Practice and Homework Book Authors Peggy Morrow Maggie Martin Connell Publisher Claire Burnett Elementary Math Team Leader Diane Wyman Publishing Team Lesley Haynes Enid Haley Ioana Gagea Lynne Gulliver Stephanie Cox Judy Wilson Product Manager Kathleen Crosbie Design Word & Image Design Studio Inc. Typesetting Computer Composition of Canada Inc. Copyright © 2008 Pearson Education Canada, a division of Pearson Canada Inc. All Rights Reserved. This publication is protected by copyright, and permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise. For information regarding permission, write to the Permissions Department. ISBN-13: 978-0-321-43803-4 ISBN-10: 0-321-43803-5 Printed and bound in Canada. 3 4 5 -- WC -- 11 10 09 08 Contents UNIT 1 UNIT 2 UNIT 3 Patterns and Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . Lesson 1 Lesson 2 Lesson 3 Lesson 4 Lesson 5 Patterns in Charts Extending Number Patterns Representing Patterns Equations Involving Addition and Subtraction Equations Involving Multiplication and Division 2 4 6 8 10 Whole Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Lesson 1 Lesson 2 Lesson 3 Lesson 4 Lesson 5 Lesson 6 Lesson 7 Lesson 8 Lesson 9 Lesson 10 Lesson 12 Lesson 13 Whole Numbers to 10 000 Comparing and Ordering Numbers Sorting Numbers Estimating Sums Using Mental Math to Add Adding 3-Digit Numbers Adding 4-Digit Numbers Estimating Differences Using Mental Math to Subtract Subtracting 3-Digit Numbers Subtracting 4-Digit Numbers Solving Addition and Subtraction Problems 12 14 16 18 20 22 24 26 28 30 32 34 Multiplication and Division Facts . . . . . . . . . . . . . . . . . . . Lesson 1 Lesson 2 Lesson 3 Lesson 4 Lesson 5 Lesson 7 Lesson 8 Lesson 9 Lesson 10 Using Doubles to Multiply Multiplying by 1, by 0, and by 10 Using Skip Counting to Multiply Other Strategies for Multiplying Using Patterns in a Multiplication Chart Using Arrays to Divide Relating Multiplication to Division Dividing by Numbers from 1 to 9 Pose and Solve Problems 36 38 40 42 44 46 48 50 52 iii UNIT 4 UNIT 5 Measurement. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Lesson 1 Lesson 2 Lesson 3 Lesson 4 Lesson 5 Lesson 6 Lesson 7 Lesson 8 Lesson 9 Lesson 10 Lesson 11 Lesson 13 Lesson 1 Lesson 2 Lesson 3 Lesson 4 Lesson 5 Lesson 9 Lesson 10 Lesson 11 Lesson 12 Lesson 13 Lesson 14 6 iv 54 56 58 60 62 64 66 68 70 72 74 76 Fractions and Decimals . . . . . . . . . . . . . . . . . . . . . . . . . . . . Lesson 7 Lesson 8 UNIT Calendar Time Exploring Time Telling Time Elapsed Time Telling Time to the Minute The 24-Hour Clock Covering Shapes Exploring Area Measuring Area in Square Centimetres Estimating and Measuring Area Finding Area in Square Metres Exploring Rectangles with Equal Areas Fractions of a Whole Fraction Benchmarks Exploring Fractions of a Set Finding a Fraction of a Set Relating Fractional Parts of Different Wholes and Sets Comparing and Ordering Unit Fractions Comparing and Ordering Fractions with the Same Numerator or Denominator Exploring Tenths Exploring Hundredths Equivalent Decimals Adding Decimals to Tenths Subtracting Decimals to Tenths Adding and Subtracting Decimals to Hundredths 78 80 82 84 86 88 90 92 94 96 98 100 102 Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Lesson 1 Lesson 2 Lesson 3 Lesson 5 Lesson 6 Lesson 7 Objects in Our World Constructing Prisms Exploring Nets Symmetrical Shapes Line Symmetry Sorting by Lines of Symmetry 104 106 108 110 112 114 UNIT 7 UNIT 8 Data Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Lesson 1 Lesson 2 Lesson 3 Lesson 4 Reading Pictographs and Bar Graphs Drawing Pictographs Drawing Bar Graphs Comparing Pictographs and Bar Graphs 116 118 120 122 Multiplying and Dividing Larger Numbers . . . . . . . . . . . Lesson 1 Lesson 2 Lesson 3 Lesson 5 Lesson 6 Lesson 7 Lesson 8 Lesson 9 Lesson 10 Lesson 11 Exploring Multiplication Patterns Estimating Products Using Models to Multiply Other Strategies for Multiplication Using Patterns to Multiply Multiplying a 3-Digit Number by a 1-Digit Number Estimating Quotients Division with Remainders Using Base Ten Blocks to Divide Another Strategy for Division Math at Home 124 126 128 130 132 134 136 138 140 142 145 v To the Teacher This Practice and Homework Book provides reinforcement of the concepts and skills explored in the Pearson Math Makes Sense 4 program. There are two sections in the book. The first section follows the sequence of Math Makes Sense 4 Student Book. It is intended for use throughout the year as you teach the program. A two-page spread supports the content of each core lesson in the Student Book. In each Lesson: Quick Review summarizes the math concepts and terminology of the Student Book lesson. Try These presents questions the student can use to check understanding of the math concepts and skills in each lesson. The right page is the “homework” page, to be completed by the student with the assistance of a family member. Stretch Your Thinking presents an extension question. Math at