Targeting Maths for Victoria Year 5 Teaching Guide Contents Gloria Harris Garda Turner Introduction Planning and Assessment Records Term 1 Term 2 Term 3 Term 4 Student Book Answers BLMs Term Planners PASCAL PRESS Targeting Maths for Victoria Year 5 Teaching Guide Gloria Harris Garda Turner PASCAL PRESS Copying for educational purposes The Australian Copyright Act 1968 (the Act) allows a maximum of one chapter or 10% of this book, whichever is the greater, to be copied by any educational institution for its educational purposes provided that that educational institution (or the body that administers it) has given a remuneration notice to Copyright Agency Limited (CAL) under the Act. 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Copying of the blackline master pages The purchasing educational institution and its staff are permitted to make copies of the pages marked as blackline master pages, activity cards and assessment pages, beyond their rights under the Act, provided that: 1. the number of copies does not exceed the number reasonably required by the educational institution to satisfy its teaching purposes; 2. copies are made only by reprographic means (photocopying), not by electronic/digital means, and not stored or transmitted; 3. copies are not sold or lent. For those pages not marked as blackline master pages, activity cards or assessment pages the normal copying limits in the Act, as described above apply. Targeting Maths for Victoria Year 5 Teaching Guide Written by Garda Turner and Gloria Harris Copyright © Blake Publishing 2006 ISBN: 1-74020-173-6 ISBN: 978-1-74020-173-5 Published by Pascal Press PO Box 250 Glebe NSW 2037 (02) 8585 4044 www.pascalpress.com.au Publisher: Katy Pike Managing Editor: Garda Turner Series editor: Amanda Santamaria Designed and typeset by The Modern Art Production Group Cover illustration by Nahum Ziersch Printed by Green Giant Press Contents About the program iv Introduction v Using the 4-page Teaching Guide unit vi Year Planners — Scope and Sequence viii Outcomes xii Assessment Record Sheets xiv Topic Term 1 Thousands Addition Subtraction Multiplication Fractions Patterns Length Time Prisms and Pyramids 2D Shapes Graphs Student pages Term 2 Whole Number Addition Division Decimals and Percentages Chance Number Patterns Volume and Capacity Mass 3D Objects 2D Shapes Bar Graphs and Data (2 (6 (10 (14 (18 (22 (26 (29 (32 (35 (38 (44 (47 (50 (54 (58 (61 (64 (68 (72 (76 (80 - - 5) 9) 13) 17) 21) 25) 28) 31) 34) 37) 41) 46) 49) 53) 57) 60) 63) 67) 71) 75) 79) 83) 2 6 10 14 18 22 26 30 34 38 42 Topic Student pages Term 3 Whole Number (86 - 88) Addition and Subtractions (89 - 91) Multiplication (92 - 95) Division (96 - 99) Fractions (100 - 102) Decimals (103 - 105) Patterns (106 - 109) Area and Perimeter (110 - 113) Angles (114 - 117) Position (118 - 121) Line Graphs and Mean (122 - 125) 46 50 54 58 62 66 70 74 78 82 86 Term 4 Whole Number Division Addition and Subtraction Multiplication, Division and Chance Fractions and Percentages Patterns Area and Length Measurement Space Graphs 90 94 98 102 106 110 114 118 122 126 130 (128 - 131) (132 - 135) (136 - 139) 134 138 142 (140 (144 (148 (152 (155 (158 (163 146 150 154 158 162 166 170 - 143) 147) 151) 154) 157) 162) 165) Targeting Maths Teaching Guide Year 5 iii The Targeting Maths program Back to Contents In creating the Targeting Maths scheme, we set out to do three things. 1 Provide a resource that is completely VELS compliant and that enables teachers to fully implement the CSF II syllabus. 2 Create child-friendly workbooks that are exciting and motivational for all children, whatever their abilities. 3 Provide teachers with a program that is easy-to-use, thorough in its coverage and comprehensive in the extra resources that it provides. A program that is truly enjoyable for all. Using the Targeting Maths program for Years 3-6 Topic-based term programs The student books from Year 3 to Year 6 are laid out as four terms of topicbased units of work. Each unit is 3 or 4 pages long. Grouping topics together allows the class to work on a topic solidly, giving better continuity. It is also easier for the teacher to individualise programs to suit the needs of students. Having clearly defined terms of work makes it easier to assess the progress of students. The contents pages in the student books clearly show the 4 terms of work. The topics are in bold. Many teachers told us they wanted topics to be easy to find, so they could alter the program to suit their needs. Features of the student book • Topic-based units of work • Easy to follow instructions • Exciting, colourful pages and creative activities that appeal to all ability levels • Dictionary of mathematical terms in each student book • Problem solving activities • Easy to achieve measurement activities • Regular challenging extension activities Maths Lab CD-Rom — more than 20 motivating maths games and activities to reinforce essential maths concepts. Lab Icons indicate which game will help students understand the concept being taught. The Targeting Maths for Victoria Planning CD-Rom contains: • The complete Teaching Guide to make programming easier. • Additional Blackline Masters, 44 in all. • Student book answers in an easy-to-print format. iv Targeting Maths Teaching Guide Year 5 Student book units of work The focus page Each unit begins with a focus page. The large focus picture grabs children's attention with a high-interest or real-life situation. • Focus pages are good for all ability levels as they include open-ended questions and active participation. Even the weakest student can perform the task because the visual image is so helpful. • Focus pages are also useful for revision. Return to the page and use it for mental warm-ups before a lesson. Photos • Photos of real things are an exciting feature of the scheme and serve to connect maths to real life. Outcomes • The outcome number and the relevant skills and indicators are written in full at the base of each page. Mathematical language • Information notes reinforce mathematical language and important facts. Problem solving • Problem solving strategies such as looking for patterns appear regularly. The other strategies covered include drawing a diagram, trial and error and working backwards. Teaching Guide units Each unit of work in the student book is matched by a 4-page Teaching Guide unit. The teaching resources include:• Syllabus outcomes, skills and indicators clearly stated for each unit • Teach and discuss section introduces each topic with a class discussion • Teaching notes for the other pages in the unit • Oral and mental activities — mental strategies give students a sound base for their problem solving • Activity bank of extra hands-on and group activities • List of easily located resources needed for the unit • Two photocopiable activity cards for individual, pairs or group work — especially useful for extension or fast-finishers • An assessment blackline master at the end of each unit. Every unit is cross-referenced to the Targeting Maths Blackline Master series for all the additional materials you may need for consolidation, extension or extra assessment. Assessment • Revision assessment page at the end of every unit of the Teaching Guide. • Term assessments in the student book. Targeting Maths Teaching Guide Year 5 v Using the 4-page teaching guide unit The teaching guide is broken into units of work. Each unit is laid out in the same format for ease of use and is directly linked to 3 – 5 pages of the student book. The teaching resources provided, as part of each unit, include teaching notes, oral, mental and hands-on activities, two activity cards and an assessment blackline master. The sequence of units provides a guide to the order of presentation. This follows the same order as suggested in the year and term planners. However, this is flexible and teachers can choose their own progression through the course. Relevant Student Book pages. Teaching notes for the focus page and other pages in the Student Book. The large illustration on the focus page is the basis for a class discussion of the topic. Outcomes and Standards covered in this unit. The key words that students need to understand. A list of all extra materials used in any of the activities. Additional work sheets in Targeting Maths blackline master books. Answers to the assessment page in the Teaching Guide. vi Targeting Maths Teaching Guide Year 5 Mental and oral strategies that can be used to introduce the lesson, or as mental warm-ups that reinforce previous learning and basic facts. The Activity Bank provides a range of practical activities for the unit that present the mathematical content in a variety of ways. Changing the presentation of a topic can support students with different learning styles or who are struggling with the concept. Activity Cards are designed for individuals, pairs or small groups. This information is clearly marked on each card. The two Activity Cards can be used as reinforcement; for fast-finishers; for homework or for fun. The Assessment page can be used to assess students’ understanding of a topic and to determine areas which need reinforcement. Targeting Maths Teaching Guide Year 5 vii Back to Contents Year Planner — Term 1 Mental and Oral Strategies Teaching Focus (student pages) Supporting Activities from Teaching Guide Thousands pp 2–5 Place value; Make that number; In order; Pass it on; How many people in each town?; The Greevy Galaxy Number study; Which one is best? Abacus Addition drill; Measure and add; Go shopping; Number Buzz; Show-bag spree; Cross the river Add up and down; Add around the room Subtraction grids, containers showing mass Subtraction table drill; Number lines; Missing numbers; Mass of groceries; Number patterns using subtraction; Crossnumber puzzle What's my number?; Change Cartons, bags, drill grids Shopping for a large number; Roll a multiple; Pot luck; Teams; Daylight ferry; Multiple patterns Counting by multiples; Buzz Dice, catalogues, number cards Memory; Fraction dominoes; Equivalent bars; Media search; Lost pieces; Plan a farm Guess my number; Equivalents for !2, !4 Blank playing cards, fraction dominoes, grid paper Pattern block puzzle; Patterns in multiples; Complete a pattern; Odd man out; Regular polygons; Find a pattern What's my pattern?; Look around Building blocks, match sticks, octagonal pattern blocks My measurements; Guinness Book of Records; World geography; Odometer readings; Around the town; Measure a kilometre How far?; Millimetres to kilometres Coloured pencils, street directories, trundle wheels Collect timetables; Rewrite timetable; Home appliances; Elsewhere; Timeline; Play with time Rewrite the clock; Elapsed time Classroom clocks, timetables Cross-sections; Models; Nets; 3D in the home; Euler's rule; Humpty Dumpty What am I? (I); What am I? (II) Models of common prisms and pyramids, plasticine, drinking straws, pipe cleaners Enlarge and reduce; Tessellation; Shapes within shapes; Shapes in the environment; Tangram puzzles; Barrier games What am I?; Mini-shapes Pattern blocks, cm grid paper Picture graph; Tally that; Choose a symbol; Bar graph towers; Missing data; Tell the story Count by ...; Divide by ... Reference books, building blocks Thousands Numbers in words Ten thousands Place value Addition pp 6–9 Two-digit addition Addition facts Addition algorithms Number lines Subtraction pp 10–13 Subtraction of money Subtraction strategies Subtraction methods Checking answers Multiplication pp 14–17 Factors Multiples Multiplication Multiplication by one-digit numbers Fractions pp 18–21 Fraction equivalence Fractions of groups and wholes Fractions on a number line Tenths Patterns pp 22–25 Geometric patterns More steps Pattern tables Patterns in words Length pp 26–28 Length Kilometres Millimetres, centimetres, metres Time pp 29–31 Twenty-four hour time Changing times Daylight saving Prisms and Pyramids pp 32–34 Prisms and pyramids Comparing 3D objects Drawing prisms and pyramids 2D Shapes pp 35–37 Special quadrilaterals Properties of quadrilaterals Regular shapes Graphs pp 38–41 Picture graph Drawing a picture graph Tally marks Bar graph viii Resources Targeting Maths Teaching Guide Year 5 Year Planner — Term 2 Teaching Focus (student pages) Supporting Activities from Teaching Guide Mental and Oral Strategies Whole Number pp 44–46 Roman numbers; Number line; State areas; Live number line; Palindromes; Sort the numbers Odometer readings; Roman numerals Wall map of Australia, toilet paper roll, blank cards, rope Shopping grab; Total height; Total age; Shopping game; Super holiday bargains; How did you do that? Random adding; The same ones Calculator, Blu-tack, blank cards Throw and divide; Musical groups; Bargain shopping; Pass it on; Toothpick puzzle; Only one allowed Count multiples; What's my number? Calculators, dice, shopping catalogues Bingo; Memory; Environmental percentages; Lotto; Farmer's dilemma; Add 'em up Comparing; Aligning Memory pack cards, newspapers, magazines Synonyms of chance; Arrange in order; Determine outcomes; Family chance; Even chances; Match the statement Number patterns; Statements of change Coins, thesaurus, blank flashcards Number families; Make an equation; Make my number; Story time; Magic sums; Two-way stretch Number patterns; Number clues Number cards What's my volume?; Same volume, different shapes; How many fit in a m3?; Litres everyday; That's a lot of lunchboxes; How big is a cup? Calculate volume; Litres and millilitres Cubic centimetre blocks, rectangular boxes, isometric dot paper, metre rods, fabric, empty containers, litre measures What's my mass?; Size and mass; Double a recipe; Weigh it up; Different volume, same mass; School bag survey Total 1 000 g; Subtract from 1 000 g Standard masses 50 g, 100 g, 500 g, 1 kg, scales, litre measures, large containers, empty dry food packages Different views; This is my view; Area of nets; Footprint; Make a tetrahedron; Five questions Give me four; What will I need? Models of 3D objects, centimetre cubes, photocopies of 3D nets, blank cards, scissors, glue Large scale drawing; Triangle patterns; Rigid triangles; Tessellating patterns; Star in a circle; How many triangles? Circle words; Circle facts Pairs of compasses, coloured pencils, rope or string, pattern blocks, geostrips Graphs in the environment; Graphs in class; Interview; Tell a story; Sunny days; Critical data Label axes; Scale on graphs Large sheet of graph paper Roman numerals Comparing numbers Rounding thousands Addition pp 47–49 Addition of money Addition problems Four-digit addition Division pp 50–53 Division facts Dividing mentally Division algorithms Problem solving Decimals and Percentages pp 54–57 Hundredths Percentages Using percentages Decimals Chance pp 58–60 Chance Chance experiment What is the chance? Number Patterns pp 61–63 Using a table Find the value Number patterns Volume and Capacity pp 64–67 Volume Cubic measure Litres Capacity Mass pp 68–71 Mass Grams and kilograms Estimating mass Mass problems 3D Objects pp 72–75 3D objects in real life Nets 3D views Perspective 2D Shapes pp 76–79 The circle Drawing circles Types of triangles Triangles and scale Bar Graphs and Data pp 80–83 Bar graph Horizontal bar graph Gathering data Representing data Targeting Maths Teaching Guide Year 5 Resources ix Year Planner — Term 3 Supporting Activities from Teaching Guide Whole Number pp 86–88 House prices; Population figures of Australian cities; Reading numbers; Bingo; Twenty questions; Domino puzzle; Squared Read and add challenge Hundred thousands Place value Roman numerals to 1 000 Addition and Subtraction pp 89–91 Just a minute; Travel bug; Calculator practice; Tables rugby; Hundreds multiplication; Going to a party; Up the ladder; Telephone numbers to remember; Stamp it Random operations; Prime number 'Buzz' Calculators, coloured pencils, dice Divide a large number; Mystery quotient; Mind reading; What am I?; Famous numbers; Even only Four for one; Divide the class Reference materials Fraction bars; Pizza day; Fraction of a book; Divide and conquer; Sort them out!; Making one Sort the fraction; Divide my number Coloured pencils, 100 m ball of string, trundle wheel, pizza Number line; Calculator; Currency conversion; Measure heights; Puzzle math words; Guess and check Twenty questions; Next whole number Calculators, tape measures Number pattern strings; Think of a number; Number patterns to meet; Pattern draw; Work systematically; Mystery rules Number patterns; Number pattern stories Pattern blocks, objects for patterning, beads, string Draw to size; Different square metres; Perimeters in the playground; Hectares in the playground; 12 squares; Cabin for sale Perimeters; Areas Square centimetre overlay, centimetre grid paper, coloured pencils, trundle wheel, chalk, calculators Study the clock; Study a compass; Study the classroom door; Draw a square; Barrier game; Three into one Angles on the clock; Sum of angles Protractors, class clock Street directory; Treasure Island; Playground square; Classroom map; Pot of gold; Use scale Classroom as map; Scale calculations Coloured pencils, various maps, compasses Weather graphs; Local temperature; Number line of possibility; Change the scale; Every graph tells a story; What's happening here? True or false; Study a large number Weather graphs, weather thermometer Multiplication pp 92–95 Division Division signs and zero Remainders Problem solving Fractions pp 100–102 Equivalent fractions Making equivalent fractions Ordering fractions Decimals pp 103–105 Decimal addition and subtraction Multiplication of decimals Division of decimals Patterns pp 106–109 Shape pattern Making patterns Number fact patterns Number patterns Area and Perimeter pp 110–113 Area and perimeter Area of a rectangle Hectares Large areas Angles pp 114–117 Angles Types of angles Measuring and drawing angles Angle sum Position pp 118–121 Map reading Coordinates Scale Compass bearings Line Graphs and Mean pp 122–125 Line graphs Reading a line graph Drawing a line graph Mean Newspapers, atlases Dice, state maps, calculators Take it!; Down on the farm; Skip to my Lou! Division pp 96–99 Resources Related facts; Add around the class Addition Addition and Subtraction Using addition and subtraction Money multiplication Multiplication algorithms Three-digit multiplication Interesting numbers x Mental and Oral Strategies Teaching Focus (student pages) Targeting Maths Teaching Guide Year 5 Year Planner — Term 4 Mental and Oral Strategies Resources Teaching Focus (student pages) Supporting Activities from Teaching Guide Whole Number pp 128–131 Model large number; Vertical figure; Really cold!; Largest number; Make mine bigger; Shop till you drop True or false; Give me a number between Coloured pencils, MAB blocks, newspapers, calculators, dice Dividing by 10; Lotto answers; Best value; Quick tables practice; Very sneaky; Divisibility rules – OK? Multiples 'Buzz'; Add what? Supermarket catalogues, empty box Everyday averages; Supermarket catalogues; Random number sentences; Practice; Number table; Class average Thigh, clap, snap, snap; Short methods Catalogues, addition and subtraction squares – blank, number cards, operation sign cards, calculators Teacher versus class; Predictions Opaque bags, marbles (or counters), coloured pencils, number cards 1 – 100, money Large numbers Working with large numbers Negative numbers Ordinal numbers Division pp 132–135 Matching quotients Inverse checking Four-digit division Dividing by 10 Addition and Subtraction pp 136–139 More addition More subtraction Averages Order of operations Multiplication, Division and Chance Averages backwards; Door check; Change from $5 or $1; Blackboard race; What chance?; Postcode pp 140–143 Money multiplication Division with money Chances are Most likely detectives Fractions and Percentages pp 144–147 Gather percentages; Dicey mixed numbers; Give the first answer; Twenty questions using decimals; Time and time again; What percentage? Percentages; Stand up! Calculators, dice Secret numbers; Calculator practice; Important destinations; Back home again; Calculator words; New number system Oral number sentences; What's my rule? Calculators, cm grid paper Half a shape – perimeter; Half a shape – area; List the perimeters; Mystery shapes; Perimeter/Area; Rearrange me Short methods; Quick perimeters Measuring tools, scissors Time a minute; Record personal measurements; Use measuring instruments; Dominoes with measurements; Letter spacing; Volume of irregular shapes True or false; Time left Medicine measures, blocks, stopwatch, measuring instruments, blank cards Designs in 2D shapes; Rigid shapes; Construction practice; 2D shapes in real life; Enlarge; Geoboard squeeze Quiz; Study the clock Protractors, photocopies of 2D shapes, compass and protractor board, geostrips, split pins Which graph to use?; What is the data?; Read a double graph; Useful data; Lamington drive; Make it right Divisibility test; Division with remainders Centimetre grid paper Percentages Everyday percentages Changing fractions Decimal patterns Patterns pp 148–151 Number sentences What is my value? Tables and patterns Following patterns Area and Length pp 152–154 Mixed areas Perimeter rules Estimating length Measurement pp 155–157 Measuring instruments Timetable Cubic centimetres Space pp 158–162 Diagonals What am I? Lines Shape and position Map reading Graphs pp 163–165 Graphs At the vet My graph Targeting Maths Teaching Guide Year 5 xi Outcomes Outcome Pages in student book NUMBER Numbers, counting and numeration 4.1 Use place-value knowledge to read, write and order negative whole numbers and decimal numbers from thousandths to millions. 2, 3, 4, 5, 45, 46, 54, 86, 87, 103, 14, 109, 128, 129, 130, 131, 150, 151 4.2 Compare and order common fractions. 20, 21, 100, 101, 102, 104, 144, 145 4.3 Rename common fractions as decimals and percentages. 21, 54, 55, 56, 144, 145 Mental computation and estimation 4.1 Recall automatically basic multiplication and division facts, simple common fraction facts and frequently used common fraction, decimal and percentage equivalences. 15, 16, 18, 19, 50, 53, 55, 56, 92, 93, 96, 97, 135, 136, 137, 145 4.2 Use knowledge of place-value and number properties to increase the range of computations which can be carried out mentally. 6, 7, 11, 16, 17, 51, 92, 93, 135, 138 4.3 Use estimation strategies to check the results of written or calculator computations. 11, 47, 48, 57, 98, 99, 137 Computation and applying number 4.1 Use written methods to add and subtract decimal numbers. 10, 12, 13, 47, 49, 56, 91 4.2 Use written methods to multiply and divide whole numbers. 8, 9, 12, 17, 52, 94, 97, 98, 132, 133, 134, 138, 140, 141, 142 4.3 Use models to illustrate the four operations with common fractions, and develop written methods for carrying out these operations. 19, 20, 132, 146, 149 4.4 Analyse a problem situation which may involve several different operations, decimal numbers, negative whole numbers and common fractions; express the problem symbolically and choose appropriate computational methods to solve it. 13, 48, 53, 89, 90, 91, 95, 99, 105, 108, 133, 147 Number patterns and relationships 4.1 Generate and investigate number sequences which may involve fractions, decimals and combinations of operations, using a calculator where appropriate. 22, 23, 24, 25, 49, 63, 107, 108, 109, 147, 150, 151 4.2 Specify multiples and factors of whole numbers. 14, 15, 95, 133 4.3 Construct, verify and complete number sentences involving the four operations, brackets, decimal numbers and fractions. 62, 134, 139, 148, 149 SPACE Shape and space 4.1 Recognise, describe and represent parallel, perpendicular, horizontal and vertical lines, ight angles, and angles greater than or less than 90 degrees (multiples of 45 degrees). 36, 115, 116, 117, 160 4.2 Analyse, explain and compare the spatial properties of lines, angles, polygons, polyhedra and cross-sections using conventional spatial terms. 32, 33, 35, 36, 37, 72, 76, 77, 78, 79, 158, 159, 161, 62 4.3 Make congruent copies of given three-dimensional objects. 34, 74 4.4 Draw conventional representations of prisms, pyramids, cylinders and cones. 34, 159 4.5 Visualise, explain and represent 'what is not seen' of an object. 32, 73, 74 4.6 Visualise, test and describe transformations of shapes. 106, 107 4.7 Enlarge (or reduce) two-dimensional shapes and simple three-dimensional objects. 79 Location 4.1 Use and understand conventional location language including distance and direction. 118, 121 4.2 Use informal coordinate systems (positive numbers only) and intermediate compass points to specify location or give directions. 121, 119, 161, 162 4.3 Visualise and find paths to satisfy specifications on maps, grids and mazes. 27, 120 4.4 Interpret formal maps and make detailed maps and plans. 118, 120, 121, 162 4.5 Use a simple scale (for example, 1 centimetre for each metre) when making, interpreting and using maps and plans. 112, 120 xii Targeting Maths Teaching Guide Year 5 Outcomes Outcome Pages in student book MEASUREMENT Measuring and estimating 4.1 Choose attributes and standard units appropriate to the task. 28, 65, 68, 69, 70, 154 4.2 Make judgments about the relative size of objects based on comparison to known benchmarks or standard units. 26, 27, 64, 65, 113 4.3 Draw and construct objects using accurate measurements. 77, 111, 112 4.4 Use measuring instruments, reading simple scales and measuring accurately to the nearest marked gradation, taking into account the degree of exactness required. 28, 67, 77, 78, 114, 116, 117, 152, 155 Time 4.1 Use and construct timetables and use and analyse calendars. 31, 156 4.2 Estimate, measure and calculate time elapsed (duration). 30, 156 4.3 Tell the time accurately using analogue clocks and digital clocks. 29, 30, 31 Using relationships 4.1 Measure and compare the perimeter and area of regular and irregular polygons. 28, 110, 111, 153 4.2 Investigate the relationship between area and perimeter and calculate the area of a polygon. 110, 111, 112, 113, 152 4.3 Investigate and compare the volume and mass of objects. 64, 65, 71, 157 CHANCE AND DATA Chance 4.1 Examine the outcomes from simple chance experiments and data on familiar events to order outcomes and events from least to most likely. 58, 142, 143 4.2 Use and interpret numerical statements which quantify chance. 60 4.3 Use language of chance in everyday situations. 58, 59, 60, 142 Posing questions and collecting data 4.1 Design and prepare surveys and experiments to answer questions or test conjectures and predictions. 80, 164, 165 4.2 Collect and record data systematically. 41, 81, 82, 83, 165 Summarising and presenting data 4.1 Prepare tabular displays of discrete and continuous data. 40, 81, 165 4.2 Prepare visual displays of discrete and continuous (measurement) data using a range of graphical methods. 39, 40, 87, 124, 163, 165 4.3 Compare, order and summarise data sets using simple numerical methods. 41, 82, 123, 125 Interpreting data 4.1 Extract and interpret numerical information contained in tables, data displays and databases. 38, 41, 81, 122, 123, 124, 163, 164 4.2 Interpret, discuss and compare data displays, including how well they communicate information. 41, 80, 163, 164 REASONING AND STRATEGIES Mathematical reasoning 4.1 Make and test simple conjectures in each mathematics strand. 9, 10, 38, 49, 125, 164, 165 4.2 Make judgments about the accuracy of reasoning and results and modify working accordingly. 5, 67, 70, 82, 83 4.3 Use and interpret simple mathematical models. 44, 56, 88, 100, 109, 111, 112, 120, 142, 144, 145, 154, 155 Strategies for investigation 4.1 Generate mathematical questions from presented data and from familiar contexts. 26, 39, 51, 63, 99, 107, 121, 128, 129 4.2 Clarify the essential nature of a task or problem and identify key information in the context under consideration. 25, 75, 88, 117, 151, 152 4.3 Use a range of strategies for inquiry when responding to tasks and problems. 73, 138, 157 4.4 Communicate own responses to tasks and problems appropriate for this level to others. 59, 71, 73, 107, 139, 154 Targeting Maths Teaching Guide Year 5 xiii Assessment of Outcomes Record Sheets Student name _________________________________________________________________ Date ______________________________________ Outcomes Stage 4 NUMBER Numbers, counting and numeration 4.1 Use place-value knowledge to read, write and order negative whole numbers and decimal numbers from thousandths to millions. 4.2 Compare and order common fractions. 4.3 Rename common fractions as decimals and percentages. Mental computation and estimation 4.1 Recall automatically basic multiplication and division facts, simple common fraction facts and frequently used common fraction, decimal and percentage equivalences. 4.2 Use knowledge of place-value and number properties to increase the range of computations which can be carried out mentally. 4.3 Use estimation strategies to check the results of written or calculator computations. Computation and applying number 4.1 Use written methods to add and subtract decimal numbers. 4.2 Use written methods to multiply and divide whole numbers. 4.3 Use models to illustrate the four operations with common fractions, and develop written methods for carrying out these operations. 4.4 Analyse a problem situation which may involve several different operations, decimal numbers, negative whole numbers and common fractions; express the problem symbolically and choose appropriate computational methods to solve it. Number patterns and relationships 4.1 Generate and investigate number sequences which may involve fractions, decimals and combinations of operations, using a calculator where appropriate. 4.2 Specify multiples and factors of whole numbers. 4.3 Construct, verify and complete number sentences involving the four operations, brackets, decimal numbers and fractions. SPACE Shape and space 4.1 Recognise, describe and represent parallel, perpendicular, horizontal and vertical lines, right angles, and angles greater than or less than 90 degrees (multiples of 45 degrees). 4.2 Analyse, explain and compare the spatial properties of lines, angles, polygons, polyhedra and cross-sections using conventional spatial terms. 4.3 Make congruent copies of given three-dimensional objects. 4.4 Draw conventional representations of prisms, pyramids, cylinders and cones. 4.5 Visualise, explain and represent 'what is not seen' of an object. 4.6 Visualise, test and describe transformations of shapes. 4.7 Enlarge (or reduce) two-dimensional shapes and simple three-dimensional objects. Location 4.1 Use and understand conventional location language including distance and direction. 4.2 Use informal coordinate systems (positive numbers only) and intermediate compass points to specify location or give directions. 4.3 Visualise and find paths to satisfy specifications on maps, grids and mazes. 4.4 Interpret formal maps and make detailed maps and plans. 4.5 Use a simple scale (for example, 1 centimetre for each metre) when making, interpreting and using maps and plans. xiv Targeting Maths Teaching Guide Year 5 Student name _________________________________________________________________ Date ______________________________________ Outcomes Stage 4 MEASUREMENT Measuring and estimating 4.1 Choose attributes and standard units appropriate to the task. 4.2 Make judgments about the relative size of objects based on comparison to known benchmarks or standard units. 4.3 Draw and construct objects using accurate measurements. 4.4 Use measuring instruments, reading simple scales and measuring accurately to the nearest marked gradation, taking into account the degree of exactness required. Time 4.1 Use and construct timetables and use and analyse calendars. 4.2 Estimate, measure and calculate time elapsed (duration). 4.3 Tell the time accurately using analogue clocks and digital clocks. Using relationships 4.1 Measure and compare the perimeter and area of regular and irregular polygons. 4.2 Investigate the relationship between area and perimeter and calculate the area of a polygon. 4.3 Investigate and compare the volume and mass of objects. CHANCE AND DATA Chance 4.1 Examine the outcomes from simple chance experiments and data on familiar events to order outcomes and events from least to most likely. 4.2 Use and interpret numerical statements which quantify chance. 4.3 Use language of chance in everyday situations. Posing questions and summarising data 4.1 Design and prepare surveys and experiments to answer questions or test conjectures and predictions. 4.2 Collect and record data systematically. Summarising and presenting data 4.1 Prepare tabular displays of discrete and continuous data. 4.2 Prepare visual displays of discrete and continuous (measurement) data using a range of graphical methods. 4.3 Compare, order and summarise data sets using simple numerical methods. Interpreting data 4.1 Extract and interpret numerical information contained in tables, data displays and databases. 4.2 Interpret, discuss and compare data displays, including how well they communicate information. REASONING AND STRATEGIES Mathematical reasoning 4.1 Make and test simple conjectures in each mathematics strand. 4.2 Make judgments about the accuracy of reasoning and results and modify working accordingly. 4.3 Use and interpret simple mathematical models. Strategies for investigation 4.1 Generate mathematical questions from presented data and from familiar contexts. 4.2 Clarify the essential nature of a task or problem and identify key information in the context under consideration. 4.3 Use a range of strategies for inquiry when responding to tasks and problems. 4.4 Communicate own responses to tasks and problems appropriate for this level to others. Targeting Maths Teaching Guide Year 5 xv Student pages 2–5 Back to Contents Thousands Learning focus • Revise numbers to one thousand. Stress the place value of each digit. • Introduce thousands. Show students how to write 4-digit numbers with a space between the thousands and hundreds digits. • Make digit cards. Use four at a time for students to say/read/write numbers. Make the largest/smallest number you can using these four digits. • Ensure that all students understand that whole numbers do not start with zero. If a zero digit card is used they cannot make a small whole number by starting with a zero. • When discussing question three have students suggest a strategy they can use to make sure that no numbers are omitted. VELS: NUMBER Outcomes and Standards Numbers and Numeration 4.1 Use place-value knowledge to read, write and order negative whole numbers and decimal numbers from thousandths to millions. Reasoning 4.2 Make judgments about the accuracy of reasoning and results and modify working accordingly. • Reads and writes whole 4-digit numbers. • Reads, writes and orders 5-digit numbers. • Represents the structure of whole numbers to 5-digits. • Understands the structure of 5-digit numbers. • Uses checking procedures when calculating. Key words zero, four-digit, abacus, ascending, descending, digit Student page 3 • Make sure students refer back to page 2 for questions 1 and 4. • Have students spell some of the more difficult number words, eg forty, eighty etc. Make a class spelling chart of number words. Display the chart for future reference. • Practise writing 4-digit numbers on the board. Pay particular attention to the use of and. • Show an abacus. Make numbers on it, have students say the number and vice versa. Student page 4 • Introduce tens of thousands. Write several examples on the board. What are these numbers? • When students are reading five-digit numbers accurately name the place-value column — tens of thousands or ten thousands. • Remind them that there is still a space between the thousands digit and the hundreds digit. Student page 5 abacus, digit cards • On the board write a five-digit number, eg 35 826. Have students tell you the value of each digit. Write the values on the board. 30 000 + 5 000 + 800 + 20 + 6 • Repeat several times. Additional work sheets Answers for assessment page 5 Targeting Maths Upper Primary Numeration and Fractions • Place Value and Estimation — Unit 1 1 a 9 640 b 4 069 c Teacher check d Teacher check 2 a eight thousand five hundred and twenty-seven b six thousand two hundred and five c five thousand and forty-three d nine thousand and one 3 a 24 381 b 59 146 4 Teacher check 5 a 19 605, 24 063, 31 517, 47 014 b 18 509, 18 950, 19 085, 19 580, 19 850 6 a 30 000 + 7 000 + 500 + 60 + 4 b 10 000 + 5 000 + 80 + 6 7 1 036, 1 063, 1 306, 1 360, 1 603, 1 630, 3 016, 3 061, 3 106, 3 160, 3 601, 3 610, 6 013, 6 031, 6 103, 6 130, 6 301, 6 310 Resources 2 Targeting Maths Teaching Guide Year 5 Mental and Oral Strategies Number study Which one is best? Write the number 15 738 on the board. What is the value of the 7? (700) What is the place value of the 7? (hundreds) How many tens in the number? (1 573) How many thousands? (15) Place a number on the board, to 50 000. Which numeral would you prefer for – a) hours of homework? b) days on holiday? c) kg of chocolate? d) desks to scrub? e) dollars to pay back? Activity Bank Place value Make that number Dictate numbers for students to write down in vertical format. Check that numerals are being written with units under units, tens under tens etc. and that they are leaving a space between thousands and hundreds. Give students number cards with one digit per card. Organise groups of 5 students, each group to have the same digits on cards. On a signal, give a command to make a number, eg larger than 10 000, smaller than 25 000, largest number, smallest number, number divisible by 5, even number, odd number. Students rearrange themselves and call ‘Stop!’ when done. Reward the fastest group. In order Pass it on Give groups of students cards with numerals to 100 000 written on them. On a signal, give a command for them to arrange in ascending or descending order. Children call ‘Stop!’ when done. As they become more proficient, make groups larger and larger. Start with a number, add, subtract or multiply by 10, 100 or 1 000 and pass it on. eg Teacher, 5 multiply by 10, pass it on; Child 1, 50, add 100, pass it on; Child 2, 150, multiply by 10, pass it on; Child 3 1 500, subtract 1 000, pass it on; etc. Targeting Maths Teaching Guide Year 5 3 Activity Card 1 How Many People in Each Town? ✎ JERAL has a population 10 times the village of GEMMA, which has 2 360 people. STRATHEN has 1 000 more than JERAL. HENTIN has 1 200 more than FERNIE and 600 less than MOONEY. FERNIE has one tenth the population of STRATHEN. MOONEY has half the population of BERRIE. The city with the largest population is the capital city. Which is the capital city? Activity Card 2 ✎ The Greevy Galaxy Label the planets according to their distance from the Greevy. Crang = 15 100 km; Twan = 1 202 km; Yoho = 2 850 km; Briny = 19 770 km; Groop = 3 080 km; Friep = 11 500 km; Stam = 2 560 km; Trill = 17 050 km; Droop = 5 100 km. Greevy 4 © Blake Publishing — Targeting Maths Teaching Guide 5 This page may be reproduced by the original purchaser for non-commercial classroom use. Assessment Name __________________________________________ Thousands Date _____________________________ 6 0 9 4 1 Use these digit cards to write: a the largest number. ___________ b the smallest number. ___________ c two numbers between 6 000 and 7 000. ___________ ___________ d three numbers less than 5 000. ___________ ___________ ___________ 2 Write in words. a 8 527 b 6 205 c 5 043 d 9 001 3 Write the numbers under the abacus. a 4 Draw each number on an abacus. b Tth Th H T O a Tth Th H T O b Tth Th H T O 17 392 Tth Th H T O 43 815 5 Write in ascending order. a 31 517 19 605 24 063 47 014 b 19 085 18 509 19 850 18 950 19 580 6 Expand. a 37 564 = ___________ + ___________ + ___________ + ___________ + ___________ b 15 086 = ___________________________________________________ 7 Write all the four-digit numbers you can make using the digits 6, 1, 0, 3. © Blake Publishing — Targeting Maths Teaching Guide 5 This page may be reproduced by the original purchaser for non-commercial classroom use. 5 Student pages 6–9 Addition Learning focus VELS: NUMBER Outcomes and Standards • What is addition? Make a list of responses on the board. • Ask students to suggest words that would indicate addition. Make a class list. • Give oral examples of problems to be solved by addition. eg Sam has 34 model cars and Uncle Jay gives him another 27 to add to his collection. How many does he now have? • Work the example on the board. Point out the positioning of the numbers and the + sign on the left-hand side of the algorithm. • Look at page 6 and discuss the focus picture. Read the questions to ensure that students know what to do. • Allow students to work mentally if they are confident. Setting out can be done in workbooks for those who do not want to work mentally. • For question 6 stress that estimation does not mean an exact answer. Student page 7 Mental Computation 4.2 Use knowledge of place-value and number properties to increase the range of computations which can be carried out mentally. Computation and Applying Number 4.2 Use written methods to multiply and divide whole numbers. Reasoning 4.1 Make and test simple conjectures in each mathematics strand. • Adds mentally using appropriate strategies. • Uses appropriate mental strategies when adding 2-digit numbers. • Uses appropriate written methods for addition. • Uses a variety of strategies and methods for addition. • Provides evidence for own ideas and assertions. • Students orally double all numbers to 20. Practise near doubles. • Explain the split strategy. Write examples on the board for practice. • Explain the compensation strategy. Work practice examples on the board. • Explain the jump strategy. Work practice examples on the board. • Before starting page draw attention to the fact notes on the student page and encourage referral to them. Key words • Introduce number lines. Show by example how to make jumps for addition. • Write one example, eg 238 + 519. Ask students how they would work it on the number line. • Show all responses. • Stress that no one method is better than another, eg 200 + 500 + 30 + 10 + 8 + 9 is equally as valid as 238 + 500 + 10 + 19. strategies, split, compensation, number line, algorithm Resources calculators, addition blanks, coloured pencils, catalogues Additional work sheets Targeting Maths Upper Primary Operations and Number Patterns • Addition — Unit 1 6 Student page 8 • Work addition examples on the board. Have students come to the board to scribe. • Revise column (place value) headings for two columns and three columns. • Ensure that carry numbers are clearly written at the top of the next column. • Stress the importance of writing answer numbers in their correct place. Student page 9 Answers for assessment page 9 1 a 70 b 145 c 92 b ice-creams and cakes 4 Teacher check 6 a 65 b 93 c 122 d 75 8 a 563 b 1 012 c 1 001 d 2 a toffee apples and biscuits 3 a 210 b 129 5 a 31 b 23 c 43 d 53 7 a 95 b 125 c 100 d 79 713 e 866 9 864 Targeting Maths Teaching Guide Year 5 Mental and Oral Strategies Add up and down Add around the room Place a column of figures on the board. Have students individually add them working up the column, only giving the total as they go. Check by adding down the column. eg 5 + 7 + 3 + 8 + 2 + 6 = 5, 12, 15, 23, 25, 31. Check 6, 8, 16, 19, 26, 31. Time each effort. Students should individually keep their own times to try to better them through the week. Start with a number, eg 7, and give the command for each child around the room to add a single number, eg 6. Time the whole process for the class and keep a record of the time to try to beat. Reward the whole class when time is beaten. Activity Bank Addition drill Measure and add Prepare photocopied addition blanks with 10 given digits in place. When all are ready, give the number to be added to all and the command to begin. Have students estimate then measure the length of 6 of their coloured pencils in mm and obtain the total length by adding. This can also be done with multiples of other items, eg pieces of chalk etc. 7 9 12 18 4 25 13 10 19 31 +8 +12 Go shopping Number Buzz Use supermarket catalogues and go shopping with a given amount. Allow a set time for students to ‘spend’ the given amount exactly (rounded). Around the room students add a given number, eg 7, until a given limit is reached. When the limit is reached, eg 50, the student says Buzz and the next student is out, but they may come back in if they can beat a standing student with an answer. Targeting Maths Teaching Guide Year 5 7 Activity Card 3 ✎ Show Bag Spree Your dad will give you $25 to buy Show Bags at the fair. Which ones will you buy to get the most for your money? Big Fizz $4.75 Grub Bug $8.50 Channel 6 $6.60 Spars Bars $10.00 Whizz Bits $4.50 Floppy Slop $6.75 Healthy Heaps $9.25 Miles of Music $11.50 Activity Card 4 ✎ Cross the River Get from one side of the river to the other using the cheapest path. Check using a calculator. 