TM TG Yr5-p.00i-xv.qxd - 4js

TM TG Yr5-p.00i-xv.qxd - 4js
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
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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
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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.
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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
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$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 = _____
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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
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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? __________
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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
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9
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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.
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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.
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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? ___________
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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.
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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.
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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
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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
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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.
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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
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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.
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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
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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
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= 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.
_____________________________
_________________________________
_________________________________
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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
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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 _______
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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
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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 = __________
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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
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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
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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? ____________
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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?
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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.
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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
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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 __________
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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
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$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
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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
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✎
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. ___________ ___________ ___________ ____________
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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
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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.
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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
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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
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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
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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?
_______________
_______________
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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
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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 ________________
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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
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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. _______________________
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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
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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 _________ .
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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
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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? _______________
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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? ________
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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
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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? ______
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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
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✎
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?
_________
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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
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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?
_____________________
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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
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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.
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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
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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 = ___
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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
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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
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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
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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
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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
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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
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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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