Home The second section of the book, on pages 145 to 156, consists of 3 pull-out Math at Home magazines. These fun pages contain intriguing activities, puzzles, rhymes, and games to encourage home involvement. The perforated design lets you remove, fold, and send home this eight-page magazine after the student has completed Units 3, 6, and 8. vi To the Family This book will help your child practise the math concepts and skills that have been explored in the classroom. As you assist your child to complete each page, you have an opportunity to become involved in your child’s mathematical learning. The left page of each lesson contains a summary of the main concepts and terminology of the lesson. Use this page with your child to review the work done in class. The right page contains practice. Here are some ways you can help: • With your child, read over the Quick Review. Encourage your child to talk about the content and explain it to you in his or her own words. • Read the instructions with (or for) your child to ensure your child understands what to do. • Encourage your child to explain his or her thinking. • Some of the pages require specific materials. You may wish to gather items such as a centimetre ruler, index cards, a measuring tape, scissors, number cubes labelled 1 to 6, and paper clips. Many of the Practice sections contain games that will also improve your child’s math skills. You may have other ideas for activities your child can share with the rest of the class. The Math at Home pull-out pages 145 to 156 provide more fun activities. vii TU T D E N B OO 1 K S UNIT 1 Patterns in Charts Xxx LESSO N me hoo l Quick Review At Sc At Ho Look at this hundred chart. ➤ There is a pattern in the circled numbers. The pattern rule is: Start at 3. Count on by 3s. ➤ There is a pattern in the positions of the squares with circles. The pattern rule is: The squares with circles lie along every third diagonal. The diagonals go 1 down, 1 left. Try These 1. Look at the squares with circled numbers on this hundred chart. a) Describe the position pattern. __________________________ __________________________ b) Write the number pattern. __________________________ c) Write a pattern rule for the number pattern. ___________________________ _____________________________________________________________ d) Circle numbers to complete the pattern on the hundred chart. 2 Practice 101 102 103 104 105 106 107 108 109 110 Circle these numbers. b) Start at 102. Count on by 5s. Put an X on each number. c) Write the numbers that have both an X and are circled. 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 ________________________ 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 1 2 3 4 5 6 7 1 1 2 3 4 5 6 7 2 2 4 6 8 10 12 14 3 3 6 9 12 15 18 21 4 4 8 12 16 20 24 28 5 5 10 15 20 25 30 35 6 6 12 18 24 30 36 42 7 7 14 21 28 35 42 49 1. a) Start at 102. Count on by 2s. ________________________ d) Write the pattern rule for the number pattern in part c. ________________________ 2. Look at the squares with circled numbers in this multiplication chart. a) Write a pattern rule for the position pattern. _____________________________ _____________________________ _____________________________ b) Write a pattern rule for the number pattern. _____________________________________________________________ _____________________________________________________________ Stretch Your Thinking Follow this position rule. Put an X in the squares on the chart. The squares with an X lie along every third diagonal, starting at the first diagonal. The diagonals go 1 down and 1 right. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 3 TU T D E N B OO 2 K S UNIT 1 Extending Number Patterns LESSO N Quick Review me At Sc At Ho ➤ Here is a pattern of squares drawn on dot paper. l hoo Square Number of Dots on Perimeter 1 4 2 8 3 12 4 16 5 20 ^^^^^^^^^^^^^^^^^^^^^^^^^ One pattern rule for the number of dots on the perimeter is: Start at 4. Add 4 each time. Another pattern rule for the number of dots is: Multiply the square number by 4. ➤ The number of dots on any perimeter is a number we get when we start at 0 and skip count by 4. For the 10th square, skip count by 4 ten times: 4, 8, 12, 16, 20, 24, 28, 32, 36, 40 The 10th square will have 40 dots on its perimeter. Try These 1. a) Complete the table for this pattern. Triangle Number of Dots on Perimeter 1 2 3 4 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ b) Write the pattern rule. ________________________________________________ c) Which triangle will have 21 dots? __________ 30 dots? __________ d) Will any triangle have 22 dots? ____ Why or why not? ______________________ 4 Practice 1. a) Complete the table for this pattern of Figure Perimeter (units) 1 6 regular hexagons. Figure 1 Figure 2 Figure 3 Figure 4 The side length of each hexagon is 1 unit. b) Write the pattern rule for the perimeters. __________________________________ 2 3 4 ^^^^^^^^^^^^^^^^^^^^^^^^^^^ c) Which figure will