85c $5.35 $6.25 $1.35 $7.90 $8.60 $4.25 95c 70c $3.10 $3.50 $1.70 8 $2.60 60c © Blake Publishing — Targeting Maths Teaching Guide 5 This page may be reproduced by the original purchaser for non-commercial classroom use. $5.20 ÷ X _ + Assessment Name __________________________________________ Addition Date _____________________________ 1 Goods sold by Sam’s Stunning Super Store last Friday. Biscuits 59 Toffee apples 43 Iceblocks 65 Cakes 86 Ice-creams 27 a ice-creams + toffee apples = ___________ Working b cakes + biscuits = ___________ c ice blocks + ice-creams = ___________ 2 Which two items together equal: a 102? b 113? 3 a Add the three highest scores. ___________ b Add the three lowest scores. ___________ 4 Estimate how many items were sold altogether. 5 Use doubles and near doubles. a 15 + 16 = _______ b 12 + 11 = _______ c 21 + 22 = _______ d 15 + 23 + 15 = _______ 6 Use the split strategy. a 28 + 37 = _____ b 59 + 34 = _____ c 65 + 57 = _____ d 27 + 48 = _____ c 72 + 28 = _____ d 47 + 32 = _____ 7 Use the compensation strategy. a 56 + 39 = _____ 8 a 317 + 246 b 82 + 43 = _____ b 529 + 483 c 706 + 295 d 425 + 288 e 187 + 679 9 Use the number line. 375 + 489 = _____ © Blake Publishing — Targeting Maths Teaching Guide 5 This page may be reproduced by the original purchaser for non-commercial classroom use. 9 Student pages 10–13 Subtraction Learning focus VELS: NUMBER Outcomes and Standards Computation 4.1 Use written methods to add and subtract decimal numbers. 4.2 Use written methods to multiply and divide whole numbers. 4.4 Analyse a problem situation which may involve several different operations, decimal numbers, negative whole numbers and common fractions; express the problem symbolically and choose appropriate computational methods to solve it. Reasoning 4.1 Make and test simple conjectures in each mathematics strand. Mental Computation 4.2 Use knowledge of place-value and number properties to increase the range of computations which can be carried out mentally. 4.3 Use estimation strategies to check the results of written or calculator computations. • Uses knowledge of number properties to subtract mentally. • Provides evidence about what is true in a mathematical inquiry. • Uses number properties to subtract mentally. • Uses front end estimation. • Uses written methods and a variety of strategies to subtract. • Uses inverse relationships for checking answers. Key words cents, change, cheapest, estimate, number line, algorithm Resources subtraction grids, containers showing mass • Revise simple subtraction. 81 • Stress the ‘read from the top’ rule. eg – 27 “1 – 7” not “7 – 1”. • Allow students to discuss the method they might use. Discuss the merits of each. • Do not use calculators unless they are really needed by a special group. • If written algorithms are required write them in workbooks. • Look at page 10 and discuss it. Ensure students are familiar with the notion of change. Student page 11 • Teach jump strategy and compensation strategy for subtraction. Practise them on the board. • When would we use each strategy? • After question 5 have the class discuss any patterns they have observed. • Revise estimation. Stress again that it is NOT an exact answer. In fact students who do work exact answers could be penalised at this stage to ensure that they understand the concept of estimation. Student page 12 • Draw number lines on the board. Students can pose problems and you work the answers using the number lines and vice versa. • Practise trading in tens and hundreds. Work many examples on the board before attempting question 3. Student page 13 • Why do we check answers? How do we check answers? • Discuss inverse operations. • Show how to use addition to check subtraction. Answers for assessment page 13 1 2 3 4 5 6 52, 7, 71, 13, 56, 34, 9, 45, 20, 66, 73, 28 Teacher check a 71 b 122 c 249 d 285 a 264 b 434 c 235 d 176 e 165 627, 333, 257, 70 207 Additional work sheets Targeting Maths Upper Primary Operations and Number Patterns • Subtraction — Unit 1 10 Targeting Maths Teaching Guide Year 5 Mental and Oral Strategies What’s my number? Change Clues: I am less than 30, even, and the difference between my digits is 4. (26) What change do I receive from $20 after spending – $5.50, $6.75, $12.80? I am the sum of 15, 2 and the difference between 11 and 3. (25) I am thirteen less than the sum of 15 and 24. (26) Calculate change by ‘counting on’. Answers can be given orally or written. Activity Bank Subtraction drill Number lines Using grids which show 10 numbers, students practise subtractions of a given number from an array of mixed numerals. eg Place a number line on the board and have students demonstrate and explain subtraction. They choose the size of the jumps. eg 285 – 159 = 15 18 23 20 11 28 17 28 24 16 –9 –5 9 126 50 135 100 185 285 Missing numbers Mass of groceries On the board, write an algorithm with missing digits. Have students work out the missing digits then explain how they did the problem. Have students bring empty cartons, bags and containers from the cupboards at home. Hold them up, covering the mass written on the container with your hand. Students guess the original mass, using terms ‘more’ and ‘less’ to guide them. 355 –260 168 * * Targeting Maths Teaching Guide Year 5 Add to check. 11 Activity Card 5 ✎ Number Patterns Using Subtraction Add four more terms to the following number patterns. a 860, 760, 650, 530, 460, ________ , ________ , ________ , ________ b 347, 328, 309, ________ , ________ , ________ , ________ c 1 007, 999, 991, ________ , ________ , ________ , ________ d 34, 31, 33, 30, 32, ________ , ________ , ________ , ________ e 66, 50. 36, 24, ________ , ________ , ________ , ________ f 110, 120, 117, 107, 110, ________ , ________ , ________ , ________ g 97, 84, 71, ________ , ________ , ________ , ________ h 250, 235, 230, 215, ________ , ________ , ________ , ________ Activity Card 6 ✎ Crossnumber Puzzle Across 1. 307 + 19 3. 52 – 22 5. 15 less than 400 7. 4 π 9 – 7 8. 17 π 3 9. 150 – 35 10. 65 + 19 12. 10 π 11 13. Sum of 275 and 45 14. 830 + 260 + 35 17. 5 π 3 18. 180 less than 1 000 19. 6 π 5 π 2 20. Three dozen 12 Down 1. 45 less than 400 2. 7 π 9 3. 14 of 100 4. 210 – 15 6. 3 π 3 π 3 π 3 7. 70 π 3 + 4 11. = 3 000 + 4 π 3 13. 250 + 70 – 2 15. 102 + 3 16. 11 π 5 π 1 18. 12 of 160 1 2 5 3 4 6 7 8 9 10 11 12 13 14 17 15 18 19 © Blake Publishing — Targeting Maths Teaching Guide 5 This page may be reproduced by the original purchaser for non-commercial classroom use. 20 16 Assessment Name __________________________________________ Subtraction Date _____________________________ 1 Complete. 71 26 90 32 75 53 28 64 39 85 92 47 –19 2 Estimate the answers. a 64 – 18 = _____ b 59 – 21 = _____ c 81 – 32 = _____ d 94 – 68 = _____ 3 Use the number lines. a 154 – 83 = _____ b 238 – 116 = _____ c 508 – 259 = _____ d 473 – 188 = _____ 4 Work the algorithms then add to check the answers. a 527 – 263 b 852 – 418 c 610 – 375 d 346 – 170 e 923 – 758 Check a 263 + b __ __ __ + c __ __ __ + d __ __ __ + e __ __ __ + 5 Complete the path. Work backwards to check. 760 - 133 - 294 - 76 - 187 6 After Jules won 168 marbles he owned 375. How many did he begin with? __________ © Blake Publishing — Targeting Maths Teaching Guide 5 This page may be reproduced by the original purchaser for non-commercial classroom use. 13 Student pages 14–17 Multiplication Learning focus • Revise factors. A factor is a whole number which can divide into another whole number without any remainder. • Work examples on the board. eg What are some factors of 24? • Revise multiples. A multiple is the product of two or more factors. • Work examples on the board. Tell me some multiples of 7. • Show how one number may be a factor of several larger numbers. Student page 15 VELS: NUMBER Outcomes and Standards Number Relationships 4.2 Specify multiples and factors of whole numbers. Mental Computation 4.1 Recall automatically basic multiplication and division facts, simple common fraction facts and frequently used common fraction, decimal and percentage equivalences. 4.2 Use knowledge of place-value and number properties to increase the range of computations which can be carried out mentally. Computation 4.2 Use written methods to multiply and divide whole numbers. • Finds and uses factors of whole numbers. • Generates and recognises multiples of whole numbers. • Recalls multiplication and division facts. • Uses number properties to generate multiples. • Multiplies whole numbers without using a calculator. Key words factor, product, multiple, double, digit cards Resources catalogues, number cards, dice Additional work sheets Targeting Maths Upper Primary Operations and Number Patterns • Multiplication — Unit 1 14 • The first multiple of any number is the number itself (8 π 1 = 8). • Look at the fact box and revise the words product and multiple. • Show how to multiply by 2, 4 and 8 by using doubles. Work examples on the board. eg 17 π 8 = 17 doubled (34), doubled (68), doubled (136). Student page 16 • Discuss the fact box. Apply the ‘tricks’ to examples suggested by the students. • Work an example like question 1 on the board to help students write instructions. This does not come easily to many students. eg I doubled 16 to get 32, then again to get 64 then again to get 128. That is my answer. Student page 17 • Break down a multiplication into its parts, eg 37 π 6 means 7 π 6 and 30 π 6. • Work many examples on the board. • Work two-digit by one-digit and three-digit by one-digit numbers. • Point out the example in the fact box so students can use it if they need to. Answers for assessment page 17 1 a 1, 2, 3, 4, 6, 8, 12, 24 (any four) b 1, 2, 4, 5, 8, 10, 20, 40 (any four) c 1, 3, 5, 9, 15, 45 (any four) 2 a 3, 6, 9, 12, 15, 18 b 5, 10, 15, 20, 25, 30 c 7, 14, 21, 28, 35, 42 d 12, 24, 36, 48, 60, 72 e 50, 100, 150, 200, 250, 300 3 a 96 b 160 c 248 d 432 e 840 4 a 252, Teacher check b 1 740, Teacher check c 290, Teacher check 5 a 515 b 288 c 4 347 d 4 072 6 Teacher check Targeting Maths Teaching Guide Year 5 Mental and Oral Strategies Counting by multiples Buzz Students count by 3s, 4s, 6s up to π10 or π12 etc. as practice for multiplication. Practise forwards and backwards. Time students who wish to compete. State a factor, eg 3. Count by ones around the classroom. For every multiple of the given factor, students say ‘buzz’ (or ‘fizz’) eg 3π table. 1, 2, buzz, 4, 5, buzz. They sit when they make a mistake. The last standing is the winner. Activity Bank Shopping for a large number Roll a multiple Using shopping catalogues, find the cost of multiple items from a grocery list, eg 4 tins of asparagus at $2.55 a tin. Students form groups of four. Each roll a die and multiply by the number rolled. eg 3 π 5 π 2 π 6 = 180. Write the score for each multiplication. Keep a running total. The first group to reach 1 000 wins. Pot luck Teams Deal out number cards with numbers to 20 on them, 4 to a student. See who can make the largest or the smallest total using mixed operations. How many ways can the class be assigned to teams without any children being left out? Allow children to arrange themselves in teams of 3, 4, 5, 6, 7, 8, 9, 10 etc. Discuss factors of the class total, number needed to add to make even teams and what teams are possible when 1 or 2 etc. are absent. Targeting Maths Teaching Guide Year 5 15 Activity Card 7 ✎ Daylight Ferry FARES: Adults – 80c each way; Children – 50c each way; Pensioners – 60c each way TICKETS SOLD TODAY PRICE 20 adults both ways ________________ 10 adults one way ________________ 15 children both ways ________________ 5 pensioners both ways ________________ 5 pensioners one way ________________ Total ________________ ✎✎✎✎✎ Activity Card 8 Multiple Patterns On this hundred chart, circle multiples with the given colour. 1. Multiples of three – yellow 2. Multiples of six – green 3. Multiples of five – red 4. Multiples of four – purple 5. Multiples of eight – blue. Describe your findings. 16 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 © Blake Publishing — Targeting Maths Teaching Guide 5 This page may be reproduced by the original purchaser for non-commercial classroom use. Assessment Name __________________________________________ Multiplication Date _____________________________ 1 Write 4 factors in each tree. 24 40 45 2 Write the first 6 multiples of: a 3. _____ _____ _____ _____ _____ _____ b 5. _____ _____ _____ _____ _____ _____ c 7. _____ _____ _____ _____ _____ _____ d 12. _____ _____ _____ _____ _____ _____ e 50. _____ _____ _____ _____ _____ _____ 3 Multiply by 8 mentally. a 12 ______ b 20 ______ c 31 ______ d 54 ______ e 105 ______ 4 Work each one mentally then write how you did it. a 63 π 4 = _______ _____________________________________________ b 87 π 20 = _______ _____________________________________________ c 58 π 5 = _____________________________________________ 5 a 75 π 7 _______ b 96 π 3 c 483 π 9 d 509 π 8 6 The answer is 56. Write the problem. © Blake Publishing — Targeting Maths Teaching Guide 5 This page may be reproduced by the original purchaser for non-commercial classroom use. 17 Student pages 18–21 Fractions Learning focus • Draw the diagram from page 18 on the board. Use it for practice in recognising fraction parts. • Ensure that students recognise each bar as one whole. • How can three thirds be equal to eight eighths? Discuss. • Students answer (and ask) questions about the diagram. Student page 19 VELS: NUMBER Outcomes and Standards Mental Computation 4.1 Recall automatically basic multiplication and division facts, simple common fraction facts and frequently used common fraction, decimal and percentage equivalences. Computation 4.3 Use models to illustrate the four operations with common fractions, and develop written methods for carrying out these operations. Numbers and Numeration 4.2 Compare and order common fractions. 4.3 Rename common fractions as decimals and percentages. • Uses common fractions in addition and subtraction facts. • Uses simple common fractions in addition and subtraction facts where fractions have related denominators. • Finds fractional parts of discrete collections. • Locates fractions on a number line. • Finds fractional parts of collections and quantities. • Compares and orders common fractions. • Converts a simple common fraction to a decimal. Key words fraction, equivalent, equivalence, nought, decimal Resources • Fractions can be part of a group or part of a whole, eg half the class (group) or half an orange (whole). • Practise this concept in the classroom. eg How many is half the desks? How many pages in half of this book? How many is one third of the windows? etc. • Draw diagrams on the board to practise simple addition 1 3 and subtraction. eg Draw 6 balls. What is 6 + 6 ? 5 2 What is 6 – 6 ? Student page 20 • On the board draw a long number line 0 to 1. How would we show halves? (Divide it into two equal parts.) How would we show thirds? (Divide it into three equal parts.) etc. 1 • Where would we write 5 ? What must you do first? • For the problem solving, encourage students to draw diagrams in their workbooks as an aid if it is needed. Student page 21 • What is a tenth? Where do we use tenths? (money particularly) • Point out that our number system is a decimal one where tenths play a prominent part. • Practise the correct reading of decimals, eg nought point 5 etc. Answers for assessment page 21 1 Teacher check 2 5 9 6 2 a 10 , 0.2 b 10 , 0.5 c 10 , 0.9 d 10 , 0.6 3 Teacher check 2 4 3 7 4 a 3 b 6 c 4 d 12 5 a= b< c> d= e< 6 a $2 b $15 1 e 4 6 f 12 4 g 6 1 h 8 blank playing cards, fraction dominoes, grid paper, newspapers Additional work sheets Targeting Maths Upper Primary Numeration and Fractions • Common Fractions — Unit 1 18 Targeting Maths Teaching Guide Year 5 Mental and Oral Strategies Guess my number — 20 questions Questions such as ‘Is it more than 50?’ are asked until the class is close to the target you have previously set. Encourage creative questions such as ‘is it odd, even, prime’ etc. Good listening and reasoning exercise. Equivalents for 21 , 41 Can the students go all around the class giving equivalent fractions for 12 or 14 ? If a student gives an incorrect equivalent the rest of the class must quickly acknowledge the error. Activity Bank Memory Fraction Dominoes On a pack of blank playing cards, write many equivalent fractions for 1, 12 , 14 , 34 . Up to 6 students can play on the floor or a large table. All cards are face down. Students turn over two cards, if they are equivalent they keep the pair and have another turn. If they are not equivalent, they are turned face down again. Everyone tries to remember where they are to use later for their turn. Take turns around the group. The player with the most pairs at the end wins. Use commercial or homemade fraction dominoes to practise matching equivalents. Equivalent bars Media search Use grid paper. Students make a bar 24 units long to equal one whole. Using more 24 unit bars colour and label sections to show halves, quarters, thirds, sixths, twelfths, eighths, similar to page 18. Cut fraction pieces and paste them down on paper to show addition number sentences. Record the number sentences. Display pages in the classroom. From newspaper or commercial advertisements and articles, cut out sections that refer to fractions. Discuss them as a class. Make posters to display in the classroom. Targeting Maths Teaching Guide Year 5 19 Activity Card 9 1 2 1 4 3 4 5 6 1 2 1 4 1 4 5 6 1 4 Lost Pieces The children have lost some parts of these pattern block shapes. Draw in the missing parts to help them. 1 2 1 2 3 8 1 3 2 3 7 8 1 4 1 2 5 6 1 2 1 4 5 6 1 4 1 4 1 2 Activity Card 10 Plan a Farm On a farming lot: • 1 4 of the land is to be used for a house. • • • 1 8 1 3 3 8 for utilities. for growing vegetables . for animals. Mark each area as you would plan it for your farm. What will you do with the space left over? Illustrate each area you plan. © Blake Publishing — Targeting Maths Teaching Guide 5 This page may be reproduced by the original purchaser for non-commercial classroom use. 3 4 1 2 5 6 5 6 20 ✎ 1 2 5 6 5 6 1 2 1 4 ✎ Assessment Name __________________________________________ Fractions Date _____________________________ 1 On the diagram colour to show: a 3 1 b 6 5 3 d 4 1 c 12 2 Write the fraction and the decimal. a b d c _ . 10 = 0 ____ _ . 10 = 0 ____ _ . 10 = 0 ____ _ . 10 = 0 ____ 3 Write these fractions on the number line. 1 1 b 3 a 2 3 4 c 4 1 d 6 e 12 0 1 1 3 1 1 b 6 + 6 =— 3 2 f 12 – 12 = — 4 a 3 + 3 =— e 4 – 4 =— 5 Use 10 c 4 1 2 4 + 4 =— d 12 + 12 = — 5 h 8 – 8 =— 1 g 6 – 6 =— 2 5 7 6 >, < or = to make these true. 1 6 a 2 ____ 12 5 b 0.4 ____ 10 c 1 6 a Jodi has $12 and spent 6 of it. How much is spent? ___________ 6 2 8 ____ 8 9 d 10 ____ 0.9 1 1 e 3 ____ 2 1 b Will was given $20 and saved 2 of it. How much did he spend? ___________ © Blake Publishing — Targeting Maths Teaching Guide 5 This page may be reproduced by the original purchaser for non-commercial classroom use. 21 Student pages 22–25 Patterns Learning focus • Where do we see patterns? • Why are some patterns important? Discuss places where patterns are mathematically important, eg in architecture. • Look at the steps in the picture. Can you see a pattern? Discuss. Two steps are being added each time. • Make sure that students know it is not an accumulative total. The number of blocks is for each step. • On the board do a 1 + 1 pattern. Describe it in several ways. Add 1 to previous number. 1 times table. Progressive counting etc. Student page 23 VELS: NUMBER Outcomes and Standards Number Patterns and Relationships 4.1 Generate and investigate number sequences which may involve fractions, decimals and combinations of operations, using a calculator where appropriate. Investigation 4.2 Clarify the essential nature of a task or problem and identify key information in the context under consideration. • Describes and tests a rule which produces a given number pattern or sentence. • Verifies rules for sequences which relate each element to the previous element. • Generates and investigates sequences. • Uses rules which involve a combination of operations to make a sequence. • Works out elements according to their position in sequence. • Allow use of blocks. • Explain that when drawing the steps only the faces need be shown (not 3D). • Revise what was done on page 22. Student page 24 • Have match sticks available for use if needed. • Work pattern A as a class. Student page 25 • Work question 1 A as a class. Students can suggest the types of words which will be used to describe the patterns. • Write a word list on the board. • Use octagonal pattern blocks or stencils if available. If not, cut out cardboard octagons for students to trace around. Answers for assessment page 25 1 2 3 4 6, 10, 14, 18, 22, 26, 30, 34, 38, 42 Teacher check (π4 +2) a 50 b 82 c 402 Teacher check Key words geometric, pattern, numeral, octagon Resources building blocks, match sticks, octagonal pattern blocks Additional work sheets Targeting Maths Upper Primary Operations and Number Patterns • Number Patterns — Unit 1 22 Targeting Maths Teaching Guide Year 5 Mental and Oral Strategies What’s my pattern? Look around Give a number pattern orally. eg 2, 5, 8, … Have different students continue it for another 5 terms. Have another student state the pattern in words. Can students identify this pattern in real life? Look around the classroom and find geometric patterns in the building or the equipment, eg windows/panes of glass, cupboards/pigeon holes. Students state the pattern in words as well as numbers. A student gives a number pattern and other students guess to which aspect of the classroom they are referring. Activity Bank Pattern block puzzle Patterns in multiples Students can use pattern blocks to make a geometric pattern and record it in table form, eg hexagons. Teach children to look for patterns in numbers everywhere. Joined Hexagons 1 2 Sides 6 11 16 21 3 4 What is the pattern of digits in the ones column of each multiplication table? 2 = 2, 4, 6, 8, 0 and repeat. 3 = 3, 6, 9, 2, 5, 8, 1, 4, 7, 0 and repeat. What are the patterns in other sets of multiples? Complete a pattern Odd man out Work in pairs. One student makes an incomplete repeating geometric pattern with pattern blocks. The other student completes the pattern to the satisfaction of the first student. Give students a pattern of numbers with one mistake. They work out which term does not belong. Use numbers in order: eg 7, 14, 21, 27, 35, or random, eg 21, 35, 27, 7, 14. Students can also make up the patterns. They then swap roles. Targeting Maths Teaching Guide Year 5 23 Activity Card 11 ✎ Regular Polygons On a sheet of paper draw the regular polygons from a triangle, 3 equal sides, up to an octagon, 8 equal sides. Complete a table showing the number of equal sides, equal angles and axes of symmetry. Triangle Square Pentagon Hexagon Heptagon Octagon Sides Angles Axes of symmetry What is the pattern you can see? ________________ How many axes of symmetry has a decagon? ________________ Activity Card 12 Find a Pattern ✎ Search this square for patterns consisting of FIVE terms. Circle the numbers. 24 2 3 6 9 12 15 5 21 2 4 7 10 27 16 4 4 6 8 6 11 14 17 6 14 8 15 18 5 5 24 256 12 3 64 16 18 20 10 19 7 4 16 20 22 24 26 28 9 2 4 8 16 32 30 31 11 22 1 25 20 15 10 5 13 Write the remaining numbers here. ____ ____ ____ ____ ____ ____ Arrange them into a pattern. © Blake Publishing — Targeting Maths Teaching Guide 5 This page may be reproduced by the original purchaser for non-commercial classroom use. Assessment Name __________________________________________ Geometric Patterns Date _____________________________ Jemma is making shapes using match sticks. 1 Fill in this table for Jemma’s shapes. Shape 1 2 3 4 5 6 7 8 9 10 Number of matches 2 a Describe the pattern in words. b Describe it a different way. 3 How many match sticks are needed for the: a 12th shape? _________ b 20th shape? _________ c 100th shape? _________ 4 a Draw your own shape pattern. b Fill in the table for your pattern. Shape Number of matches c Describe it in words. © Blake Publishing — Targeting Maths Teaching Guide 5 This page may be reproduced by the original purchaser for non-commercial classroom use. 25 Student pages 26–28 Length Learning focus VELS: MEASUREMENT Outcomes and Standards Measuring 4.1 Choose attributes and standard units appropriate to the task. 4.2 Make judgments about the relative size of objects based on comparison to known benchmarks or standard units. 4.4 Use measuring instruments, reading simple scales and measuring accurately to the nearest marked gradation, taking into account the degree of exactness required. Location 4.3 Visualise and find paths to satisfy specifications on maps, grids and mazes. Relationships 4.1 Measure and compare the perimeter and area of regular and irregular polygons. • Estimates by comparison with standard units. • Selects appropriate units to specify a quantity. • Finds the shortest route between two places on a map. • Uses standard units to measure length. • Uses measuring instruments for exact measurements. • Calculates the perimeter by adding lengths. • Discuss kilometres. Why do we need kilometres? • Name some things that are measured in kilometres. Write a list on the board. • Take the class for a walk to measure one kilometre. Students can be in groups. Each group has a trundle wheel and a note pad and pencil. Get them to work in 100 metre lots both in counting, recording and in using the trundle wheel. Student page 27 • Teach 1 000 metres = 1 kilometre. 1 • Discuss parts of a kilometre. How many metres in 2 1 a kilometre? … 4 of a kilometre? etc. • Before working questions 4, 5 and 6 work some examples on the board. Student page 28 • Revise abbreviations used for measurements. Make a class chart and display. • Look carefully at the fact box and remind students that it is there for them to refer to. • Work many examples of conversions on the board until students feel capable of working examples in the text. • Revise perimeter. Stress that it is the distance around the outside of a shape — add the lengths of all the sides. Answers for assessment page 29 1 2 3 4 5 6 7 Teacher check a 750 m b 20 cm c 60 km a 70 b 730 c 68 d 131 e 2 000 a 6 000 b 11 000 c 7 800 d 600 e 841 a 6 b 3.19 c 51. 4 d 2 000 e 7 000 a 9 b 26 c 8.5 d 16.5 a 144 mm, 14.4 cm b 104 mm, 10.4 cm Key words estimate, distance, metre, kilometre, centimetre, millimetre, measure, perimeter, length, width Resources coloured pencils, street directories, trundle wheels, atlas, encyclopedia, Internet Additional work sheets Targeting Maths Upper Primary Measurement • Length — Unit 1 26 Targeting Maths Teaching Guide Year 5 Mental and Oral Strategies How far? Millimetres to kilometres Guess (estimate) the length of various classroom distances, such as from one student to another, from the door to a desk, from the classroom to the Library. Build up awareness about real distances that are in the students’ immediate environment. Start with a number of millimetres in the millions and divide by ten to get centimetres, by 100 to get metres, by 1 000 to get kilometres. Make calculations the other way — kilometres to metres to centimetres to millimetres. Activity Bank My measurements Guinness Book of Records Allow students to measure each other’s vital statistics, eg, hand span, length of little finger, length of foot, length of arm, arm span, step. Make a chart. Research the world’s records to find records that are about length. Who is the world’s tallest man? … shortest woman? … longest animal? … shortest fish? etc. World geography Odometer readings From an atlas or encyclopedia, find the heights of the world’s tallest mountains in metres. Graph them and make posters for the classroom. Have students write down the odometer readings from the family car every morning or every night. Discuss the distance being travelled each day. Children can watch the odometer while a parent is driving and note places that are within 1 km of home, within 5 km of home etc. There are many other lengths to do with geographical features that can be researched. Targeting Maths Teaching Guide Year 5 27 Activity Card 13 Street ry Directo Around the Town Work with a partner. Use a Street Directory for the area in which you live. 1. Find your suburb or town. 2. Locate your school. 3. Using the scale given in the directory, find 2 places that are less than 1 kilometre from your school and 5 places that are less than 5 kilometres from your school. 4. How far away from your school is the Railway Station, the Main Shopping Centre and the Hospital? Activity Card 14 J Measure a Kilometre ✇ How far is one kilometre around your school? Use a trundle wheel and with a partner, measure out a distance around your school equal to one kilometre. You will need to measure around a given area a certain number of times, eg around the soccer ground twice. 28 © Blake Publishing — Targeting Maths Teaching Guide 5 This page may be reproduced by the original purchaser for non-commercial classroom use. Assessment Name __________________________________________ Length Date _____________________________ 1 Name two lengths that are measured in: a millimetres. _________________________ _________________________ b centimetres. _________________________ _________________________ c metres. _________________________ _________________________ d kilometres. _________________________ _________________________ 2 Estimate the distance: a walked by Sam. ________ 0 1 km 0 1m 0 100 km b jumped by Fred. ________ c cycled by Joc. ________ 3 Change to millimetres. a 7 cm _______ b 73 cm _______ c 6.8 cm _______ d 13.1 cm______ e 2 m _______ 4 Change to centimetres. a 60 m ________ b 110 m _______ c 78 m ________ d 6 m ________ e 8.41 m______ 5 Change to metres. a 600 cm ______ b 319 cm ______ c 5 140 cm_____ d 2 km ________ e 7 km _______ 6 Change to kilometres. a 9 000 m __________ b 26 000 m __________ c 8 500 cm __________ d 16 500 m __________ 7 Measure the dimensions of each shape. Write the perimeter in millimetres and then in centimetres. a b P = __________ mm, P = __________ cm P = __________ mm, P = __________ cm © Blake Publishing — Targeting Maths Teaching Guide 5 This page may be reproduced by the original purchaser for non-commercial classroom use. 29 Student pages 29–31 Time Learning focus VELS: MEASURMENT Outcomes and Standards Time 4.1 Use and construct timetables and use and analyse calendars. 4.2 Estimate, measure and calculate time elapsed (duration). 4.3 Tell the time accurately using analogue clocks and digital clocks. • Uses 12-hour and 24-hour time. • Tells the time on analogue and digital clocks. • Uses 12-hour and 24-hour time. • Calculates time elapsed. • Uses a calendar. • Tells the time accurately. Key words twenty-four hour time, leap year, earliest, latest, daylight saving Resources classroom clock, timetables, map of Australia Additional work sheets Targeting Maths Upper Primary Measurement • Time — Unit 2 30 • Why is twenty-four hour time sometimes used? Discuss. • Who uses twenty-four hour time? • Draw a clock on the board with the 24-hour times written around the outside, eg above the 1 hour write 13 etc. • Use the board clock to practise time conversions. What is the 24-hour time at 2:30 p.m.? If it is 1715 what is the p.m. time? • Show students that 24-hour time is written always using four digits (usually without a break between the hours and minutes). However they may see it written in slightly different ways. eg 0730 may be written as 7:30 or 07:30. Digital clocks will usually show the colon. • Practise throughout the day. Using 24-hour time tell me the time now … when will we go to Library? Student page 30 • Use the information on page 29 to work questions 1, 2 and 3. • Revise a.m. and p.m. times. Look at the fact box. Time before midday is a.m. time. After midday is p.m. time. • If possible have a clock in the classroom which does show 24-hour time. Otherwise draw one on cardboard and display it so students can use it as a reference. Student page 31 • Discuss daylight saving. Tell the students the arguments for and against it, eg it makes the curtains fade. • Make a poster with For and Against arguments listed. • Encourage students to ask for opinions at home and then hold another class discussion. • Point out that Queensland does not have daylight saving so for people living on the border there is quite some confusion. Answers for assessment page 33 1 a 0730 b 1715 c 2040 d 1115 e 0100 f 1645 g 2205 h 1810 (colons can be used) 2 a 4 a.m. b 1 p.m. c 7:20 p.m. d 7:15 a.m. e 9:10 p.m. f 10:30 a.m. g 4:05 p.m. h 11:55 p.m. 3 a 3:45 p.m. b 5:30 p.m. c 6:10 p.m. d 7 p.m. e 8:05 p.m. 4 a 1000 b 1220 c 1400 d 1607 e 1715 (colons can be used) 5 a last Sunday, October b last Sunday, March 6 Teacher check 7 a 8:28 b 8:03 8 a 28 or 29 b depends on whether it is a leap year Targeting Maths Teaching Guide Year 5 Mental and Oral Strategies Rewrite the clock Elapsed time Rewrite the times on your classroom clock to twenty-four hour time. Refer to activities in the school day using twenty-four hour time. eg The bus will leave at 13:15. Ask children to give the difference in time from 13:10 to 14:55, where the calculation is straightforward. Graduate to times such as 17:20 to 18:05. Count on to the next hour, then to the given ending time. Say an a.m. or p.m. time and students write the 24-hour time and vice versa. Activity Bank Collect timetables Rewrite timetable Have students gather timetables from buses, trains, ferries or planes where twenty-four hour time is used. Display them in the classroom. Discuss time between departures. Use twenty-four hour time to rewrite the class or school timetable. Which time annotation do students prefer? Use the timetables for children to write their own problems. The class reads and solves the problems. Home appliance Elsewhere Have students gather a list of all the appliances at home which use twenty-four hour time. Are there different methods of displaying the time? eg 00:22 or 24:22. How many appliances in their homes have to be changed when daylight saving began or ended? Don’t forget the car! Display a map of Australia with the various time zones marked. Targeting Maths Teaching Guide Year 5 Stop sometimes during the day to ask what children in another Australian state may be doing. Discuss whether daylight saving must be taken into consideration. 31 Activity Card 15 Timeline ✎ Write down the times at which you begin the following daily activities on a school day. Rise and dress Arrive school Take lunch Complete homework Eat dinner Eat breakfast Begin lessons Leave school Have play or recreation Go to bed Leave home for school Take recess Arrive home Watch TV Construct a timeline at least 24 cm in length. Label it according to the day’s times. Write the above activities on the timeline. Compare yours with a friend’s. Activity Card 16 ✎ Play with Time We write the time thirty minutes and thirteen seconds past nine in the evening as 21:30:13 hours minutes seconds Write the following times in twenty-four hour time. 1 twenty-seven minutes and fifteen seconds past seven in the morning 2 three minutes and fifty seconds past eleven at night 3 twenty-five minutes to three in the afternoon 4 What is the following time in words? 12:34:56 5 What might 01:23:45, 6-7-09 mean in 2009? 32 © Blake Publishing — Targeting Maths Teaching Guide 5 This page may be reproduced by the original purchaser for non-commercial classroom use. Assessment Name __________________________________________ Time Date _____________________________ 1 Write these times in 24-hour time. a 7:30 a.m. ______ b 5:15 p.m. ______ c 8:40 p.m. ______ d 11:15 a.m. ______ e 1:00 a.m. ______ f 4:45 p.m. ______ g 10:05 p.m. ______ h 6:10 p.m. ______ 2 Write these times as a.m. and p.m. a 04:00 ______ b 13:00 ______ c 19:20 ______ d 07:15 ______ e 21:10 ______ f 10:30 ______ g 16:05 ______ h 23:55 ______ 3 Yoko arrived home from school at (a) 15:45. She watched television until (b) 17:30 and then did her homework until (c) 18:10. Her dad arrived home at (d) 19:00 so the family ate dinner at (e) 20:05. Write all the times using a.m. or p.m. a __________ b __________ c __________ d __________ e __________ 4 Seb’s friend Sam arrived at (a) 10 a.m. They played marbles until (b) 12:20 p.m. when Mum called them for lunch. At (c) 2 p.m. she took them to the cinema. The film ended at (d) 4:07 p.m. Sam arrived home at (e) 5:15 p.m. Write all the times using 24-hour time. a __________ b __________ c __________ d __________ e __________ 5 In NSW when does Daylight Saving: a begin? ____________ b end? _______________ 6 a Write two reasons why many people like Daylight Saving. b Write two reasons why many people do not like Daylight Saving. 7 a When Tilly woke up the morning Daylight Saving started the clock showed 7:28. What did she change it to? _______________ b When Tomas woke up the morning Daylight Saving ended his clock showed 9:03. What did he change it to? _______________ 8 a How many days in February? __________ b Explain your answer. © Blake Publishing — Targeting Maths Teaching Guide 5 This page may be reproduced by the original purchaser for non-commercial classroom use. 33 Student pages 32–34 Prisms and Pyramids Learning focus • Have many models of prisms and pyramids. Allow time for students, in small groups, to handle and discuss the models. • What is a prism? • What is a pyramid? • Revise — a prism has two identical end faces (their shape names the prism) and all other faces are rectangles; a pyramid has one base face (its shape names the pyramid) and all other faces are triangles. • What is a cross-section? Ensure that students know that the cross-section is to be at the red mark. Student page 33 VELS: SPACE Outcomes and Standards Shape and Space 4.2 Analyse, explain and compare the spatial properties of lines, angles, polygons, polyhedra and crosssections using conventional spatial terms. 4.3 Make congruent copies of given threedimensional objects. 4.4 Draw conventional representations of prisms, pyramids, cylinders and cones. 4.5 Visualise, explain and represent 'what is not seen' of an object. • Recognises, describes and names 3D objects. • Represents 'what is not seen' of an object. • Describes a 3D object in detail. • Classifies objects according to properties. • Makes congruent copies of 3D objects. • Draws conventional representations of prisms and pyramids. Key words prism, pyramid, three-dimensional, crosssection, face, corner, edge Resources • Revise faces, edges and corners. • Using models have students show the faces, edges and corners. • How can you be sure that you have counted all of them? • For questions 2 and 3 students could work in groups and have models they can handle in order to explore similarities and differences. Student page 34 • Make sure that all students have sharp pencils and are using a ruler. • Have spare sheets of isometric dot paper and blank paper for use in question 2. • Many students will need help with their drawings! Answers for assessment page 37 1 a rectangular prism, 6, 12, 8 b square pyramid, 5, 8, 5 c pentagonal prism, 7, 15, 10 d triangular pyramid, 4, 6, 4 e hexagonal pyramid, 7, 12, 7 f triangular prism, 5, 9, 6 2 Teacher check 3 Pyramids are named according to the shape of their base. 4 Teacher check models of common prisms and pyramids, plasticine, drinking straws, pipe cleaners, fishing line, magazines Additional work sheets Targeting Maths Upper Primary Space and Chance and Data • Space 3D — Unit 1 34 Targeting Maths Teaching Guide Year 5 Mental and Oral Strategies What am I? (I) What am I? (II) One student gives clues using the properties of a 3D object. After three clues the others must guess the object. The one to guess then chooses another object and gives the clues. Give a student the name of a 3D object on a small card. The other students guess what it is, using only ‘Yes’/ ‘No’ questions. eg Do you have 5 faces? Activity Bank Cross-sections Models Students model prisms and pyramids using plasticine or clay. Use fishing line to slice through a model to display a cross-section. Students trace the cross-section onto card and display the 3D object and the tracing. Use coloured drinking straws and cut pieces of pipe-cleaners as ‘joiners’ for students to make ‘see-through’ models of all 3D objects. Allow students to cut drinking straws accurately (equally) to make edges. Give them a quantity of pipe cleaners cut to about 4 cm long. They should bend them to 90 degrees to use as joiners at vertices. Label and display the models on a table or shelf. Nets 3D in the home Use plastic 3D models for students to draw around faces to form the nets for the models. Search magazines for photographs of items used in homes, which demonstrate use of various regular 3D objects. Cut out the nets and fold up to form the 3D object. No gluing together for this activity. Targeting Maths Teaching Guide Year 5 Rooflines may be prisms or pyramids. Soft furnishings and appliances may be any shape. Students cut out and arrange their choices neatly under headings on posters. Display. 35 ✎ Activity Card 17 Euler’s Rule Euler’s Rule states that the sum of Faces and Vertices = Edges plus Two Check this rule by filling the table below for the 3D objects above. Name Faces Vertices Edges 4 6 hexagonal prism triangular prism rectangular prism square pyramid What 3D shape is not drawn or named on the table? Activity Card 18 Humpty Dumpty Using clay or plasticine, build a 3D object with straight edges and flat faces. Cut it carefully into four pieces with straight cuts, using fishing line. Have a friend put it back together again! 36 © Blake Publishing — Targeting Maths Teaching Guide 5 This page may be reproduced by the original purchaser for non-commercial classroom use. Assessment Name __________________________________________ 3D Objects Date _____________________________ a b c d f e 1 Complete the table. Name Number of faces Number of edges Number of corners a b c d e f 2 What is the difference between a pyramid and a prism? 3 How are pyramids named? 4 Draw: a a triangular prism. b a square pyramid. © Blake Publishing — Targeting Maths Teaching Guide 5 This page may be reproduced by the original purchaser for non-commercial classroom use. 37 Student pages 35–37 2D Shapes Learning focus VELS: SPACE Outcomes and Standards Shape and Space 4.1 Recognise, describe and represent parallel, perpendicular, horizontal and vertical lines, right angles, and angles greater than or less than 90 degrees (multiples of 45 degrees). 4.2 Analyse, explain and compare the spatial properties of lines, angles, polygons, polyhedra and cross-sections using conventional spatial terms. Investigation 4.1 Generate mathematical questions from presented data and from familiar contexts. • Classifies shapes according to properties. • Recognises, describes and names common 2D shapes. • Recognises and describes parallel lines. • Uses geometrical language. • Generates mathematical questions. • Explains and compares using conventional spatial terms. Key words quadrilateral, rhombus, kite, parallelogram, trapezium, parallel, diagonal, octagon, pentagon, hexagon • Teach — 2D shapes are plane shapes that have only two dimensions, height (length) and breadth (width). They do not have depth. • They are named according to the number of sides. • Four-sided shapes are called quadrilaterals. • Draw each of the special quadrilaterals on the board. • Revise the properties of a square and a rectangle. • Teach the distinguishing features of the others. Parallelogram — opposite sides parallel and equal. Kite — two pairs of adjacent equal sides. Trapezium — one pair of opposite parallel sides. Rhombus — all sides equal and opposite angles equal (a square pushed out of shape). • Remind students that regular means to have all sides equal and all angles equal. Irregular is to have sides and angles of different sizes. Student page 36 • Make sure that students know to use only the words from the Word Bank for question 1. • Teach diagonal — a line drawn from one corner to another corner of a shape. Dispel the myth that any sloping line is a diagonal. • Point out that a shape can have many diagonals. • Ensure that rulers are being used to draw the diagonals. Student page 37 • On the board draw all shapes to 10 sides. • Beside each shape write its name. (7 sides heptagon; 9 sides nonagon; 10 sides decagon) • Make a class chart of shapes and their names. Display for students to use as a reference. Answers for assessment page 41 1 a rhombus b pentagon c parallelogram d hexagon 2 Teacher check 3 a rectangle, kite b Teacher check c A has two equal diagonals; B has two diagonals that are perpendicular to each other. Resources pattern blocks, cm grid paper, magazines Additional work sheets Targeting Maths Upper Primary Space and Chance and Data • Space 2D — Unit 2 38 Targeting Maths Teaching Guide Year 5 Mental and Oral Strategies What am I? Mini-shapes A student describes a shape giving one property at a time. On the board, draw several polygons on top of one another. Students name any other shapes they can see and count how many squares, triangles, rectangles etc. there are. The class tries to guess the shape. The first student to guess the shape gives the next lot of clues. Include diagonals and angle properties in the list of properties. Activity Bank Enlarge and reduce Tessellations Students copy special quadrilaterals from 1 cm squared paper to 5 mm squared paper, or to 2 cm squared paper. What changes? Using a limited number, eg 4, 8, 12, of pattern blocks of rhombuses, kites or trapeziums, students make a tessellated pattern. They write down how the pattern was formed. What happens to the perimeter, area, properties of the shape? Colour the patterns and make a class display. Shapes within shapes Shapes in the environment Examine the properties of a kite, rhombus, trapezium etc. when diagonals have been drawn. What types of triangles are formed? Are they right-angled? Do they have three equal sides? … two equal sides? In home style magazines, find pictures of special quadrilaterals used in homes, furniture, construction etc. Make posters, each with a different heading and paste on the pictures. Targeting Maths Teaching Guide Year 5 39 Activity Card 19 Tangram Puzzles Use all seven pieces of a tangram to make animals, buildings, people or flowers. Draw around the puzzle to show the outline only. Ask other students to use all seven tans to reconstruct your puzzle. Activity Card 20 Barrier Games Two students sit back to back on the floor. Student 1 secretly makes a pattern using 20-30 pattern blocks including quadrilaterals. Student 2 is not to see the pattern. Student 1 then instructs Student 2 to make the same pattern using verbal instructions only. When Student 2 has completed the task, they look at Student 1’s pattern and make comparisons. 40 © Blake Publishing — Targeting Maths Teaching Guide 5 This page may be reproduced by the original purchaser for non-commercial classroom use. Assessment Name __________________________________________ 2D Shapes Date _____________________________ 1 Name each shape. a b d c 2 Draw: a a trapezium b a kite c a regular quadrilateral d a triangle e an irregular octagon f an irregular pentagon 3 A B a Name each shape. b Draw the diagonals in each shape. c Write one fact about the diagonals for each shape. A B © Blake Publishing — Targeting Maths Teaching Guide 5 This page may be reproduced by the original purchaser for non-commercial classroom use. 41 Student pages 38–41 Graphs Learning focus VELS: DATA Outcomes and Standards Interpreting Data 4.1 Extract and interpret numerical information contained in tables, data displays and databases. Reasoning 4.1 Make and test simple conjectures in each mathematics strand. Presenting and Summarising Data 4.1 Prepare tabular displays of discrete and continuous data. 4.2 Prepare visual displays of discrete and continuous (measurement) data using a range of graphical methods. 4.3 Compare, order and summarise data sets using simple numerical methods. Investigation 4.1 Generate mathematical questions from presented data and from familiar contexts. Collecting Data 4.2 Collect and record data systematically. • Reads and interprets data presented in graphs. • Makes and tests simple conjectures. • Displays data in an organized form. • Generates mathematical questions from presented data. • Presents collected data in a table. • Displays data in a picture graph. • Records data systematically. • Finds the lowest and highest values of a data set. • Interprets information in tables. • • • • • What is a graph? Why are graphs used? Where do you see graphs? How many types of graphs can you think of? Look at the graph on page 38 and find the key. Why is there a key? What does this key mean? • Have students discuss the symbol used. Ask for reasons why one symbol represents 4. Why not one symbol for one cake? • Is this graph easy to interpret? Why? • Make sure that the students look at the title and the labels on the axes. Student page 39 • • • • Students use the graph on page 38 as a model. Some may need help with choosing a suitable key. Discuss the scale and what can/cannot be used and why. Encourage sensible questions for question 3. Student page 40 • Introduce tally marks. Show how they are written in bundles of 5 to make counting easy. • Have class count to 100 in fives. • Practise tally marks on the board. Student page 41 • Introduce the bar graph. Why do you think it is called a bar graph? • Look at both axes and discuss their importance. • Ensure that students know it is a follow-on from page 40. Answers for assessment page 45 1 a 18, 15, 11, 4, 16 b 64 2 Teacher check 3 Teacher check Key words picture graph, symbol, scale, key, tally mark, bar, title Resources reference books, building blocks Additional work sheets Targeting Maths Upper Primary Space and Chance and Data • Graphs — Unit 1 42 Targeting Maths Teaching Guide Year 5 Mental and Oral Strategies Count by … Divide by … Practise use of 1 symbol equivalent to a number of items, Divide by 4s, 6s or 8s by counting backwards by these numbers. eg Start at different numbers, eg 58, so that a remainder is found: 58, 54, 50, 46, 42, 38, 34, 30, 26, 22, 18, 14, 10, 6, 2. Remainder = 2. = 4 sunny days. Count by 4s,(6s, 8s) for tables practice up to a given number. Activity Bank Picture graphs Tally that Find picture graphs which are used in atlases and other reference materials. Study their use and advantages over other graphs for the same purpose. In pairs, children read to each other. Have one student tally the number of times ‘and’ or ‘the’ is heard in the reading. Change ‘reader’ and ‘tallier’ roles and compare results. Choose a symbol Bar graph towers Give a picture graph scenario. Ask students to draw suitable symbols for use in picture graphs. Discuss their suitability in terms of ease of comprehension, ease of division into parts, and ease of drawing. Display best efforts. Represent numbers in a bar graph by having students build towers using coloured blocks. Discuss suitable scales, eg 1 block = 5 items. Targeting Maths Teaching Guide Year 5 43 ✎ Activity Card 21 ________________________ 50 All the data for this graph has been lost. 40 30 Make it up for Professor Badger. 20 10 0 Missing Data ___ ___ ___ ___ ___ ___ ________________________ Don’t forget to name the graph, and to label the axes to tell him what information is meant to be on the graph. Activity Card 22 ✎ Tell the Story This graph reports some information which was gathered from a survey of children about their favourite activities. Write a report for the newspaper about this survey. What conclusions could you as a reporter come to after studying this data? Why are children interested in these activities? Internet activities Crafts Sport Music Reading 44 Key © Blake Publishing — Targeting Maths Teaching Guide 5 This page may be reproduced by the original purchaser for non-commercial classroom use. = 10 students Assessment Name __________________________________________ Graphs Date _____________________________ The school canteen kept a tally of fruit sold on Monday. Fruit Tally apples bananas oranges pears mandarins Total 1 a Complete the total column. 555111 555 55 1 1111 555 1 b How many pieces of fruit were sold altogether?__________ 2 Draw a picture graph of the information. Don’t forget the key. _________________________________ 3 Draw a bar graph to show the information. Remember to write the title and to label the axes. _____________________________ _________________________________ _________________________________ © Blake Publishing — Targeting Maths Teaching Guide 5 This page may be reproduced by the original purchaser for non-commercial classroom use. 45 Student pages 44–46 Whole Number Back to Contents Learning focus • • • • • Teach Roman numerals to 100. Show how the symbols are grouped in threes and then change. Stress the ‘one before, three after’ aspect. Allow plenty of class practice using the board. Make a poster of the Roman symbols and display it so students can use it for reference. • What is the greatest difference between the Roman system and our decimal system? The use of zero. • Ensure that the students know that our system is called the Hindu-Arabic system. Student page 45 VELS: NUMBER Outcomes and Standards Numeration 4.1 Use place-value knowledge to read, write and order negative whole numbers and decimal numbers from thousandths to millions. Reasoning 4.3 Use and interpret simple mathematical models. • Uses and interprets simple mathematical models. • Reads, writes, compares and represents the structure of whole numbers to 5-digits. • Uses place value knowledge to round numbers for calculations. Key words Roman, numerals, Hindu-Arabic, value, rounding Resources wall map of Australia, toilet paper roll, blank cards, rope Additional work sheets Targeting Maths Upper Primary Numeration and Fractions • Number Systems — Unit 1 46 • Draw a number line on the board — from 2 000 at one end to 3 000 at the other. • Say a number and have a student write where it will be placed. The class agree or disagree with the placement. • How do we determine whether one number is larger than another? We look at the numerals in turn from the left. • Reinforce place-value columns. Student page 46 • Teach how to round numbers. The fact box can be referred to. • If a number ends in 0, 1, 2, 3 or 4 the number stays the same. If it ends in 5, 6, 7, 8 or 9 add 1. • When rounding to thousands the place number to look at is the hundreds number. eg In 2 678 because the hundreds number is a 6 we will add 1 to the thousands; 3 000. In 5 309 because the hundreds number is a 3 we will leave it; 5 000. Answers for assessment page 49 1 a V b XXIII c XI d XVIII e XIII f IX g XXXIV h XC i LVI j XXIX k XL l LXXII m LXXXVI n C o LXI 2 a 6 b 15 c 22 d 91 e 64 f 43 g 70 h 37 i 19 j 88 3 Teacher check 4 a 15 031 b 70 001 c 91 119 5 a 2 672 b 13 804 c 9 260 d 34 161 6 a 9 620 b 43 062 c 77 677 d 2 921 7 a 5 068 b 18 209 c 26 003 d 41 695 8 a 300 b 700 c 3 600 d 8 400 e 2 200 9 a 4 000 b 1 000 c 7 000 d 5 000 e $12 000 f $ 21 000 g $8 000 h $36 000 Targeting Maths Teaching Guide Year 5 Mental and Oral Strategies Odometer readings Roman numerals Write a number in the tens of thousands on the board, eg 34 587. Ask which number will change when the vehicle has travelled another — 1 km, 10 km, 100 km, 1 000 km, 10 000 km. Students can either write answers (practise using km and leaving a space between the number and the measurement) or answer orally around the class. Give quick tables questions but students answer in Roman Numerals, eg 7 π 6 = XLII. Activity Bank Roman numbers Number line Change the labels on things around the classroom so that they use Roman numerals, eg the clock, chapter headings, encyclopaedia volumes, chapter numbers. Unroll a roll of toilet tissue on the playground. Count the sheets and round off to an equal number of tens, discarding the rest. Calculate what each sheet would be worth if the entire line equalled 10 000 or 1 000 000. Mark the half-way point, then mark each sheet with its equivalent on the number line. Discuss the size of these numbers in dollars, metres, people. Students can write the date, question numbers etc. in Roman numerals. State areas Live number line Use an atlas to find the area of each Australian state. Round the areas off to the nearest thousand km2. On a wall map of Australia, laid on the floor, model the areas using base 10 materials, where a cube = 1 000 000 km2, a flat = 100 000 km2 etc. Make a 3 m – 4 m number line with a strip of paper or a rope. Label the ends, eg 0 and 10 000. Hand out five cards with numbers written on them and have students stand along the number line where they think their number belongs. Time each group and reward quick groups. Targeting Maths Teaching Guide Year 5 47 ✎ Activity Card 23 30-11-03 Palindromes Words or numbers which can be read backwards as well as forwards are called palindromes. MUM, DAD, EVE, LEVEL are palindromes. The 30th November, 2003 can be written as a palindromic number 30 – 11 – 03. Write four other dates that are palindromes. Which palindromic dates have occurred in your life? What is the next palindromic date in your life? Write four Roman numerals that are palindromes? 53035 L E V LE Activity Card 24 ✎ Sort the Numbers Sort the following numbers into their correct boxes. 14 570 14 068 15 606 15 001 Round to 15 000 48 13 875 25 248 16 003 4 884 Palindromes 15 876 28 280 14 841 15 249 < 15 000 © Blake Publishing — Targeting Maths Teaching Guide 5 This page may be reproduced by the original purchaser for non-commercial classroom use. 16 010 17 025 Multiples of 5 Assessment Name __________________________________________ Whole Numbers Date _____________________________ 1 Change to Roman numerals. a 5 ______ b 23 ______ c 11 ______ d 18 ______ e 13 ______ f 9 ______ g 34 ______ h 90 ______ i 56 ______ j 29 ______ k 40 ______ l 72 ______ m 86 ______ n 100 ______ o 61 ______ 2 Change to Hindu-Arabic numerals. a VI ____ b XV ____ c XXII ____ d XCI ____ f XLIII ____ g LXX ____ h XXXVII ____ i XIX ____ e LXIV ____ j LXXXVIII ____ 5 000 4 000 3 A = 4 500 B = 4 900 C = 4 200 D = 4 750 E = 4 361 4 Circle the larger number. a 15 031 13 699 b 7 643 70 001 c 19 991 91 119 5 Add 100. a 2 572 _______ b 13 704 _______ c 9 160 _______ d 34 061 _______ b 43 162 _______ c 77 777 _______ d 3 021 _______ b 17 209 _______ c 25 003 _______ d 40 695 _______ 6 Subtract 100. a 9 720 _______ 7 Add 1 000. a 4 068 _______ 8 Round to the nearest 100. a 293 _____ b 715 _____ c 3 640 _____ d 8 448 _____ e 2 199 _____ 9 Round to the nearest thousand. a 3 694 _________ b 1 407 _________ c 7 198 _________ d 5 379 _________ e $11 997 _______ f $20 603 _______ g $8 009 ________ h $36 217 _______ © Blake Publishing — Targeting Maths Teaching Guide 5 This page may be reproduced by the original purchaser for non-commercial classroom use. 49 Student pages 47–49 Addition Learning focus VELS: NUMBER Outcomes and Standards Computation 4.1 Use written methods to add and subtract decimal numbers. 4.4 Analyse a problem situation which may involve several different operations, decimal numbers, negative whole numbers and common fractions; express the problem symbolically and choose appropriate computational methods to solve it. Estimation 4.3 Use estimation strategies to check the results of written or calculator computations. Number Relationships 4.1 Generate and investigate number sequences which may involve fractions, decimals and combinations of operations, using a calculator where appropriate. Reasoning 4.1 Make and test simple conjectures in each mathematics strand. • Uses written methods to add decimal numbers. • Uses front end estimation. • Selects relevant information to solve a problem. • Uses front end estimation. • Investigates number patterns. • Understands the roll of place value in written methods for addition. • Presents statements about own findings. Key words estimate, actual, approximate, exact Resources calculator, Blu-tack, blank cards, supermarket catalogues • Revise addition of money. Insist on $ not the American dollar sign with two lines. • When adding money always put the sign in the answer and the decimal point to separate the dollars and cents. • Point out that the students are making their own choices but no two days are to be the same. • Discuss different ways to work problems. Is one way always the only correct way? Encourage the students to change their methods where possible. • If the class has a slower group, allow them to use a calculator for the whole page. • At the end of the lesson share responses to question 2 c. Student page 48 • Revise the compensation strategy. • Stress the importance of writing numerals in their correct place-value columns when adding more than two numbers. Why? • Practise estimation on the board. Stress that an estimate is NOT an exact answer. Ensure that students know why estimates are done and used. • Depending on class ability level some initial help may be needed for the Trial and error question. Student page 49 • Teach place values in four-digit numbers. • Why must we keep numbers in their correct columns? • Have a class discussion about where large numbers can be approximated, eg a crowd at a football game. When is it possible to approximate and when are exact answers needed? Discuss. • Look at the lack of signs for question 5. How do we know that we are to add? Answers for assessment page 53 1 a b 2 a 3 a 4 a 5 a 57, 101, 83, 36, 92, 45, 74, 110 92, 73, 98, 115, 61, 76, 114, 47 861 b 743 c 1 017 d 501 e 724 5 730 b 12 285 c 11 471 d 5 010 e 9 305 9, 90, 900, 9 000 b 8, 80, 800, 8 000 c 7, 70, 700, 7 000 $12.12 b $8.46 c $14.33 d $25 e $20.58 Additional work sheets Targeting Maths Upper Primary Operations and Number Patterns • Addition — Unit 1 50 Targeting Maths Teaching Guide Year 5 Mental and Oral Strategies Random adding The same ones Add students’ house numbers around the class. Each student gives the number of their house then the answer when it is added to the previous total. Estimate the total before beginning. Repeat another day in another order and check that the same total is reached if the same students are present. Practise orally adding numbers using the same digit in the ones place. eg 7 + 6 = 13, 17 + 6 = 23, 47 + 6 = 53, 817 + 256 – must always end in a …(3). Use other combinations. Can be a game where the additions are done around the class. Students sit as they make an error. The winner can choose the next combination. Activity Bank Shopping grab Total height Blu-tack cards depicting supermarket items (from catalogues) around the room. In 20 seconds a student grabs as many cards as possible and adds their total. The total is recorded on a chart. At the end of the week the champion shopper is rewarded! Measure (in cm) every child in the class. Estimate total height. Total their heights in small groups, then add all groups together to get the total height of the class. What distance around the school would they cover, lying head to toe? How many storeys high? Total age Shopping game Students work out their ages in months. Work same exercise as for Total height. What would be as old as our total ages? Set a total, eg $55.60. Students use shopping catalogues to find as many items as they can which when added together will total the set amount. They are only allowed one of any item. The one with the greatest number of items is the winner. Targeting Maths Teaching Guide Year 5 51 Activity Card 25 ÷ X _ + ✎ Super Holiday Bargains! With $2 000 to spend at the holiday resort, Bib and Bub have many choices. Study the brochure and plan how you and a friend would like to spend that $2 000 in 5 days. Luckily, air tickets and accommodation are already paid. Hire car per day $8 5.50 Lunches $14 each Dinners $45 each Snorkelling lessons $16 hr Surfing lessons $18 hr Magazines $6.50 ea Haunted house visit $25 ea Movies $12.50 ea Activity Card 26 ✎ How Did You Do That? ÷ X _ + 4 1 Use the digits 1, 2, 3, 4, 5, 6, 7, 8, 9 and use addition signs to make the largest possible total and the smallest possible total. 3 eg 12 + 3 + 45 + 67 + 8 + 9 = 144 2 Now use addition signs in other places to make a total of 99. 6 7= 2 1 2 3 4 5 6 7 8 9 3 Use addition signs and subtraction signs to total 100. 1 2 3 4 5 6 7 8 Find as many answers as you can. 52 © Blake Publishing — Targeting Maths Teaching Guide 5 This page may be reproduced by the original purchaser for non-commercial classroom use. 9 Assessment Name __________________________________________ Addition Date _____________________________ 1 a b 91 38 55 82 +19 26 64 73 17 12 57 79 38 +35 41 63 26 80 2 a 574 236 + 51 b 9 53 + 681 c 407 82 + 528 d 35 374 + 92 e 3 a 2634 + 3096 b 8715 + 3570 c 9578 + 1893 d 1091 + 3919 e 4308 + 4997 c 4 + 3 = _____ b 3 + 5 = _____ 4 a 6 + 3 = _____ 88 629 + 7 60 + 30 = _____ 30 + 50 = _____ _____ + _____ = _____ 600 + 300 = _____ 300 + _____ = _____ _____ + _____ = _____ 6000 + 3000 = _____ _____ + _____ = _____ _____ + _____ = _____ Nachos $5.87 5 Burrito $6.25 Taco $3.54 Miso soup $4.92 Find the cost of: Working a Burrito + Nachos = __________ b Taco + Miso Soup = __________ c Nachos + Taco + Miso Soup = __________ d 4 Burritos = __________ e one of each item = __________ © Blake Publishing — Targeting Maths Teaching Guide 5 This page may be reproduced by the original purchaser for non-commercial classroom use. 53 Student pages 50–53 Division Learning focus VELS: NUMBER Outcomes and Standards Mental Computation 4.1 Recall automatically basic multiplication and division facts, simple common fraction facts and frequently used common fraction, decimal and percentage equivalences. 4.2 Use knowledge of place-value and number properties to increase the range of computations which can be carried out mentally. Investigation 4.1 Generate mathematical questions from presented data and from familiar contexts. Computation and Applying Number 4.2 Use written methods to multiply and divide whole numbers. 4.4 Analyse a problem situation which may involve several different operations, decimal numbers, negative whole numbers and common fractions; express the problem symbolically and choose appropriate computational methods to solve it. • Automatically recalls multiplication and division facts. • Uses place value to extend division facts. • Generates mathematical questions from familiar context. • Divides whole numbers by one-digit whole numbers without a calculator. • Selects relevant information to solve a problem. • Recalls and uses division facts. Key words • • • • Revise division. When do we use division? Encourage many different examples. Have much oral practice. This is an exercise where students can work in pairs, discussing probable answers before working them out exactly. • Students to work divisions in their workbooks. Student page 51 • Have students examine the ‘tricks’ in the first fact box. • Practise these on the board and orally. • Then look at the tricks in fact box two and practise. Will these tricks work with all even numbers? Student page 52 • Write the divisibility tests on a chart and display. • Practise each divisibility test orally until students are familiar with them. • Work divisions on the board. Make sure that students know where and how to write any remainders — especially the ‘carry over’ numbers. Student page 53 • Quick oral practice of 4, 7, 8 and 9 times tables. • Suggest students lightly pencil in a path before colouring it. • Estimate the answers to the problems first. Answers for assessment page 57 1 2 3 4 5 6 a a a a a a h 7 a 13 b 27 c 39 d 46 r 3 e 15 r 8 16 b 12 c 22 d 46 e 96 12 b 13 c 16 d 25 e 52 86, 138, 106, 354 b 84, 102, 213 c 132, 636, 516 13 b 24 c 17 d 13r3 e 25r1 112 b 141 c 162 d 229 e 116 f 131r3 g 120r7 172r2 i 223r3 j 132 84 b 76 division, divisibility, remainder Resources calculators, dice, shopping catalogues Additional work sheets Targeting Maths Upper Primary Operations and Number Patterns • Division — Unit 1 54 Targeting Maths Teaching Guide Year 5 Mental and Oral Strategies Count multiples My number Practise tables by counting by a given number as a class. Count backwards as well. Discuss how to use counting multiples to calculate division. I have 3 digits, factors of 4 and 3, and am less than 110. What am I? Prepare several examples. Allow students to give their own examples to the class. Activity Bank Throw and divide Musical groups In groups of 4, each student throws a die 3 times. Multiply the scores. Divide this by the number on a fourth throw. Write down all working and each member of the group checks others for correctness. Reward students who have 5 correct answers at the end of the game. Outdoors, allow students to move around freely for 5 seconds, then call ‘threes’ and students form into groups of 3. Left-overs may remain in the group. Immediately call ‘fives’ and groups reform into groups of 5. Continue calling various numbers and discuss the class size and the groups which can be made equally and those which cannot (factors and multiples). Bargain shopping Pass it on From shopping catalogues, find products which are offered in different sizes. Work out which is the best value, eg 3 kg for $4.50 or 2 kg $3.20. Think of a number, make a calculation and pass it on. eg 15 multiply by 3, pass it on; 45, divide by 9, pass it on; 5 add 17 pass it on; etc. Place an upper limit on answers. Targeting Maths Teaching Guide Year 5 55 Activity Card 27 Toothpick Puzzle 13 toothpicks form 4 squares. Remove 1 toothpick to make 3 squares. Remove 1 and move 2 toothpicks to new positions to form 5 squares. Activity Card 28 ✎ 13 Only One Allowed 52 324 51 Place the numerals 1, 2, 3, 4 and 5 in each column and row. A numeral can only appear once in any column, row or diagonal. Use trial and error. 56 © Blake Publishing — Targeting Maths Teaching Guide 5 This page may be reproduced by the original purchaser for non-commercial classroom use. Assessment Name __________________________________________ Division Date _____________________________ Work mentally. 1 Divide by 10. a 130 ______ b 270 ______ c 390 ______ d 463 ______ e 158 ______ b 60 ______ c 110 ______ d 230 ______ e 480 ______ b 104 ______ c 128 ______ d 200 ______ e 416 ______ 2 Divide by 5. a 80 ______ 3 Divide by 8. a 96 ______ 4 Colour the numbers that are: a divisible by 2. 86 138 221 106 354 b divisible by 3. 84 92 102 213 334 c divisible by 4. 132 142 282 636 516 5 a 6 a f 7 6 78 7 784 6 789 b b g 4 96 5 705 8 967 a Ali has 756 reels of cotton to put into 9 bags. How many in each bag? ________ Working c c h d 5 85 4 648 3 518 d i 7 94 3 687 4 895 e e j 3 76 6 696 7 924 b There are 608 children to put onto 8 buses. How many on each bus? ________ Working © Blake Publishing — Targeting Maths Teaching Guide 5 This page may be reproduced by the original purchaser for non-commercial classroom use. 57 Student pages 54–57 Decimals and Percentages Learning focus VELS: NUMBER Outcomes and Standards Number and Numeration 4.1 Use place-value knowledge to read, write and order negative whole numbers and decimal numbers from thousandths to millions. 4.3 Rename common fractions as decimals and percentages. Mental Computation and Estimation 4.1 Recall automatically basic multiplication and division facts, simple common fraction facts and frequently used common fraction, decimal and percentage equivalences. 4.3 Use estimation strategies to check the results of written or calculator computations. Reasoning 4.3 Use and interpret simple mathematical models. • Writes, compares and orders numbers with decimal fractions. • Converts a simple fraction to a decimal and/or a percentage. • Automatically recalls frequently used fractions, decimals and percentage equivalences. • Interprets percentages. • Rounds decimals to the nearest whole number to check. • Uses written methods to add and subtract decimal numbers. Key words fraction, decimal, ascending, descending, percentage, discount Resources Memory pack cards, newspapers, magazines Additional work sheets Targeting Maths Upper Primary Numeration and Fractions • Percentages — Unit 1 58 • Look at the diagrams on page 54. Count the squares. • How many little squares are there in one big square? What fraction of the big square is each little square? • Talk about hundredths. Where are hundredths used? • Revise the writing of decimals. Always write a zero before a decimal point if there are no whole numbers, eg 0.5. Make sure the decimals point is written in the middle of the numbers not on the line. • Teach that when there are hundredths there are two numbers after the decimal point. Give the place values; tenths followed by hundredths. • How do we distinguish small decimal numbers from large decimal numbers? Practise many examples on the board. Student page 55 • Teach what a percentage is (a part out of 100). • Students give examples of use of percentages. • Ensure that they understand that the whole is 100% — so anything less than 100% means less than the whole. • Practise some matching of fraction to decimal to percentage. • Revise the meanings of ascending and descending. Student page 56 • Let children attempt question 1, then stop and mark it. Discuss the common fractions. Give oral examples and encourage students to give examples too. • Tell them they can use hundredths where it is appropriate, eg when dealing with dollars or metres, but to change to common fractions for other measures, eg years or hours. Student page 57 • Discuss the setting out for algorithms on page 57. • Stress that for addition and subtraction the decimal points must be directly underneath each other. • Decimal points to be written in the middle of numbers, not on the line. DON’T forget to write the decimal point in the answer. • Estimate in whole numbers only, so take decimal to the nearest whole number. Answers for assessment page 61 24 41 18 8 1 a 100 , 0.24, 24% b 100 , 0.41, 41% c 100 , 0.18, 18% d 100 , 0.08, 8% 2 Teacher check 3 a $5 b 10 cm c 15 min d 30c e 3 months f 18 hours 4 a 17; 16.8 b 13; 12.3 c 10; 9.62 d 19; 18.74 e 13; 12.99 f 6; 6.4 g 3; 3.2 h 1; 1.54 i 1; 1.24 j 1; 1.46 5 a $4.96 b $4.04 Targeting Maths Teaching Guide Year 5 Mental and Oral Strategies Comparing Aligning List twenty common percentages, decimals and fractions on the board. Which is largest, 1 smallest, equal to, larger than 2 , 1 closest to 4 etc? Read decimal fraction numbers to students. They write them down vertically, decimal point under decimal point. Practise ragged ends. Activity Bank Bingo Memory Students choose 9 common fractions to write in a 3 π 3 square. You then read out equivalent fractions/decimals/percentages. Students cross off theirs as they are said. The student who is last to cross off a fraction wins. See page 19, Teacher’s Guide. Add cards with simple percentages to the pack. Environmental percentages Lotto From newspapers and magazines, cut out any advertisements where percentages appear. Collate to make posters with equivalent fractions written on them as well. Place cards from Memory pack in a hat. Students draw out one each. ‘Prize’ goes to the one who draws out a match to a previously hidden fraction/decimal/ percentage numeral. Targeting Maths Teaching Guide Year 5 59 Activity Card 29 ✎ Farmer’s Dilemma 1 In his will, a farmer left 2 his property to 1 his eldest son, 3 to his middle son and 1 9 of his property to his youngest son. They first tried to divide 17 cows, but no-one wanted a fraction of a cow. A neighbour solved the problem for them by some very original thinking. What did the neighbour do? Activity Card 30 Add ’Em Up ✎ Travel around the trail and add together all the decimal numbers less than 5. 2.5 7.4 4.3 3.75 5.05 6 4.8 3.7 11.5 3.09 60 3.56 0.95 4.9 6.5 © Blake Publishing — Targeting Maths Teaching Guide 5 This page may be reproduced by the original purchaser for non-commercial classroom use. Assessment Name __________________________________________ Decimals and Percentages Date _____________________________ 1 Write each as a fraction, a decimal and a percentage. a b c d a 100 = 0. ____ = ____ % b 100 = 0. ____ = ____ % c 100 = 0. ____ = ____ % d 100 = 0. ____ = ____ % b c d 2 Colour. a 0.73 0.04 55% 3 a 50% of $10 = ______ d 10% of $3 = ______ 17% b 10% of 1 m = ______ c 25% of 1 hour = ______ e 25% of 1 year = ______ f 75% of 1 day = ______ 4 First estimate answers in whole numbers, then work actual answers. b 7.6 c 2.74 d 4.91 a 8.9 0.9 1.86 5.19 6.4 . . . + 1 5 + 3 8 + 5 02 + 8.64 Est. f 9.2 – 2.8 Est. Est. g 5.8 – 2.6 Est. Est. h 3.28 – 1.74 Est. Est. i 6.03 – 4.79 Est. e 2 1 + 9 .60 .15 .24 Est. j 7.30 – 5.84 Est. 5 Meri bought grapes for $3.17 and peaches for $1.79. a How much did she spend? ____________ b How much change did she get from $9? ____________ © Blake Publishing — Targeting Maths Teaching Guide 5 This page may be reproduced by the original purchaser for non-commercial classroom use. 61 Student pages 58–60 Chance Learning focus • • • • • Discuss garage sales — why, when, where, types etc. Are you sure to be able to buy a …? What would be impossible to buy at a garage sale? Do we take chances when we hold a garage sale? Why? What type of chances do we take? Student page 59 VELS: CHANCE Outcomes and Standards Chance 4.1 Examine the outcomes from simple chance experiments and data on familiar events to order outcomes and events from least to most likely. 4.2 Use and interpret numerical statements which quantify chance. 4.3 Use language of chance in everyday situations. Investigation 4.4 Communicate own responses to tasks and problems appropriate for this level to others. • Uses language of chance in everyday situations. • Analyses outcomes from simple experiments. • Recognises the likelihood of events occurring. • Makes simple predictive statements. • Communicates own responses to tasks. • Assigns the values from nought to one to the probability of events occurring. • Uses and interprets common probability statements. • Group children into harmonious groups of four. • Make sure each group has coins (or play coins) and a box. • Tell them they must close their eyes or the experiment will not be valid. • Discuss the types of observations they might write about (sensible ones). • Hold a class discussion at the end of the experiment to share outcomes. Student page 60 • • • • These results will vary depending on class make-up. Show students how to make numerical values. If 0 is ‘impossible’ and 1 is ‘certain’ where will fifty-fifty be? Demonstrate by placing some chance words on a 0 to 1 number line on the board. Answers for assessment page 65 1 Teacher check 2 Answers will vary. Teacher check 3 2 red, 2 green, 2 yellow, 1 red and 1 green, 1 red and 1 yellow, 1 yellow and 1 green 4 a 1 in 6 b 1 in 2 c 1 in 2 5 a have all blue balls b not put yellow balls in the bag (or open eyes) Key words chance, experiment, prediction, influence, combination, probability Resources coins, thesaurus, blank flashcards Additional work sheets Targeting Maths Upper Primary Space and Chance and Data • Chance and Data — Unit 1 62 Targeting Maths Teaching Guide Year 5 Mental and Oral Strategies Number patterns Statements of chance Give a number pattern and have students work out the rule in order to continue the series for three more terms. eg 5, 6, 8, 11, 15, *, * ,*. Have students make predictions about the day’s activities. Check at the end of the day, or next day, to see whose predictions were correct. Allow students to give their own patterns for others to work out. Activity Bank Synonyms of chance Arrange in order Use a thesaurus to gather a list of synonyms for such words as ‘certain’, ‘possible’, etc. Make all the synonyms into flashcards. Write a list and display it in the classroom. Arrange on a continuum to express the variations of words of chance. Look up the antonyms of the main chance words and make pairs. Determine outcomes Family chance What items can you use to arrive at an outcome? eg dice, lotto balls, coin toss, spinners. Students ask their families for instances where chance has been used in their lives. Have students suggest experiments to be carried out. These can be done as a class or in groups and the outcomes discussed. Targeting Maths Teaching Guide Year 5 These stories can then be shared with the class. 