have a perimeter of 22 units? ______ 34 units? ______ d) Predict the perimeter of the 10th figure. ___________________________ e) Will any figure have a perimeter of 40 units? Explain. _______________ _____________________________________________________________ 2. a) Complete the table for Figure this pattern. Perimeter (units) Area (square units) 1 Figure 1 2 Figure 2 Figure 3 3 Figure 4 4 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ b) Write the pattern rule for the areas. _____________________________________________________________ _____________________________________________________________ Stretch Your Thinking 1. a) Which figure in question 2 will have a perimeter of 60 units? ___________ What will its area be? ___________________________________________ b) Which figure in question 2 will have an area of 81 square units? __________ What is its perimeter? ___________________________________________ 5 TU T D E N B OO 3 K S UNIT 1 Representing Patterns LESSO N Quick Review Here is a pattern. From the table, the Squares in a Figure increase by 2. Here are 2 different ways to build this pattern: me At Sc At Ho Figure 1 2 3 4 Squares in Figure 2 4 6 8 l hoo +2 +2 +2 ^^^^^^^^^^^^^^^^^^^^^^^^^ Pattern 1 Pattern 2 The pattern rule for the number of squares in a figure is: Start at 2. Add 2 each time. Try These 1. a) Use counters to build this pattern. Figure Record the pattern below. 1 2 3 4 Counters in a Figure 1 3 5 7 ^^^^^^^^^^^^^^^^^^^^^^^^^ b) What is a pattern rule? ____________________________________________________________ 6 Practice 1. a) Use toothpicks to build this pattern. Figure Draw the pattern below. 1 2 3 4 Toothpicks in a Figure 2 4 6 8 ^^^^^^^^^^^^^^^^^^^^^^^^^ b) Write a pattern rule. ____________________________________________ c) How many toothpicks would be in the eighth figure? ________________ 2. a) Use counters to build this pattern. Record the pattern below. Figure 1 2 3 4 Counters in a Figure 2 5 8 11 ^^^^^^^^^^^^^^^^^^^^^^^^^ b) Build the pattern in a different way. Record the pattern below. c) Write a pattern rule: ____________________________________________ Stretch Your Thinking Choose a pattern rule. Complete the data in the table. Draw the pattern below. Figure Squares in a Figure 1 2 3 4 ^^^^^^^^^^^^^^^^^^^^^^^^^ 7 TU T D E N B OO 4 K S UNIT 1 Equations Involving Addition and Subtraction LESSO N Quick Review =6 ➤ Use counters. Take away all but 6 counters. Count the counters you took away. So, 15 – 9 = 6 ➤ Draw a picture. 15 – 9 = 6 ➤ Use guess and test. Guess: = 7 Test: 15 – 7 = 8 This is too low. Guess: = 9 Test: 15 – 9 = 6 This is correct. Try These 1. Use counters to solve each equation. Rewrite each equation. Replace the symbol with the correct value. a) 8 + = 40 b) 25 – ______________ c) + 17 = 24 ______________ 8 = 15 ______________ d) – 25 = 20 ______________ l hoo Here are 3 ways to solve this subtraction equation: 15 – Put out 15 counters. me At Sc At Ho Practice 1. Write an equation for each set of counters. _____________________________ a) b) + _____________________ = 2. Use counters to solve each equation. a) –8=8 b) = ______ 7 + = 24 c) 15 – = 13 = ______ = ______ 3. Draw a picture to solve each equation. a) 19 – = 14 b) = ______ + 5 = 16 = ______ 4. Use guess and test to solve each equation. a) 53 + = 68 = ______ b) 37 – = 14 = ______ 5. Write a story problem you could solve using the equation: 20 = 38 – Solve the equation. ________________________________________________________________ ________________________________________________________________ Stretch Your Thinking Solve: 126 + + 847 = 1000 = _____ 9 T E N T B OO UD 5 K S UNIT 1 LESSO N Equations Involving Multiplication and Division Quick Review Divide the counters into 4 equal groups. ➤ Draw a picture. 4 3 = 12 ➤ Use mental math. Think of a related division fact. What do we divide 12 by to get 4? 12 ÷ 3 = 4 So, 4 3 = 12 Try These 1. Use counters to solve each equation. a) 5 c) = 20 = ______ b) 24 ÷ ÷3=6 = ______ d) e) 2 3 = = ______ 10 = 12 =6 = ______ 8 = 32 = ______ f) 7 6 = = _______ l hoo Here are 3 ways to solve this multiplication equation: 4 ➤ Use counters. Put out 12 counters. me At Sc At Ho Practice 1. Write a multiplication and division equation for each picture. a) b) _________________________ _________________________ _________________________ _________________________ 2. Draw a picture to solve each equation. a) 9 = 18 = ______ b) 14 ÷ =2 c) = ______ 6 = 12 = ______ 3. Use mental math to solve each equation. a) 9 = 81 = ______ b) 21 ÷ = 3 = ______ c) 3 = 27 = ______ 4. Write a story problem that could be solved by using this equation: 28 ÷ = 7. Solve the problem. ________________________________________________________________ ________________________________________________________________ ________________________________________________________________ Stretch Your Thinking Use these numbers and some of these symbols: 3, 4, Write as many different equations as you can. , , ÷, =. 