63 Activity Card 31 ✎ Even Chances Make a list of things which have a fifty-fifty chance of coming true. Study this picture to give you clues. Activity Card 32 Match the Statements Match the following statements about your class with the outcome terms on the board. • One in six families have white cars. • All cars use unleaded petrol. • One in ten students in my class are left-handed. • My friends all eat pizza. • Two out of three students have brothers. • Five out of ten families have two children. • In 20 throws of a die, I will throw 10 sixes. • In twenty throws of a die I will throw two ones. • My teacher ate chocolate last night. 64 ✎ usually certain always good chance possible probable likely never fifty-fifty sometimes unlikely © Blake Publishing — Targeting Maths Teaching Guide 5 This page may be reproduced by the original purchaser for non-commercial classroom use. Assessment Name __________________________________________ Chance Date _____________________________ 1 Write two happenings under each heading. Impossible Unlikely Fifty-fifty Probable Certain 2 Write a chance word for each level on the probability line. 1 0 A B C D E F A B C D E F G H G H 3 In a bag there are two red balls, two green balls and two yellow balls. You choose two balls without looking. Write all the possible results. 4 What are the chances that you picked: a two red balls? _____________ b two different balls? _____________ c two balls of the same colour? _____________ 5 How could you be sure to: a pick two blue balls? b not pick a yellow ball? © Blake Publishing — Targeting Maths Teaching Guide 5 This page may be reproduced by the original purchaser for non-commercial classroom use. 65 Student pages 61–63 Number Patterns Learning focus VELS: NUMBER and DATA Outcomes and Standards Number Patterns and Relationships 4.1 Generate and investigate number sequences which may involve fractions, decimals and combinations of operations, using a calculator where appropriate. 4.3 Construct, verify and complete number sentences involving the four operations, brackets, decimal numbers and fractions. Investigation 4.1 Generate mathematical questions from presented data and from familiar contexts. • Prepares tabular displays of data. • Verifies rules for number sequences. • Constructs and verifies number sentences. • Solves number puzzles with missing numbers. • Continues and describes number patterns. • Generates mathematical questions. Key words • What are unknowns? Discuss as a class. Make sure students understand this concept before progressing. • Write a statement on the board and draw the table. eg Use question 1 as an example and change the numbers. How will we fill in the table? • Have one student fill in the table as the class tells them the next term. • Does the table help us solve the problem? How? • Can you tell me another problem where filling in a table will help us solve it? • Discuss all problems suggested by the students. • Students will feel very clever at this stage if you suggest that they are ‘doing algebra’. Student page 62 • • • • Go through the process of how to check. Work many examples on the board. Why do we check answers? What will you do if you think an answer is wrong? Student page 63 • • • • Tell students to work out the rule first. Apply it to the other numbers to make sure that it works. Complete the pattern. Depending on class this is a page that students can work in pairs. This is especially applicable to question 2. • As an alternative, when students have completed question 2, each pair can present their patterns on the board for the class to solve. Answers for assessment page 69 1 a table, number sentence, rule, pattern Resources number cards Additional work sheets b 2 a 3 a 4 a 1 2 3 4 5 6 30 24 18 12 6 0 12 c 72 d 5 20 b 39 c 72 d 67 e 94 f 4 g 113 h 6 57 b 18 +11; 46, 57, 68, 79, 90 b ÷ 2; 80, 40, 20, 10, 5 Targeting Maths Upper Primary Operations and Number Patterns • Number Patterns — Unit 2 66 Targeting Maths Teaching Guide Year 5 Mental and Oral Strategies Number patterns Number clues Give a pattern of numbers in pairs. Have students work out the pattern and give the next three pairs. Give clues for students to work out a number. eg I am 3 times the sum of 4 and 5; I am two less than the sum of 14 and 18; My tens are four more than my ones and I am between 50 and 60, etc. eg 2,6; 3,9; 4, __ ; __ , __ ; __ , __ Activity Bank Number families Make an equation Give out two number cards to each student. Have them hold them so that others can see them. Call out a number pattern, eg odd numbers divisible by 3. All children who hold those cards must find each other and stand together. They collect a point if they belong in the given group. Deal out six number cards to a group of students. Have them arrange the cards to form an equation. eg With a 4, 6, 3, 2, 13, 10 students could make 4 π 6 + 2 – 3 = 13 + 10. Make my number Story time Draw a number between ten and fifty from the ‘hat’. With a time limit of one minute, students write equations for the number. Reward the most innovative equations. Give three numbers that can be connected in some way, eg 24, 45, 21. Targeting Maths Teaching Guide Year 5 Have students make up a story to use those numbers. eg After spending $21 of my $45 holiday allowance, I had $24 remaining. 67 Activity Card 33 Magic Sums Place the numbers 2 – 9 in the circles, so that two of the numbers add up to the third number. π + ✎ = + = ÷ = Replace each symbol with a numeral. Activity Card 34 Two-Way Stretch Powers of 2 Odd Numbers ✎ Multiples of 5 Three numbers that add to 20 Factors of 20 The sum of the first two is a factor of the third. Use numbers between 2 and 15 in the above table to obey the clues. Use guess and check. 68 © Blake Publishing — Targeting Maths Teaching Guide 5 This page may be reproduced by the original purchaser for non-commercial classroom use. Assessment Name __________________________________________ Number Patterns Date _____________________________ 1 Sonia had 90 goldfish to sell. The first day she sold 30. Each day after that she sold 6 less than the day before. a Complete the table. Day 1 Goldfish sold 30 b How many did she sell on day 4? _______ c How many had she sold altogether on day 3? _______ d How many days did it take to sell all the fish? _______ 2 Check the answer for each question. a π 7 = 140 b 92 – = 53 = ___ ÷ 6 = 12 = ___ Check e c = ___ Check f 13 π – 19 = 75 Check = 52 g Check Check = ___ Check = 114 = ___ + 103 = 216 h 120 ÷ = ___ = ___ d 47 + Check = 20 = ___ Check 3 Write a number sentence to solve each problem. a John saves stamps. He has 143. How many more must he save to have 200? ____ + = ____ b Nada’s hens laid 72 eggs. How many hens does she have if each hen laid 4 eggs? ____ ÷ = ____ = ____ = ____ 4 Write the rule and complete the pattern. a b 13 24 35 640 320 160 © Blake Publishing — Targeting Maths Teaching Guide 5 This page may be reproduced by the original purchaser for non-commercial classroom use. Rule __________ Rule __________ 69 Student pages 64–67 Volume and Capacity Learning focus VELS: MEASUREMENT Outcomes and Standards Using Relationships 4.3 Investigate and compare the volume and mass of objects. Measuring and Estimating 4.1 Choose attributes and standard units appropriate to the task. 4.2 Make judgments about the relative size of objects based on comparison to known benchmarks or standard units. 4.4 Use measuring instruments, reading simple scales and measuring accurately to the nearest marked gradation, taking into account the degree of exactness required. Reasoning 4.2 Make judgments about the accuracy of reasoning and results and modify working accordingly. • Orders prisms according to volume. • Measures volume by counting cubes. • Selects appropriate unit to help estimate and measure. • Makes judgements about relative size. • Uses standard units to measure capacity. • Uses known sizes of familiar things to make estimates. • Links key features to own experiences. • Reads linear scales of measuring instruments. • Reconciles unreasonable statements. Key words volume, cubic centimetre, cubic metre, litre, capacity, millilitre Resources cubic centimetre blocks, rectangular boxes, isometric dot paper, metre rods, fabric, empty containers, litre measures Additional work sheets Targeting Maths Upper Primary Measurement • Volume and Capacity — Unit 1 70 • What is volume? The amount of space something occupies. • Why do we need to be able to measure volume? Allow students to give many examples. Add to their list if they omit important reasons. • Have cubic centimetre blocks for students to handle and examine. Ensure they know that one block is 1 cm π 1 cm π 1 cm. 1 block occupies 1 cm3 of space. • Volume can be measured in cm 3. How will we measure the volume of our models? Count the cm3. • Students can work in pairs for this exercise. Student page 65 • Ensure that each pair has a small rectangular box and plenty of cm3 blocks. • Discuss estimates. Stress that estimates are not meant to be exact. • Class works questions 1 – 4 before making the cubic metre. If at all possible also have a box which is approx 1 m3. • Have fun! How many of you can fit into a cubic metre? etc. Student page 66 • Define capacity — how much a container can hold. Teach that capacity can be measured in litres and millilitres. • Ensure students know 1 000 mL = 1 L and the correct symbols L and mL. Student page 67 • Plan for this lesson well ahead so children can bring in many containers from home. There will need to be several 1 litre measuring jugs as well. • Each group has a litre measure and chooses 6 containers that are different from one another. • This is a good outside activity! Answers for assessment page 73 1 2 3 4 5 6 7 8 9 a 16 cm3 b 18 cm3 c 36 cm3 96 Teacher check 1 1 a2L b8L c 2 L d32 L a 4 000 mL b 10 000 mL c 250 mL d 6 500 mL Teacher check Teacher check Teacher check a 2 L 50 mL b 12 L 330 mL Targeting Maths Teaching Guide Year 5 Mental and Oral Strategies Calculate volume Litres and millilitres How many cubes do I need to fill a shape 5 cm long, 4 cm high and 2 cm wide? Make sure those students who cannot understand this concept get a chance to fill the shape and see that it has 4 levels of 5 cm by 2 cm. Mentally convert litres to millilitres and vice versa. How many litres in 2 000 mL? … 1 500 mL? How many millilitres in 3 L? … 6.5 L? Activity Bank What’s my volume? Same volume, different shapes Have students bring in well-known and littleknown liquids containers from the kitchen or bathroom at home. Cover the label where the volume is mentioned. Holding the container up, ask students to give you the volume in mL. Give clues by saying only ‘more’ or ‘less’. Students start to take notice of familiar containers, eg soft drink cans, and should use known sizes of containers to guess unknown ones. With a given number of cubes, have students build many different shaped 3D models. Record dimensions of different models of the same volume. How many fit in a m 3? Litres everyday How many school bags will stack into the cubic metre you have built? Make a poster illustrating all the products we buy in litres. Write a list of other familiar objects. Students estimate how many of these objects could fit into the cubic metre. Find advertisements where capacities are mentioned. Targeting Maths Teaching Guide Year 5 Discuss whether it is better value to buy 2 π 500 mL bottles or one litre bottle of any product. 71 Activity Card 35 That’s a lot of Lunchboxes ✎ 1 Use a calculator to find how many cubic centimetres (cm3) there are in a cubic metre. 100 cm π 100 cm π 100 cm. Record your answer as cm3. 2 Calculate how many cubic centimetres in your lunch box, using a calculator, or building the same sized model with cubic centimetre blocks(shorts). 3 Divide the number of cm3 in the cubic metre by your lunchbox’s volume to find out how many lunchboxes will fit into a cubic metre. Activity Card 36 How big is a cup? With a friend, collect about five cups of various types, including a measuring cup from a kitchen. Collect coffee cups, tea cups, styrofoam cups, plastic cups and mugs, picnic mugs. Line them up from holds least to holds most. Check your estimate of size by measuring each capacity using a mL measuring cup. Discuss which one you should use when the recipe says ‘1 21 cups milk’. Why? 72 © Blake Publishing — Targeting Maths Teaching Guide 5 This page may be reproduced by the original purchaser for non-commercial classroom use. ÷ X _ + Assessment Name __________________________________________ Volume and Capacity Date _____________________________ 1 These models are made from cubic centimetre blocks. What is the volume of each. a b c Volume = __________ Volume = __________ Volume = __________ 2 You have an empty box which is 8 cm long, 4 cm high and 3 cm wide. How many cubic centimetre blocks will fit inside it? __________ 3 Name an object which would have a volume of about: a 1 m3. _____________ b 2 m3. _____________ c 1 2 m3. _____________ 4 Write as litres. a 2 000 mL ______ b 8 000 mL ______ c 500 mL _______ d 3 500 mL ______ 5 Write as millilitres. a 4 L ______ b 10 L ______ 1 4 c L ______ 1 d 6 2 L ______ 6 Name three things you would measure in litres. a c b 7 Name three things you would measure in millilitres. a c b 8 Name two containers that would hold about: a 1 L. b 1 2 L. 9 How much altogether? a 400 mL + 700 mL + 950 mL = _______ L _______ mL b 2 L 800 mL + 1 L 580 mL + 7 L 950 mL = _______ L _______ mL © Blake Publishing — Targeting Maths Teaching Guide 5 This page may be reproduced by the original purchaser for non-commercial classroom use. 73 Student pages 68–71 Mass Learning focus • Define mass. Ask students for examples. • What do we use to find mass? If possible have several different types of scales available. • What measurements do we use to state the mass of something light? … heavy? Students should be able to use grams and kilograms. Tonnes may be talked about. • Students give examples of light and heavy objects. • Revise 1 000 g = 1 kg. • Make a class list of mass words. Student page 69 VELS: MEASUREMENT Outcomes and Standards Measuring and Estimating 4.1 Choose attributes and standard units appropriate to the task. Reasoning 4.2 Make judgments about the accuracy of reasoning and results and modify working accordingly. Using Relationships 4.3 Investigate and compare the volume and mass of objects. Investigation 4.4 Communicate own responses to tasks and problems appropriate for this level to others. • Uses standard units to measure mass. • Selects appropriate unit to specify a quantity. • Reconciles and adjusts unreasonable statements. • Investigates and compares the volume and mass of objects. • Presents outcomes and results of own inquiries. Key words mass, gram, weigh, weight, kilogram • Teach how to convert from grams to kilograms (÷ by 1 000) and kilograms to grams (π by 1 000). • Practise many examples on the board. • How do we round to the nearest hundred grams? Revise numbers up to 50 go down and numbers 50 – 99 go up, eg 248 g is 200 g and 259 g is 300 g to the nearest 100 g. Practise. • The Challenge could be set for homework. Student page 70 • Name familiar everyday items. The class calls out the measurement that would be used to find the mass — grams or kilograms. • Have standard masses available. Each child should have the opportunity to heft these — especially 100 g, 500 g, 1 kg. • If standard masses are not available use sand in bags (matchboxes for 100 g) to make some. Student page 71 • The experiment is best carried out in the playground if possible. • Each group will need a set of scales. • Be sensitive when grouping for question 2. • Depending on class ability calculators could be used for question 3. Answers for assessment page 77 1 Resources standard masses 50 g, 100 g, 500 g, 1 kg, scales, litre measures, large containers, empty dry food packages Additional work sheets Targeting Maths Upper Primary Measurement • Mass — Unit 1 74 3 1 1 a A 1 4 kg, B 8 kg, C 2 4 kg, D 1 kg 160 g , E 1 2 kg b D, A, E, C, B c 13 kg 630 g 2 Teacher check 3 a g b g c kg d g e kg f kg g g h g i kg 4 a 3 000 g b 9 000 g c 28 000 g d 4 500 g e 10 250 g f 2 200 g g 12 650 g 1 1 5 a 5 kg b 2 kg c 43 kg d 1 2 kg e 17 4 kg 3 f 25 4 kg g 16 kg 295 g 6 Teacher check Targeting Maths Teaching Guide Year 5 Mental and Oral Strategies Total 1 000 g Subtract from 1 000 g Give students three items in grams to total mentally, eg 150 g, 220 g, 350 g. What mass will be needed to total 1 kg? (1 000 g). Use ‘easy totals’ to assist by adding the 350 g + 150 g = 500 g first. Practise subtracting grams from 1 kg (1 000 g). Use a story. I use 125 g butter from the kilogram butter pack. How much butter is left? Activity Bank What’s my mass? Size and mass Have students bring in empty dry-food packets from home. Hold up each item, covering the label which shows mass. Students study its size and discuss what was in it. They then guess what was the mass of the product. Arrange dry food packages in order of their mass when they were full. Double a recipe Weigh it up Take a simple children’s recipe which uses grams of ingredients. How much of each ingredient would be needed if we double the recipe? … triple the recipe? … halve a recipe? Make a list of different, easily obtainable substances on the board, eg, flour, sugar, milk. Discuss why some products have less mass than others in the same sized package. Students imagine a cup of each substance and order them from lightest to heaviest. Using kitchen scales, allow students to weigh a kitchen measuring cup of the substances and compare the results with their estimated order. Targeting Maths Teaching Guide Year 5 75 Activity Card 37 Different Volume, Same Mass Use balance scales, standard 500 g mass and plastic bags. With a friend, gather together a number of articles to make the mass of 500 g. Collect sand, stones, rice, pencils, apples or other pieces of fruit. Place the items into plastic bags when 500 g is measured. Label the bags. Discuss how different items have different volume, but the same mass. Activity Card 38 ✎ School Bag Survey 1 Choose five items from your school bag today. 2 Weigh them and record their masses. 3 What is the mass of your school bag with the items taken out? Item Mass 4 What items do you use up during the day? 5 What is the difference between the mass of your bag on the way to school and the way home? 76 Total © Blake Publishing — Targeting Maths Teaching Guide 5 This page may be reproduced by the original purchaser for non-commercial classroom use. Assessment Name __________________________________________ Mass Date _____________________________ 1 a Write the mass of each container in kilograms. A ___________ B ___________ C ___________ D ___________ E ___________ A 1 200 g b Order the containers from lightest to heaviest. D 1 160 g E 1 500 g c What is the total mass of the B 8 000 g C 2 750 g containers? ___________ 2 Write 5 objects in each column. Under 100 g About 500 g About 1 kg More than 10 kg 3 Would you use g or kg to find the mass of: a a pencil? ____ b your pencil case? ____ c a pony? ____ d a pie? ____ e a full suitcase? ____ f a baby? ____ g a peg? ____ h a box of popcorn? ____ i a lounge chair? ____ 4 Change to grams. a 3 kg ______ b 9 kg ______ 1 e 10 4 kg _____________ c 28 kg ______ f 2 kg 200 g ___________ 1 d 4 2 kg ____ g 12 kg 650 g __________ 5 Change to kilograms or kilograms and grams. a 5 000 g _______ b 2 000 g _______ c 43 000 g ______ d 1 500 g _______ e 17 250 g _____________ f 25 750 g _____________ g 16 295 g _____________ 6 Estimate the mass of each. a b c d © Blake Publishing — Targeting Maths Teaching Guide 5 This page may be reproduced by the original purchaser for non-commercial classroom use. e 77 Student pages 72–75 3D Objects Learning focus VELS: SPACE Outcomes and Standards Shape and Space 4.2 Analyse, explain and compare the spatial properties of lines, angles, polygons, polyhedra and crosssections using conventional spatial terms. 4.3 Make congruent copies of given threedimensional objects. 4.5 Visualise, explain and represent 'what is not seen' of an object. Investigation 4.2 Clarify the essential nature of a task or problem and identify key information in the context under consideration. 4.3 Use a range of strategies for inquiry when responding to tasks and problems. 4.4 Communicate own responses to tasks and problems appropriate for this level to others. • Classifies and compares shapes and objects. • Predicts various nets for 3D objects, • Makes decision about which outcomes to save. • Communicates own responses to tasks. • Accurately builds a model from a drawing. • Represents what is not seen of an object • Clarifies the essential nature of a task and identifies key information. Key words names of 3D objects, net, views, perspective • Talk about the shapes of 3D objects in real life. • Write a list of 3D objects, eg cube, pyramid. The class can carry out a school search for items that are based on objects on the list. • Remind them that items may not be the exact shape, eg a funnel is based on a cone. • After the search discuss which shapes are used most / least often and why. Student page 73 • Nets are like an architect’s plans. Architects use plans to build a house. Nets are plans used to build a 3D object. • Give each student a photocopy of a net and have them make the object. • Display all the objects and discuss their nets. Student page 74 • Have models of square pyramids, cylinders, triangular prisms and cones available to be passed around the room. Students can use them for question 1. • Show how to determine top, side and front views. Make sure that students understand that a top view is from exactly overhead. • Working in groups is possible for question 2 if there are not enough blocks for each child. Student page 75 • Have many examples of perspective drawing available. If possible make a display for the classroom. • Discuss when perspective is and isn’t used and why. • Draw some easy examples on the board, eg a road lined by trees, and have students practise on paper. • Why do the trees get smaller? Why does the road become narrower? Answers for assessment page 81 Resources 1 Teacher check 2 a b models of 3D objects, centimetre cubes, photocopies of 3D nets, blank cards, scissors, glue 3 square pyramid, Teacher check 4 Teacher check c Additional work sheets Targeting Maths Upper Primary Space and Chance and Data • Space 3D — Unit 1 78 Targeting Maths Teaching Guide Year 5 Mental and Oral Strategies Give me four What will I need? Write one number fact on the board. Have students write or say 3 more that are related, making four related facts. eg You write 6 + 8 = 14; they write 8 + 6 = 14, 14 – 6 = 8, 14 – 8 = 6. Or you write 4 π 7 = 28 and they write the 3 extra π and ÷ facts. Name a 3D object and have students tell you what 2D shapes you will need to make it, eg cube, 6 square faces. Expand on four facts with multiplication and division by using fractions, eg 5 π 7 = 35, 1 5 of 35 = 7, etc. Activity Bank Different views This is my view Draw the view of a classroom item not normally seen from that view, eg a chair from the bottom, a blackboard from the top. Students identify it. Show a top view of a model of cubes on the board. Students build the model. Discuss how there could be different models. Students draw a classroom item from a different perspective on the board and the class guesses what it is. Area of nets Footprint Students draw nets on cm grid paper. Count the number of squares in all faces of the net. Explain that this is called surface area. Compare total area of the net with its base area. Explain that the area that an item stands upon is its footprint. Many items are bought because they have a small footprint, ie they do not take up too much space on a desk or bench. Students write a list of such items and where they would be used. Share lists with the class. Targeting Maths Teaching Guide Year 5 79 Activity Card 39 Glue Make a Tetrahedron Using this triangle, make the nets of two triangular pyramids. Glue them together at the base. This is called a tetrahedron. How many faces? How many corners? How many edges? Activity Card 40 Five Questions 1 On a set of blank cards, draw 3D objects. 2 Players shuffle the cards. 3 Player 1 draws a card. 4 In five questions, Player 2 must identify what object is held, by asking only yes/no questions. 5 If a student guesses wrongly, they exit the game until next round. 6 Player 2, if successful, next draws a card. 7 Player 3 has the chance to guess, and so on. 8 Those who guess correctly get 5 points. 80 © Blake Publishing — Targeting Maths Teaching Guide 5 This page may be reproduced by the original purchaser for non-commercial classroom use. Assessment Name __________________________________________ Views and Nets Date _____________________________ 1 Write the names of three real-life items that are shaped like: a a cone. b a cube. c a cylinder. d a pyramid. e a triangular prism. 2 Draw the top, front and side views. Object Top view Front view Side view a b c 3 Draw and name the 3D object you can make from this net. 4 Draw 2 different nets for a cube. © Blake Publishing — Targeting Maths Teaching Guide 5 This page may be reproduced by the original purchaser for non-commercial classroom use. 81 Student pages 76–79 2D Shapes Learning focus • Draw several large circles on the board. Teach the names of the parts of a circle as you draw them in. • Why are circles 2D shapes? • Draw more circles (leave the marked ones on view) and have students come to the board to mark parts as you say them. • Write the circle words on a chart and display it in the room for students to use as reference. • Where are circles used? Why? Student page 77 VELS: SPACE and MEASUREMENT Outcomes and Standards Shape and Space4.2 Analyse, explain and compare the spatial properties of lines, angles, polygons, polyhedra and crosssections using conventional spatial terms. 4.7 Enlarge (or reduce) two-dimensional shapes and simple three-dimensional objects. Measuring 4.4 Use measuring instruments, reading simple scales and measuring accurately to the nearest marked gradation, taking into account the degree of exactness required. • Uses knowledge of a shape to construct a figure. • Uses geometrical language to classify shapes. • Uses a pair of compasses • Explains and compares spatial properties. • Uses a square grid to reduce or enlarge a 2D shape. Key words circle, circumference, quadrant, diameter, radius, sector, semicircle, compasses, equilateral, isosceles, scalene, right-angled Resources • How do we draw a circle? • Explain that the instrument is really called a pair of compasses but common usage is simply compass. • Demonstrate how to hold the compass by the top only (never the arms) and twirl with the finger tips. Allow plenty of practice on scrap paper. This is quite a hard skill for some children to master. • Show how to mark off the radius then position the compass and draw the circle. • On the board demonstrate how to draw the daisy pattern. Student page 78 • Remind students that a triangle is a three-sided polygon. • Work question 1, then discuss it to ensure that all students have the correct measurements. • As a class work questions 2 and 3. Discuss the definitions. Student page 79 • • • • Teach that some sides are marked to show that they are equal. After question 1 discuss the need for working to a scale. When is scale used? Why? When can you use this method? – when drawing in maps or diagrams etc. Answers for assessment page 85 1 Teacher check 2 Teacher check 3 a, g are red b, h are blue c, e are green d, f are yellow pairs of compasses, coloured pencils, rope or string, pattern blocks, geostrips Additional work sheets Targeting Maths Upper Primary Space and Chance and Data • Space 2D — Unit 2 82 Targeting Maths Teaching Guide Year 5 Mental and Oral Strategies Circle words Circle facts From a dictionary, list words derived from the Latin circulus. Discuss the connections. How many axes of symmetry has a circle? Through how many degrees do I turn in making a circle? How many right angles in a circle? How many diameters can a circle have? Which 3D objects have circular faces? What is the plural of radius? How many radii make a diameter? Activity Bank Large scale drawing Triangle patterns Students work in small groups. They draw a circle without compasses on the playground. Use pattern blocks to make patterns using only triangles. Each group has a different type of triangle. Use rope or string with chalk. What would we call the rope? (the radius) Who drew the best circle? Which triangles make the best patterns? Rigid triangles Tessellating patterns Using geostrips, make a square and a triangle. Which is the rigid shape? Is it always true? Where are triangles used because they are the strongest shape? (in building) Using pattern blocks again, make a tessellating triangle pattern, suitable for a tiled floor. Children do a search in the school for places where triangles have been used for strength. Targeting Maths Teaching Guide Year 5 Remind students that tessellations have no gaps or overlaps. Display the patterns. 83 Activity Card 41 ✎ Star in a Circle 1 Draw a circle with a radius of 6 cm. 2 Keeping the same radius, mark off six points around the circle. They should fit exactly. 3 Join point 2 to point 4, point 4 2 to point 6 and point 6 to point 2. 4 Then join point 1 to point 3, point 3 to point 5 and point 5 to point 1. 5 How many triangles in your star? 6 Colour the star to highlight the design. 4 3 5 1 Activity Card 42 How Many Triangles? 6 ✎ Count them, then draw two more lines and have a friend count the new triangles. Compare results. 84 © Blake Publishing — Targeting Maths Teaching Guide 5 This page may be reproduced by the original purchaser for non-commercial classroom use. Assessment Name __________________________________________ Circles and triangles Date _____________________________ 1 Use these circles to clearly label: a a centre. e a semicircle. b a radius. f a sector. c a diameter. g a quadrant. d a circumference. 2 Use a pair of compasses to draw a circle with a radius of 4 cm and x as the centre. Make a pattern in the circle. x 3 Colour the scalene triangles blue, the equilateral triangles yellow, the isosceles triangles green and the right-angled triangles red. a b f c g d e h © Blake Publishing — Targeting Maths Teaching Guide 5 This page may be reproduced by the original purchaser for non-commercial classroom use. 85 Student pages 80–83 Bar Graphs and Data Learning focus VELS: DATA Outcomes and Standards Posing Questions and Collecting Data 4.1 Design and prepare surveys and experiments to answer questions or test conjectures and predictions. 4.2 Collect and record data systematically. Interpreting Data 4.1 Extract and interpret numerical information contained in tables, data displays and databases. 4.2 Interpret, discuss and compare data displays, including how well they communicate information. Summarising and Presenting Data 4.1 Prepare tabular displays of discrete and continuous data. 4.2 Prepare visual displays of discrete and continuous (measurement) data using a range of graphical methods. 4.3 Compare, order and summarise data sets using simple numerical methods. Reasoning 4.2 Make judgments about the accuracy of reasoning and results and modify working accordingly. • Prepares surveys and questions. • Extracts information contained in data displays. • Interprets scales and data in bar graphs. • Collects and records data systematically and displays it in a table and bar graph. • Finds lowest and highest values of a data set. • Recognises unreasonable statements. • Displays data in organised forms. Key words bar graph, axis, axes, key, survey, label Resources large sheet of graph paper • Why do we draw graphs? Discuss. • Where do you find graphs? Who uses graphs? Discuss. • Examine the graph on page 80. In what way is this graph different? Two colours are used. • You are going to decide what this graph is about. Don’t rush! Read all the questions and think carefully before you start. • Some students may need help with this task. Be prepared to start them on their way. Student page 81 • Prepare a simple bar graph for the board. Draw it two ways — horizontal bars and vertical bars. • Invite questions and statements about the graphs. • Do they show the same information? • Which one do you prefer? Why? Student page 82 • Revise tally marks. Ensure that students record in bundles of five. • Discuss ways that they can be sure that all letters are counted and each letter is only counted once. Student page 83 • For question 1 encourage drawing of different graphs. You could have set groups drawing a picture graph, a vertical bar graph or a horizontal bar graph. • Encourage students to write meaningful questions. Share questions with the class when finished. • For question 3 draw the table on the board. Students can copy it after the survey has been completed. Answers for assessment page 89 1 2 3 4 5 6 7 8 a 17 b 23 c 31 d 11 e 5 f 8 95 Teacher check a chocolate b mango chocolate, strawberry, vanilla strawberry or chocolate Teacher check Teacher check Additional work sheets Targeting Maths Upper Primary Space and Chance and Data • Graphs — Unit 1 86 Targeting Maths Teaching Guide Year 5 Mental and Oral Strategies Label axes Scale on graphs Given a topic, have students nominate appropriate labels for axes to show information on that topic. How do I show 50 children play soccer when I only have 5 cm space? eg, Topic: Sea water temperature. Axes: horizontal — Day, vertical — Temperature. Give other numbers to show and other space to fit. Ask students to work out the scale, eg 10 players = 1 cm. Give the scale, eg 2 cm = 5 cars, and ask the questions. eg How many cars in 4.8 cm? How will I show 23 cars? Activity Bank Graphs in the environment Graphs in class Look in newspapers and articles for bar graphs. Students each present a graph to the class and tell them what it is showing. Make a poster to display them in the class. Add an explanation for each graph. Various charts in your classroom can be used as bar graphs. Homework completed, rewards, points, money raised or spelling mistakes are often displayed on charts. Students work in small groups to turn them into bar graphs. Interview Tell a story Write five meaningful questions you could ask about the sports survey on page 81. Use the information you gathered in your survey to draw a bar graph. Pretend you are a current events reporter. Write a short story to report the findings which are shown in the graph. You may interview an important person for an opinion on the stunning findings! Interview a classmate after they have finished the survey. Ask them about their results and whether there were any surprises in their findings. Did they anticipate these results? Targeting Maths Teaching Guide Year 5 87 Activity Card 43 ✎ Sunny Days Use the information from this picture graph to make a bar graph. Days of Sunshine = 5 days Days of Sunshine Months January Days March May July September November Jan Mar May Activity Card 44 Critical Data Jul Sept Nov ✎ Be critical of what you read. Use reasoning to check if you think each ‘B’ statements is true or false in the light of its ‘A’ statement. Compare your answers with a friend’s. A The population of Sydney is over 4 million in 2003. B The population of NSW is no more than 4 million. True / False A The average temperature of Brisbane in March was 34º C. B In Brisbane last March, twelve days were over 34º and 12 days were under 34º. True / False A The boys lost 4 soccer matches in 6 rounds. B The boys had a win/lose ratio of 4 to 2. True / False A The average rainfall in September was 22 mm per week. B 184 mm of rain fell in September. True / False A David’s pocket money goes mostly on CDs. B Of David’s $50 pocket money, he has spent $30 on CDs. True / False A Australia’s population will probably reach 30 million in 2010. B Our population has risen from 18 million to 20 million in the last 5 years. True / False 88 © Blake Publishing — Targeting Maths Teaching Guide 5 This page may be reproduced by the original purchaser for non-commercial classroom use. Assessment Name __________________________________________ Bar Graphs Date _____________________________ The canteen at Pascal Primary recorded the flavours of ice-cream sold. 1 Complete the table for the numbers of ice-creams sold during the survey. Ice-cream flavour a vanilla b strawberry c chocolate d raspberry e mango f lime Tally Total 5 5 5 11 5 5 5 5 111 5555551 551 5 5 111 17 2 How many ice-creams were sold altogether? _________ 3 Draw a horizontal bar graph for these results. Ice-cream flavours sold Ice-cream flavours lime mango raspberry chocolate strawberry vanilla 0 5 10 15 20 25 30 Number sold 4 Which was the: a most popular ice-cream sold? _______________ b least popular ice-cream sold? _______________ 5 List the three most popular ice-cream flavours in order. ___________________________ 6 Name a flavour that is at least twice as popular as raspberry. ______________________ 7 One flavour has to be dropped from the list. Which one should it be? ________________ Why? 8 Give one reason why this survey was done. © Blake Publishing — Targeting Maths Teaching Guide 5 This page may be reproduced by the original purchaser for non-commercial classroom use. 89 Student pages 86–88 Back to Contents Whole Number Learning focus • Introduce hundred thousands. • Remind students to leave a space between the hundreds and thousands numbers — NO COMMAS, eg 154 679. • “Discover” that the first three numbers are thousands, eg 754 219 is seven hundred and fifty-four thousand etc. • Have plenty of oral practice at reading six-figure numbers which have been written on the board. • Discuss the use of ‘K’ when writing numbers. Where do you see it used? • If possible have some advertisements where K is used to pass around the class. VELS: NUMBER Outcomes and Standards Number and Numeration 4.1 Use place-value knowledge to read, write and order negative whole numbers and decimal numbers from thousandths to millions. Reasoning 4.3 Use and interpret simple mathematical models. Investigation 4.2 Clarify the essential nature of a task or problem and identify key information in the context under consideration. • Writes, compares and orders whole numbers to 6-digits. • Models different representations of whole numbers. • Orders whole numbers to 6-digits. • Represents the structure of whole numbers to 6-digits. • Uses and interprets simple mathematical models. • Identifies key information in investigations. Key words expensive, expanded notation, round, Roman numerals Resources newspapers, atlases Additional work sheets Targeting Maths Upper Primary Numeration and Fractions • Number Systems — Unit 1 • Numbers to 999 999 — Unit 1 90 Student page 87 • Draw a place-value chart on the board and beside it write several numbers to hundreds of thousands. • Have students come to the board to write a number in the correct columns. • The value of a digit is NOT its place value. This concept needs to be practised often as students find it difficult. eg In 72 619 the value of the 2 is 2 000. It is in the thousands place. • Revise expanded notation. Student page 88 • Revise rounding rules — 0, 1, 2, 3, 4 stay the same; 5, 6, 7, 8, 9 add 1. • Practise rounding to the ten thousands place on the board. The important place to look at is the thousands place. That determines what will happen to the ten thousands place. • Revise Roman numerals learnt to date. • Introduce the new Roman numerals. • Practise using them on the board. Answers for assessment page 93 1 2 3 4 Teacher check a 500 b 7 c 10 d 9 000 e 60 000 f 200 000 518 075, 347 209, 300 279, 92 304, 66 514, 5 382, 1 016, 964 a 200 000 + 60 000 + 7 000 + 300 + 50 + 4 b 80 000 + 1 000 + 90 + 6 c 500 000 + 4 000 + 200 + 8 5 Teacher check 6 a 255 b 400 c 820 d 1 100 e 910 f 190 g 550 h 1 500 7 a CXXX b CCCLXXX c MCD d DCXL e DLXIV f MCXC g DCCXV h CDLIX Targeting Maths Teaching Guide Year 5 Mental and Oral Strategies Reading numbers Read and add Place five large numbers using hundreds of thousands on the board. Have individual students read them aloud. Check that all numerals are being given correctly, including ‘and’. As for ‘Reading numbers’, but have each student add one to any place, eg one hundred and thirty-two thousand, four hundred and five. Add one ten. The next student has to come to the board, change the number, read out the new one and add one, eg 100. Read a list of numbers and have students write them underneath each other in the correct columns. Activity Bank House prices Population figures of Australian cities Collect real estate advertisements from weekend newspapers. Make posters complete with house pictures, writing the price in larger font. Arrange them in categories, eg $300 000 to $400 000. Discuss most expensive and least expensive. Differences in prices can be found. Find population figures from atlases. Discuss how many hundreds of thousands of people are in each city. Draw comparisons of differences. Bingo Twenty questions Give a list of 25 large numbers. Each student chooses 9 to write in their books for Bingo. Choose a number in a 10 000 range. Only answer ‘Yes’ or ‘No’ to questions students ask. The student who identifies the number chooses the next one. This is a good listening and reasoning game. Read the numbers only once to concentrate on listening skills. Targeting Maths Teaching Guide Year 5 91 Activity Card 45 Domi no Puzzle Use the double six set of dominoes (28 dominoes). Build a rectangle like the one above so that it has 7 dominoes and 42 spots. The number of spots on each square must match the number of spots on the adjacent square of the next domino. CHALLENGE: Build 4 such rectangles with the set. Activity Card 46 Squared Challenge Work with a partner. You will need a chess board and some counters. Place 8 counters on the chess board so that no two counters are on the same line, horizontally, vertically or diagonally. 