11 TU T D E N B OO 1 K S UNIT 2 Xxx Whole Numbers to 10 000 LESSO N Quick Review me At Sc At Ho l hoo You can show the number 1453 in different ways. ➤ Use Base Ten Blocks. 1 thousand 4 hundreds 5 tens 3 ones ➤ Use a place-value chart. Thousands 1 Hundreds 4 Tens 5 Ones 3 ➤ Use expanded form. 1453 = 1000 + 400 + 50 + 3 ➤ Use words. 1453 is one thousand four hundred fifty-three. The number 1453 is written in standard form. Every digit has a place value, depending on its position. Try These 1. Write each number in standard form. a) two thousand six hundred thirteen _______ b) 8000 + 600 + 40 + 1 _______ 2. Write each number in expanded form. a) 7125 ______________________ b) 2307 ______________________ 3. Write each number in words. a) 1620 ________________________________________________________ b) 3408 ________________________________________________________ 12 Practice 1. Complete the chart. Standard Form Expanded Form 2. Write each number in words. a) 3602 ________________________________________________________ b) 5045 ________________________________________________________ 3. Use each of these digits once to make each 4-digit number: 4, 2, 7, 5 a) the greatest possible number _______ b) the least possible number _______ c) the greatest number with 5 tens _______ d) the least number with 5 ones _______ Stretch Your Thinking Use 5, 3, 1, and 7 once in each number you make. Make as many 4-digit numbers as you can. ___________________________________________________________________ ___________________________________________________________________ 13 TU Comparing and Ordering Numbers T D E N B OO 2 K S UNIT 2 LESSO N Quick Review me At Sc At Ho l hoo Here are some ways to order the numbers 3261, 3621, and 2163 from least to greatest. ➤ Use a place-value chart. Thousands 3 3 2 Hundreds 2 6 1 2163 has the fewest thousands, so it is the least number. Tens 6 2 6 Ones 1 1 3 Both 3261 and 3621 have 3 thousands. Compare their hundreds. 200 < 600 So, 3261 < 3621 < means less than. > means greater than. ➤ Use a number line. 2163 2000 3261 2500 3000 3621 3500 4000 From least to greatest: 2163, 3261, 3621 Try These 1. Compare each pair of numbers. Write >, <, or =. a) 627 485 b) 2641 4824 c) 2683 2683 2. Write the numbers in order from least to greatest. 758, 709, 741 ____________________________________________________ 3. Write the numbers in order from greatest to least. 7148, 6271, 7285 ________________________________________________ 14 Practice 1. Play this game with a partner. The object of the game is to make the greater number. You will need a paper bag containing 10 cards with the digits 0 to 9. ➤ Draw a card from the bag. Record the digit in any space in the first row of your game board. Return the card to the bag. ➤ Take turns until each player fills all four spaces in a row. ➤ Compare your numbers. Write > or < in the box between the numbers. The player with the greater number wins a point. ➤ Play two more rounds. The player with the most points at the end of the game wins. Player 1 Player 2 2. a) Put your numbers from the game in order from least to greatest. _____________________________________________________________ b) Put your partner’s numbers in order from greatest to least. _____________________________________________________________ Stretch Your Thinking Make up three 4-digit numbers. Order the numbers from greatest to least. ___________________________________________________________________ 15 TU T D E N B OO 3 Sorting Numbers K S UNIT 2 LESSO N Quick Review me At Sc At Ho l hoo Here are four ways to sort these numbers. 86 225 895 300 75 1000 721 Venn Diagram Venn Diagram 1000 86 1000 225 895 300 75 86 300 721 Have 2 digits Less than 500 Venn Diagram Odd Odd Carroll Diagram Greater than 200 225 895 721 895 721 Have 3 digits 300 225 75 Digits add to less than 10 86 75 Even Odd 300 1000 225 Digits add to 10 or more 86 75 721 895 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ 1000 Try These 1. Use each Venn diagram to sort these numbers. 94 27 85 13 44 76 a) b) c) Digits add to 13 Odd 16 Even Less than 50 Multiples of 2 Even Practice 1. Sort these numbers in each Venn diagram. 421 718 246 967 358 709 626 a) Less than 900 b) Even Digits add to 16 Odd 2. Use a coloured pencil to write one more number in each part of the Venn diagrams in question 1. 3. a) Sort these numbers in the Carroll diagram. 56 101 77 84 50 126 91 105 Even Odd Multiples of 7 b) Use a coloured pencil to write another number in each box in the Carroll diagram. Not Multiples of 7 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ 4. Elmo travels to Sweden every three years. Sven visits Sweden every four years. Both men went to Sweden in 2006. Use a Venn diagram to find the year in which both men will visit Sweden again. ______________________________________ Stretch Your Thinking Choose two attributes. Label the circles. Sort these numbers in the Venn diagram. 