92 © Blake Publishing — Targeting Maths Teaching Guide 5 This page may be reproduced by the original purchaser for non-commercial classroom use. Assessment Name __________________________________________ Whole Numbers and Roman Numerals Date _____________________________ 1 Write these numbers in their correct places. a 347 209 b 964 c 5 382 d 66 514 e 518 075 f 1 016 g 92 304 h 300 279 HTh TTh Th H T O 2 Write the value of each bold numeral. a 37 518 ____________ b 614 087 ____________ c 8 916 ____________ d 29 405 ____________ e 67 290 ____________ f 213 524 ____________ 3 Write the numbers in question 1 in descending order. ________________________________________________________________________________ ________________________________________________________________________________ 4 Write in expanded notation. a 267 354 = b 81 096 = c 504 208 = 5 A house is sold for $615K. Explain what the K means. 6 Write these numbers using Hindu-Arabic numerals. a CCLV __________ b CD ____________ c DCCCXX ________ d MC ___________ e CMX __________ f CXC ___________ g DL ____________ h MD ___________ 7 Write these numbers using Roman numerals. a 130 __________ b 380 __________ c 1 400 ________ e 564 __________ f 1 190 ________ d 640 __________ g 715 __________ h 459 __________ © Blake Publishing — Targeting Maths Teaching Guide 5 This page may be reproduced by the original purchaser for non-commercial classroom use. 93 Student pages 89–91 Addition and Subtraction Learning focus • Discuss credit cards and how and why they are used. • Discuss award point systems, eg 1 point awarded for every $1 spent. Are award points a good idea? • Look at the awards on page 89 and how many points are needed to earn each award. • Revise addition of 3- and 4-digit numbers on the board. • Remind students of the importance of keeping numerals in their correct columns. Student page 90 VELS: NUMBER Outcomes and Standards Computation 4.1 Use written methods to add and subtract decimal numbers. 4.4 Analyse a problem situation which may involve several different operations, decimal numbers, negative whole numbers and common fractions; express the problem symbolically and choose appropriate computational methods to solve it. • States verbal problems symbolically in terms of the operation needed. • Selects relevant information to solve a problem. • Uses inverse relationships to solve practical problems. • Uses written methods for addition. • Uses inverse relationships for checking. Key words • Demonstrate that addition and subtraction are inverse operations. • Show how to use inverse operations as a check for answers. eg 9 + 6 = 15; 15 – 6 = 9. • Revise estimating skills. Again stress that exact answers are NOT estimates. • Ensure that students know to use page 89 for the information they need. Student page 91 • Again stress the ‘rules’ of estimation. Write examples on the board and have students estimate. Point out the error if an exact answer is given. • Revise the use of inverse operations to check answers. • Discuss ‘Working backwards’ as a problem solving strategy. Answers for assessment page 97 1 2 3 4 a 4 650 b 12 787 c 3 416 d 10 228 a 1 123 b 1 171 c 842 d 600 e 904 a 5 318 b 4 212 c 1 730 d 7 213 e 10 288 Teacher check credit card, check, estimate, inverse Resources dice, state maps, calculators Additional work sheets Targeting Maths Upper Primary Operations and Number Patterns • Addition — Unit 1 • Subtraction — Unit 1 94 Targeting Maths Teaching Guide Year 5 Mental and Oral Strategies Related facts Add around the class Give students one addition algorithm and have them give you the three others that are associated. eg 3 400 + 2 700 = 6 100; 6 100 – 3 400 = 2 700; 6 100 – 2 700 = 3 400; 2 700 + 3 400 = 6 100. Teacher starts with a number and states ‘Add 4’. Next student gives answer and states ‘Add ?’ etc. around the class. Limit the Add (or Subtract) to cater for class abilities. Activity Bank Just a minute Travel bug Students work in pairs. Supply state maps and have students plan car or plane travel around the state. How many places can you visit in 3 000 km? (or other totals). Throw two dice. Add the scores. How many number sentences can the pair make to equal that score in one minute? eg 9 (a 4 and a 5); number sentences could be 36 – 27 = 9, 3 π 3 = 9 etc. Their trips can then be presented to the class. Calculator practice Take it! Read out a short list (2 or 3) of money amounts and have students add or subtract the amounts using their calculators. Only say the numbers once. This is a good listening and concentration exercise. Students play in pairs. Each student writes 500 at the top of a piece of paper. The first player throws two dice, makes a two-digit number from the throw and subtracts it from 500. Take turns. The first student to reach 0 wins. Students can play for team points. Targeting Maths Teaching Guide Year 5 95 ✎ Activity Card 47 ÷ X _ + Down on the Farm I have $1 000 and wish to purchase 100 fowls for my new farm. Chickens cost $7.50, hens cost $25.00 each and roosters cost $30.00 each. How many of each can I buy? $25.00 $7.50 Activity Card 48 Skip to my Lou! Measure 20 m with a trundle wheel. With a stopwatch, have a friend time how long you take to skip 20 m. Calculate how many 20 m there are in 1 km. How long would you take to skip 1 km? Could you skip 1 km in that time? Why not? Repeat with other activities such as jumping. 96 © Blake Publishing — Targeting Maths Teaching Guide 5 This page may be reproduced by the original purchaser for non-commercial classroom use. $30.00 Assessment Addition and Subtraction Name __________________________________________ Date _____________________________ 1 Estimate first. a 3807 759 + 84 b Est. 9095 78 + 3614 c Est. 26 576 + 2814 d Est. 961 48 + 9219 Est. 2 Check your answers by using the inverse operation. a 716 + 407 Check b 208 + 963 Check c 564 + 278 Check d 353 + 247 Check e 657 + 247 Check 3 4 346 points 972 points 758 points 2 317 points 1 895 points Suyan saves points to spend in her Bonus Club. How many points does she need for: a lamp and bowl? __________ Working b teapot and torch? __________ c bowl and mug? __________ d lamp, torch and bowl? __________ e all the items? __________ 4 Check your answers for a, b and c. a b c © Blake Publishing — Targeting Maths Teaching Guide 5 This page may be reproduced by the original purchaser for non-commercial classroom use. 97 Student pages 92–95 Multiplication Learning focus VELS: NUMBER Outcomes and Standards Mental Computation 4.1 Recall automatically basic multiplication and division facts, simple common fraction facts and frequently used common fraction, decimal and percentage equivalences. 4.2 Use knowledge of place-value and number properties to increase the range of computations which can be carried out mentally. Computation 4.2 Use written methods to multiply and divide whole numbers. 4.4 Analyse a problem situation which may involve several different operations, decimal numbers, negative whole numbers and common fractions; express the problem symbolically and choose appropriate computational methods to solve it. Number Relationships 4.2 Specify multiples and factors of whole numbers. • Automatically recalls multiplication facts. • Uses place value to extend division facts. • Checks results of written computations. • Uses written methods to multiply whole numbers. • Defines and identifies prime numbers. • Uses a calculator to solve problems. Key words multiplication, algorithm, contracted form, expanded form, prime, composite, product Resources calculators, coloured pencils, dice Additional work sheets Targeting Maths Upper Primary Operations and Number Patterns • Multiplication — Unit 1 98 • What is multiplication? Discuss. • Students tell all the words they know that mean multiplication, eg times, multiply by, lots of etc. Write them on the board. • What sign tells us to multiply? • Do you remember the short way to multiply by 10? Practise — write answers on the board. • Extend to multiplying by lots of 10. eg To multiply by 40, add a zero and multiply by 4. • Practise multiplying by lots of 10 orally and on the board before attempting page 92. • Allow students to suggest their own strategies. Guide them in their use. Student page 93 • Write a multiplication algorithm on the board, eg 58 π 6. • Work it both ways — the extended form and the contracted form. • Have students practise both forms before attempting the page. • Revise the work backwards strategy. Student page 94 • Practise three-digit by one-digit multiplication on the board. • Particularly practise algorithms containing zeros. • Suggest that students estimate before they work the algorithms as a check for their answers. Student page 95 • Teach prime and composite numbers. • The explanations are in the fact box. Point out that 1 does not fit either definition so it is neither prime nor composite. • Read the fact boxes for square and cubed numbers. If the class ability allows you can introduce the squared and cubed indices, eg 7 2 and 5 3. • Practise finding square and cubed numbers orally (using a calculator) before beginning question 4. Answers for assessment page 101 1 a 2, 3, 5, 7, 11, 13, 17, 19 b 21, 22, 24, 25, 26, 27, 28, 30, 32, 33, 34, 35, 36, 38, 39 2 a 3 b 5 c 10 d 9 e 6 3 a 1 b 64 c 216 d 1 000 e 8 000 4 a 342 b 368 c 595 d 324 e 400 5 a 370 b 504 c 3 968 d 5 445 e 6 510 6 a $3.48 b $7.38 c $4.65 d $9.20 e $1.16, $1.64, $1.86, $0.92 Targeting Maths Teaching Guide Year 5 Mental and Oral Strategies Random operations Prime number ‘Buzz’ Write twenty-four random numbers on the board. Use operation signs written on cards. Students may choose three numbers and two operation signs to make a number sentence. Write it onto the side of the board and rub off the numbers used. Aim to make the largest total possible with the chosen digits and operation signs. This can be done mentally or orally. Count around the class by ones. When a prime number comes up student must say Buzz. If they are out the next student must say Buzz etc. Students must concentrate as they are not able to work out their answers ahead in case someone is ‘out’. Activity Bank Tables rugby Hundreds multiplication Students play in pairs. Each player in turn throws two dice. They multiply the sum of the two dice by a given number for tables practice, eg 7. They keep a running total of their answers. The first player to reach 500 is the winner. Use four dice for four students. Throw three dice. All students make the largest three-digit figure possible and write it down. Throw one more die. All students multiply the three-digit number by the single-digit number. First student to get the correct answer scores a point. First to 10 points is the winner. Going to a party Up the ladder First player chooses the secret code for a house-number, eg it can only be a prime number, or it can only be divisible by 5. Say “I live in house number 48, I’m going to the party.” Next player has to guess the code (divisible by 6) and say “I live in house Number 54. First player either lets them come along, “Sure, come along,” or “Sorry, not this time”. Keep going until all students are going to the party. Those who are accepted keep giving a statement that shows the correct code to help others work it out. On the board place a ladder of 10 calculations, eg π3, +15, –28, π12. Each student draws a number card less than 10 from a stack or bag and on the signal, beginning with that number, makes the calculations cumulatively, to reach the top. Ten quickest students are rewarded. Targeting Maths Teaching Guide Year 5 99 Activity Card 49 ✎ Telephone Numbers to Remember Make up little clues for remembering the following telephone numbers. eg 9966 3266 — Invert the 99 and read 66. Three times two is 6. 1 8482 7214 2 9396 2739 3 9018 8016 4 4248 8424 5 6848 9612 6 0414 342 516 Activity Card 50 Stamp It At the Black Stump Post Office, not many people post parcels so Mr Crowe does not keep many stamps for large amounts. He only keeps 40c and 30c stamps. Recently, several people did post large parcels. What is the least number of each stamp that Mr Crowe had to use to exactly cover the postage on these parcels? $9.60 100 $11.80 $10.20 © Blake Publishing — Targeting Maths Teaching Guide 5 This page may be reproduced by the original purchaser for non-commercial classroom use. ✎ Assessment Name __________________________________________ Multiplication Date _____________________________ 1 a Write all the prime numbers less than 20. b Write the composite numbers between 20 and 40. 2 What number squared has a product of: a 9? _____ b 25? _____ c 100? _____ d 81? _____ e 36? _____ c 6 _______ d 10 _______ e 20 _______ 4 Work these in expanded form. a 57 b 92 π 6 π 4 c 85 π 7 d 36 π 9 e 80 π 5 5 Use contracted form for these. a 74 b 168 π 5 π 3 c 496 π 8 d 605 π 9 e 930 π 7 3 Cube these numbers. a 1 _______ b 4 _______ 6 How much will they cost? Give your answer in dollars and cents. a 6 jellies at 58c each. b 9 ice-creams at 82c each. c 5 pies an 93c each. d 20 cakes at 46c each. e 2 each of the above. ___________ ___________ ___________ ____________ © Blake Publishing — Targeting Maths Teaching Guide 5 This page may be reproduced by the original purchaser for non-commercial classroom use. 101 Student pages 96–99 Division Learning focus VELS: NUMBER Outcomes and Standards Mental Computation and Estimation 4.1 Recall automatically basic multiplication and division facts, simple common fraction facts and frequently used common fraction, decimal and percentage equivalences. 4.3 Use estimation strategies to check the results of written or calculator computations. Computation 4.2 Use written methods to multiply and divide whole numbers. 4.4 Analyse a problem situation which may involve several different operations, decimal numbers, negative whole numbers and common fractions; express the problem symbolically and choose appropriate computational methods to solve it. Investigation 4.1 Generate mathematical questions from presented data and from familiar contexts. • Automatically recalls division facts. • Mentally recalls division facts. • Divides whole numbers by 1-digit whole numbers without using a calculator. • Uses front end estimation. • Selects relevant information to solve problems. • Generates maths questions from familiar context. Key words division, signs, zero, remainder • What is division? Give me some examples of where you would use division. • Write a division example on the board. eg How many 9c pencils can I buy for $2.70? • Encourage students to tell how they would work it out mentally. Allow differences in methods. • Look at the pictures and prices on page 96. • How will we work these answers? • Encourage mental working of this page. Student page 97 • What signs tell us to divide? • Look at the fact box. Allow students time to practise writing both signs, in the air, on their desks etc. • Write examples on the board where a zero must be used in the answer. • Remind them that zero is a place keeper and without it many answers would be wrong, eg 436 ÷ 4 = 109. Write it as an algorithm to show the correct placing of the zero. Student page 98 • Revise estimating. Always stress that it is a ‘near’ answer not an exact answer. • Remind them of why estimation is so helpful. Student page 99 • Discuss division in real life where allowances have to be made. eg I have 23 chair legs. How many chairs can I make? 3 Only 5 — you can’t make 4 of a chair. Or Each boat on the River Caves rides holds 6 people. How many boats are needed for 15 people? 3 are needed — one will not be full. • Have students give you examples. Answers for assessment page 105 1 a 4, 6, 9, 3, 8, 5, 7, 2 b 10, 8, 4, 6, 5, 7, 9, 3 c 3, 8, 6, 4, 9, 2, 5, 7 2 a 136 b 146 c 226 d 84 3 a 24 2 3 e 22 3 4 Resources nil Additional work sheets Targeting Maths Upper Primary Operations and Number Patterns • Division — Unit 1 102 4 5 6 7 a a a a b 11 1 2 c 17 2 5 d8 3 9 1 160 b 209 4 c 130 d 136 8 b 14 c 30 d 43 10 b 6 c 21 d 66 62 b Teacher check Targeting Maths Teaching Guide Year 5 Mental and Oral Strategies Four for one Divide the class Write a multiplication fact on the board and have students write the other three associated facts. eg 7 π 5 = 35, 5 π 7 = 35, 35 ÷ 5 =7, 35 ÷ 7 = 5. Use multiples of ten as well. Class stands in a group. How many ways can the class be divided into groups of 5? … 6? … 4? … 3? etc. Have the students move to demonstrate each division and record each on the board. Repeat on different days when the attendance alters. Activity Bank Divide a large number Mystery quotient Write a large number with many factors on the board, eg 108. Have the students find as many division number sentences as possible. Challenge! What number less than 200 has the largest number of division number sentences? Relate to factors/multiples. Choose three different 1-digit numbers. Write all the two-digit numbers you can, using these three numbers. Then add the six two–digit numbers you have made. Next find the sum of your original three numbers. Then divide the sum of the six numbers by the sum of the three numbers. Repeat all these steps for another set of three numbers, then again for another set. What is the mystery quotient each time? Mind reading What am I? Think of a number. Multiply it by 5, add 2, multiply by 3, subtract 4, add 4, divide by 3, subtract 2, divide by 5. You should end with your original number. How is this done? Students construct clues for a number they choose. Use the words multiple, odd, even, prime, composite, factor, less than, more than, sum, difference in their clues. Students give clues to the class and they guess the secret number. Targeting Maths Teaching Guide Year 5 103 Activity Card 51 ary Diction Famous Numbers ✎ Can you identify these numbers? You may need to use a dictionary or other reference material. 1 ______ dwarfs 11 Normal body temperature ______ 2 ______ Dalmatians 12 ______ degrees in a full turn 3 Sweet ______ 13 Age to get a drivers’ licence in your state ______ 4 ______ Australian States 14 ______ cards in a deck 5 Unlucky ______ 15 Legal voting age ______ 6 Number of Zodiac signs ______ 16 Points for a goal in Australian Rules football ______ 7 Days in February 2005 ______ 17 Points for a behind in Australian Rules football ______ 8 A baker’s dozen ______ 18 Number of points in the Federation Star ______ 9 ______ US States 19 Three score and ten ______ 10 Your postcode ______ 20 Telephone number for emergency ______ Activity Card 52 Even Only Use only the digits 2, 4, 6, 8, and 0 to complete the following division algorithms. 104 © Blake Publishing — Targeting Maths Teaching Guide 5 This page may be reproduced by the original purchaser for non-commercial classroom use. ✎ Assessment Name __________________________________________ Division Date _____________________________ 1 a b c 10 20 35 ÷5 25 24 80 30 72 45 56 40 15 2 a 7 ÷8 49 21 64 35 32 14 40 48 b 952 6 c 876 56 ÷7 42 63 28 4 d 904 9 756 3 Write remainders as fractions. a 4 a 3 74 6 960 b 8 c 92 b 4 5 c 837 d 87 7 9 e 75 910 d 5 4 91 680 5 How many $10 brooms can I buy for: a $80? ____ b $140? ____ c $300? ____ d $439? ____ 6 How many 30c toothbrushes can I buy for: a $3.00? ____ b $1.80? ____ c $6.30? ____ 7 a The school orders 8 buses to take its 496 pupils on an excursion. How many pupils will travel on each bus? _________ d $20? ____ 8 Write a division problem that has an answer of 174. © Blake Publishing — Targeting Maths Teaching Guide 5 This page may be reproduced by the original purchaser for non-commercial classroom use. 105 Student pages 100–102 Fractions Learning focus VELS: NUMBER Outcomes and Standards Numbers and Numeration 4.2 Compare and order common fractions. Reasoning 4.3 Use and interpret simple mathematical models. • Reads, writes and compares simple common fractions. • Interprets simple mathematical models. • Recognises simple equivalent fractions. • Writes, orders and compares simple common fractions. • Places fractions on a number line. • Discuss the shapes on page 100. Ensure that students recognise each as a whole shape. • Liken the diagrams to a pizza. We ordered one whole ham and pineapple pizza. When it was delivered it was cut into 8 pieces but it was still only one pizza. • Have students suggest examples of where one whole is divided into many parts, eg an orange at half time in a sports game. • What do we call one part of a pizza that has been cut into 8 pieces? (one out of eight — one eighth) … three parts? Point out that they are still eighths as that is how many parts the pizza was cut into. • Draw diagrams on the board and divide them into equal parts. Have students correctly name each part, eg one quarter etc. • Look at the diagrams on page 100. How many parts is each divided into. What will we call them in diagram A? (tenths) Repeat for the other diagrams. Student page 101 Key words • Teach equivalent fractions. Draw two equal shapes on the board. Divide one into quarters and one into eighths. Colour one quarter and two eighths. • Make sure that the students recognise both coloured parts 1 2 as being equal. 4 = 8 • Repeat many times. Discuss what happens to change the numerator and denominator each time. • Aim at having the students recognise that fractions are equivalent if their numerator and denominator have both been multiplied (or divided) by the same number. equivalent, numerator, denominator, order Student page 102 Resources • Draw several different shapes divided into parts on the board. • Have students colour the whole shapes calling them by their fraction names, eg three thirds, five fifths etc. • How could we show more than one whole? How would we show one and one third? • Draw many examples of mixed fractions on the board. Students can draw and class tells the fraction, you tell a fraction and students draw. coloured pencils, 100 m ball of string, trundle wheel, pizza, dice, blank cards Additional work sheets Targeting Maths Upper Primary Numeration and Fractions • Common Fractions — Unit 1 Answers for assessment page 109 6 12 15 2 4 3 1 a 9 b 15 c 24 2 3 4 5 6 a 3 b 5 c 5 Teacher check a 6 b 3 c 1 d 25 e 1 a 6 b 14 c 3 d 14 e 9 Teacher check 1 2 1 3 7 a 10, 5, 2, 4 106 5 1 3 1 b 6 , 1 3, 1 4, 2 2 Targeting Maths Teaching Guide Year 5 Mental and Oral Strategies Sort the fractions Divide my number Record about twenty random fractions on the board in a group. Have a number of students come to the board and use arrows to indicate whether each fraction is more than or less than one half. Put the ‘less than a half’ set to one side and the ‘more than a half’ set to the other side. Give a number eg 48, which has many factors. Ask students to divide by 6, divide by 8, divide by 2, divide by 12, in quick fire succession, moving around the class to different students. Sometimes ask them to divide by a divisor which will not give a whole number answer. Students say ‘Not a whole number answer.’ Discuss and check each one as it is done. Activity Bank Fraction bars Pizza day Show equivalence by demonstration using drawn fraction bars. Students draw fraction bars and colour to show given equivalent fractions. Practise often, especially for special needs students. Take a real pizza (or pizzas) to school to share with the class (or group). Discuss how to divide the pizza evenly between the whole class. Which set of children would be able to eat half the pizza, eg the blue-eyed children, if exactly half the class has blue eyes. Which children would be able to eat one quarter, one third, two thirds etc. of the pizza? Fraction of a book Divide and conquer Take a large book and see if you or the students can open the book at the halfway place, the quarter way, the third way place by visually measuring the thickness of the book first. Calculate the exact spot using the page numbers to check. Using a 100 m ball of string and a trundle wheel, divide the classroom into fractions. How many ways can you divide the room into quarters or thirds? Is the area of each fraction the same each different way? Targeting Maths Teaching Guide Year 5 107 Activity Card 53 Sort Them Out! ✎ Use small blank cards to make a set of fraction cards the same as the ones shown. Rearrange these fraction cards and record your arrangements in at least five different ways, eg all equivalent fractions together. Sum equal to ONE 15 4 2 3 8 2 4 16 20 20 8 12 10 10 6 20 Ascending order Descending order 10 6 5 9 8 12 5 15 20 12 12 16 15 Less than one half 8 More than one half Can you think of more ways to sort these fraction cards? Activity Card 54 Making One ✎ Two players. Player one throws a die twice and makes a proper fraction, with numerator less than the denominator. Player two does the same. Record your fractions. The first player to make ONE by adding any two of their fractions scores a point. The winner is the first to 10 points. 2 5 108 + 3 5 =1 © Blake Publishing — Targeting Maths Teaching Guide 5 This page may be reproduced by the original purchaser for non-commercial classroom use. 12 20 Assessment Name __________________________________________ Fractions Date _____________________________ 1 Make equivalent fractions by multiplying by 3. 2π3 2 4 a b = = = 3π3 3 5 = c 5 8 = = = c 18 = 30 = 2 Make equivalent fractions by dividing. a 10 10 ÷ 5 = = 15 b 16 = 20 3 Colour. a 1 b 3 8 3 4 a 1= 6 2 3 5 a 3 b 1= 4 = 7 = 10 b c 1 4 2 23 c 20 = c 16 = 24 12 12 d 1= 2 d 2 5 25 = e 35 = e 63 = 81 92 92 7 6 Place these fractions on the number lines. a 1 3 , 1 1 3 3 4 , , 1 3 4 0 b 1 15 , 5 6 , 1 2 10 , 1 2 1 2 1 5 0 3 7 Order from smallest to largest. a 3 4 b 13 , 1 , 2 5 1 2 , 1 22 , 1 10 , 5 6 , 3 14 © Blake Publishing — Targeting Maths Teaching Guide 5 This page may be reproduced by the original purchaser for non-commercial classroom use. 109 Student pages 103–105 Decimals Learning focus VELS: SPACE and NUMBER Outcomes and Standards Numeration 4.1 Use place-value knowledge to read, write and order negative whole numbers and decimal numbers from thousandths to millions. 4.2 Compare and order common fractions. Computation 4.4 Analyse a problem situation which may involve several different operations, decimal numbers, negative whole numbers and common fractions; express the problem symbolically and choose appropriate computational methods to solve it. • Uses written methods to add and subtract decimals. • Orders decimal numbers. • Uses written or calculator methods to multiply decimal numbers. • Uses a calculator to solve problems involving decimal numbers. Key words decimal, tallest, shortest, lightest, heaviest Resources calculators, tape measures Additional work sheets Targeting Maths Upper Primary Numeration and Fractions • Decimal Fractions — Unit 1 110 • Discuss people’s heights. What measurement do we use for height? It is wise here to talk about feet and inches as most students will have heard a height being referred to in Imperial measure, eg 5 feet 6 inches. • Explain the change to a decimal system. • Why do we need decimals when writing heights? Why not just whole metres? • What operation do we use to find difference? • Demonstrate both adding and subtracting decimals. Allow time for board practice. • Stress the importance of placing the decimal point in the answer. • Remind students that the measurement must also be placed in the answer, eg 7.32 m. Student page 104 • Decide whether you want the class to use calculators for this page. It will depend on class ability levels. • Revise place value to hundredths. • Demonstrate multiplication of decimals. • Again stress the placing of the point in the answer. Write 12 and 1.2 on the board. Have students explain the difference. Show them that forgetting the point in the answer makes the same difference. • Remind students to write a $ sign in the answers for question 4. Student page 105 • Decide whether you want the class to use calculators for this page. It will depend on class ability levels. • Demonstrate division of decimals. Allow plenty of board practice. • Suggest that the point goes into the answer first when dividing. • For question 3 remember to place the $ sign in the answers. Answers for assessment page 110 1 2 3 4 5 6 a 3.76 kg b 5.58 kg c 1.65 kg d 15.91 kg e 15.36 kg a 30.03 kg b 7.92 kg c 17.85 kg d 3.05 kg e 1.15 kg 2.64 kg, 3.57 kg, 4.29 kg, 8.05 kg, 9.15 kg a $64.35 b $40.30 c $28.38 d $73.36 e $41.92 a $1.57 b $1.29 c $1.71 d $1.29 e $0.79 a 14.5 kg b 1.95 m c 10.43 kg d 29.4 L Targeting Maths Teaching Guide Year 5 Mental and Oral Strategies Twenty questions A student or the teacher chooses a decimal number between 0 and 5. Students ask More than? or Less than? questions to guess the number. Only allow direct guesses when the target is almost reached. Next whole number I’m at 6.4 km. How much further do I go to get to 7 km? I have 4.7 L. How much more do I need to have 5 L? I have measured 3.6 m. How much more must I measure to reach 4 m? Activity Bank Number line Calculator Set out a number line on the board, beginning at 0 and going to another whole number less than 5. Six students are given a card on which is written a decimal that lies somewhere on the number line. On the signal ‘Go!’ students must arrange themselves correctly along the number line. Time each group. Use a calculator. Begin with a given decimal number, eg 3.2. How can you reach 10 using at least one of each operation sign. Record your moves. Currency conversion Measure heights Find out the Australian dollar/US dollar conversion rate to two decimal places. eg AU$1 — US$0.65. Calculate what various Australian dollar amounts are worth in American dollars with the whole class, on the board. eg AU$5 = 5 π 0.65 = US$3.25. Compare over time. In small groups, students measure their heights and record in decimal form. Divide by the number in the group to gain an average height. Who would you group together to get the tallest/shortest average of five students? Targeting Maths Teaching Guide Year 5 111 Activity Card 55 ✎ Puzzle Math Words This is a coded way to say ‘Round Up’. What could these two codes say? 3 D D A TNUOC 4 6 7= 2 Can you make similar codes for triangle, long division, times table, multiply, number line, square root? Activity Card 56 Guess and Check 23.3 11.6 . 15.6 24 9 69.3 ✎ 4 6 9 8 7 Use a decimal from the rhombus and a number from the circle with an operation sign (+, –, π or ÷) to make the answers given here. Record your number sentences. 2.6, 93.2, 3.6, 33.9, 9.9 112 © Blake Publishing — Targeting Maths Teaching Guide 5 This page may be reproduced by the original purchaser for non-commercial classroom use. Assessment Name __________________________________________ Decimals Date _____________________________ A B D C 4.29 kg 8.05 kg E 3.57 kg 9.15 kg 2.64 kg 1 a B–A 8.05 – 4.29 b D–C c A–E d A+B+C e 2 a Aπ7 4.29 π 7 b Eπ3 c Cπ5 d e D÷3 C+D+E B÷7 3 Order the weights from lightest to heaviest. 4 a 5 a 6 $7.15 π 9 4 $6.28 $8.06 π 5 b b 7 $9.03 $4.73 π 6 c c 5 $8.55 $9.17 π 8 d d 6 $7.74 e $10.48 π 4 e 8 $6.32 a Jono put 72.5 kg of onions into 5 bags. b Emma cut 9.75 m of ribbon into 5 lengths. How long is each piece? What did each bag weigh? _______________ _______________ c Sui has 7 bags of sweets each weighing d Each of 6 drums held 4.9 L of juices. How much juice altogether? 1.49 kg. What is the total weight? _______________ _______________ © Blake Publishing — Targeting Maths Teaching Guide 5 This page may be reproduced by the original purchaser for non-commercial classroom use. 113 Student pages 106–109 Patterns VELS: SPACE and NUMBER Outcomes and Standards Shape and Space 4.6 Visualise, test and describe transformations of shapes. Number Patterns 4.1 Generate and investigate number sequences which may involve fractions, decimals and combinations of operations, using a calculator where appropriate. Investigation 4.1 Generate mathematical questions from presented data and from familiar contexts. 4.4 Communicate own responses to tasks and problems appropriate for this level to others. Computation 4.4 Analyse a problem situation which may involve several different operations, decimal numbers, negative whole numbers and common fractions; express the problem symbolically and choose appropriate computational methods to solve it. Reasoning 4.3 Use and interpret simple mathematical models. • Predicts the shapes required to continue a spatial pattern. • Describes shapes required to continue a pattern. • Tests the rule that produces it. • Generates mathematical questions and communicates own responses. • Recognises and uses inverse relationships. • Describes and tests a rule which produces a number sequences. • Generates number sequences which may involve fractions and decimals. • Counts in fractional amounts. • Uses and interprets simple models. Key words pattern, table, rule, value Resources pattern blocks, objects for patterning, beads, string Additional work sheets Targeting Maths Upper Primary Operations and Number Patterns • Number Patterns — Unit 1 114 Learning focus • What is a pattern? Discuss. • If possible have students make a pattern drawn on the board by stringing beads. • Discuss how the pattern was made. Was it difficult? Why did we follow a pattern? • Would it be a pattern if we placed beads at random on the string? Demonstrate. • Draw another bead pattern on the board. Students take turns to draw the next bead. How do you know which bead comes next? • How can we work out how many beads we will need? Student page 107 • Discuss the different pattern at the top of the page. How is it different? • Have concrete materials available for students to experiment with making their own geometric patterns. • When page is completed allow students to share their patterns with the class. Student page 108 • Work question 1. When completed discuss what the students have observed. • Work question 2 and do the same. • When the rest of the page has been completed discuss each question in turn. • If students cannot tell the patterns guide them by leading questions. Student page 109 • Tell students to work out the rule first. • Then decide on the next term. Test it on the existing terms. Does it work? • Do the same for a second term. If it works the second time as well they then complete the whole pattern. • Share their own patterns with the class at the end of the lesson. Answers for assessment page 117 1 a Teacher check b 1, 4, 3, 8; 2, 8, 6, 16; 3, 12, 9, 24; 4, 16, 12, 32; 5, 20, 15, 40; 6, 24, 18, 48 2 a4 b3 3 a 240 b 180 4 a 96 b 84 c 28 d 11 e 143 f 216 g 480 h 619 i 380 j 970 k 2 160 l 5 940 5 a 4.6, 5.5, 6.4, 7.3, 8.2: Rule — add 0.9 2 1 2 1 b 1 3 , 1 3 , 1, 3 , 3 : Rule — subtract c 1.6, 3.2, 6.4, 12.8: Rule — double 1 3 Targeting Maths Teaching Guide Year 5 Mental and Oral Strategies Number patterns Number pattern stories Practise making new number patterns by adding or subtracting. Students give four terms. The class guesses the rule. Ask a question about the number pattern. eg What is the fifteenth term? Students tell a story to describe a number pattern. eg 2, 4, 6, 8. David swam 2 laps of the pool in Week 1, 4 laps in Week 2 etc. How many laps would he swim in Week 5? Activity Bank Number pattern strings Think of a number Students build number pattern strings using shapes and objects. Look for interesting combinations with a repeat of the pattern inside 10 or 12 terms. Students think of a number, add 5, subtract 3, multiply by 4, divide by 2, half that number, add 3, subtract 5. Why do we always end up with the number we started with? Discuss inverse operations. Students then write their own set of instructions where the answer is the same as the starting number. Number patterns to meet Pattern draw Begin three number patterns which will have a common term in them. Students are to find out at which number will the three patterns meet? eg, 4, 7, 10, ___ ; 4, 8, 12, ___ ; 1, 2, 4, 7, ___ . (These will meet at 16.) Have students take 20 pattern blocks out of a bag and see if they can arrange them into a line pattern. Draw and display all the line patterns made. Targeting Maths Teaching Guide Year 5 115 ✎ Activity Card 57 Working Systematically 55 1 How many digits in the numbers between 0 and 100? 66 2 How many numbers between 0 and 100 contain the digit 9? 3 How many palindromic numbers (numbers which read the same backwards as forwards) are there between 10 and 200 and between 10 and 400? 4 How many numbers between 0 and 100 have two different digits? 5 How many numbers between 0 and 100 will I write if I use 85 digits? 38 131 99 Activity Card 58 Mystery Rules In each row there is a MYSTERY RULE to find in order to complete the whole row. When you complete the row, take the prize at its end. Term 2 3 Value 1 3 Term 1 2 Value Term 116 5 6 1 2 3 4 5 2 Value 4 Term 1 3 8 9 12 20 6 7 8 9 10 37 3 4 5 11 Term 7 11 5 Value Value 4 4 6 101 7 8 17 5 9 10 23 6 7 8 9 12 15 4 5 6 7 8 10 12 33 39 25 2 3 63 © Blake Publishing — Targeting Maths Teaching Guide 5 This page may be reproduced by the original purchaser for non-commercial classroom use. Assessment Name __________________________________________ Patterns Date _____________________________ 1 a Continue the pattern. b Complete the table. 2 Complete the rules. Total 1 4 a For every there are __________ times as many 3 2 b For every 3 . there are __________ times as many 4 3 If there are 60 5 a 6 4 a 96 – 15 + 15 = ______ . how many: ? __________ b ? __________ b 84 ÷ 7 π 7 = ______ c 28 + 37 – 37 = ______ d 11 π 13 ÷ 13 = ______ e 143 π 8 ÷ 8 = ______ f 216 – 89 + 89 = ______ g 480 ÷ 20 π 20 = ______ h 619 + 94 – 94 = ______ i 38 π 10 = ______ j 97 π 10 = ______ k 216 π 10 = ______ l 594 π 10 = ______ 5 Complete each pattern and write the rule. a 1.9 b 2 c 0.1 2 3 2.8 2 1 3 0.2 3.7 Rule ________________ 2 Rule ________________ 0.4 0.8 Rule ________________ © Blake Publishing — Targeting Maths Teaching Guide 5 This page may be reproduced by the original purchaser for non-commercial classroom use. 117 Student pages 110–113 Area and Perimeter Learning focus VELS: MEASUREMENT Outcomes and Standards Using Relationships 4.1 Measure and compare the perimeter and area of regular and irregular polygons. 4.2 Investigate the relationship between area and perimeter and calculate the area of a polygon. Measuring 4.3 Draw and construct objects using accurate measurements. Reasoning 4.3 Use and interpret simple mathematical models. • Calculate perimeter by adding lengths. • Approximates area by counting squares. • Generalises formula for area of a rectangle. • Constructs shapes using accurate measurements. • Uses own short cuts to find perimeter and area. • Interprets simple mathematical models. • Makes a model using accurate measurements. • Demonstrates that shapes with the same area can have different perimeters. • Uses known sizes as standard measurements. Key words area, perimeter, measure, overlay, length, breadth, hectare, square kilometre Resources square centimetre overlay, centimetre grid paper, coloured pencils, trundle wheel, chalk, calculators Additional work sheets Targeting Maths Upper Primary Measurement • Area — Unit 1 118 • Revise area and perimeter. • Area is the size of the surface of a shape and is always measured in square measure. • Perimeter is the distance around the outside of a shape. Liken it to a fence. • Look at the character’s statement. Will this always work? • Use an overhead projector (or prepared sheets) to work some examples as a class. First use a centimetre grid overlay and then use the formula. • Remind students that when working with measurements they must be the same, eg all centimetres or all metres etc. Student page 111 • Revise: Area of a square or rectangle = length π breadth (width). • Revise: Perimeter is the sum of the lengths of all the sides. • When the page is finished discuss the answers to questions 2 and 3. • Work more on the board, eg 40 cm 2 can be 8 cm π 5 cm; 10 cm π 4 cm, 20 cm π 2 cm. Student page 112 • Have you heard of a hectare? Discuss. • What is a hectare? Look at fact box. • Discuss acres as students will be familiar with the term and will cite people who still use it. Point out that it was used in the old (Imperial) system. 1 acre is approximately 2.5 hectares (2.47). • Students can work in pairs for question 4. Student page 113 • Allow use of calculators for questions 1 and 2. • Discuss square kilometres (km 2) and where they are used (for much larger areas, eg a whole town). • Allow students to work in pairs for question 3. Answers for assessment page 121 1 b A 7 cm, 2 cm; B 5 cm, 4 cm; C 8 cm, 1.5 cm c A 14 cm 2; B 20 cm 2; C 12 cm 2 d A 18 cm; B 18 cm; C 19 cm 2 a m 2 b ha c ha d ha e m 2 f m 2 3 a 20 000 b 4 c 100 000 d 7 e 15 000 f 2.5 4 colour a, b 5 Teacher check Targeting Maths Teaching Guide Year 5 Mental and Oral Strategies Perimeters Areas How many different dimensions of a regular rectangle, square, triangle, can you give to arrive at a given perimeter? Give the perimeter, eg 20 cm and the shape, eg a triangle. Set a timer to one minute. Students write as many different side lengths that give the perimeter as they can in the set time. How many different dimensions of a rectangle or square can you give to arrive at a given area? Repeat the exercise with areas. eg A rectangle has an area of 36 cm 2. What are its dimensions? Activity Bank Draw to size Different square metres On grid paper, draw a short, fat regular shape with a given area, or a long, thin regular shape with the same area. Count the squares in rows to check the area. On the playground, draw different square metres with chalk. Use a paper template of a square metre cut in different ways, to draw around your square metre. What is the perimeter of each different square metre? Remind students that 1 m 2 = 10 000 cm 2. Perimeters in the playground Hectares in the playground Using a trundle wheel measuring metres, find the perimeter of a basketball court, the lunch area, the assembly area. Find a large area to measure and find how many circuits of that area you make in walking one half a kilometre or 1 kilometre. Find a space in the playground where you can measure a 50 m π 20 m rectangle. Mark it using witches hats. The area of this rectangle is 1 000 m 2 so 10 of these equals one hectare. Targeting Maths Teaching Guide Year 5 119 Activity Card 59 12 Square You need a 15 cm π 15 cm square grid paper. 