1514 2658 947 352 685 4109 17 TU T D E N B OO 4 K S UNIT 2 Estimating Sums LESSO N Quick Review me At Sc At Ho l hoo When a question asks “about how many,” you can estimate. Here are some ways to estimate the sum of 294 + 351. ➤ Write each number to the closest 100. 294 is closest to 300. 351 is closest to 400. 300 + 400 = 700 So, 294 + 351 is about 700. ➤ Use front-end estimation. Add the first digits of the numbers. 200 + 300 = 500 So, 294 + 351 is about 500. For a closer estimate: Think about 94 and 51. This is about 100 + 50 = 150. So, 294 + 351 is about 500 + 150 = 650. Try These 1. Estimate each sum. a) 198 + 389 b) 119 + 408 c) 640 + 192 Estimate: __________ Estimate: __________ Estimate: __________ d) 79 + 272 e) 516 + 482 f) 291 + 291 Estimate: __________ Estimate: __________ Estimate: __________ 2. William estimated 246 + 585 as 700. Is his estimate high or low? Explain. ________________________________________________________________ ________________________________________________________________ ________________________________________________________________ 18 Practice 1. About how many beads would you have if you bought these sizes: a) small and large? ______________ b) medium and jumbo? ___________ c) medium and large? ___________ d) jumbo and small? _____________ 2. The toy shop sold 117 wind-up cars and 289 battery-operated cars in one week. About how many cars did it sell? _________________________ 3. Yolanda has a desktop publishing business. She wants to print 1000 items today. She actually prints 352 brochures and 581 flyers today. a) About how many items did she print? _____________________________ b) Did Yolanda reach her goal? Explain. _____________________________________________________________ _____________________________________________________________ 4. Last summer, 227 children signed up for T-ball and 139 signed up for baseball. About how many children signed up altogether? __________ Stretch Your Thinking The estimated sum of two numbers is 1000. What might the numbers be? Give three different answers. ___________________________________________________________________ 19 TU T D E N B OO 5 K S UNIT 2 Using Mental Math to Add LESSO N Quick Review me At Sc At Ho l hoo ➤ Use mental math to add: 267 + 197 Use the strategy of make a “friendly” number. 197 is 200 – 3. Add 200, then take away 3. 200 is a friendly number 267 + 200 = 467 because it is easy to add 200. 467 – 3 = 464 So, 267 + 197 = 464 ➤ Count on to add: 271 + 580 Add 271 and 500. 271 + 500 = 771 Count on by 10s eight times. 771, 781, 791, 801, 811, 821, 831, 841, 851 So, 271 + 580 = 851 ➤ Use mental math to add: 415 + 342 Use the strategy of “adding on” from left to right. Add on hundreds, then tens, and then ones. Think: 415 + 300 + 40 + 2 Count on 3 hundreds: 415, 515, 615, 715 Count on 4 tens: 715, 725, 735, 745, 755 Then add 2: 755 + 2 = 757 So, 415 + 342 = 757 Try These 1. Use mental math to add. a) 262 + 345 = _____ b) 497 + 222 = _____ c) 370 + 163 = _____ d) 399 + 544 = _____ e) 262 + 290 = _____ f) 196 + 341 = _____ 2. Becky gathered 316 clams and Charlie gathered 286. How many clams did they gather in all? Use mental math to find out. _____ 20 Practice Use mental math. 1. Add. a) 690 + 284 = _______ b) 2131 + 3468 = _______ c) 352 + 213 = _______ d) 229 + 493 = _______ For which problems did you make a “friendly” number? __________________ 2. Look at these containers. If you bought the following groups of animals, how many toy animals would you have? a) farm animals and zoo animals _______ b) sea creatures and jungle animals _______ c) zoo animals and jungle animals ________ 3. Ridgetown has a population of 8317 people. Mayberry has a population of 1291. How many people live in the two towns? _______ 4. The cafeteria sold 123 cartons of chocolate milk and 204 cartons of white milk. How many cartons of milk were sold? _______ Stretch Your Thinking Use mental math to add: 453 + 197 + 205 = _______ Describe the strategy you used. ________________________________________ ___________________________________________________________________ ___________________________________________________________________ ___________________________________________________________________ 21 TU T D E N B OO 6 Adding 3-Digit Numbers K S UNIT 2 LESSO N Quick Review me At Sc At Ho l hoo Geraldo has 276 hockey cards and 397 baseball cards. To find how many cards Geraldo has in all, add: 276 + 397 ➤ Add from right to left. 276 397 500 160 13 673 + Add the hundreds: Add the tens: Add the ones: Add the sums: ➤ Add from right to left. Add the ones: 13 ones Regroup 13 ones as 1 ten and 3 ones. Add the tens: 17 tens Add the hundreds: Regroup 17 tens as 6 hundreds 1 hundred and 7 tens. 1 11 276 + 397 3 Geraldo has 673 cards in all. 11 276 + 397 73 276 + 397 673 Try These 1. Add. a) 295 + 104 b) 327 + 415 c) 299 + 463 d) 508 + 419 e) 285 + 79 2. There were 139 more people at the soccer game on Saturday than on Friday. On Friday there were 472 people at the game. How many people were at the game on Saturday? ____________________ 22 Practice 1. Estimate first. Circle the letters next to the examples for which the sum will be less than 900. Then, add to find all the sums. a) 738 b) 637 c) 109 d) 718 + 191 + 439 + 488 + 237 f) 482 + 519 g) 234 + 410 h) 689 + 130 i) 651 + 259 e) 367 + 662 j) 318 + 491 e) 397 + 459 j) 282 + 531 2. Estimate first. Circle the letters next to the examples for which the sum will be greater than 700. Then, add to find all the sums. a) 418 b) 526 c) 381 d) 108 + 231 + 437 + 294 + 592 f) 362 + 282 g) 583 + 199 h) 435 + 428 i) 339 + 382 3. Add: 419 + 386 Explain your strategy. ________________________________________________________________ 4. What is the greatest 3-digit number you can add to 457 without having to regroup in any place? ______ Stretch Your Thinking The sum of two numbers is 853. What might the numbers be? Find two pairs of numbers. ____________________________________________ 23 TU T D E N B OO 7 K S UNIT 2 Adding 4-Digit Numbers LESSO N Quick Review 15 hundreds is 1 thousand 5 hundreds 14 ones is 1 ten 4 ones 1000s 100s 10s 1s 1 7 5 6 +4 8 2 8 5 15 7 14 6 5 7 14 6 5 8 4 ➤ 1756 + 2469 Add from right to left. Add the ones. Add the tens. Add the hundreds. Add the thousands. Regroup. Regroup. Regroup. 1756 + 2469 5 11 1756 + 2469 25 111 111 1756 + 2469 225 1756 + 2469 4225 Estimate to check that the sum is reasonable. 1756 is close to 2000. 2469 is 4225 is close to 4000. close to 2000. 2000 + 2000 = 4000 So, the sum is reasonable. Try These 1. Find each sum. Estimate to check. a) 5558 b) 3047 + 1343 + 2828 2. Estimate each sum. a) 3276 + 4192 Estimate: _______ 24 c) 4189 + 3673 b) 1258 + 3769 Estimate: _______ d) 1847 + 5684 c) 2672 + 3409 Estimate: _______ l hoo ➤ 1756 + 4828 Use column addition. 1 me At Sc At Ho Practice 1. Play this game with a partner. You will need: 1 number cube labelled 1 to 6 ➤ Take turns rolling the number cube. On each roll, both players record the digit rolled in one of the boxes in their first addition grid. ➤ After 8 rolls, players add. The player with the greater sum wins. ➤ Repeat with the other addition grids. Player A Player B + + + + + + + + + + + + Stretch Your Thinking The sum of two 4-digit numbers is 4589. What might the two numbers be? Give two different answers. ___________________________________________________________________ 25 TU T D E N B OO 8 K S UNIT 2 Estimating Differences LESSO N Quick Review me At Sc At Ho l hoo Here are some strategies for estimating differences. ➤ Estimate: 513 – 289 To get a closer estimate, write Write each number only one number to the closest 100. to the nearest 100 513 – 300 = 213. and subtract. So, 513 – 289 is about 213. 500 – 300 = 200 So, 513 – 289 is about 200. ➤ Estimate: 4592 – 2369 Use front-end estimation. Use the digits in the thousands 4592 4000 place. Replace the other 2369 2000 digits with zeros. 4000 – 2000 = 2000 So, 4592 – 2369 is about 2000. Try These 1. Estimate each difference. a) 749 – 263 b) 504 – 327 c) 988 – 214 Estimate: __________ Estimate: __________ Estimate: ____________ d) 4580 – 1235 e) 677 – 48 f) 6896 – 1583 Estimate: ____________ Estimate: __________ Estimate: ____________ 2. Natalie estimated 584 – 126 as 400. Is her estimate high or low? Explain. _________________________________________________________________ _________________________________________________________________ _________________________________________________________________ _________________________________________________________________ 26 Practice 1. Use the data in the chart to estimate each difference. School Lunches Served Day Monday Number Served 286 Tuesday 327 Wednesday 489 Thursday 417 Friday 648 a) About how many more lunches were served on Friday than on Monday? _____________________________________________ b) About how many more lunches were served on Thursday than on Tuesday? ______________________________________________ c) About how many more lunches were served on Wednesday than on Tuesday? _____________________________________________ 2. Laleh estimated the difference of 7654 and 4111 as 4000, and Sam estimated the difference as 3500. a) How might Laleh have estimated? _____________________________________________________________ b) How might Sam have estimated? _____________________________________________________________ c) Whose estimate is better? Explain. _____________________________________________________________ Stretch Your Thinking Find a pair of 3-digit numbers that have an estimated difference of 520. ___________________________________________________________________ 27 TU T D E N B OO 9 K S UNIT 2 Using Mental Math to Subtract LESSO N Quick Review me At Sc At Ho l hoo Here are some strategies for using mental math to subtract. ➤ Use the strategy of “make a friendly number.” Subtract: 437 – 103 Subtract: 719 – 398 Subtract 100 instead of 103. Add 2 to 398 to make 400. 437 – 100 = 337 Add 2 to 719 to make 721. Then subtract 3. 