3 players each have a different coloured pencil. • Player 1 colours an area greater than 1 cm2 but less than 12 cm2. • Player 2 colours a similar area anywhere on the page. • Player 3 follows. • Players take turns to colour the same shape. • They must not colour a shape that is adjacent to one of their own colour already in place. • The first player who cannot colour a shape which does not touch their own loses. Activity Card 60 ✎ CABIN FOR SALE Fill in the measurements of this cabin for the Real Estate Agent who must describe it for sale. NB The plan is not drawn to scale. ? ? 5m 9m ? ? ? 11 m 7m ? ? 12 m 2m ? 14 m Draw a plan of your dream Holiday Cabin on separate paper. 120 © Blake Publishing — Targeting Maths Teaching Guide 5 This page may be reproduced by the original purchaser for non-commercial classroom use. Assessment Name __________________________________________ Area Date _____________________________ 1 a Measure the length and breadth of each shape. b Write the measurements on the shapes. A B C c Work out the area of each shape. A Area = _____ π _____ B Area = _____ π _____ = _____ C Area = _____ π _____ = _____ = _____ d Work out the perimeter for each shape. A P = _____________ B P = _____________ = _____ C P = _____________ = _____ = _____ 2 Square metres or hectares? a a small garden bed _____ b a city block _____ c a playing field _____ d a park _____ e a tennis court _____ f a sand pit _____ 3 Complete. a 2 ha = ___________ m2 b 40 000 m2 = ______ ha c 10 ha = ___________m2 1 d 70 000 m2 = ______ ha e 1 2 ha = __________ m2 e 25 000 m2 = ______ ha 4 Colour the shapes that are 1 ha. They are not drawn to scale. (You can use a calculator.) a b c 25 m 50 m 100 m 400 m 210 m d 100 m 125 m 800 m 5 Name an area which would be measured in km2. _______________________ © Blake Publishing — Targeting Maths Teaching Guide 5 This page may be reproduced by the original purchaser for non-commercial classroom use. 121 Student pages 114–117 Angles Learning focus VELS: SPACE and MEASUREMENT Outcomes and Standards Measuring and Estimating 4.4 Use measuring instruments, reading simple scales and measuring accurately to the nearest marked gradation, taking into account the degree of exactness required. Shape and Space 4.1 Recognise, describe and represent parallel, perpendicular, horizontal and vertical lines, right angles, and angles greater than or less than 90 degrees (multiples of 45 degrees). 4.2 Analyse, explain and compare the spatial properties of lines, angles, polygons, polyhedra and cross-sections using conventional spatial terms. Investigation 4.2 Clarify the essential nature of a task or problem and identify key information in the context under consideration. • Uses and reads the scale on a protractor to measure angles. • Draws representations of given angles. • Compares spatial properties of angles. • Uses a protractor to measure and draw angles. • Uses knowledge of a shapes properties to construct a figure. • Identifies key information. • What is an angle? Make sure students understand that it is the amount of turning between two arms at a point. Use the term vertex. • How can we measure an angle? • What measurement is used for angles? Write the word degree . • Give each child a protractor. Allow time for questions. • Point out the ‘base line’ and the centre point. Show how to use one using either a board protractor or one on an overhead projector. • Discuss the dual rows of measurement and the two starting points (inner and outer). Use the diagram on page 114. • Individual students may need a lot of help with measuring angles. Student page 115 • Teach the names of all types of angles. • Read the fact box. Tell students that it is there to refer to. • When they are drawing angles insist on the use of a ruler and sharp pencil for accuracy. Student page 116 • Revise angle types and sizes. • Give some strategies for estimation by practising many examples on the board. • Tell the students that when measuring they can extend one of the arms using a ruler, to make it easier to get an accurate reading. • When drawing an angle, draw the base line then use the protractor to mark the size of the angle. Student page 117 protractor, angle, base line, degree, vertex, acute, obtuse, reflex, revolution, straight, quadrilateral • After questions 1 and 2 are completed discuss the findings. Explain that the discrepancies are due to inaccurate measuring. • Ensure that the class agrees that the sum of the angles in a triangle is 180º. • Explain that they use this fact to answer question 4. • Repeat after question 5. (360º) Resources Answers for assessment page 125 Key words protractors, class clock Additional work sheets Targeting Maths Upper Primary Space and Chance and Data • Space 2D — Unit 1 122 1 2 3 4 5 6 a a right angle b Teacher check c 90º a acute b Teacher check c 60º a obtuse b Teacher check c 135º Teacher check Teacher check a, b Teacher check c 360º Targeting Maths Teaching Guide Year 5 Mental and Oral Strategies Angles on the clock Sum of angles Discuss the angle between the hands of a clock. One revolution = 360º, so between each numeral there is 30º. What is the angle between the hands of the clock at one o’ clock, two o’ clock etc. What is the sum of angles measuring 30º and 55º? Name two angles which add to a right angle. Name three angles which add to 180º. Activity Bank Study the clock Study a compass Write down at least ten times that the clock hands will form a right angle, a straight angle, an angle of 30º etc. If possible have compasses for students to look at. How many degrees between North and West? ... North and East? … North and South? … East and West? etc. Make angles harder depending on class ability. Name all the points that are 45º from the major points. Study the classroom door Draw a square Open the door to show 10º differences between closed and open at a right angle. Draw a 10 cm square. Draw in both diagonals and the other two axes of symmetry. How many right angles can you mark? Mark each 10º. This can also be done with cupboard doors etc. Targeting Maths Teaching Guide Year 5 Use other regular shapes and discuss the sizes and names of the angles made. 123 Activity Card 61 Barrier Game Choose a partner who has not seen this card. Without them seeing it, instruct them, in words only, to draw this diagram, giving accurate instructions. Use words like diagonal, midpoint, degrees, right angle, straight angle, straight line and names of shapes you know. Then have your partner instruct you to draw their own version of a similar diagram. Count and name the special triangles in this diagram. Activity Card 62 Three Into One Take three different coloured paper squares and fold along the diagonals. Cut along the folds to produce twelve right-angled triangles. Rearrange the triangles to make this shape. Paste it onto card in an interesting colour arrangement. Explore different ways to do this with friends. 124 © Blake Publishing — Targeting Maths Teaching Guide 5 This page may be reproduced by the original purchaser for non-commercial classroom use. Assessment Name __________________________________________ Angles Date _____________________________ For each angle: a name its type, b estimate its size, c measure its size. 1 2 3 a _____________________ a _____________________ a _____________________ b ________ c ________ b ________ c ________ b ________ c ________ 4 Draw: a a reflex angle. b a revolution. c a straight angle. 5 Use a protractor to draw an angle of: a 165º. b 38º. c 85º. 6 a Draw a quadrilateral and measure each angle. b Add the angles. c Complete. The sum of the angles in a quadrilateral is _________ . © Blake Publishing — Targeting Maths Teaching Guide 5 This page may be reproduced by the original purchaser for non-commercial classroom use. 125 Student pages 118–121 Position Learning focus • • • • VELS: SPACE Outcomes and Standards Location 4.1 Use and understand conventional location language including distance and direction. 4.2 Use informal coordinate systems (positive numbers only) and intermediate compass points to specify location or give directions. 4.3 Visualise and find paths to satisfy specifications on maps, grids and mazes. 4.4 Interpret formal maps and make detailed maps and plans. Reasoning 4.3 Use and interpret simple mathematical models. Investigation 4.1 Generate mathematical questions from presented data and from familiar contexts. • Finds given features on an unfamiliar map. • Uses simple coordinate maps and major compass points. • Understands conventional location language. • Locates coordinate points on graph paper. • Interprets formal maps. • Uses simple scales on a map to calculate distances. • Describes movement using compass points. • Sketches detailed maps with attention to direction. • Generates mathematical questions from familiar context. Key words coordinate, scale, compass, bearing, direction Resources coloured pencils, various maps, compasses Additional work sheets Targeting Maths Upper Primary Space and Chance and Data • Position and Mapping — Unit 1 126 When/why do we need to know how to read maps? What types of maps have you seen? Can you think of some things that help us to read a map? Look at the map on page 118. Discuss the use of coordinates to find places on maps. • Stress to always read the bottom number/letter before the side number/letter for mathematical purposes. This does not always happen commercially. • Tell students that there are different combinations of letters and numbers used for coordinates. • Draw a simple map on the board. Practise finding the coordinates for objects that are not at the exact spot — use the closest coordinates. Student page 119 • Revise reading coordinates. The coordinates are written in brackets with a comma between. The bottom (horizontal axis) number is first. • Students make large coloured dots so they are easily seen. Student page 120 • On a map or plan what does a scale tell us? Discuss this at length. If possible have maps and plans available where different scales are used. • Look at this map and tell me what the scale is. 1 cm = 1 km • What distance is represented by 1 mm? 1 How is 2 km represented? • Give guidelines for drawing an aerial view. Student page 121 • Revise the eight major compass directions. • If possible have compasses for the children to handle. • Make sure students know that for question 7 they have to look at page 120. Answers for assessment page 129 1 Teacher check 2 a star b triangle c marked square d black square e cross f circle 3 a 2.7 km b 5.5 km c 11 km d 8.6 km e 5 km f 11.5 km 4 Teacher check 5 a Pike's Peak b Rampant Rv c Golden Sands d Smelly Swamp d Rampant Rv e Hut D Targeting Maths Teaching Guide Year 5 Mental and Oral Strategies Classroom as map Scale calculations Place numbers along one wall of the classroom and letters along the adjacent wall. Ask students to describe who or what is at a certain coordinate that you call out. If the scale is 1 cm on paper equals 2 km on land, what is the land distance for 5 cm, … 8 cm, … 10 cm, … 25 cm on paper? Have students call out the coordinate of where they are sitting. Change the scale to 1 cm to 5 km, 1 cm to 10 km, 1 cm to 100 m, 5 cm to 10 m, etc. Activity Bank Street directory Treasure Island Study the page from the local Street Directory which shows your school. Note the important features nearby, eg the Library, the service station, the railway. Draw your own Treasure Island including buried treasure. Give mysterious directions for friends to find your treasure. In what directions do you walk from school to each interesting local feature? Playground square Classroom map On the playground, draw a one metre square. Divide it into three by three squares. Label one side with letters A B C, the adjacent one with numbers 1 2 3, providing you with nine squares with coordinates. Player One is blindfolded and starts by standing in A1. Player Two calls a coordinate to them which Player 1 must step into without seeing exactly where they are stepping. This involves visualising the nine squares. A Player is out if they don’t have at least one complete foot in the correct square. Change roles of the two Players. Measure your classroom in metres. Draw your classroom on an A4 sheet of paper. What scale will you use to fit it most appropriately? Mark the doors and windows and large furniture. Targeting Maths Teaching Guide Year 5 127 Activity Card 63 Pot of Gold 1 Two players each use centimetre grid paper 12 cm by 12 cm. 2 Label sides with letters horizontally and numbers vertically. 3 Player 1 secretly ‘buries’ a pot of gold in one of their squares. 4 Player 2 tries to locate the pot of gold in twenty guesses or less, naming coordinates. 5 Player 2 places a cross on the square they are naming to Player 1. 6 Player 1 colours in each square named by Player 2. 7 If the gold is not located in twenty guesses, the gold remains in the possession of Player 1. 8 Change roles. Activity Card 64 Use Scale Give the real length of each line using the scale given. 1 cm = 5 m ___________ 2 cm = 10 km __________ 1 cm = 3 m __________ 5 cm = 10 km ___________ 10 cm = 1 m ___________ 128 © Blake Publishing — Targeting Maths Teaching Guide 5 This page may be reproduced by the original purchaser for non-commercial classroom use. Assessment Name __________________________________________ Position Date _____________________________ 1 Draw red dots at: a (2, 2) b (5, 6) c (10, 3) d (8, 9) e (9, 0) f (3, 8) 10 9 8 ▲ 7 2 What is at: a (2, 6) ? _____________ 6 b (7, 7) ? _____________ 5 c (9, 2) ? _____________ d (4, 9) ? _____________ e (1, 1) ? _____________ f (6, 4) ? _____________ ★ ● 4 3 ✦ 2 1 ✖ 0 1 2 3 4 5 6 7 8 9 10 3 Use the scale to state the distances to the nearest half kilometre. a Safe Harbour to Twisty Twins _______ b Shallow Shoals to hut D _______ c Hut B to hut D _______ d Golden Sands to hut B _______ e Smelly Swamp to hut E _______ f Iron Cove to Finger Point _______ 4 On the back of this page draw a diagram to show the 8 main compass points. 5 On the map what is: a NE of hut A? _______________ b N of Iron Cove? _______________ c SW of Finger Point? _______________ d NW of hut D? _______________ e E of Safe Harbour? _______________ f SE of Smelly Swamp? _______________ © Blake Publishing — Targeting Maths Teaching Guide 5 This page may be reproduced by the original purchaser for non-commercial classroom use. 129 Student pages 122–125 Line Graphs and Mean Learning focus VELS: DATA Outcomes and Standards Interpreting Data 4.1 Extract and interpret numerical information contained in tables, data displays and databases. Summarising Data 4.3 Compare, order and summarise data sets using simple numerical methods. Presenting Data 4.2 Prepare visual displays of discrete and continuous (measurement) data using a range of graphical methods. Reasoning 4.1 Make and test simple conjectures in each mathematics strand. • Reads and interprets data presented on line graphs. • Summarises data using simple numerical methods. • Draws a line graph to represent data. • Discusses information presented in graphs from newspapers and magazines. • Calculates the mean of a data set. • Makes assertions about what is true. Key words graph, average, axis, axes, mean score Resources weather graphs, weather thermometer Additional work sheets Targeting Maths Upper Primary Space and Chance and Data • Graphs — Unit 2 • Chance and Data — Unit 1 130 • Discuss line graphs. Draw a simple line graph on the board. • Read the title and the labels for the axes. Why are these labels important? • In what way does this graph differ from a bar graph or a picture graph? • Show how a line graph can show a continuous happening, eg a train trip, a journey to school. • As a class examine the four graphs on page 122. Ask students for their observations. • Read the 4 statements. • Allow students time to complete the questions. • Discuss the choices made and the titles given. Student page 123 • What type of graph is this? • Revise: one axis, 2 or more axes. • Point out where the title and the labels for the axes are to be written. Student page 124 • • • • Point out that the markings on the axes have been started. Why are there two squares for each mark? What does one square on the vertical/horizontal axis stand for? Encourage all students to attempt the Challenge. They can write two questions about their graph and present them to the class. Make a class display of the collected graphs and the questions. Student page 125 • Teach the word mean. • Show how to find the mean of a group of numbers. Work many examples on the board. • Remind students that the fact box is an example. • When working question 3 encourage students to use examples which are different from those in question 2. Answers for assessment page 133 1 2 3 4 Teacher check Teacher check Teacher check 11.3 members Targeting Maths Teaching Guide Year 5 Mental and Oral Strategies True or false Study a large number Choose a range of number facts to which students answer True or False orally. eg Multiples of 3 are 12, 16, 21, 38, 45, 69, 72, 54, 55. 7 is a factor of 86. Students give oral answers to: 720 — How many 20s? … 30s? … 40s? … 80s? Take away 120 … 150 … 240. Add 50 … 60 … 35. Halve it, halve it again. Choose other large numbers to study as well. Students answer True or False after each fact is given. Activity Bank Weather graphs Local temperature Find weather graphs in newspapers and atlases. Measure the temperature outside your classroom each half hour during one day. Discuss, compare and contrast. Students choose one graph about which they write questions to present to the class. Draw a line graph to show the results. Find the mean temperature for the period. Number line of possibility Change the scale Draw a number line on the board. Label one end 0 (impossible) and the other end 1 (certain). On the line label 6 possible temperatures for the rest of the week. Choose a graph from page 123 or 124. Redraw the graph using a different scale for the vertical axis. Discuss the change that was made. Did it change the information? Targeting Maths Teaching Guide Year 5 131 Activity Card 65 ✎ Every Graph Tells A Story Tell a story about a journey for each line graph. KM M 250 – 100 – 200 – 80 – 150 – 60 – 100 – 40 – 50 – 20 – 0 9 a.m. 0 10 a.m. 11 a.m. Time 12 noon 0 min 10 min 20 min Explain the information given in each of these graphs. Height (m) Weight (kg) b AGE Degrees Time (secs) 132 AGE d DAY 50 min ✎ What’s Happening Here? c 40 min Time Activity Card 66 a 30 min DAY © Blake Publishing — Targeting Maths Teaching Guide 5 This page may be reproduced by the original purchaser for non-commercial classroom use. Assessment Name __________________________________________ Line Graphs Date _____________________________ The choirmaster marks the roll each choir practice. There are 15 members in the choir. These are the results for the last ten weeks. Week 1 2 3 4 5 6 7 8 9 10 Number present 9 15 15 8 12 11 15 10 4 14 1 Draw a line graph to show this information. 2 Give your graph a title and label the axes. 3 Write 3 questions you could ask about your graph. a b c 4 What is the mean attendance per week? ________ © Blake Publishing — Targeting Maths Teaching Guide 5 This page may be reproduced by the original purchaser for non-commercial classroom use. 133 Student pages 128–131 Back to Contents Whole Number Learning focus • Introduce the millions place. • If you write seven million using numerals how many zeros will you write? • Write many numbers on the board to show millions. • Discuss real-life situations where millions are used. • Show where spaces must be left when writing numbers in the millions — between the millions place and hundreds of thousands place AND between the thousands place and the hundreds place, eg 3 567 910. Student page 129 VELS: NUMBER and MEASUREMENT Outcomes and Standards Number and Numeration 4.1 Use place-value knowledge to read, write and order negative whole numbers and decimal numbers from thousandths to millions. Investigation 4.1 Generate mathematical questions from presented data and from familiar contexts. Measuring 4.4 Use measuring instruments, reading simple scales and measuring accurately to the nearest marked gradation, taking into account the degree of exactness required. • Reads, writes and orders whole numbers to 7-digits. • Displays place value knowledge. • Operates with negative whole numbers in everyday whole numbers and locates them on a scale. • Measures various temperatures on a Celsius scale. • Reads and writes ordinal numbers. Key words million, population, descending, round, nearest, negative, position, ordinal Resources coloured pencils, MAB blocks, newspapers, calculators, dice Additional work sheets Targeting Maths Upper Primary Numeration and Fractions • Numbers to 999 999 — Unit 1 134 • Practise writing large numbers in words on the board. • Point out the use of ‘and’, eg 1 233 456 — one million two hundred and thirty-three thousand four hundred and fifty-six. • Revise the use of hyphens between tens and units numbers. • Revise the value of a digit, eg the 3 in 235 has a value of 30. • Revise the rules for rounding (0, 1, 2, 3, 4 stay the same — 5, 6, 7, 8, 9 add 1). • Also revise which digit to look at when rounding. eg If rounding to the nearest thousand look at the digit in the hundreds place to decide whether to add 1. Student page 130 • Introduce negative numbers. • Where are negative numbers used? (weather, bank accounts, below sea level etc.) • Have much practice on the board before working this page. • NB The ‘higher’ the numeral the lower the value, eg –10 is smaller than –3. Student page 131 • Revise ordinal numbers. • Explain tied places. Remind students to refer to the fact box. Answers for assessment page 137 1 a one million three hundred and sixty-seven thousand two hundred and fifty-one b seven million nine hundred and fiftythree thousand five hundred and eight 2 a 300 000 b 3 000 3 a 1 367 000 b 7 954 000 4 a 900 000 + 10 000 + 5 000 + 600 + 20 + 4 b 2 000 000 + 400 000 + 70 000 + 3 000 + 900 + 10 + 8 5 a –2 b 3 c 1 d –3 e –1 6 a 4ºC b –2ºC c 0ºC 7 –8, –3, –2, 0, 1, 4, 10 8 a 9th, 11th b 2nd, 4th c 19th, 21st 9 a 7th b 3rd c 12th 10 12th Targeting Maths Teaching Guide Year 5 Mental and Oral Strategies True or false Give me a number between Give a number fact that is relevant to your aims this week, eg 1 000 000 is 10 hundreds of thousands, and students place hands on shoulders if true, hands in the air if false. A good way to give a movement break! Give me a number between zero and minus 5 … between 10th and 20th … between 100 000 and 1 000 000. How many correct answers can the class give in one minute? Activity Bank Model large number Vertical figures Using base 10 blocks where a cube = 1 000 000, a flat = 100 000 etc., model the numbers for the population figures on page 128. Then compare them altogether with one city eg Perth. Sydney is nearly four times as big. etc. Have students write vertically, large numbers which you dictate. Make sure they place millions under millions, thousands under thousands etc. When they are proficient at this, include decimals up to two places. Really cold! Largest number From newspapers, collect temperature figures from cities like Moscow, Toronto, Detroit, Oslo in our summer months or Thredbo, Charlotte Pass in our winter months. Discuss how many degrees colder these are than your classroom temperature. Take the temperature in the fridge and the freezer to compare. What is the largest number that can be recorded on your calculator? What happens when you try to add to that? Targeting Maths Teaching Guide Year 5 Explore other large numbers (adding, multiplying etc.) using a calculator. 135 Activity Card 67 ✎ Make Mine Bigger 4 With a partner, use a die to create a number in the millions. 3 Throw #1 is the ones digit, throw #2 is the tens digit, throw #3 is the hundreds digit and so on. Take turns to make your throws. Keep a record of your digits after each throw. 6 7= 2 Read your numbers to each other. The larger number wins. Winners can challenge other winners in the class. Activity Card 68 ✎ $ Shop Till You Drop! $ $ $ $ $ ÷ X _ + Mum spent exactly $50 on food for the weekend. The items we could see in the trolley were crackers $3.75, bread $2.85, cheese, $4.65, Drink $3.50, Ham $6.25, Chocolate $4.90, Pasta $ 3.75. There are 5 more items in the bottom of the trolley. What are they and what are their costs? 1 2 3 4 5 136 © Blake Publishing — Targeting Maths Teaching Guide 5 This page may be reproduced by the original purchaser for non-commercial classroom use. Assessment Name __________________________________________ Whole Numbers Date _____________________________ 1 Write in words. a 1 367 251 b 7 953 508 2 Give the value of the 3 in the above two numbers. a b 3 Round the numbers in question 1 to the nearest thousand. a b 4 Expand a 915 624 = 900 000 + b 2 473 918 = 5 Write the value of each letter. –4 0 a 0 d a 5 e c b c d 6 Colour the higher temperature. a b –7ºC b 4ºC –2ºC e c –5ºC 0ºC –3ºC 7 Write in ascending order. 1, –3, –8, 4, 0, –2, 10 8 Write the position before and after: a ______ 10th ______ b ______ 3rd ______ c ______ 20th ______ b a tied 1st? ______ c a tied 10th? ______ 9 What position comes after: a a tied 5th? ______ 10 There are 12 runners. What position is last? ______ © Blake Publishing — Targeting Maths Teaching Guide 5 This page may be reproduced by the original purchaser for non-commercial classroom use. 137 Student pages 132–135 Division VELS: NUMBER Outcomes and Standards Computation 4.2 Use written methods to multiply and divide whole numbers. 4.3 Use models to illustrate the four operations with common fractions, and develop written methods for carrying out these operations. 4.4 Analyse a problem situation which may involve several different operations, decimal numbers, negative whole numbers and common fractions; express the problem symbolically and choose appropriate computational methods to solve it. Number Relationships 4.2 Specify multiples and factors of whole numbers. 4.3 Construct, verify and complete number sentences involving the four operations, brackets, decimal numbers and fractions. Mental Computation 4.1 Recall automatically basic multiplication and division facts, simple common fraction facts and frequently used common fraction, decimal and percentage equivalences. 4.2 Use knowledge of place-value and number properties to increase the range of computations which can be carried out mentally. • Divides whole numbers by whole 1-digit numbers. • Interprets the remainder when dividing by a whole number. • Uses written methods to multiply and divide whole numbers. • Uses inverse relationships. • Finds factors of whole numbers. • Divides whole numbers by 1-digit whole numbers. • Completes number sentences. • Recalls multiplication and division facts. • Uses place value to extend facts. Learning focus • Teach the word quotient as being the answer when one number is divided by another. • Ask What is the quotient when 31 is divided by 5? First student answers and asks a question of second student who answers and asks a question of third etc. • Revise 3-digit numbers ÷ 1-digit numbers. • Revise remainders written as ‘r’ and as a fraction, 1 eg 41 ÷ 4 = 10r1 or 10 4. • Demonstrate how to match up the three parts which belong together. Student page 133 • Stress the advisability of checking answers. • How will we check division answers? Use multiplication to check division, eg 35 ÷ 5 = 7; check 5 π 7 = 35. • Revise factors. How can we find out if a number is a factor of another number? (if it divides exactly into the given number) Discuss. Practise orally. Student page 134 • What is a prediction? • How can we make sensible predictions? • Discuss digit patterns for some tables, eg table for 5 always ends in a 0 or 5. • Revise estimation. Again stress that an estimate is NOT an exact answer. • Work many 4-digit numbers ÷ 1-digit numbers on the board. • You may have to work with a small group if there are still students who are having difficulties. Student page 135 • Is there an easy way to divide by 10? Give students 1 minute to discuss this in pairs. • Write the rule on the board. • When working with money remind students to put the point in the answer and to use the $ sign. Without the $ sign the answer is wrong! Key words Answers for assessment page 141 quotient, inverse, predict 1 2 3 4 5 6 7 8 Resources supermarket catalogues, empty box Additional work sheets Targeting Maths Upper Primary Operations and Number Patterns • Division — Unit 1 138 a a a a a a a a 6 b 17 c 9.3 d 7.6 e 54.2 74c b $3.89 T bF cF 90 b 220 c 200 d 20 130r5 b 218 c 93r4 d 74r2 209 b 186 c 76 d 84 9 b 9 c 8 d 9 e 52 f 37 g 86 h 4 79 b 93 Targeting Maths Teaching Guide Year 5 Mental and Oral Strategies Multiples ‘Buzz’ Add what? Count around the room by ones, with students saying ‘Buzz’ each time they encounter a multiple of a given number. eg Multiples of 3; One, Two, Buzz, Four, Five, Buzz, Seven etc, up to a given number. Anyone making a mistake is out and sits down. So that students don’t stop participating, make a rule that if a seated person beats another to saying their number, they rejoin the standing group. WARNING! This can become noisy but is very participatory, so limit this activity. What can you add to a particular number to make it divisible by a given number. eg What has to be added to 37 to make it divisible by 7? Activity Bank Dividing by 10 Lotto answers Use calculators to see ÷10 in action. Describe what students see. Use calculators to see if ÷40 is the same as ÷10 and then ÷4. On small pieces of paper in a ‘hat’, are written 30 numbers from 100 to 500. On drawing out a number a student must return to their desk and write 5 number sentences using π or ÷ with that number as the answer. Swap with a partner to check. Best value Quick tables practice From supermarket catalogues or advertisements, find prices for multiple items, eg 6 for $2.10. Work out the cost of one item. Where pricing allows work out if it is better to buy six lots of one, or the pack of six. Have blank tables like this one in bulk, available to be given out quickly. Write the numbers to be placed on the table on the board and give a time limit for finishing. π 7 10 8 Targeting Maths Teaching Guide Year 5 9 4 6 10 3 8 50 139 Activity Card 69 Very Sneaky When they aren’t watching, you can sneak off with tazos from someone’s box. You may only tell them what is the difference, and the sum, of the original number of tazos and the number taken. 27 32 18 22 Player 1: 1 Secretly choose a box and a secret number to take. 2 Mentally subtract the secret number of tazos. 3 Then add the secret number to the original number in the box. 4 Now tell the group your two numbers. They must work out from which box you sneaked the tazos and the secret number. Continue with all players taking a turn to ‘sneak’ tazos. Successful ‘detectives’ collect a token. Activity Card 70 Divisibility Rules - OK? _____ _____ _____ _____ _____ _____ Use the digits 1 to 6 in the blanks to form a six-digit number. Follow these rules: 1 The first two digits (from the left) must make a number divisible by 2. 2 The first three digits must make a number divisible by 3. 3 The first four digits must make a number divisible by 4. 4 The first five digits must make a number divisible by 5. 5 The six-digit number must be divisible by 6. Use your knowledge of divisibility rules! (Student Book page 52) 140 © Blake Publishing — Targeting Maths Teaching Guide 5 This page may be reproduced by the original purchaser for non-commercial classroom use. ✎ Assessment Name __________________________________________ Division Date _____________________________ 1 a 10 b 60 10 c 170 10 d 93 10 e 76 10 542 2 How much will 1 book cost if 10 cost: a $7.40? ___________ b $38.90? ___________ 3 True or false. a 764 ÷ 6 = 127r2 _____ b 958 ÷ 3 = 326r1 _____ c 506 ÷ 4 = 104 _____ 4 Estimate these answers. a 275 ÷ 3 ______ b 916 ÷ 4 ______ c 837 ÷ 5 ______ d 169 ÷ 8 ______ c d 5 Estimate before working the answer. a 7 b 915 Est. 3 654 Est. 6 562 Est. 8 594 Est. 6 Check these answers using multiplication. a 4 b 836 Check 5 c 930 Check π 4 9 d 684 Check π 5 7 588 Check π 9 π 7 7 Fill in the missing numbers. a 7 π ____ = 63 b ____ π 6 = 54 c 8 π ____ = 64 d ____ π 9 = 81 e 3 π ____ = 156 f 7 π ____ = 259 g 10 π ____ = 860 h ____ π 13 = 52 8 a 395 oranges must fit into 5 boxes. How many in each box? _________ b There are 7 men carrying boxes containing 651 books. How many books does each man carry? _________ © Blake Publishing — Targeting Maths Teaching Guide 5 This page may be reproduced by the original purchaser for non-commercial classroom use. 141 Student pages 136–139 Addition and Subtraction Learning focus VELS: NUMBER Outcomes and Standards Computation 4.1 Use written methods to add and subtract decimal numbers. 4.2 Use written methods to multiply and divide whole numbers. Numeration 4.1 Use place-value knowledge to read, write and order negative whole numbers and decimal numbers from thousandths to millions. Estimation 4.3 Use estimation strategies to check the results of written or calculator computations. Investigation 4.3 Use a range of strategies for inquiry when responding to tasks and problems. 4.4 Communicate own responses to tasks and problems appropriate for this level to others. Number Relationships 4.3 Construct, verify and complete number sentences involving the four operations, brackets, decimal numbers and fractions. • Uses written methods for addition. • Uses written methods to subtract decimal numbers. • Uses place value knowledge to model different whole numbers. • Round decimal numbers to nearest whole number to estimate. • Increases the range of computation which can be carried out mentally. • Calculates using addition. • Uses a range of strategies for inquiry. • Verifies and completes number sentences involving brackets. • Communicates own responses to problems. Key words average, order of operations, brackets Resources catalogues, addition and subtraction square blanks, number cards, operation sign cards, calculators Additional work sheets Targeting Maths Upper Primary Operations and Number Patterns • Addition — Unit 1 • Subtraction — Unit 1 142 • Revise all addition strategies. • On the board write several horizontal addition algorithms. • Have students write them on the board vertically then work the answers. • Why is it important to make sure that numerals are in their correct place-value column? Discuss. • Read all the numbers on page 136 orally. Discuss the use of zero. Student page 137 • Revise all subtraction strategies. • On the board write several horizontal subtraction algorithms. • Have students write them on the board vertically and then work the answers. • These subtractions are money so again stress the importance of placing the decimal point to separate the dollars and cents. • Also stress the importance of writing the $ sign in the answer. • Remind students to estimate first in question 2 and that an estimate is not an exact answer. Student page 138 • • • • Teach how to find an average. Work many examples on the board. Remind students to refer to the fact box when necessary. Discuss the necessity to change all measurements to the same name, eg 1 m 32 cm becomes 132 cm; 4 yr 7 mth becomes 55 months. Student page 139 • Teach order of operations. Have students read together the fact box. Encourage questions to help understanding. • Work many examples on the board until students are comfortable with not simply working from left to right. eg 3 + 6 π 2 = 15 • Work one question at a time. Some students may need ongoing help to complete the page. Answers for assessment page 145 1 2 3 4 5 6 7 a 10 371 b 1 660 c 7 173 d 19 293 a 356 b 576 c $5.69 d $14.45 2 1 a 9 b 47 c 8 d 3 e 10 6 f 44 3 a 2 b 50 c 13 d 45 e 50 f 1 a 9 b 32 c 4 d 16 e 7 f 0 8 kg 16 Targeting Maths Teaching Guide Year 5 Mental and Oral Strategies Thigh, clap, snap, snap Short methods Students clap both thighs, clap both hands, snap fingers on right hand, snap fingers on left hand. On the ‘Thighs’, teacher gives a starting number. First student adds a predetermined number to the teacher’s number and gives their answer on the next ‘Thighs’. eg (Adding 9) 20, clap, snap, snap; 29, clap, snap, snap, 38, clap, snap, snap … etc. as far as the class can go. Review short methods to add single digits. Double, plus or minus one. eg 5 + 6 = 5 + 5 + 1 = 11. Add 9 : add ten minus 1. Add 8 : add 4 and 4 again. Add 17 : add 10 and 7 more. Add groups of 10 : 3 + 8 + 4 + 7, (3 + 7) = 10 + 8 + 4 = 22. Add known addends : 5 + 7 + 6 + 7 = 11 + 14 = 25. Activity Bank Everyday averages Supermarket catalogues Use everyday classroom situations to calculate averages as a class. eg What is the average attendance for the week? … average number of spelling mistakes made in a test? … average age? Use a set of catalogues, found in mailboxes, to have a shopping spree. With a $50 note, what will you buy to take on a picnic for 2 adults and 2 children? Random number sentences Practice squares With a set of number and operation sign cards, deal four numbers and three operations to individual children or a small group. They make a number sentence using brackets and remembering the order of operations. Who can make the largest or smallest answer with their set of cards? On photocopied blanks for these ‘squares’, give quick practice with addition or subtraction. The advantage is that these are self-correcting. 29 15 18 9 Subtraction squares are harder as the bottom row numbers must be able to be subtracted from the top row numbers. Targeting Maths Teaching Guide Year 5 143 Activity Card 71 ✎ Complete the Table Numbers between Sum Difference The numbers are 50 and 100 135 5 65, 70 50 and 100 156 12 40 and 80 114 10 10 and 100 90 60 100 and 200 205 55 100 and 200 262 42 500 and 1 000 1 585 85 Activity Card 72 ÷ X _ + Class Average ✎ 1 Guess the average number of children in the classes of your school. 2 Survey the teachers to find the exact number of children in each class. 3 Divide the total number of children by the number of classes you surveyed using a calculator. 4 Record your findings. 5 Is any class an average-sized class? 6 Survey your friends about other topics to find averages, eg pets, foot length, kilometres from school. 144 © Blake Publishing — Targeting Maths Teaching Guide 5 This page may be reproduced by the original purchaser for non-commercial classroom use. Assessment Name __________________________________________ Addition and Subtraction Date _____________________________ 1 a 7036 384 + 2951 b 863 207 + 590 c 361 5867 + 945 d 8230 4197 + 6866 2 a 643 – 287 b 850 – 274 c $ c 8.64 – 2.95 d $ c 24.30 – 9.85 3 Find the average of each set of scores. a 9, 7, 11 ____ b 53, 41 ____ c 11, 8, 6, 7 ____ d 1, 0, 3, 9, 2 ____ e 11, 21, 6, 14, 7, 3 ____ f 38, 43, 52 ____ b 5 π (8 + 2) = ______ c 49 ÷ 7 + 6 = ______ e 8 + 7 π 6 = ______ f 28 ÷ 4 – 6 = ______ 4 a 6 – 12 ÷ 3 = ______ d 5 π (16 – 7) = ______ 5 Show your working for these. a 27 ÷ (5 + 4) + 6 = ________ b (9 + 7) π (24 ÷ 12) = ________ = ________ = ________ c 8 + 6 – 3 π 4 + 2 = ________ d 37 + 21 ÷ 3 – 28 = ________ = ________ = ________ e 4 π 3 π 2 ÷ 8 + 4 = ________ f (2 + 3) π (4 + 5) π (6 – 6) = ________ = ________ = ________ 6 The cat weighs 4 kg, the dog weighs 11 kg, the rabbit weighs 2 kg and the goose weighs 15 kg. What is their average weight? _____________________ 7 In the weekly tests Iva scored 19 for maths, 15 for spelling, 17 for language and 13 for science. What was his average mark? _____________________ © Blake Publishing — Targeting Maths Teaching Guide 5 This page may be reproduced by the original purchaser for non-commercial classroom use. 145 Student pages 140–143 Multiplication, Division and Chance Learning focus • Examine the picture on page 140. Allow students to tell stories about it. • Read the price list carefully. • Read the questions. What operation will you be using to work these answers? • Revise the multiplication algorithm on the board. • Because we are working in money what must we remember to do? (decimal point and $ sign). Student page 141 VELS: NUMBER and CHANCE Outcomes and Standards Computation 4.2 Use written methods to multiply and divide whole numbers. Chance 4.3 Use language of chance in everyday situations. Reasoning 4.3 Use and interpret simple mathematical models. • Uses written methods to multiply money. • Uses written methods to divide money. • Adjust unreasonable statements and results. • Uses written methods for the four operations. • Uses language of chance in everyday situations. • Interprets simple mathematical models. • Examines the outcomes from simple chance experiments. Key words multiplication, change, approximate, survey, predict, chance Resources opaque bags, marbles (or counters), coloured pencils, number cards 1 – 100, money Additional work sheets Targeting Maths Upper Primary Space and Chance and Data • Chance and Data — Unit 1 146 • Ensure that students know they are using the information on page 140. • Revise the division algorithm on the board. Again remind students about the special notation for money answers. • After question 3 stop and discuss the answer. • After question 4 allow students to share their examples with the class. Student page 142 • • • • The survey must be done before the examples are worked. Write the results of the class survey on the board in the table. Allow students to copy it into their books (question 2). Work and mark question 1. Write the results into another table on the board. • Discuss and compare the two tables. • Share the answers to question 4a when it is completed. Student page 143 • Ensure that the class is divided into harmonious groups of three. • Each group needs an opaque bag and the marbles (or counters). • Explain carefully what is to be done. • On completion have a class discussion about the results. Answers for assessment page 149 1 a 3 640 b 2 718 c 4 560 d 2 065 e $18.72 f $54.45 g $19.48 h $76.80 3 2 a 172 b 175 4 c 94 d 99 f 1.50 g $1.49 h $1.42 3 a 10 b 12 4 Teacher check 5 Teacher check 3 8 e $1.67 Targeting Maths Teaching Guide Year 5 Mental and Oral Strategies Teacher v class Predictions Each child has a number card on which is written a number between 30 and 100. From a ‘hat’ you (teacher) draw a number card on which is a number less than 11. Each time you draw a card from the hat, a given student divides his/her number by yours, shows their number card and gives the answer aloud. The class gains a point for each correct answer, the teacher gains a point for each incorrect answer. When an event of interest is nearing, make a prediction about the result and have each child state their view of the predicted outcome; eg our football team will win this week. Children individually state, Certain, Likely, etc. After the event, check the predictions and the children’s views about their certainty or otherwise. Activity Bank Averages backwards Door check Discuss how averages are determined and working backwards. Wait at the door and as children exit, have them make a statement using a ‘chance word’ which you give them. eg likely, ‘It is likely that I will be back in this classroom today.’ Give the signal ‘Pass!’ if their answer is correct. Reward creative responses. Present ‘average’ problems that can only be solved by working backwards. Jenni wants to have an average of 90% on her science tests. She has scores of 84, 96 and 85. What must she get in the next test? Change from $5 or $1 Blackboard race Organise frequent practice at giving change from these amounts as they are amounts children handle regularly. Give them the change, either verbally, on paper or with plastic money, and ask how much they spent to get that change. Class is in three teams. Place algorithms on the board for three students and have them work answers in competition. This allows you to see strengths and weaknesses clearly. Ask students to explain their working if appropriate. First finished and correct scores a point for their team. Targeting Maths Teaching Guide Year 5 147 Activity Card 73 ✎ What Chance? Use the given words in original sentences. LIKELY: My next door neighbour _______________________________ . HIGHLY LIKELY: The under 12s ________________________________ . CERTAIN: My hair is _________________________________________ . UNLIKELY: _____________________________________ for two weeks. IMPOSSIBLE: ___________________________ on his roof. POSSIBLE: ___________________________ for three days. CERTAIN: _______________________ to grow to 200 cm. UNLIKELY: Jet planes __________________________ . Activity Card 74 e Postcod Book Postcode Detectives ✎ Use a postcode booklet or the postcode list in the back of the Phone Book. 1 What Victorian town has a post code to match these clues? Begins with S. Can be divided equally by 10, 30 and 60. Contains the number for 3 dozen. Sum of digits is 12. It is __________________________________________ 2 What NSW town has a postcode to match these clues? Begins with T. Can be divided evenly by 10, 30, 90. Has a digit sum of 9. All digits are under 5. It is __________________________________________ 2 Complete your detective work by finding these places in the atlas. 148 © Blake Publishing — Targeting Maths Teaching Guide 5 This page may be reproduced by the original purchaser for non-commercial classroom use. Assessment Name __________________________________________ Operations and Chance Date _____________________________ 1 a 728 π 5 b 906 π 3 c 570 π 8 d 295 π 7 e $3 . 1 2 π 6 f $6 . 0 5 π 9 g $4 . 8 7 π 4 h $9 . 6 0 π 8 2 a e 3 3 516 5 $8.35 b f 4 703 7 $10.50 a Eggs are being packed into half-dozen boxes. How many boxes are needed for 57 eggs? _________ c g 6 564 6 $8.94 d h 8 795 9 $12.78 b At the boarding kennels there are 4 dogs to a run. How many runs are needed for 45 dogs? _________ 4 Predict six things that may occur in the next school holidays. a b c d e f 5 a Place the six happenings on this number line above the line. 0 1 Definitely will not happen Definitely will happen b Write chance words under each one, eg probable. © Blake Publishing — Targeting Maths Teaching Guide 5 This page may be reproduced by the original purchaser for non-commercial classroom use. 149 Student pages 144–147 Fractions and Percentages VELS: NUMBER Outcomes and Standards Numeration 4.2 Compare and order common fractions. 4.3 Rename common fractions as decimals and percentages. Reasoning 4.3 Use and interpret simple mathematical models. Mental Computation 4.1 Recall automatically basic multiplication and division facts, simple common fraction facts and frequently used common fraction, decimal and percentage equivalences. Number Patterns 4.1 Generate and investigate number sequences which may involve fractions, decimals and combinations of operations, using a calculator where appropriate. Computation 4.3 Use models to illustrate the four operations with common fractions, and develop written methods for carrying out these operations. 4.4 Analyse a problem situation which may involve several different operations, decimal numbers, negative whole numbers and common fractions; express the problem symbolically and choose appropriate computational methods to solve it. • Recognises simple percentages. • Converts a simple fraction to a percentage. • Interprets percentages. • Renames common fractions as decimals and percentages. • Automatically recalls percentage equivalence. • Interprets percentages. • Finds fractional parts of a discrete collection. • Adds and subtracts fractions. • Describes and tests a rule which produces a given number sentence. • Uses a calculator to solve problems involving decimal numbers. Key words percentage, decade, ingredients, mixed number, numerator, denominator Resources Learning focus • What is a percentage? • Where are percentages used? Make a list of student suggestions on the board. • Why do we use percentages? • Show students how the percent sign is made up of the parts of 100 — a zero, a stroke (for 1) and a zero, 010. • Explain that a percentage is always out of 100. Why is 100 a good number to use? • If I ate 20% of a cake how much is left? 20 + 80 = 100 so 80% is left. Work many examples. • Teach that all of anything is 100%. Student page 145 • Draw the table from question 1 on the board. • Fill it in as a class. Discuss all the answers. • Students copy into their books and use it to answer other questions. • Before working question 4 make sure students know dozen, decade. • For question 4 point out that large units can be broken down into smaller units, eg 12 months in 1 year. Student page 146 • Draw diagrams on the board showing common fractions, eg halves, thirds, quarters etc. • How many halves in 1 whole? … quarters? … thirds? … fifths? etc. • How will we change the recipe? Discuss. • Teach how to change improper fractions into mixed fractions. Work LOTS on the board before attempting question 3. Student page 147 • Students each need a calculator to work this page. • The page can be worked as a whole class exercise and discussed as each question is completed. • If working individually stop after question 5 and discuss the multiplication. Write some rules. • After question 9 stop to discuss the division. Write some rules. Answers for assessment page 153 1 a 100 b, c Teacher check d 32 e 32% 1 10 1 25 2 a 50%, 2, 0.5(0) b 100, 10, 0.1(0) c 25%, 100, 0.25 75 calculators, dice Additional work sheets Targeting Maths Upper Primary Numeration and Fractions • Percentages — Unit 1 150 3 4 5 6 3 20 1 d 75%, 100, 4 e 100, 5, 0.2(0) a 6 b 10c c 75 d $2.50 e 20 f 9 Teacher check 1 2 3 3 3 a 1 3 b 1 5 c 1 10 d 5 4 e 4 8 a 76 b 59 c 16.4 d 150 e 720 f 850 j 5.3 k 0.17 l 9.28 m 5.16 n 2.26 o g1 h6 i6 j6 g 1 210 h 694 i 3.2 0.583 p 0.794 Targeting Maths Teaching Guide Year 5 Mental and Oral Strategies Percentages Stand up! Find 50% of … 25% of … 10% of … 100% of etc. Use quantities as well as numbers. Various percentages of the class stand up … hop to the door … sit back to front etc. Stand up the back 50%. Stand up the front 25%. Stand up the tallest 10%. Stand up 100% of the class. Stand up 50% of the boys. One number can be 50% of something, yet 25% of something else. eg 30 is 50% of 60, 25% of 120. Students can make up the questions. Activity Bank Gather percentages Dicey mixed numbers Make a poster with students’ contributions of percentage signs from their environment — newspapers, advertisements, signs from the shops. Discuss each example; where it was used; why it was used; how it was used etc. In pairs, students throw two dice. The first throw is the numerator, the second is the denominator. Write the fraction. Classify it as ‘Proper’ or ‘Improper.’ If improper, change it to a mixed number. What is the largest fraction that can be thrown with two dice in this way? Give the answer first Twenty questions using decimals Give the answer, eg 57, and ask what multiplication or division using decimals could have been the question. Choose a decimal between 0 and 10 and have the class guess the number, eg 6.9. Encourage thoughtful questioning, eg is it even. Use only the clues, ‘higher’ or ‘lower’ to guide the questioning. Use only 10 or 100. Targeting Maths Teaching Guide Year 5 151 Activity Card 75 ✎ Time and Time Again With your partner, decide on five tasks to complete ten times each — eg, write a three-letter word ten times; say ‘fee, fi, fo, fum’ ten times; draw a five pointed star ten times. 1 Time each other in seconds. 2 Divide the time for each activity by 10 using a calculator to work out the time for each repetition. Task Repetitions 3 Divide the number of repetitions by the time to work out how many repetitions per second. 4 Total the time per repetition column. 5 The player with the shortest time, wins. Time per repetition Repetitions per second Activity Card 76 ✎ What Percentage? What percentage of each item is shaded? Give estimates only and match the shape to the list. Less then 10% Just over 50% Between 40% and 50% About 75% Nearly 20% About 25% Between 50% and 75% Almost 100% 152 © Blake Publishing — Targeting Maths Teaching Guide 5 This page may be reproduced by the original purchaser for non-commercial classroom use. Assessment Name __________________________________________ Fractions and Percentages Date _____________________________ a How many small squares? _________ 1 b Colour 17% red. c Colour 51% green. d How many squares are not coloured? _________ e What percentage is this? _________ 2 Fill in the table. Percentage Hundredths Fraction in lowest terms Decimal 50 100 a b 10% 1 4 c 0.75 d e 20% 3 a b c d e f g h i j Find: 50% of 10% of 75% of 25% of 20% of 75% of 50% of 10% of 20% of 25% of 1 year. _____ months $1. _____ 1 m. _____ cm $10. _____ 1 century. _____ years 1 dozen. _____ 1 fortnight. _____ week 1 hour. _____ minutes April. _____ days 1 day. _____ hours 4 Colour diagrams to show: 1 1 a 2 – 4 = ______ 3 b 3 – 5 = ______ c 2 – 8 = ______ 5 Change to mixed numbers. 4 7 13 23 35 a 3 = ____ b 5 = ____ c 10 = ____ d 4 = ____ e 8 = ____ 6 a 7.6 π 10 = _____ b 5.9 π 10 = _____ c 1.64 π 10 = ____ d 15 π 10 = _____ e 7.2 π 100 = ____ f 8.5 π 100 = ____ g 12.1 π 100 = ___ h 6.94 π 100 = ___ i 32 ÷ 10 = ______ j 53 ÷ 10 = ______ k 1.7 ÷ 10 = _____ l 92.8 ÷ 10 = ____ m 516 ÷ 100 = ____ n 226 ÷ 100 = ____ o 58.3 ÷ 100 = ___ p 79.4 ÷ 100 = ___ © Blake Publishing — Targeting Maths Teaching Guide 5 This page may be reproduced by the original purchaser for non-commercial classroom use. 153 Student pages 148–151 Patterns Learning focus VELS: CHANCE Outcomes and Standards Number Patterns and Relationships 4.1 Generate and investigate number sequences which may involve fractions, decimals and combinations of operations, using a calculator where appropriate. 4.3 Construct, verify and complete number sentences involving the four operations, brackets, decimal numbers and fractions. Computation 4.4 Analyse a problem situation which may involve several different operations, decimal numbers, negative whole numbers and common fractions; express the problem symbolically and choose appropriate computational methods to solve it. Counting 4.1 Use place-value knowledge to read, write and order negative whole numbers and decimal numbers from thousandths to millions. • Solves number puzzles expresses in words. • Constricts and verifies number sentences. • Recognises and uses inverse relationships. • Uses rules to generate a sequence. • Describes and tests rules for a sequence. • Counts in decimal fractional amounts. • Uses rules to generate a sequence. • Identifies key information to complete a task. Key words number sentence, value, substitute, rule Resources calculators, cm grid paper Additional work sheets Targeting Maths Upper Primary Operations and Number Patterns • Number Patterns — Unit 2 154 • Play “I am thinking of …” with one step then two steps. Eg I am thinking of a number that when it is divided by 7 the answer is 12.” (84) “… divided by seven and 14 is added the answer is 19.” (35) • Start with teacher generated sentences and then allow students to present the clues. • How do we work them out? Work through several examples. • Ensure that the students understand the role that inverse operations play. • Point out that we are finding unknowns. (algebra) Student page 149 • Work question 1 mentally. Work the first two examples as a class. • In question 2 show how to write the sentences using opposites. Work examples on the board. • Tell students that question 3 refers to question 2 answers. If they find a question 2 answer wrong work it again. Student page 150 • Have centimetre squared paper available for students to draw the patterns if necessary. • Discuss the patterns. • Complete the table and stop. Discuss what is happening. • Students can then complete the page (drawing diagrams if they wish). Student page 151 • Students work out all the rules before drawing any lines. This will give them a check on their decisions. • Question two could be worked with a partner. At the end of the lesson each pair can present one (or more) of their patterns to the class who has to guess the rule. • For question 3 draw a lamp on the board. Write a two-step rule under it and encourage students to put in a number for the class to decide what number comes out. • This can be a class/team game. Answers for assessment page 157 1 a 36 ÷ 3 – 7 = 5 b ( 7 + 15) π 2 = 44 c 9 π 10 – 37 = 53 2 a 10 b 3 c 10 9 4 1 3 a 10 b 14.9 c 1.3 d 12.8 e 8 f 2 4 9 1 4 a 10 + 10 = 1 b 14.9 – 6.5 = 8.4 c 1.3 π 7 = 9.1 4 3 1 d 12.8 ÷ 8 = 1.6 e 8 – 8 = 8 f 3 1 3 1 1 2 1 4 + 3 14=4 5 a 2 4 , 3 4 , 3 4 , 4 4 (+ 2 ) b 5.2, 4.4, 3.6, 2.8 (– 0.8) Targeting Maths Teaching Guide Year 5 Mental and Oral Strategies Oral number sentences What’s my rule? Give students quick two part number sentences to work, eg Add 4 and 7 and subtract 3. Give a series of numbers and have students identify the rule you are using. Review the four processes in this way. eg 2, 5, 8, 11 (+ 3); 1, 7, 49, 343 (π 7) Also practise multiplication and division, eg 3 π 8 ÷ 4. Activity Bank Secret numbers Calculator practice Students think of a number and give a twopart clue to its ‘identity’. eg My number is one quarter of 68 minus the sum of 7 and 6. A student has to give the number sentence and the answer to identify the secret number. Give students practice using calculators. Orally dictate a number sentence for students to work and write down their answer when completed. Important destinations Back home again Choose a number, eg 108, as a destination. Have students collectively make a number of interesting ways in which you can arrive at this number. eg Begin at 10, square it and add two fours. Display each set on a chart drawn on the board for that number. From 108 (previous activity) how do we work backwards (using opposites) to arrive ‘home’ again? eg From 108, subtract two fours and find the square root. Arrive at 10. Targeting Maths Teaching Guide Year 5 This is also a good listening skills activity. It can be done in teams where the team with most correct answers to a question gain a point. This can be worked for every expression written on the chart. 155 Activity Card 77 ✎ Calculator Words ÷ X _ + Work each of the following on a calculator. Remember order of operations. Turn the calculator upside down and write the ‘word’ obtained. 1 (20 π 20) + 59 π 3 π 4 = ______________ 2 (69 + 77 π 200) π 5 = ______________ 6=G 3 20 π 30 + (2 π 9) = ______________ 7=L 4 11 π 7 π 100 +18 = ______________ 5=S 5 8 π 3 π (20 π 7 + 6) = ______________ 8=B 6 Make up one of your own. ______________ Activity Card 78 ✎ New Number Systems Invent your own number system. • Your number system could be based on another number other than 10. • Decide how to show the equivalent of Hindu-Arabic ones, tens, hundreds. • Make up other symbols for your digits. Ones Tens Hundreds • Draw four numbers on the abacuses using your system. # ☯ k ∞ • Ask a partner to work out the Hindu-Arabic m ^^ @ ~~ equivalents to the new numbers you have drawn. a 156 b c © Blake Publishing — Targeting Maths Teaching Guide 5 This page may be reproduced by the original purchaser for non-commercial classroom use. d Assessment Name __________________________________________ Patterns Date _____________________________ 1 Write a number sentence and find each number. I am thinking of a number: a so that when I divide it by 3 and subtract 7 the answer is 5. Number sentence b so that when I add 15 and double it the answer is 44. Number sentence c so that when I multiply it by 10 and subtract 37 the answer is 53. Number sentence 2 a + 9 = 37 – 18 b 17 π = _____ = 14 + 37 = _____ 3 Rewrite using opposites to find the value of 1 a + 10 = 1 b ▲=9π8 ▲ = _____ . – 6.5 = 8.4 π 7 = 9.1 c 1 10 = _____ = _____ = _____ = _____ = _____ = 1– ÷ 8 = 1.6 d c 82 – e 3 1 – 8 = 8 f + 3 14 = 4 = _______ = _______ = _______ = _____ = _____ = _____ 4 Substitute your values into the questions to check your answers in question 3. 9 1 a 10 + 10 = 1, true b c d e f 5 Complete the pattern and write the rules. a 1 14 Rule 3 14 1 b 24 7.6 6.8 6 Rule © Blake Publishing — Targeting Maths Teaching Guide 5 This page may be reproduced by the original purchaser for non-commercial classroom use. 157 Student pages 152–154 Area and Length Learning focus VELS: MEASURMENT Outcomes and Standards Measuring 4.4 Use measuring instruments, reading simple scales and measuring accurately to the nearest marked gradation, taking into account the degree of exactness required. Using Relationships 4.1 Measure and compare the perimeter and area of regular and irregular polygons. 4.2 Investigate the relationship between area and perimeter and calculate the area of a polygon. Investigation 4.2 Clarify the essential nature of a task or problem and identify key information in the context under consideration. 4.4 Communicate own responses to tasks and problems appropriate for this level to others. Reasoning 4.3 Use and interpret simple mathematical models. • Uses measuring instruments accurately. • Calculates the area of a polygon. • Calculates perimeter by adding lengths. • Devises own shortcuts for finding perimeter. • Uses a range of strategies for inquiry. • Chooses attributes and standard units appropriate to the task. • Uses and interprets simple mathematical models. • Presents outcomes and results of own inquiries. Key Words area, dimensions, perimeter, equilateral, isosceles, average Resources measuring tools, scissors Additional work sheets Targeting Maths Upper Primary Measurement • Length — Unit 1 • Area — Unit 1 158 • Revise how to find the area of a square and a rectangle. Draw the shapes on the board. • Draw an irregular shape on the board, eg like one of the ones on page 152. • How will we work out the area of this shape? • Encourage children to make suggestions and write them all. Apply some suggestions to your shape. Does it work? • When it has been established that we work 2 (or more) areas and add (subtract) them, draw more shapes where the separate areas will be added or subtracted to give total area. Clearly show working. • Revise perimeter — what it is and how to work it out. Student page 153 • Revise perimeter. • After questions 1 and 2 have been completed discuss the ‘rules’ for squares and rectangles. • Point out that the rules make it easier but you can always add the lengths of all the sides if you forget the rules. • Remind students about equilateral and isosceles triangles. Student page 154 • Have many measuring instruments available for use by students. • Encourage them to swap instruments regularly so they experience using them all. • Why do we have so many different instruments to help us measure length? • Revise averages — what they are and how to work them out. Answers for assessment page 161 1 a 4 cm, 5 cm, 2 cm, 2 cm, 2 cm, 7 cm b outside; 6 cm, 5 cm, 6 cm, 5 cm inside; 4 cm, 1.5 cm, 4 cm, 1.5 cm 2 a 24 cm2 b 24 cm2 3 22 cm 4 a length of side π 4 b (length + breadth) π 2 5 a 280 mm b 28 cm c 0.28 m 6 answers will vary — Teacher check 7 a 26 mm b 4.4 cm c 5.03 m d 72 km 8 Teacher check Targeting Maths Teaching Guide Year 5 Mental and Oral Strategies Short methods Quick perimeters Review the short methods for multiplying and give oral practice. • 3π6+5x6=8π6 • π 10, add a 0 or move the decimal point one place to the right • π 5 = half of x 10 • π 4 = double and double again etc. Perimeter of a rectangle = 2 π long side plus 2 π short side Perimeter of square = 4 π side. Give quick oral practice working out the perimeters of regular quadrilaterals. Activity Bank Half a shape — perimeter Half a shape — area Is the perimeter of half a 4 cm square exactly half the perimeter of the 4 cm square? Draw a square to prove your answer. Is the area of half of a 4 cm square exactly half the original area? Draw a square and prove your answer. Work this exercise for other 2D shapes. Also repeat for other regular shapes. List the perimeters Mystery shapes Take a walk around your school and list the places where builders or contractors would have applied their knowledge of perimeter. Have students draw regular quadrilateral shapes. They work out the perimeter and the area. Given this information, other students are to work out the dimensions of that shape, eg P = 20 cm, A = 24 cm2. The shape is a rectangle 6 cm π 4 cm. Work out the perimeter of designated areas, eg the handball court. Targeting Maths Teaching Guide Year 5 159 Activity Card 79 ✎ Perimeter /Area The area of the square base of this triangular pyramid is 81 cm 2. The triangular sides are equilateral triangles. What is the perimeter of the whole net? Cut out the triangles and arrange them like this: Explain how you could work out the area of this shape. Activity Card 80 Rearrange Me Turn the 5 small squares into 1 big square. • Cut out the 5 square shape. • Cut it along the dotted lines. • Arrange the pieces into 1 square. How will the area of the large square compare to the area of the 5 smaller squares? Hint: You can turn and slide the pieces but you can’t flip them. 160 © Blake Publishing — Targeting Maths Teaching Guide 5 This page may be reproduced by the original purchaser for non-commercial classroom use. Assessment Name __________________________________________ Area and Length Date _____________________________ B A 1 Carefully measure the dimensions of both shapes. Write the measurement on the shapes. 2 Work out each shaded area. a Area = b Area = 3 What is the perimeter of A? P= 4 Write the rule for finding the perimeter of: a a square. b a rectangle. 5 Measure the length of this page. Write it in: a mm. __________ b cm. __________ c m. __________ 6 What instrument would you use to measure: a the width of a door? _______________ b a person’s height? _________________ c the length of a tennis court? ________ d the length of a park? ______________ 7 Find the average. a 17 mm, 24 mm, 27 mm, 36 mm _________ b 1.9 cm, 8.6 cm, 3 cm, 7.2 cm, 1.3 cm _________ c 4.23 m, 8.64 m, 5.07 m, 2.18 m _________ d 65 km, 92 km, 59 km _________ 1 8 Name 3 items in the room which are approximately 2 m long. a b c © Blake Publishing — Targeting Maths Teaching Guide 5 This page may be reproduced by the original purchaser for non-commercial classroom use. 161 Student pages 155–157 Measurement Learning focus VELS: MEASURMENT Outcomes and Standards Measuring 4.4 Choose attributes and standard units appropriate to the task. Reasoning 4.3 Use and interpret simple mathematical models. Time 4.1 Use and construct timetables and use and analyse calendars. 4.2 Estimate, measure and calculate time elapsed (duration). Using Relationships 4.3 Investigate and compare the volume and mass of objects. Investigation 4.3 Use a range of strategies for inquiry when responding to tasks and problems. • Uses and interprets simple mathematical models. • Chooses and explains the choice of instruments when measuring. • Reads timetables correctly. • Estimates the time taken to complete a task. • Prepares a timetable. • Counts cubes to measure volume. • Uses a range of strategies for inquiry. Key words instrument, timetable, cubic centimetres, volume, capacity, dimensions Resources medicine measures, blocks, stopwatch, measuring instruments, blank cards Additional work sheets Targeting Maths Upper Primary Measurement • Time — Unit 2 • Volume and Capacity — Unit 1 162 • What do we measure? Students will come up with a long list. Write it on the board. • What do we use to measure things? Again a long list can be made. • Look at each item on the first list and choose instruments from the second list that can be used to measure the item. • Students can be taught a little of the history of measures, eg a hand span, a foot etc. • Mention special measuring devices. Students name some and tell what they are used for, eg special x-ray machines that measure bone density. Student page 156 • • • • • Discuss timetables. Are they necessary? Who relies on a timetable? Where and when do you or your family use a timetable? What types of timetables are there? Look at the timetable on page 156. Discuss what the timetable is for and the time units used. Student page 157 • • • • • Form class into harmonious groups! Make sure each group has the necessary equipment. If possible work question 1 outside as there will be spilt water. At the end of question 1 come together to discuss findings. Questions 2 and 3 can be worked individually. Answers for assessment page 165 1 measuring instruments will vary for this question — these are only possibles: a tape measure, centimetres b stopwatch, seconds c measuring jug, litres d scales, grams e medicine glass, millilitres f ruler, centimetres g clock, hours h teaspoon, grams i protractor, degrees j steel tape, metres 2 a 6 cm3 b 5 km c 4:00 a.m. d 72 mL e 9 ha f 200 L g 43 m2 h 250 g i 10:00 p.m. j 19 mm 3 a 10:15 a.m. b 5:05 p.m. c 11:30 p.m. d 2:10 a.m. 4 a 14:00 b 18:20 c 9:07 (09:07) d 21:51 e 11:50 f 1:00 (01:00) (these can be written without the colon) 5 a 8 cm3, 8 mL b 24 cm3, 24 mL c 15 cm3, 15 mL d 72 cm3, 72 mL Targeting Maths Teaching Guide Year 5 Mental and Oral Strategies True or false Time left Review all measurements of length, mass, 1 time, capacity. Make statements such as ‘2 2 metres equals 150 cm.’ ‘I use scales to measure sugar.’ Hands up if its true, hands in laps if it’s false. It’s 9:53 a.m. How many minutes until 10:15 a.m.? Count on to the hour and then past it. How many minutes until recess at 10:45 a.m.? How many hours and minutes until we go home? Activity Bank Time a minute Record personal measurements Work with a small group at a time. Time one minute on a stopwatch while students count a minute to estimate. They say ‘Time’ when they guess the minute has gone by. After the minute has gone by and after they have all said ‘Time’, tell the student who was closest to the real minute. Have students record as many measurements about themselves as they can: height, weight, size of head, clothing sizes, temperature, time of birth (ask at home), how much blood is in them (seek information). Allow them another try to make an adjustment to their timing. Make a class chart under the various headings. Allow students to give you their measurements privately if they wish. Use measuring instruments Dominoes with measurements Allow plenty of access to measuring instruments in the classroom. Use a height measure on the wall. Use scales when possible and needed. Use trundle wheels to find distances around the school. Use a metre stick for measurements around the classroom. Children need lots of hands-on practice with instruments. Using blank cards make a set of dominoes with a decimal measure on the end of one card (1.47 m) and the matching measurement without the decimal point (147 cm) on the end of another card. Play dominoes in groups of four. Targeting Maths Teaching Guide Year 5 163 Activity Card 81 LETTER Spacing ✎ Print each title in its space. Use decorative letters. Measure the space allowed and allocate an equal space to each letter so that they fit accurately. 1 AUSTRALIA 2 CHINA 3 MURRAY RIVER Activity Card 82 Volumes of Irregular Shapes 1 Use a marked kitchen liquid measure containing water to measure the volume of small items collected from the classroom. 2 Mark the height of the liquid before and after the item is submerged in the container. 3 Calculate the difference in the water levels in millilitres. 4 Record the volumes. 5 Discuss other ways that the liquid can be measured to determine the volume of the item. 164 © Blake Publishing — Targeting Maths Teaching Guide 5 This page may be reproduced by the original purchaser for non-commercial classroom use. Assessment Name __________________________________________ Measurement Date _____________________________ 1 Complete this table. Object to measure Measuring device Measurement centimetres a length of a curtain b time of 100 m race c liquid in a large bottle d weight of a cake e a dose of medicine f the width of a book g time spent at a party h a spoonful of salt i degrees in an angle j length of a school yard 2 Use the short form to write: a 6 cubic centimetres __________ b 5 kilometres __________ c 4 o’clock in morning __________ d 72 millilitres __________ e 9 hectares __________ f 200 litres __________ g 43 square metres __________ h 250 grams __________ i j 10 o’clock at night __________ 19 millimetres _________ 3 Write using a.m. or p.m. a 10:15 _________ b 17:05 _________ c 23:30 _________ d 02:10 _________ 4 Write using 24-hour time. a 2 p.m. ____________ b 6:20 p.m. ____________ c 9:07 a.m. ____________ d 9:51 p.m. ____________ e 11:50 a.m. ___________ f 1:00 a.m. ____________ Volume in cm3 Capacity in mL 5 Complete. Prism a 2 cm π 4 cm π 1 cm b 4 cm π 3 cm π 2 cm c 5 cm π 1 cm π 3 cm d 6 cm π 3 cm π 4 cm © Blake Publishing — Targeting Maths Teaching Guide 5 This page may be reproduced by the original purchaser for non-commercial classroom use. 165 Student pages 158–162 Space Learning focus VELS: SPACE Outcomes and Standards Shape and Space 4.1 Recognise, describe and represent parallel, perpendicular, horizontal and vertical lines, right angles, and angles greater than or less than 90 degrees (multiples of 45 degrees). 4.2 Analyse, explain and compare the spatial properties of lines, angles, polygons, polyhedra and cross-sections using conventional spatial terms. 4.4 Draw conventional representations of prisms, pyramids, cylinders and cones. Location 4.2 Use informal coordinate systems (positive numbers only) and intermediate compass points to specify location or give directions. • Explains and compares spatial properties of 2D shapes. • Describes a 3D object in detail. • Classifies shapes and objects according to properties. • Uses conventions for drawing 2D shapes and 3D objects. • Identifies lines in the environment. • Locates coordinate points on graph paper. • Classifies shapes according to properties. • Uses coordinate systems to specify locations. • Interprets formal maps. Key words diagonal, vertex, reflex, position, horizontal, vertical, oblique, parallel, perpendicular Resources protractors, photocopies of 2D shapes, compass and protractor for board, geostrips, split pins Additional work sheets • What is a diagonal? A diagonal is a straight line that is drawn inside a shape from one corner to another. Dispel the myth that it is any sloping line. • What is a decagon? Draw one on the board. • When drawing a decagon for the Challenge tell the students that it does not have to be a regular decagon. Student page 159 • Read the word bank. • Discuss each word; what it means. Have students draw each shape on the board. • Erase drawings before they attempt question 1. • Insist on the use of rulers and sharp pencils for question 2. Student page 160 • • • • Draw examples of different lines on the board. Explain that the word oblique can be used instead of diagonal. Revise vertical, horizontal and oblique lines. Talk about looking at the horizon. This is the easy way to remember horizontal lines. • Revise parallel lines (straight lines that never meet). • Teach perpendicular lines. Stress that the lines do not have to be vertical and horizontal — they just must meet at right angles. Student page 161 • • • • Revise how to read a grid. Read bottom number before the side number. Tell students to use rulers to draw in the lines. For Draw a diagram suggest that they try shapes that do not appear on page 161 — or at least make the shapes different. Student page 162 • Study the map. How is this grid different from the one on page 161? • Grid uses letters and numbers. Still read bottom before side. • Discuss the fact that students will see coordinates which are written differently — sometimes a side letter or number will come first. For school purposes tell them to always read/write the bottom number or letter first. Answers for assessment page 169 1 Teacher check diagonals; 2, 5, 9, 14, 20 2 a triangular pyramid b cone c octagon d isosceles triangle e trapezium f triangular prism 3 Teacher check Targeting Maths Upper Primary Space and Chance and Data • 2D — Unit 1, Unit 2 166 Targeting Maths Teaching Guide Year 5 Mental and Oral Strategies Quiz Study the clock Give the properties of a 2D shape, including sides, angles, axes of symmetry, diagonals. Students identify it. Play in teams and award points. Give the time when the angle between the hands of a clock is a reflex angle. Encourage students to also give the details for the class to guess. Students can estimate the size of the reflex angle. Point out the 270º angle (three right angles) as this is an aid to estimation of size. Activity Bank Designs in 2D shapes Rigid shapes Give students photocopies of large 2D shapes. Which ones will contain a star (stars) when all diagonals are drawn? Colour them appropriately. Show how diagonals will make a non-rigid shape into a rigid shape. Build rigid shapes using geostrips and split pins. Which shape is rigid to start with? Construction practice 2D shapes in real life Give practice constructing squares, rectangles and triangles using rulers and protractors. Drawings should be labelled with dimensions. Have students check each other’s work for accuracy by checking measurements. Give students photocopied 2D shapes on larger pages. Ask them to add details and colour which show the 2D shape in the environment, eg windows in a church, rooflines, a plan of a garden area. Targeting Maths Teaching Guide Year 5 167 Activity Card 83 Enlarge ✎ Enlarge this shape by redrawing it on the larger grid. Be careful to match every important point so that the shape is maintained exactly. Draw the axes of symmetry and colour it attractively. Activity Card 84 Geoboard Squeeze On a 10 π 10 geoboard create a regular triangle, square, pentagon, hexagon, heptagon, nonagon and a decagon using rubber bands. Is it possible to fit all the shapes without any overlapping? 168 © Blake Publishing — Targeting Maths Teaching Guide 5 This page may be reproduced by the original purchaser for non-commercial classroom use. Assessment Name __________________________________________ Space Date _____________________________ 1 Draw the diagonals for these shapes and fill in the table. Shape Quadrilateral Pentagon Hexagon Heptagon Octagon Number of diagonals 2 What am I? a I have 4 faces. They are all triangles. _________________ b I have 1 flat surface and 1 curved surface. _________________ c I have 8 sides, 8 angles and 20 diagonals. _________________ d I have 3 sides. Two sides are equal. _________________ e I have 4 sides. One pair of sides is parallel. _________________ f I have 5 faces and 6 corners. 2 faces are triangles. _________________ 3 Draw: a some vertical lines. d a pair of parallel lines. b some horizontal lines. c three oblique lines. e two lines that are perpendicular to each other. © Blake Publishing — Targeting Maths Teaching Guide 5 This page may be reproduced by the original purchaser for non-commercial classroom use. 169 Student pages 163–165 Graphs Learning focus VELS: DATA Outcomes and Standards Summarising and Presenting Data 4.1 Prepare tabular displays of discrete and continuous data. 4.2 Prepare visual displays of discrete and continuous (measurement) data using a range of graphical methods. Interpreting Data 4.1 Extract and interpret numerical information contained in tables, data displays and databases. Posing Questions and Collecting Data 4.1 Design and prepare surveys and experiments to answer questions or test conjectures and predictions. 4.2 Collect and record data systematically. Reasoning 4.1 Make and test simple conjectures in each mathematics strand. • Constructs bar graphs to represent given data. • Extracts and interprets information from data. • Interprets graphical displays. • Suggests new questions arising from data. • Gives own ideas for mathematical inquiry. • Designs surveys, collects and records data. • Prepares data tables and chooses a graphical display. • Present statements about own findings. Key words graph, axes, tally, survey, information Resources • Why do we use graphs? • Lead children to discuss the effect of visual literacy and its uses. • Look at page 163, first graph. What type of graph is this? • Why is there a key? Is this a good key? Discuss. • Could we use one symbol to represent one meal? Why? • Does this graph need labels on the axes? Why? • When the page is finished look at the answers for questions 2b and 3d. Let students read their answers and discuss them as a class. Student page 164 • • • • Look at the graph on page 163. What type of graph is this? In what way does it differ from the graphs on page 162? Without reading the question can you tell me what the graph is about? • What does the graph need to give us more information? • Revise how to find the mean of a set of scores. Student page 165 • The class will probably need help to get started with this task. • Make a class list of the types of entertainment that might have been visited. • From the list the students choose five types. • Tell the students that they are to choose a cross-section of people. 10 children only can be surveyed. • Why do I limit the number of children? • At the end of the task allow students to show their graphs and discuss their findings. Answers for assessment page 173 1 2 3 4 a 6 b 10 c 11 d 9 e 19 f 17 a 72 b 12 Teacher check a 13, 26, 9, 20, 7 b Teacher check c Teacher check centimetre grid paper Additional work sheets Targeting Maths Upper Primary Space and Chance and Data • Graphs — Unit 1 170 Targeting Maths Teaching Guide Year 5 Mental and Oral Strategies Divisibility tests Division with remainders If my number is divisible by 5 (or another given number) students clap once. If it is not they remain silent. This can be done as a competition with students being ‘out’ when they make an error. Those ‘out’ help identify others who make errors. Give about 5 numbers before changing divisor. Review divisibility rules for 3, 4, 5, 6, 7, 8, 9, 10. What is the remainder when … is divided by 6, 7, 8, 9? A good way to practise tables. Activity Bank Which graph to use? What is the data? Redraw the graph on page 163 as a line graph. Is this information suitable for a line graph? Why or why not? With a horizontal axis marked in letters A to J and a vertical axis marked in kg from 100 to 150, what could be the title of the graph? Students discuss what they know from the labels on the axes. Make up several more sets of data and have students guess each other’s graph titles. Read a double graph Useful data Find or make a bar graph where two columns are used for each item on the horizontal axis. Ask students what data could be displayed using two columns, eg minimum and maximum temperatures for a city. Discuss where we might see such a graph used (on a tourist brochure advertising a city). Make a list of data which would be useful for the following people; cinema owners, car salesmen, market researchers, rail administrators, travel salesmen, toy shop owners, hotel owners. Students then draw their own double bar graph. Targeting Maths Teaching Guide Year 5 From the list choose one person and write ten survey questions which would help them find the data they need. 171 Activity Card 85 ✎ Lamington Drive Time 9 a.m. 10 a.m. 11 a.m. 12 noon 1 p.m. 2 p.m. 3 p.m. Total Lamingtons made 4 doz 6 doz 9 doz 12 doz 16 doz 16 doz 22 doz Draw the most appropriate type of graph to display this information. First decide on a key or scale. Label the axes. Write a title. Activity Card 86 Make It Right ✎ Read the following statements. Underline any part of a statement that is not logical. Rewrite the statement with something logical in its place. 