721 – 400 = 321 337 – 3 = 334 So, 719 – 398 = 321 So, 437 – 103 = 334 ➤ Use the strategy of “counting on.” Subtract: 441 – 230 Count: 230 330 430 440 441 +100 +100 So, 441 – 230 = 211 +10 +1 = 211 Try These 1. Use mental math to subtract. a) 427 – 299 = _______ b) 625 – 495 = _______ c) 586 – 397 = _______ d) 256 – 101 = _______ e) 748 – 403 = _______ f) 462 – 202 = _______ g) 4272 – 2150 = _______ h) 7758 – 3547 = _______ i) 6894 – 1673 = _______ 2. Laslo travelled 637 km on Saturday and 402 km on Sunday. How much farther did he travel on Saturday than on Sunday? Use mental math to find out. ________ 3. The hot dog stand served 250 hot dogs on Friday and 481 on Saturday. How many more hot dogs were served on Saturday than on Friday? Use mental math to find out. _____________ 28 Practice 1. Use mental math to find each difference. Then use the letters next to the differences to solve the riddle. What did King Tut say when he was scared? 543 – 260 = ________ (B) 622 – 415 = ________ (E) 894 – 517 = ________ (N) 583 – 298 = ________ (I) 499 – 354 = ________ (M) 314 – 189 = ________ (U) 532 – 220 = ________ (T) 847 – 606 = ________ (Y) 684 – 302 = ________ (W) 717 – 402 = ________ (Z) 536 – 199 = ________ (C) 632 – 421 = ________ (F) 947 – 624 = ________ (L) 231 – 111 = ________ (A) 285 382 120 377 312 145 241 145 125 145 145 241 Stretch Your Thinking Describe two ways to find 4000 – 3894. ____________________________________________________________________ ____________________________________________________________________ ____________________________________________________________________ ____________________________________________________________________ 29 UNIT 2 TU Subtracting 3-Digit Numbers T D E N B OO S K 10 LESSO N Quick Review me At Sc At Ho l hoo There are 300 seats in the theatre. One hundred eighty-four seats are on the main floor. The rest are in the balcony. To find how many seats are in the balcony, subtract: 300 – 184 9 ➤ You can use place value to subtract. 2 10 10 You cannot take 4 ones from 0 ones. 300 There are no tens to regroup. – 184 Regroup 1 hundred as 10 tens. Regroup 1 ten as 10 ones. 9 Subtract the ones. 2 10 10 Subtract the tens. 300 – 184 Subtract the hundreds. 116 ➤ You can use mental math to subtract. Count on from 184 to 300. 184 284 294 300 +100 +10 +6 You can check by adding. Add: 184 + 116 = 300 = 116 Try These 1. Subtract. a) 465 – 213 b) 786 – 229 c) 574 – 197 d) 600 – 211 e) 238 – 79 2. Find the difference. Use mental math. 30 a) 400 – 174 = _______ b) 500 – 189 = _______ c) 347 – 215 = _______ d) 701 – 500 = _______ e) 428 – 299 = _______ f) 152 – 107 = _______ Practice 1. Subtract. Check your answers. a) 836 b) 726 – 451 Check: – 538 c) Check: 736 – 528 Check: 2. Use mental math to find each difference. a) 400 – 263 = ______ b) 501 – 248 = ______ c) 450 – 231 = ______ 3. Estimate first. Then subtract the numbers for which the difference will be less than 300. a) 591 b) 436 – 375 – 168 c) 624 – 235 d) 716 – 371 e) 327 – 79 4. Ms. Green’s class collected 600 cans for recycling. Mr. Hso’s class collected 427 cans. How many more cans did Ms. Green’s class collect? ___________ 5. Sanil’s school had a book sale. On Monday they sold 697 books. On Tuesday they sold 842 books. How many more books did they sell on Tuesday? ____________ Stretch Your Thinking The difference of two numbers is 329. What might the numbers be? Find two pairs of numbers. ___________________________________________________________________ 31 UNIT 2 TU Subtracting 4-Digit Numbers T D E N B OO S K 12 LESSO N Quick Review 2053 – 997 6 9 14 1 10 4 13 9 14 1 10 4 13 2053 – 997 6 2053 – 997 1056 Check. ➤ By adding: 997 + 1056 2053 ➤ By estimating: 2000 – 1000 = 1000 1000 is close to 1056. So, the answer is reasonable. The sum should be the number you started with. Try These 1. Subtract. a) 4532 – 2121 b) 5726 – 248 c) 7243 – 5685 d) 4029 – 388 2. Subtract. Check your answer. a) 32 9354 – 3287 Check: b) 7600 – 1452 Check: l hoo Subtract: 2053 – 997 You can use place value to subtract from right to left. Subtract the tens. Regroup 1 ten as Regroup 1 thousand Subtract the hundreds. as 10 hundreds. 10 ones. Regroup 1 hundred Subtract the thousands. Subtract the ones. as 10 tens. 4 13 me At Sc At Ho Practice 1. Estimate. Then subtract. a) 3059 b) 5138 – 2298 – 4479 c) 8209 – 5919 d) 5439 – 3216 Estimate: _______ Estimate: _______ Estimate: _______ Estimate: _______ 2. Manjit and Irene like to collect acorns. Manjit collected 1286 acorns and Irene collected 898. How many more acorns did Manjit collect than Irene? ______ 3. Play this game with a partner. You will need: 1 number cube paper pencils ➤ Each player draws a subtraction grid like this: ➤ Take turns rolling the number cube. After each turn, both players record the digit rolled in any box in their grid. ➤ After 8 rolls, players subtract. The player with the greater difference wins. Play 5 or more games. Stretch Your Thinking A 3-digit number is subtracted from a 