1 After visiting the movies, Jake had $2.50 in change, so he took a taxi home. 2 The plane left Melbourne at 5:30 p.m. and arrived in Sydney at 4:45 p.m. 3 The difference between the tallest and the shortest student in our class is 2 cm. 4 If you double any two-digit number, you will get an answer between 0 and 50. 5 The mean minimum temperature at Thredbo in July is expected to be 18ºC. 6 In June 2004 the Australian dollar is worth 65¢ in US currency. 7 If you double the length and width of a cake, you double the amount of cake. 8 I scored 80% in Maths for 3 weeks running so if I score 100% this week, my average will be 90%. 172 © Blake Publishing — Targeting Maths Teaching Guide 5 This page may be reproduced by the original purchaser for non-commercial classroom use. Assessment Name __________________________________________ Graphs Date _____________________________ A scientist studied spiders found in six areas. These are the results. 1 How many were found in each area? Area A B a A ____ b B ____ c C ____ C d D ____ e E ____ f F ____ 2 a What is the total number D E of spiders found? ____________ F b What is the mean number found 0 5 10 15 20 per area? ____________ Number of Spiders 3 Is this information best shown in a bar graph, picture graph or line graph? ______________________ Why? ______________________________________________ ___________________________________________________________________________ 4 This tally chart shows information gathered by the local butcher. Monday Sales chops sausages steak mince roast Tally 5 5 111 555551 5 1111 5555 5 11 Total a Complete the Total column. b Represent this information on a graph. c Does this represent the butcher’s total number of sales for Monday? _____ Why? _________________ ______________________ ______________________ © Blake Publishing — Targeting Maths Teaching Guide 5 This page may be reproduced by the original purchaser for non-commercial classroom use. 173 Year 5 Student Book Answers Page 2 Page 6 1 a 1 237, 3 567, 2 045 b 2 a 7 321, 7 653, 5 420 b 3 1 237, 1 273, 1 327, 1 372, 1 2 317, 2 371, 2 713, 2 731 4 4 025, 4 052, 4 205, 4 250, 4 5 042, 5 204, 5 240, 5 402, 5 5 Sue, 1 237 6 Karl, 5 024 Sue Tom 723, 1 732, 2 137, 2 173 502, 4 520, 5 024 420 Page 3 1 a 7 312, 7 635, 5 402 b 1 273, 3 576, 2 054 2 a seven thousand three hundred and twelve b seven thousand six hundred and thirty-five c five thousand four hundred and two 3 a 3 271 b 5 736 c 4 052 d 2450 e 7 312 4 a Sue b Tom c Karl d Karl e Sue 5 a three thousand one hundred and seventy-two b one thousand seven hundred and twenty-three c two thousand three hundred and seventeen d seven thousand two hundred and thirteen Challenge 64 Page 4 1 a 25 147 b 61 492 2 Teacher check 3 a b c d e 4 7 8 3 6 1 3 4 9 7 2 5 1 6 4 5 2 6 3 1 c 45 384 d 14 827 9 7 5 6 8 4 a 19 651, 23 749, 30 543 b 60 157, 79 872, 93 065 c 50 947, 51 230, 51 803 Page 5 1 coloured yellow: 60 000, 7 000, 300, 90, 4 coloured green: 40 000, 6 000, 500, 30, 9 coloured pink: 70 000, 3 000, 600, 40, 5 coloured purple: 50 000, 4 000, 900, 50, 7 2 a sixty-seven thousand three hundred and ninety-four b forty-six thousand five hundred and thirty-nine c seventy-three thousand six hundred and forty-five d fifty-four thousand nine hundred and fifty-seven 3 a 73 645, 67 394, 54 957, 46 539 4 Teacher check 5 Teacher check 6 a 10 000 b 99 999 Challenge 75 039 174 1 a Sam b Terry 2 a 153 b 129 d 134 e 177 3 a Sam + Terry c Sam + Suzie 4 a 255 b 170 5 a Sam + Mary + Ahmed 6 a Teacher check (430) c 143 f 114 b Jill + Ahmed b Jill + Ahmed + Suzie b 425 Page 7 1 a 17 b 23 c 31 e 35 f 69 g 87 i 43 j 57 k 267 2 a 77 b 89 c 98 e 93 f 117 g 112 i 143 j 125 3 a 68 b 74 c 121 e 95 f 155 g 171 4 a 84 b 99 c 94 e 132 f 96 g 140 i 97 5 a 108 b $1.48 c 151 Challenge a 163 b 186 c 142 Teacher check strategies d 49 h 113 d 65 h 88 d h d h 99 118 92 181 Page 8 1 a 172 b e 251 2 a 455 b e 787 f i 947 j 3 a $5.22 b e $8.40 f Challenge $34.20 161 c 230 d 273 669 694 848 $9.39 $6.21 c g k c g d 892 h 718 551 913 920 $4.14 $10.62 d $6.06 h $14.49 Page 9 1 a 977 b 794 e 957 f 999 2 a 224 b 184 3 Teacher check 4 Teacher check 5 Teacher check c 856 g 574 c 843 d 909 d 803 Page 10 1 a cherry tart, fruit tart b 2 a chocolate bear b c gingerbread man 3 a 8c b 12c c 4 a 54c b No: any 2 cakes cost more 40c, 19c, 27c cherry tart 15c than 99c Targeting Maths Teaching Guide Year 5 Pages 2– 19 Page 11 1 a 11 b 19 c 29 d e 27 f 32 g 56 h i 23 2 a 24 b 54 c 32 d e 44 f 18 g 44 h 3 a 28 b, c Teacher check 4 a 24 b, c Teacher check 5 a 12, 65, 49, 23, 77, 56, 34, 8 b 12, 50, 21, 8, 15, 61, 34, 53 6 Teacher check 7 a 197 b 298 c 123 d e 178 f 283 g 411 h i Teacher check Challenge a Teacher check (630) b 631 b Teacher check 25 22 61 19 349 183 Page 12 1 a e 2 a e 3 a e i 4 a e 84 265 234 217 472 457 261 478 288 b f b f b f j b 173 239 418 245 194 272 146 162 c 119 d 122 c g c g 219 347 284 183 d 264 c 304 d 579 d 392 h 281 Page 13 1 a 364 b 287 c 242 d 137 2 a 13 b 371 c A – D = 304 d B – C = 358 e B – D = 291 f D – C = 47 g E – A = 115 h E – B = 128 i E – C = 486 j E – D = 419 k because second number is larger than first 3 585, 408, 189 Work backwards: 396 Page 14 24 15 28 63 60 72 2, 3, 24, 4, 6, 12, 8 15, 3, 5 2, 4, 7, 14 3, 9, 7, 21 2, 15, 3, 4, 6, 5, 30, 20, 12 2, 3, 24, 9, 4, 36, 6, 12, 8 Page 15 1 a 4, 8, 12, 16, 20 c 9, 18, 27, 36, 45 e 20, 40, 60, 80, 100 Targeting Maths Teaching Guide Year 5 b 7, 14, 21, 28, 35 d 11, 22, 33, 44, 55 2 top row 3, 6, 20 middle row 9, 7, 8 bottom row 49, 160 3 a 16, 20, 28, 36, 44, 60 b 15, 20, 25, 35, 45, 60 c 27, 36, 45, 54, 63, 81 d 14, 21, 28, 35, 49, 63 4 a 28 b 38 c 46 d 70 e 134 5 a 32 b 48 c 96 d 168 e 284 6 a 48 b 96 c 120 d 216 e 504 Challenge a 96 b 160 c 288 d 640 Page 16 1 a 128 b 410 c 1 240 e 1 560 Teacher check methods 2 a π8 54, 30, 78, 8, 45, 28 π4 24, 34 π7 46, 62, 7, 37, 20 π3 23, 10, 32, 20, 6 π9 61, 12 π6 40, 26, 46, 34, 15, 6, 35, 16 b 28 Challenge Teacher check d 424 Page 17 1 a e 2 a e i 3 a 469 288 2 460 1 335 5 472 1 068 b f b f j b 504 368 2 082 2 265 5 624 2 142 c g c g 855 637 6 632 2 655 d h d h c 2 188 265 234 4 102 2 340 d 5 173 Page 18 1 a f 2 a 3 a 4 a f 5 a e 2 8 2 2 b 4 c 12 d 3 e 6 b 12 b 2 b % 6 g 12 ! c 4 c 2 c ! 4 h ! 6 b @ 6, 12 $ d 1 d 2 d 1%2 i @ 8 c 12 @ e 6 e 6 e ! 3 j 12 ) d ^ 8, 12 ( c # 6 h % 6 c ! 3 h 0 c circle 3 f circle 2 d 12 $ e 1 d @4 e [email protected] $8 @4, #6, $8, 12 ^ 12 ) f $ 6, 12 * Page 19 1 a # 4 b @ 3 f ^ 8 g 12 % 2 a # 6 b 12 & f 0 g @ 6 3 a circle 2 b circle 2 d circle 1 e circle 5 4 Teacher check Challenge a # 8 b 12 % c $8 #6 d @8 175 Year 5 Student Book Answers Page 20 1 Teacher check 2 a !3 @3 0 c ! 1#2 1&2 0 12 3 a 2 b 3 4 Teacher check b 1 0 !6 #6 $6 1 !3 1%2!2 0 c 7 %6 1 d 3 1 a 0.1 b # 0 = 0.3 c %0 = 0.5 d @0 = e * 0 = 0.8 2 Teacher check colouring a 0.7 b 0.4 c 0.9 d 0.6 e 3 a 0.3, # 0 b 0.9, (0 c 0.6, ^0 d 0.1, !0 4 a @ 3 b ! 8 c ! 6 d # 5 e f $ 6 g 1*2 h # 4 i 1!2 j k % 6 l $ 8 5 a = b > c > d < e f = g < h = i < j Draw a diagram Teacher check 0.2 0.5 2! &8 5 15 6 18 7 21 8 24 9 27 10 30 4 16 5 20 6 24 7 28 8 32 9 36 176 7 29 8 33 9 37 10 41 D 1 6 2 11 3 16 4 21 5 26 6 31 7 36 8 41 9 46 10 51 Page 25 1 Teacher check 2 A number of shapes π B number of shapes π C number of shapes π D number of shapes π 3 a 31, 46, 61, 76 c 201, 301, 401, 501 4 a Teacher check b 1 2 3 4 8 15 22 29 c Teacher check e 141, 351 2 3 4 5 + + + + 5 36 1 1 1 1 b 41, 61, 81, 101 6 43 7 50 8 57 9 64 10 71 d number of shapes π 7 + 1 c 600 m g 200 km d 13 km h 466 km 10 40 Teacher check Teacher check Colour b, e, f a 5 km b 1 km c 9 km d 21 km e 15 km a 3 km 200 m b 8 km 746 m c 2 km 460 m d 11 km 803 m e 4 km 55 m f 36 km 203 m 6 a 6 000 m b 10 000 m c 4 000 m d 17 000 m e 43 000 m f 1 615 m g 3 750 m h 9 208 m i 28 085 m 7 a 59 km b 84 km c 72 km d 98 km e 276 km f length 180 km (approx.) width 60 km (approx.) Challenge Teacher check Page 28 Page 24 B 6 25 1 2 3 4 5 b step π 4 A 5 21 Page 27 add three more each time multiply the step number by 3 step π 3 36 b 60 c 150 30 b 45 c 165 3 12 4 17 1 a 200 m b 333 m e 40 km f 73 km i 933 km 2 Teacher check Page 23 2 8 3 13 Page 26 1 a 2 b 4 c 6 d 8 2 2, 4, 6, 8, 10, 12, 14, 16, 18, 20 3 a add two more each time b multiply the step number by 2 c step π 2 4 a 30 b 40 c 200 5 a 20 b 110 1 4 2 9 = < Page 22 3 a b c 4 a 5 a 6 a 1 5 d 1)2 1 Page 21 1 Teacher check 2 1 2 3 4 3 6 9 12 C 1 3 2 5 3 7 4 9 5 11 6 13 7 15 8 17 9 19 10 21 1 4 2 7 3 10 4 13 5 16 6 19 7 22 8 25 9 28 10 31 1 red a, g; yellow d, e; blue b, c, f, h 2 a 30 mm b 120 mm c 55 mm e 217 mm f 3 000 mm 3 a 5 cm b 7.2 cm c 9.8 cm . e 38 5 cm f 200 cm g 591 cm 4 a 7m b 12 m c 8.15 m e 58.13 m f 2.61 m g 11.15 m d 68 mm d h d h 16 cm 1 204 cm 3.72 m 17 000 m Targeting Maths Teaching Guide Year 5 Pages 20 – 39 5 A C 6 A C 80 mm, 8 cm 158 mm, 15.8 cm 12.8 m, 1 280 cm 23.3 m, 2 330 cm B D B D 2 190 mm, 19 cm 94 mm, 9.4 cm 11.18 m, 1 118 cm 21.14 m, 2 114 cm A B C D E Page 29 Page 33 1 a Coin Collecting b Upholstery c First Aid d Pet Care e Face Painting f Bread Making g Vegetable Growing h Banjo Playing i Toy Making j Basket Weaving 2 Coin Collecting, Upholstery, First Aid, Pet Care 3 Bread Making 4 a Toy Making and Basket Weaving. b There is only a 5 minute gap. 1 A cube, 6, 12, 8 square pyramid, 5, 8, 5 rectangular prism, 6, 12, 8 triangular pyramid, 4, 6, 4 pentagonal pyramid, 6, 10, 6 triangular prism, 5, 9, 6 hexagonal prism, 8, 18, 12 2 Teacher check 3 Teacher check Page 30 1 8:15 a.m., 9:45 a.m., 10:20 a.m., 11:50 a.m., 12 noon, 2:25 p.m., 4:10 p.m., 5:05 p.m., 6:00 p.m., 8:05 p.m. 2 a 10:15 b 14:00 c 11:45 d 12:20 e 19:05 f 16:25 g 13:50 h 22:05 i 20:00 j 18:10 3 Banjo Playing 4 a 9:00 a.m. b 2:00 p.m. c 10:00 p.m. d 1:00 p.m. e 8:20 p.m. f 11:40 p.m. g 10:10 a.m. h 4:15 p.m. i 6:15 a.m. j 8:30 a.m. k 12:45 p.m. l 1:00 a.m. 5 a 09:00 b 11:00 c 02:30 d 10:30 e 01:15 f 07:45 g 21:00 h 18:00 i 15:30 j 21:40 k 23:10 l 17:45 Page 31 1 a Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec 31 28/29 31 30 31 30 31 31 30 31 30 31 Summer Autumn Winter b 28 days or 29 days in a leap year 2 a 92 b 92 c 91 d 90 or 91 e 365 f 366 3 Teacher check 4 Teacher check 5 Teacher check 6 a 8:20 b 7:05 7 5 8 a 3 p.m. b 1 p.m. c 4 p.m. 9 a 7 a.m. b 6 a.m. Spring cube rectangular prism pentagonal pyramid hexagonal prism Targeting Maths Teaching Guide Year 5 G Page 34 Teacher check Page 35 Square C, J Kite G, M Rectangle B, I Parallelogram E, N, P Rhombus D, H, L Trapezium A, F, K, O Page 36 1 a equal, right b equal, right c equal, parallel, equal d parallel e equal, parallel, equal f equal 2 a Teacher check (2 on each) b Teacher check c 2 Challenge Teacher check Page 37 1 a pentagon, 5 sides c octagon, 8 sides e triangle, 3 sides 2 Teacher check b quadrilateral, 4 sides d hexagon, 6 sides Page 38 d 3:30 p.m. Page 32 1 A C E G Sum. F B square pyramid D triangular pyramid F triangular prism 1 a 26 b 20 c 14 d 28 e 20 2 a Chocolate eclairs b more symbols 3 Apple slices 4 a ! 4 of symbol b # 4 of symbol 5 too many cake to draw if 1-to-1 correspondence 6 a No b Teacher check 7 Teacher check Page 39 Teacher Check 177 Year 5 Student Book Answers 37 9 10 11 12 13 14 15 16 15 Page 43 Page 40 1 Jazz Pop Classical Rock Childrens 55551 555554 551 55555552 555 2 3 4 5 6 6, 15, 12, 20, 14, 18, 5 easy to show one part of five Teacher check a 14 b 20 c 11 a Wednesday b Teacher check 7 Teacher check 21 29 11 17 a 3 18 a circle 5 19 a 1 Mangoes picked: Teacher check 2 a Sunday Tuesday Wednesday Thursday Friday Saturday 3 4 5 6 b 97 a Wednesday Teacher check Teacher check Teacher check 52 51 5553 55553 5552 55552 4 c 7 more picked b Saturday Page 42 1 a 7 510 b 1 057 2 a two thousand six hundred and forty-one b seven thousand and fifty-four 3 a 5 134 b 2 061 4 a 35 b 67 5 a 75 b 112 6 a 94 b 90 7 a 697 b 802 c 787 8 a 46c b 4c c 31c d 24c e 75c 178 b 4 b circle 2 b c 44 d 29 b 7, 14, 21, 28 c 1 758 c 1 d 90 Page 41 Monday a 11 b 29 a 283 b 337 264 colour 1, 2, 4, 7, 14, 28 a 9, 18, 27, 36 a 64 b 120 a 384 b 296 2 244 7 6 18 23 17 22 4 20 3, 0.3 21 a 9, 13, 17, 21, 41 b number of shapes π 4 + 1 22 a cm b m c 23 a 3 000 b 600 c e 7.4 f 27 000 24 34 m 25 a 19:15 b 26 a 11:28 a.m. b 27 a Teacher check, 5, 9, 6 b 28 a trapezium b rhombus c = number of sticks cm d km 40 d 391 03:42 10:10 p.m. Teacher check, 5, 8, 5 kite Page 44 1 a e i m 2 a e i m 3 a e i 4 a e II III XX LXX 3 5 90 60 XV XLIII XCIX 18 75 b f j n b f j n b f VII I L C 6 3 40 80 XIII LXVI b 12 f 47 c g k o c g k o c g IV VIII XC XL 4 8 20 100 XI LXXXII d h l p d h l p d h IX V LX XXX 2 9 70 30 XIX XXXIV c 21 g 96 d 58 h 69 A c D d B 92 180 40 009 c 60 547 g 28 011 d 80 604 h 91 111 = > c < g = d < h > Page 45 1 a C b e E 2 Teacher check 3 a 17 065 b e 29 751 f i 70 006 4 a > b e = f Targeting Maths Teaching Guide Year 5 Pages 40 – 53 5 a 6 a 7 a Draw 8 568 b 3 256 c 19 903 7 750 b 5 106 c 36 068 4 020 b 8 951 c 55 687 a table Teacher check d 24 165 d 99 899 d 31 156 Page 46 1 a 800 b 400 c 900 d 300 e 600 f 300 g 35 100 h 56 600 i 90 800 j 63 200 2 a 5 000 b 7 000 c 4 000 d 8 000 e 2 000 f 9 000 g 24 000 h 57 000 i 86 000 j 63 000 k 31 000 l 92 000 3 Colour red: 3 694 3 718 3 748 3 732 Colour blue: 3 554 3 639 3 619 3 640 Colour yellow: 3 467 3 499 3 549 3 507 4 a Teacher check b Honda $19 000, Mercedes $47 500, Renault $7 000, BMW $38 500, Rolls Royce $22 000, Suzuki $12 500 c Ford $9 500, Holden $17 500, Pulsar $12 500, Subaru $26 000 Page 47 1 Teacher check — each combination to be different 2 a $41 (or thereabout) b $42.08 c Teacher check Page 48 1 a 83, 97, 36, 54, 75, 102, 110, 48 b 75, 108, 60, 91, 63, 99, 116, 47 c 75, 42, 87, 100, 118, 51, 114, 69 2 a 692 b 684 c 342 d 1 317 e 862 3 a 673 b 1 055 c 870 d 803 Trial and error Amanda 193, Nat 206, Lynda 285 Many answers possible. Page 49 1 a 8, 80, 800, 8 000 b 9, 90, 400 + 500 = 900, 4 000 + 5 000 = 9 000 c 7, 30 + 40 = 70, 300 + 400 = 700 3 000 + 4 000 = 7 000 2 a 6 976 b 9 278 c 9 980 d 8 971 e 7 671 f 8 165 g 9 873 h 13 996 3 Teacher check 4 Teacher check 5 a 5 873 b 5 723 c 7 670 d 9 384 e 4 136 f 14 845 Look for patterns Teacher check Targeting Maths Teaching Guide Year 5 Page 50 1 a K, 1, 3, 4, 6 d 2 g K, 4, 6 2 a 2 3 Teacher check b K, 1, 3, 5, 6 e K, 1, 3, 6 c K, 1, 4, 6 f 2, 5 b 6 c 6 Page 51 1 a 7 b 9 e 4&0 f 6(0 i [email protected] j 13!0 m 48 n 61(0 2 a 16 b 18 e 32 f [email protected] i [email protected] (!5) j 84^0 m 74 n 25$0 3 a 18 b 45 f 134 g 91!2 4 a 16 b 19 f 63 g 85 5 a 14 b 15 f 34 g 45 6 a 39 b 41, 1 7 Teacher check (!5) (#5) (@5) c h c h c h c c 10 d g 8$0 h k 12*0 l o 92&0 c 22 d g 10*0 ($5) h k 96 l o 47 34 d 38 185!2 i 346 23 d 27 41!4 i [email protected] 17 d 22 51!8 i 90$8 13 d 19, 2 13 9!0 37%0 48 20$0 (@5) 52^0 (#5) e 72 e 54 e 21 Page 52 1 a 84, 76, 138, 610 b 90, 110, 680 c 95, 170, 315 d 63, 81, 72, 213, e 116, 220, 208, 340, 132, 504 2 a 19 b 19 c 13 r 3 d e 28 f 11 r 1 g 20 r 3 h 3 a 231 b 112 c 113 d e 374 f 141 g 141 h 4 a 121 r 4 b 244 r 2 c 214 r 1 d e 114 r 5 f 113 r 1 g 219 r 1 h i 368 r 1 j 147 r 1 Challenge 11 105, 306 14 r 3 11 r 3 128 116 110 r 6 318 r 1 Page 53 1 4 48, 120, 92, 216, 308, 656 7 49, 217, 182, 357, 406, 735 8 64, 128, 304, 520, 912, 736 9 54, 108, 351, 414, 297, 855 2 a 35 b 19 c 129 d 187 Challenge 3 π 12 = 36, 12 π 3 = 36, 36 ÷ 12 = 3, 36 ÷ 3 = 12 7 π 13 = 91, 13 π 7 = 91, 91 ÷ 13 = 7, 91 ÷ 7 = 13 9 π 12 = 108, 12 π 9 = 108, 108 ÷ 12 = 9, 108 ÷ 9 = 12 4 π 54 = 216, 54 π 4 = 216, 216 ÷ 54 = 4, 216 ÷ 4 = 54 8 π 43 = 344, 43 π 8 = 344, 344 ÷ 43 = 8, 344 ÷ 8 = 43 179 Year 5 Student Book Answers Page 54 Page 58 1 100 2 a 10, 0.10 b 47, 0.47 c 52, 0.52 e 24, 0.24 f 36, 0.36 g 75, 0.75 i 61, 0.61 j 83, 0.83 k 3, 0.03 m 8, 0.08 n 99, 0.99 o 1, 0.01 3 0.01, 0.03, 0.08, 0.10, 0.11, 0.16, 0.20, 0.47, 0.52, 0.61, 0.75, 0.83, 0.99 4 a b d 16, 0.16 h 20, 0.20 l 11, 0.11 0.24, 0.36, 1 a 3 in 10 b 2 in 5 (4 in 10) Page 60 Teacher check Page 55 1 a 10, 10% b 47, 47% c 52, 52% d 16, 16% e 24, 24% f 36, 36% g 75, 75% h 20, 20% i 61, 61% j 83, 83% k 3, 3% l 11, 11% m 8, 8% n 99, 99% o 1, 1% 2 99%, 83%, 75%, 61%, 52%, 47%, 36%, 24%, 20%, 16%, 11%, 10%, 8%, 3%, 1% 3 Teacher check 1 1 27 4 2 , 0.5, 50%; 10 , 0.10, 10%; 100 , 0.27, 27%; 91 9 33 100 , 0.91, 91%; 100 , 0.09, 9%; 100 , 0.33, 33% Draw a diagram Teacher check, 20%, 25%, 5%, 70%, 75% 50 Page 59 c 1 in 5 (2 in 10) d 1 in 10 2–6 Teacher check 99 100 1 100 Page 56 1 impossible, poor chance, fifty-fifty, good chance, certain 2 Teacher check 1 1 a 100 , 2 b 20 1 e 100 , 5 2 a 50c b e 6 hr f i 10c j m 45 min n 3 a $2 b 4 a $20, $60 b Challenge a $20 c 30 min e $8.80 g $8.50 i 20 m (2 000 25 100 , 1 4 30 min $1 10 yr 9 mth $1 $3, $9 c 75 100 , 3 4 c g k o c c 6 mth 15 min $1 30 9c $5, $15 b d f h 14 days 1m 1 yr $3 c g c g 36.5 16.30 4.5 4.31 d 10 100 , 1 10 d 50 cm h 3 l 20 cm d $3 d 15c, 45c Page 57 c $20.65 g $2.15 1 1 2 2 4 3 6 4 8 5 10 , 5 2 1 24 2 18 3 12 4 6 ,4 1 5 2 10 3 15 4 20 5 25 3 4 6 30 a 30 b 105 1 2 3 4 5 6 7 8 $70 $61 $52 $43 $34 $25 $16 $7 d h d h 7.84 13.81 3.5 5.71 d $18.13 a $16 b $308 Page 62 1 a g m s 2 a d 4 99 12 286 19 b 8 h 3 n 63 c 7 i 4 o 73 d 17 j 4 p 186 b π 7 = 56, 8 c + 63 = 102, 39 e 21 k 29 q 7 f 19 l 75 r 18 ÷ 10 = 12, 120 Page 63 1 a 20, 24, 28, 32 Rule — b 24, 12, 6, 3 Rule — c 64, 55, 46, 37 Rule — d 81, 243, 729, 2 187 Rule — e 25, 36, 49, 64 Rule — f 52, 65, 78, 91 Rule — 2 Teacher check cm) 1 Teacher check estimates a 12.8 b 14.8 . e 18 92 f 16.54 2 a 2.2 b 3.5 e 1.9 f 3.32 i 2.74 j 3.64 3 a $18.59 b $13.48 e $2.49 f $2.87 Page 61 add 4 or π 4 table halve or ÷ 2 subtract 9 π by 3 next square number + 13 Page 64 1 Teacher check 2 A 24 B E 14 F 3 A 24 cm3 B E 14 cm3 F 4 D, B, F, A, C, G. 36 30 36 cm3 30 cm3 E, H C G C G 21 15 21 cm3 15 cm3 D H D H 60 12 60 cm3 12 cm3 Page 65 Teacher check 180 Targeting Maths Teaching Guide Year 5 Pages 54– 76 Page 66 Page 71 1 A 500 mL B 1 000 mL C 3 000 mL E 2 000 mL F 1 500 mL 2 D, A, B, F, E, C 3 a 5L b 9L c 4L 4 a 12 000 mL b 31 000 mL c 1 200 mL d 5 950 mL 5 circle bin: bucket, watering can, bath 6 a 1 L 600 mL b 13 L 835 mL c D 250 mL d 20 L c 180 g, 720 g Page 72 Teacher check Page 73 28 L 0 mL Page 67 1–2 Teacher check Trial and error Put into the bucket 3 π 1 L measures. 1 1 Fill the 2 L measure and pour into the 5 L twice. 1 That leaves 100 L in the 2 L measure so pour it into the bucket (now 3 L 100mL). Pour into the bucket 2 π 30 mL measures. There is now 3 L + 100 mL + 60 mL = 3 L 160 mL in the bucket. Page 68 1 A 33 kg B 2 a 2 000 g b e 5 000 g 3 a 0 kg 500 g d 1 kg 120 g 4 a 6 400 g b e 4 900 g f 5 a 500 g b 1 Teacher check 2 Teacher check 3 a 84 kg b 2 271 g, 2 kg 271 g 1 d 8 2 kg 1 a cube b square pyramid Teacher check drawings 2 a b c cylinder Trial and error Teacher check Page 74 1 a b c d 107 kg C 12 400 g D 27 kg 12 000 g c 3 000 g d 11 000 g b 1 kg 400 g c 5 kg 700 g e 3 kg 680 g 5 300 g c 4 200 g d 3 700 g 2 500 g 46 kg 2 a Page 69 1 A 2 kg, 3 kg, 5 kg, 11 kg, 12 kg C 500 g, 1 120 g, 1 400 g, 3 680 g, 5 700 g 2 B 46 kg, 27 kg, 16 kg, 10 kg, 8 kg D 6.4 kg, 5.3 kg, 4.9 kg, 4.2 kg, 3.7 kg, 2.5 kg 3 a 2 000 g b 9 000 g c 24 000 g d 17 000 g e 1 250 g f 3 500 g g 9 750 g h 31 600 g i 15 000 g j 25 500 g k 46 250 g l 53 750 g 4 a 13 kg b 64 kg c 19 kg d 38 kg 1 1 e 8 2 kg, 8 kg 500 g f 21 2 kg, 21 kg 500 g 1 3 g 2 4 kg, 2 kg 250 g h 10 4 kg, 10 kg 750 g i 9 kg 240 g j 16 kg 175 g k 5 kg 812 g 5 a 709 g b 800 g c 500 g d 900 g e 300 g f 700 g g 200 g Challenge Teacher check Page 75 1 a To show perspective. Yes. b The back one. It is further away but looks the same size. c Because it is much further away at the top of the picture. 2 Teacher check 3 Teacher check Page 76 Page 70 1 a g b kg f g g kg 2 Teacher check 3 Teacher check b c kg h g Targeting Maths Teaching Guide Year 5 d g i kg e g j kg 1 a centre d semicircle g diameter 2 Teacher check b circumference e sector c radius f quadrant 181 Year 5 Student Book Answers 8 9 10 11 12 13 14 15 Page 77 Teacher check Page 78 1 a all 49 mm b 60 mm, 40 mm, 40 mm c 70 mm, 49 mm, 40 mm 2 a three b two c no 3 one 4 Teacher check 1 red: e, j; yellow: c, g, h, i, k; blue: b, f, l; green; a, d, g 2 Teacher check Page 80 1 two lots of information on each column 2 lighter colour is data for week 1 and darker colour is data for week 2 3–8 Teacher check Teacher check Page 82 1 H I J K L M N 4 8 2 3 4 2 12 O P Q R S T U 4 2 8 6 1 4 V W X Y Z 2 a A b F, G, T, W c Q, V, X, Z 3 100 4 5 5 Teacher check 6 Teacher check Teacher check Page 84 a 58 b a LXXVI b a 3 259 b a 22 009 b a 4 000 b 1 000 44, 76, 90, 65, 87, 58, a 9 793 b 182 d 20 a 26, 30, 34, 38; +4 b 51, 40, 29, 18; -11 a 8 cm3 b 20 cm3 a 9L b 30 L a 3 000 mL b 5 100 mL a 7 000 g b 10 500 g a kg b kg c g cylinder Top Side 1 3 - 3 equal sides scalene triangle Sandwiches made Teacher check b 2 equal sides b Sandwiches; Number made Page 86 1 a short way of writing thousand 2 make ads shorter etc. 3 A $445 000 B $384 000 C $705 000 D $298 000 E $375 000 F $402 000 G $599 000 4 D, E, B, F, A, G, C 5 A four hundred and forty-five thousand dollars C seven hundred and five thousand dollars F four hundred and twenty thousand dollars Page 87 Page 83 1 2 3 4 5 6 7 16 17 18 19 20 21 22 23 24 a c 25 a c Page 81 18 3 3 2 8 1 1 to Contents Page 85 Page 79 A B C D E F G Back a 58 b 95 a 17 b 249 117 a 14, 0.14, 14% b Teacher check a 91 b 1 c 3 a 19.9 b 4.4 c 3.65 Teacher check a 7 b 55 94 XLIX 20 004 7 915 c 73 000 123, 102 4 362 d 28 000 1 a 9 b 2 5 1 c 4 6 d e 5 8 2 f 0 8 g 9 4 3 h 6 i 0 7 0 j 2 Teacher check 3 Teacher check 4 a 50 b 100 e 4 000 f 3 i 100 000 j 900 000 7 6 8 3 9 0 9 2 0 3 6 5 4 2 0 4 6 0 3 5 c g k 5 000 20 000 300 3 8 2 9 6 5 1 0 0 8 d 60 000 h 500 000 l 9 000 Targeting Maths Teaching Guide Year 5 Pages 77– 97 5 7 651, 8 139, 15 384, 26 290, 60 573, 99 003 104 317, 200 394 6 a 500 000 + 10 000 + 7 000 + 800 + 40 + 6 b 700 000 + 60 000 + 9 000 + 100 + 20 + 8 c 900 000 + 30 000 + 4 000 + 50 + 8 d 900 000 + 40 000 + 9 000 + 600 + 1 Page 88 1 A $450 000 B $380 000 E $380 000 F $420 000 2 a CD b computer 3 a 200 b 500 e 400 f 300 4 a CC b D e CCC f DC 5 a CX b CCL e CCCXX f DCCXC i DXX j DCCCLXIX Challenge Teacher check C G c c g c g c g k $710 000 $600 000 house 700 900 CM CD DCLXXX CDXXXV CMLVIII D $300 000 d d h d h d h l racquet 1 000 800 MM DCCC CMXL DCLXXIV CDXCI Page 89 1 a 8 094 e 14 165 i 7 856 b 9 470 f 7 404 j 18 620 c 4 005 g 6 103 d 7 113 h 10 796 Page 90 1 a 4 514 b 5 495 c 5 204 2 a 4 089 b 690 3 a lamp, luggage, chess set b 572 Challenge a 23 667 b $118 335 8 160 b 710 5 645 f 8 044 2 191 b 369 backwards 425 a a a a $2.90 $9 $18.90 $22.50 b b b b $1.70 $3.20 $25.20 $14.50 c 3 577 d 1 644 g 467 h 5 444 c 3 307 Joe; 1 849 Ben c c c c $9.80 $6.40 $22.80 $8 d d d d $3.20 $15.20 $9 $15 Page 93 1 a $1.45 e $1.36 2 a $2.94 e $6.08 3 Teacher check Work backwards Page 95 1 colour red—17, 19, 29, 37, 47, 59 colour yellow—15, 16, 18, 25, 26, 27, 28, 35, 36, 38, 39, 45, 46, 48, 49, 55, 56, 57, 58 2 a 2, 3, 5, 7 b 2 3 a 13 b 23 c 37 d 53 e 101 4 a 14 b 33 c 51 d 62 e 81 5 a green—1, 4, 9, 16, 25, 36, 49, 64, 81, 100 b purple—1, 8, 27, 64 Challenge a 1 024, 1 089, 1 156, 1 225, 1 369, 1 444, 1 521, 1 600, 1 681, 1 764, 1 849, 1 936 b 1 331, 1 728, 2 197, 2 744 c 20 164, 20 449, 20 736 1 2 3 4 5 Page 92 1 2 3 4 1 a 0, 63, 35, 21, 56, 42, 28, 49 b 8, 32, 24, 16, 36, 12, 28, 40 c 30, 42, 54, 36, 0, 24, 48, 6 2 a 6, 3 b 86, 05 c 2, 7 d 7, 8 e 6, 0 3 a 2 169 b 4 890 c 3 744 d 1 876 e 4 152 f 2 285 g 5 769 h 784 4 a 721 b 2 910 c 4 064 d 4 140 e 4 140 f 0 g 4 450 h 3 000 Challenge a 26 075 430 486 b 54 265 276 242 Page 96 Page 91 1 a e 2 a Work Page 94 b $2.24 c $6.72 d $4.56 b $1.44 f $2.70 c $1.80 g $4.20 d $4.41 a 9 b a 2 b a 8 b a 9 b Teacher check 5 5 10 5 c c c c 7 6 9 7 d d d d 3 9 7 4 e e e e 8 8 4 3 Page 97 1 a 5, 9, 1, 6, 2, 8, 10, 3, 7, 4 b 6, 1, 9, 2, 5, 7, 3, 10, 4, 8 c 4, 8, 5, 10, 3, 9, 6, 2, 7, 1 2 a 24 r 2 b 14 r 3 c 159 d 139 r 3 e 115 f 85 g 156 h 129 r 4 3 a 209 b 109 r 4 c 230 r 2 d 130 r 4 e 97 f 120 r 5 g 73 r 1 h 141 r 1 i 209 r 3 Challenge Teacher check 3 iceblocks and 4 masks Targeting Maths Teaching Guide Year 5 183 Year 5 Student Book Answers Page 98 1 Answers can vary a 10 b 20 c 20 d 70 e 80 f 80 g 100 h 180 i 200 j 30 2 a 32! 3 b 16$ 5 c 9% 7 d 148# 4 e 114$7 f 153# 6 g 100&8 h 297 i 70$ 5 j 58^ 9 k 61& 8 3 2 π 252, 3 π 168, 4 π 126, 6 π 84, 7 π 72, 8 π 63, 9 π 56, 12 π 42, 14 π 36, 18 π 28, 21 π 24 and all the reverse groups (252 π 2 etc): 22 groupings 58 minutes a 42 b $2 a 33 b 36 132 59 116 Teacher check Page 100 4 2 1 A 12 B 5 1 2 E 5 F 3 3 2 I 4 J 4 2 a K b G e L f J 2 2 3 a 6 b 5 = 1 2 1 e 5 = 10 f 2 = 4 Teacher check 5 Teacher check Page 101 16 48 4 20 12 16 1 4 2 7 2 3, 3 9, 1 a e i 2 a e 3 a e 4 a 8 e 8 4 6 1 3 8 20 4 12 8 16 1 5 2 9 6 12 , 10 12 , b f j b f b f b 3 f 9 4 4 10 2 4 4 6 c 1 2 3 4 Gonk, Sonk, Wonk, Dronk, Monk, Tronk centimetres a 0.82 m b 4.08 m c 1.93 m d 0.23 m a 11.9 m b 9.39 m c 21.29 m Page 104 D 8 1 H 2 2 L 10 d I 2 3 = d 6 8 1 a 2.4 e 1.9 i 2.4 2 a $2.74 3 a 6.4 kg e 6.8 kg Challenge Joe 3 4 = b f j b b 1.3 4.9 1.5 $2.28 5.9 kg c g k c c 1.4 1.2 1.2 $1.53 8.8 kg d h l d d 1.9 1.3 3.8 $1.26 7.68 kg $3.88, Jill $2.88, Jamie $1.88 Page 106 c g k c 1 2 5 6 16 24 16 40 8 24 3 4 2 d h l d 6 1 1 2 3 4 5 6 2 3 4 5 a 30 a 3 a 300 600 24 32 4 8 8 40 3 8 1 c 5 , 15 6 3 g 10 , 5 c 9 g 9 2 d 8 , 16 2 4 h 4, 8 d 9 h 25, 2 3 6 9 12 15 18 2 4 6 8 10 12 6 12 18 24 30 36 b 20 c 15 b 2 b 200 d 45 e 8 f 16 Page 107 1 a each shape fully coloured c each are the same 2 a 10 b 7 c 1 3 Teacher check 4 a0 1 2b0 1! 4 !4 !2 c 0 1# 4 !2 @3 b all of it d 56 1 b e 100 1 @3 1 !4 Page 103 Page 105 6 C 6 4 G 10 2 K 6 c F Page 102 184 b 12, ! @3, %6, 1!3, 1#4 1 a show centimetres (hundredths), 100 cm = 1 m b 417, 290, 483, 335, 506, 98 2 a 31.2 kg b 165.6 kg c 318.6 kg d 81.9 kg e 94.5 kg f 7.8 kg, 11.7 kg, 18.9 kg, 27.6 kg, 35.4 kg 3 a 21.69 b 24.75 c 61.12 d 60.39 . . . e 66 42 f 24 29 g 48 12 h 15.87 4 a $45.30 b $17.73 c $36.16 d $77.40 e $48.56 Challenge 304.2 kg Page 99 1 2 3 4 5 6 7 Challenge a ! 5, &0, #4, 1!2 2 1! 2 3 2! 4 c for every there are twice as many 0 d Teacher check 2 Teacher check 3 a 4 b 40 44 48 52 56 60 64 68 72 c 20 d 30 is not a multiple of 4 Targeting Maths Teaching Guide Year 5 Pages 98– 117 Page 108 1 a e i j 16 b 24 c 63 d 55 84 f 100 g 92 h 77 the original number does not change Teacher check (addition undoes subtraction and vice versa) 2 a 3 b 10 c 9 d 8 e 8 f 20 g 80 h 63 i the original number does not change j Teacher check (multiplication undoes division and vice versa) 3 a 70 b 90 c 80 d 50 e 120 f when multiplying by 10 add a zero 4 a 530 b 890 c 670 d 1 130 e 5 160 5 a 16, 26, 36, 36, 56 b 13, 23, 23, 33, 43 c 9, 29, 29, 49, 49 d 15, 25, 35, 45, 75 e Teacher check 6 a 16, 26, 36, 46 b 7, 17, 27, 37, 47 c 5, 15, 25, 35, 45 d 6, 16, 26, 36, 46 Challenge 31 34 37 40 43 46 49 52 55 58 Page 109 1 a ! 6, !7, !8, !9, !0, 11 ! ; add 1 to denominator b 1.5, 1.8, 2.1, 2.4, 2.7, 3; add 0.3 c 2, 1# 4, 1!2, 1!4, 1, #4; subtract !4 . d 3 2, 6.4, 12.8, 25.6, 51.2, 102.4; double e 24, 22.5, 21, 19.5, 18, 16.5; subtract 1.5 2 Teacher check Page 112 1 a ha b m2 f ha g m2 2 a 3 ha b 7 ha 3 a 20 000 m2 c 170 000 m2 4 Teacher check 5 a 500 m c 1 000 (1 km) 6 a 6 ha b 4 e 54 ha c h c b d ha d m2 e ha 2 ha i m 12 ha d 36 ha 50 000 m2 215 000 m2 b 400 m d 1 100 m (1.1 km) ha c 9 ha d 12 ha Page 113 1 colour b, c, d, f 2 a 25 500 m2 b 21 600 m2 c 23 575 m2 d 32 500 m2 e 16 000 m2 f 12 ha 3 a Teacher check b NSW 800 642 km2, QLD 1 730 648 km2, VIC 227 416 km2, WA 2 529 875 km2, SA 983 482 km2, TAS 68 401 km2, NT 1 349 129 km2 c Western Australia, Tasmania Page 114 1 a 40º b 80º e 65º f 160º Challenge Teacher check c 50º g 135º d 120º h 100º obtuse straight acute c right g obtuse k straight d reflex h right l reflex F T c F d F 1 a 45º b 90º f 90º g 68º 2 Teacher check c 110º h 162º Page 115 Page 110 1 a e 2 a c e 3 a e 4 a c e 4 Teacher check 5 Teacher check Challenge Teacher check 2 24 cm b 14 25 cm2 f 36 6 cm, 4 cm 3 cm, 3 cm 5 cm, 5 cm 20 cm b 18 20 cm f 30 6 π 4 = 24 cm2 3 π 3 = 9 cm2 5 π 5 = 25 cm2 2 2 cm c 9 cm d 24 cm cm2 b 7 cm, 2 cm d 8 cm, 3 cm f 12 cm, 3cm cm c 12 cm d 22 cm cm b 7 π 2 = 14 cm2 d 8 π 3 = 24 cm2 f 12 π 3 = 36 cm2 Page 111 1 Teacher check 2 a 8 π 3 = 24 cm2 b 12 π 2 = 24 cm2 c 6 π 4 = 24 cm2 d They are all the same 3 a 8 + 3 + 8 + 3 = 22 cm b 12 + 2 + 12 + 2 = 28 cm c 6 + 4 + 6 + 4 = 20 cm d They are all different Targeting Maths Teaching Guide Year 5 2 1 a acute b e revolution f i revolution j 2 Teacher check 3 a T b e T f Page 116 d 60º i 25º e 140º Page 117 1 2 3 4 5 a 50º, a 90º, 180º a 50º a 90º, b 74º, 100º, 30º 30º, 60º b 180º b 180º b 35º c 40º 100º, 103º, 67º; 360º 115º, 92º, 79º; 360º d 40º 185 Year 5 Student Book Answers Draw a diagram 1 Teacher check 2 pentagon 540º, hexagon 720º 3 pentagon 108º, hexagon 120º Page 124 Page 118 1 a lighthouse b store d ferry e Lake Omo 2 a C6 b I7 d G1 e B4 3 a E5, E6 b G3, G4 (G5) c Teacher check 4 Answers will vary a kiosk b library d Island Wharf e castle g Ferry Street Wharf c f c f library cliffs J6 G6 c store f Beauty Beach h church Page 119 crazy Page 120 1 a 2 km b 6 km c 10 km e 6 km f 16.5 km g 6 km 2 27 km (approx) 3 Teacher check d 4.5 km h 2 km Page 121 1 2 3 4 5 a a a a a d g 6 a 7 a d Draw panda b kingfisher kingfisher b puppies wolf b monkey tiger b rhinoceros north-west b north-east south-east e north-east south-east h south-east east b east north-east b north-west south-west a diagram Teacher check c south-west f south-west c west c south-east Page 122 1 a D b A 2 Teacher check c B d C 1 Teacher check 2 Temperatures for 12 hours 3 Temperature in degrees Celsius, Time 4 a 1 p.m. b 10 p.m. Challenge Teacher check Page 125 1 a 7 b 16 . 2 a 76 b 20 e 10.5 mm f 7 3 Teacher check c 17 d 7% 6 c 12 months e 19 d 9# 5 kg Page 126 1 2 3 4 5 6 7 8 9 10 11 12 13 14 thousand; $243 000 a 50 b 8 000 a 450 b 1 300 a 3 019 b 12 958 a $3.20 b $11.10 a 612 b 1 740 11, 13, 17, 19 a 33 b 51 7, 5, 8, 11, 2, 12, 9 a 60 r 6 b 227 r 1 25 a @ 5 b # 8 a @ 3, $6 b $ 8, @4 a b 15 a 2.12 b 12.70 16 5, 8, 11, 29, 44, 59 c 400 000 d 70 000 c 715 d 961 c $44.50 c 4 767 c 24.42 d 7.4 Page 127 17 18 19 20 21 22 a 6 cm, 2 cm b 16 cm c 12 cm2 a ha b ha c m2 d m2 Teacher check; product must be 10 000 Teacher check 28° 6 5 4 3 Page 123 1 a Chairs sold in 1 year b Month, Number sold 2 a 375 b February 3 a 100 b January c Teacher check; no money after Christmas 4 a 250 b 225 c 175 5 a December b March c September 6 a June and August 7 3 000 186 2 1 0 1 2 3 23 4 N 24 Teacher check Targeting Maths Teaching Guide Year 5 Pages 117– 137 Page 128 1 Board A has numbers in the hundred thousands, board B has numbers in the millions 2 a Sydney b Cairns 3 a Adelaide b Cairns c Newcastle d Sunshine Coast 4 Teacher check Page 129 1 a three hundred and twenty-seven thousand seven hundred b two hundred and thirty-six thousand three hundred c three million six hundred and ten thousand eight hundred 2 a Newcastle, Gold Coast, Canberra, Woollongong, Sunshine Coast, Hobart, Geelong, Cairns 3 a 300 000 b 3 000 000 c 300 4 a Melbourne b Geelong 5 a 1 088 000 b 1 546 000 c 3 611 000 d 1 244 000 e 4 253 000 6 a 100 000 b 300 000 c 200 000 d 400 000 e 200 000 f 500 000 g 200 000 h 300 000 7 a D b B c A d C Challenge Teacher check Page 130 1 a –5 b 1 2 Teacher check 3 a 1°C b Challenge a d g j c 5 0°C $3 –$2 –$5 –$6 c b e h k d –3 e 2 5°C –$4 $7 $10 $2 d c f i 0°C $10 –$3 $5 Page 131 1 1st, 2nd, 3rd, 4th, 5th, 6th, 7th, 8th, 9th, 10th 2 a 5th b 10th c 1st d 3rd e 9th f 6th g 4th h 9th 3 a 9th, 11th b 6th, 8th c 1st, 3rd d 19th, 21st e 14th, 16th f 30th, 32nd g 12th, 14th h 28th, 30th i 17th, 19th 4 a 3rd b 5th c 8th d 4th e 10th 5 dog, kangaroo = lizard, cat, wombat Challenge Teacher check Page 132 1 2 3 4 Cb A (K) d E (G) a Bf Targeting Maths Teaching Guide Year 5 5 6 7 8 9 10 11 12 D (F) h H (L) c F (D) e I (J) g G (E) k L (H) l K (A) i J (I) j Page 133 1 a 53 (53 π 6) c 99 (99 π 8) e 39 (39 π 4) g 87 (87 π 6) i 183 (183 π 3) k 175 (175 π 5) 2 210 5, 6, 7, 10: 280 378 6, 7, 9: 450 5, b d f h j 83 (83 π 5) 57 (57 π 7) 79 (79 π 9) 119 (119 π 8) 139 (139 π 7) 5, 7, 8, 10: 315 5, 7, 9: 6, 9, 10: 504 6, 7, 8, 9 Page 134 1 a 375 e 125 2 a 1 157 e 1 296 i 760 r 4 m 698 r 3 Challenge b f b f j n a 6 250 107 r 1 1 483 1 798 516 r 7 1 000 r 3 97 582 c g c g k 187 r 2 93 r 6 1 209 884 507 r 1 b d h d h l 248 4 992 150 83 r 3 1 792 1 609 733 r 3 c 163 7 1141 Page 135 1 a oil can $13.05 c timer $13.94 e wok $21.09 2 a 7 b 9 e 5r9 f 9r3 3 a 15 b 27 e 39 r 2 f 76 r 4 4 a $5 b $7.90 e 28c f 94c i $5.91 j $7.23 Challenge $394.69, $105.31 b jug $9.57 d scales $25.40 c 3 d 4r7 c g c g k d h d h l 95 516 r 3 $3.60 $1.12 $12.36 86 489 r 5 15c $3.35 $29.79 Page 136 1 a 1 777 e 9 639 i 2 748 b 1 711 f 4 773 j 12 867 c 8 833 g 8 602 d 8 259 h 6 190 B $8.06 F $5.08 C $80.94 G $9.27 D $35.70 H $46.89 Page 137 1 A $7.39 E $2.76 I $6.95 187 Year 5 Student Book Answers 2 a $2.31 b $4.19 c $6.51 d $27.64 e $1.11 f $39.50 g $45.24 h $73.99 3 a $3.12 b 1 321 Challenge a 97 654 + 2 + 1 = 97 657 b 1 245 – 976 = 269 Page 143 Page 138 1 A 55% B 63% C D 28% E 76% F 2 Teacher check 3 a Gourmet Goodies b c Frozen Fancy Lamb d Draw a diagram Teacher check 1 a f 2 a 3 a 4 a c Trial 7 b 7 22 g 7 . 95 b 12.6 [email protected] 6 b 49! 3 8 mm 1 m 9 cm and error 17, 18 c h c c b d 7 d 27 40 i 12 . 105 5 18# 4 7 yr 10 mth Teacher check e 11 j 10 Teacher check Page 144 c g b d f b d f h j 18 d 66 55 h 12 19 – (6 + 2) = 11 18 ÷ (9 – 3) = 3 18 ÷ (6 ÷ 3) = 9 16 ÷ 4 + 7 = 11 12 ÷ 3 + 8 = 12 8 + 3 π 8 = 32 6 + 8 – 14 = 0 12 π 3 = 36 a a a a $30.80 $24.64 $18.48 $27.72 50 100 25 100 0.50 0.25 10% 75 100 10 100 1 2 1 4 3 4 1 10 20% 20 100 1 5 0.20 1 a 50% b 25% c 75% d e b b b b $49.50 $39.60 $29.70 $44.55 c c c c $26.50 $21.20 $15.90 $23.85 d d d d $17.40 $13.92 $10.44 $15.66 Page 141 1 a Nocturnal House b Cart Ride c Cable Car d Aquarium e Aquarium 2 a $99.36 b added amounts from q2 p140 c Teacher check d $0.64 3 a 9 b Teacher check (33 ÷ 4 = 8 r 1 so extra car needed) 4 Teacher check 2 Teacher check 3 Teacher check 4 a 45 b 30 c $6 d 1 e 3 f 9 Challenge Shoes $35 $52.50 $43.75 Shirt $28 $42 $35 1 a b c d e f g h $38.50 $30.80 2 people 1 kg 150 mL 25 g 3 4 people 2 kg 300 mL 50 g 6 1! 2 15 !2 pkt 2! 2 teasp 4# 7! 2 !4 pkt 1! 4 teasp 2 a 1! 2 b , 2# 4 c d , [email protected] 3 Page 142 1 Teacher help with survey 2 a A 9 177 B 1 773 E $21.39 F 5 661 I 41 J 42 b, c, d teacher check 3 Teacher check 188 0.75 0.10 Page 146 Page 140 1 2 3 4 Quick Fix Snacks Delight Stew Page 145 Page 139 1 a 25 b 0 e 8 f 12 2 a (7 + 8) ÷ 3 = 5 c 6 π (4 + 2) = 36 e (7 + 9) ÷ 4 = 4 3 a 5 + 22 – 16 = 11 c 6 – 20 ÷ 4 = 1 e 63 – 3 = 60 g 3 π 2 + 34 = 40 i 10 + 6 = 16 4 Teacher check 5 Teacher check 41% 7% C $45.76 G $3.88 D 103 r1 H 961$ 0 e ,$ 5 f , 1& 8 3 a e i m 1! 2 3# 4 8! 3 5# 8 b f j n 1! 4 1% 6 2# 7 7& 0 , 1% 6 c [email protected] 5 g 45 ! k 5! 6 d 1# 0 h 26 % l [email protected] 9 Targeting Maths Teaching Guide Year 5 Pages 137– 153 Page 147 1 a e 2 a e 3 a e 4 a e 5 a e i 6 a e 7 a e 8 a e 9 a e 10 a e i m q 76 decimal 34.5 decimal 130 decimal 218 decimal 52 80.7 855 8.2 decimal 0.76 decimal 5.64 decimal 0.642 decimal 6.9 12.2 8.91 4.06 0.37 Page 150 b 93 point moves b 16.7 point moves b 920 point moves b 472 point moves b 65 f 610 j 8 705 b 4.9 point moves b 0.15 point moves b 2.19 point moves b 0.716 point moves b 1.8 f 0.73 j 3.3 n 5.58 r 0.123 c 82 1 place to the c 93.9 1 place to the c 750 2 place to the c 896 2 place to the c 38 g 990 k 7 572 c 6.5 1 place to the c 0.94 1 place to the c 7.28 2 place to the c 0.18 2 place to the c 9.3 g 0.87 k 2.13 o 3.65 s 0.95 d 16 right d 25.5 right d 410 right d 1 502 right d 68.3 h 320 d left d left d left d left d h l p t 5.7 0.38 8.73 0.59 2.6 3.12 7.96 0.68 0.221 Page 148 1 A ■ π 2 + 9 = 23; ■ = 7 B ◗ ÷ 2 – 8 = 5; ◗ = 26 C ❖ π 6 + 2 = 56; ❖ = 9 D (● + 7) ÷ 3 = 11; ● = 26 E (❁ – 9) π 9 = 81; ❁ = 18 F ❏ π 7 ÷ 4 = 14; ❏ = 8 2 Teacher check Page 149 1 a 11 b 7 e 7 f 11 i 3 j 54 2 a 1# 4 c 7.8 ÷ 3 = 2.6 5 + !5 = $5 e # g 25.2 ÷ 6 = 4.2 8 – #8 = [email protected] i 3% 3 Teacher check Challenge a ★ = 7 b b d f h j c 72 d 7 g 44 h 39 k 30 l 7 . . . 18+23=41 3.4 π 5 = 17 10.25 – 7.63 = 2.62 2.51 π 9 = 22.59 2! 2 + 1!4 = 3#4 ★=8 Targeting Maths Teaching Guide Year 5 1 a 14 2 3 2 8 10 2 0 b 6 4 12 4 5 14 6 c 20 7 18 10 6 16 8 9 22 14 8 20 12 10 24 16 3 a 34 b 26 4 a 18 b 22 c 12 . 5 a 1 5 mm b 5 6 7 8 9 10 32 33.5 35 36.5 38 39.5 c d e f during day 11 yes; because when tried it produces correct answer 24.5 mm to make it easier to write the rule Page 151 1 a 43, 52, 61, c [email protected] 3, 3, G e 27, 9, 3, I 2 Teacher check 3 a A 9 B b A 54 B c A 30 B d A –6 B e A 123 B b 43.2, 129.6, 388.8, J d 12.5, 62.5, 312.5, L f 25.8, 33.6, 41.4, K H 0 60 28 –20 152 C C C C C 8! 2 16 12 6 27! 2 D D D D D 37! 2 39 [email protected] 0 37 41# 0 E E E E E 12 15# 4 13# 4 10# 4 [email protected] 4 Page 152 1 a b c d e 2 a e 3 a 3 cm, 2 cm, 1 cm, 4 cm, 4 cm, 2 cm 8 cm, 5 cm, 3 cm, 2 cm, 5 cm, 3 cm 6 cm, 2 cm, 3 cm, 1 cm, 9 cm, 3 cm outside: 5 cm, 4 cm, 5 cm, 4 cm; inside: 2 cm, 2 cm, 2 cm, 2 cm outside: 10 cm, 2 cm, 10 cm, 2 cm; inside: 7 cm, 1 cm, 7 cm, 1 cm 10 cm2 b 30 cm2 c 21 cm2 d 16 cm2 13 cm2 16 cm b 26 cm Page 153 1 a 12 m b 48 cm c 40 m d 15.2 cm e length of side π 4 2 a 20 m b 18 cm c 32 m d 7 cm e 2 π (length + breadth) 3 a 39.62 m b 89.6 cm Challenge equilateral triangle: 3 π length of side isosceles triangle: 2 π length of equal side + length of third side 189 Year 5 Student Book Answers Page 154 Page 157 1 Answers will vary a ruler b c trundle wheel d e tape measure f g odometer h i tape measure j 2 a cm b m c e m f mm g i cm (m) j m 3 Teacher check 4 Teacher check 5 a 115 cm, 97 cm, 109 cm b 1.15 m, 0.97 m, 1.09 m c 107 cm (1.07 m) d Cassie Work backwards 96 km 61 m 1 a–e Teacher check f 1 cm3 makes water rise 1 mL 2 8 mL 8 cm3 3 6 mL 6 cm 3 24 mL 24 cm 3 18 mL 18 cm builders’ tape tape measure ruler builders’ tape trundle wheel m d cm km h m Page 155 Teacher check part b of each question 1 a thermometer 2 a stopwatch 3 a measuring jug 4 a scales 5 a measuring tape 6 a clock 7 a scales 8 a scales 9 a tape measure 10 a protractor 11 a ruler 12 a measuring spoons 13 Teacher check Page 156 1 a 11:59 a.m . b 1:00 p.m. c 1:09 p.m. d 12:31 p.m. 2 a 12 minutes b 12 minutes 3 a 4 minutes b 9 minutes c 9 minutes d 21 minutes e 41 minutes f 37 minutes g 50 minutes h 100 minutes 4 1:09 p.m., 1:14 p.m., 1:20 p.m., 1:29 p.m., 1:34 p.m., 1:46 p.m., 1:50 p.m., 1:55 p.m. 5 a 25 minutes b 25 minutes c 25 minutes 6 Ferry B 7 12:40, 12:44, 12:49, 12:55, 13:04, 13:09, 13:21, 13:25, 13:30 Challenge Teacher check 190 3 a 1 000 mL (1L) b 10 cm π 10 cm π 10 cm (other answers) c Teacher check Challenge Teacher check Page 158 1 Teacher check 2 0 2 5 Challenge 36 9 14 20 Page 159 1 a angle c pentagon e triangular prism g equilateral triangle i parallelogram k square pyramid 2 Teacher check b d f h j l triangular pyramid cube hexagon cylinder trapezium pentagonal prism Page 160 1 a horizontal c parallel e vertical g diagonal 2 Teacher check 3 Teacher check Challenge Teacher check b perpendicular d perpendicular f parallel Page 161 1 a c e Draw trapezium b equilateral triangle kite d right-angled triangle rhombus f parallelogram a diagram Teacher check Page 162 1 a Burnie b Waratah d Campbell Town e Hastings 2 a C9 b H2 c C5 3 a National Park b national parks d capital city 4 Teacher check (answers will vary) 5 a I3 b I5 c F8 (G8) d G1 e I7 f G3 c f d c Deloraine Richmond E8 ocean Targeting Maths Teaching Guide Year 5 Pages 154– 168 Page 163 1 a 80 b 50 2 Teacher check 3 Teacher check c 25 d 75 e 345 Page 164 1 line graph 2 a Pets treated in one week b Number of pets; Days 3 a 24 b 14 c 9 4 18# 7 5 a Friday b Sunday 6 Teacher check 7 Teacher check 8 Teacher check 20 a 32.4, 97.2, 291.6; π3 b 6! 3, 6, [email protected]: –!3 21 a 26 m b 36 m2 22 a, b Teacher check c side π 3 23 a m b mL c ha d kg 24 1L e cm Page 168 25 a pentagon 26 a 310º 27 a (1, 5) b (3, 4) e-h Teacher check 28 a 11, 7, 20, 14, 3 c 55 e black b 5 diagonals b Teacher check c (2, 2) d (5, 5) b Teacher check d multistriped f Teacher check Page 165 Teacher check Page 166 1 2 3 4 5 6 7 8 9 10 11 12 13 14 three hundred and sixty-four thousand five hundred and twenty 200 000 + 70 000 + 3 000 + 500 + 90 + 1 –4 –3 –2 –2ºC a 1st, 3rd b 11th a 146 b a 7 385 b $2.70 a 9 b a 25 b a $18.90 b Teacher check a 4 out of 8 –1 0 1 2 3 4 18th, 20th 188 2 320 977 7& 8 8 $9.80 c 6 c $15.60 d 24 b 1 out of 8 Page 167 15 a 50% b 25% c 10% 1 2 1 4 1 10 d 20% 1 5 16 a c 17 a 18 a 19 a 0.5 0.25 0.1 0.2 colour 2 blue colour 10 green [email protected] 5 b 3! 4 83 b 629 3 b 10 Targeting Maths Teaching Guide Year 5 b d c c c colour 5 red 15% 5# 0 d 7! 9 . 28 d 2.57 1.7 d 1 191

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