4-digit number. The difference is 426. What could the two numbers be? Give two answers. ___________________________________________________________________ ___________________________________________________________________ 33 UNIT 2 T Solving Addition and Subtraction Problems E N T B OO UD S K 13 LESSO N Quick Review me At Sc At Ho l hoo Jakob delivered 2472 flyers in March, 3854 in April, and 1962 in May. How many flyers did Jakob deliver in all? ➤ Add: 2472 + 3854 + 1962 2 1 2472 3854 + 1962 8288 Add the ones. Add the tens. Regroup. Add the hundreds. Regroup. Add the thousands. Jakob delivered 8288 flyers. Jakob was paid $165 for his work. He bought a pair of skates for $119. Later, he bought a hockey stick for $18. How much money did Jakob have left? ➤ Subtract: 5 15 165 119 46 3 16 46 Then subtract 18 from the result: 18 28 Jacob has $28 left. Try These 1. Add. a) 4723 6415 + 3027 b) 8962 3471 + 536 c) 1357 2468 + 2389 d) 4572 3002 + 5679 2. Estimate to check each answer in question 1. Show your work. 34 a) ___________________________ b) ___________________________ c) ___________________________ d) ___________________________ Practice 1. Maddy had $1467 in her bank account. She withdrew $247 one week and $135 the next week. How much money did Maddy have left in her account? ________________________________________________________________ 2. Play this game with a partner. You will need a number cube labelled 1 to 6. ➤ Take turns to roll the number cube. On each roll, both players record the digit rolled in one of the boxes in the first addition grid. ➤ After 12 rolls, add. The player with the greater sum wins. ➤ Repeat with the other grids. Player A Player B + + + + + + + + Stretch Your Thinking The sum of three 4-digit numbers is 5638. What might the numbers be? __________________________________________ 35 TU T D E N B OO 1 K S UNIT 3 Xxx Using Doubles to Multiply LESSO N Quick Review ➤ Use doubling to multiply by 4. To find 4 5: First find 2 5, then double. 2 5 = 10 4 5 = 20 double 25 ➤ Use repeated doubling to multiply by 8. To find 8 3: First find 2 3, then double, then double again. 23=6 4 3 = 12 8 3 = 24 45 ➤ Begin with a fact you know. Double one of the factors, then multiply. You know 3 4 = 12. Double the factor 3, then multiply: 6 4 = 24 (double of 12) Or, double the factor 4, then multiply: 3 8 = 24 (double of 12) When you double a factor, the product doubles. Try These Use doubling to multiply. a) 2 7 = 14 4 7 = _____ b) 4 3 = 12 8 3 = _____ c) 3 5 = 15 __________ 2. Double one of the factors each time to get a product. Then check the circle if the product is double the one in the box. a) 4 3 = __________ __________ 36 b) 2 5 = __________ __________ c) 5 3 = __________ __________ l hoo Doubling is a strategy you can use to multiply. 1. me At Sc At Ho Practice 1. Use doubling to multiply. a) 2 9 = 18 4 9 = _____ 2. Find each product. a) 2 6 = _____ 4 6 = _____ 8 6 = _____ b) 3 3 = 9 c) 6 5 = ____ ___________ ___________ b) 2 9 = _____ 4 9 = _____ 8 9 = _____ c) 2 7 = _____ 2 14 = _____ 2 28 = _____ 3. Use repeated doubling to multiply. a) 8 6 = b) 8 5 = c) 9 8 = ____________ ____________ ____________ ____________ ____________ ____________ _____________ _____________ _____________ 8 6 = _____ 8 5 = _____ 9 8 = _____ 4. What could each missing number be? Find as many answers as you can. a) = 18 b) = 36 ______________________________ ________________________________ ______________________________ ________________________________ ______________________________ ________________________________ ______________________________ ________________________________ Stretch Your Thinking Multiply. 1. 2 2 = _____ 4 2 = _____ 8 2 = _____ 16 2 = _____ 32 2 = _____ 2. 2 5 = _____ 4 5 = _____ 8 5 = _____ 16 5 = _____ 32 5 = _____ 37 TU Multiplying by 1, by 0, and by 10 T D E N B OO 2 K S UNIT 3 LESSO N Quick Review bowls 1 = fish 5 fish in all Also, 1 × 5 = 5 When 1 is a factor, the product is always the other factor. Think: 7 groups of 0 is 7 × 0. 7 bowls 0 = fish 0 fish in all Also, 0 × 7 = 0 Think: 4 groups of 10 is 4 × 10. 4 10 = When 0 is a factor, the product is always 0. 40 fish in all When 10 is a factor, the product is always the other factor with a zero added. a) 6 1 = ______ b) 7 1 = _______ c) 4 1 = _______ 2. a) 6 0 = ______ b) 3 0 = _______ c) 2 0 = _______ 3. a) 7 10 = ______ b) 8 10 = _______ c) 4 10 = _______ tanks fish Also, 10 × 4 = 40 Try These Multiply. 1. 38 l hoo Think: 5 groups of 1 is 5 × 1. 5 me At Sc At Ho Practice 1. Find each product. a) 1 4 = _______ b) 0 0 = _______ c) 0 7 = _______ d) 5 10 = _______ e) 6 0 = _______ f) 10 6 = _______ g) 0 4 = _______ h) 7 10 = _______ i) 1 1 = _______ 2. Find each missing number. a) 4 ____ = 0 b) ____ 6 = 6 c) 7 ____ = 70 d) ____ 1 = 1 e) ____ 5 = 50 f) ____ 4 = 4 g) 1 ____ = 10 h) ____ 1 = 3 i) 2 ____ = 2 a) 5 ____ 1 = 5 b) 1 ____ 1 = 1 c) 6 ____ 10 = 60 d) 10 ___ 3 = 30 e) 4 ____ 1 = 5 f) 0 ____ 2 = 0 g) 1 ____ 4 = 4 h) 1 ____ 1 = 2 i) 7 ____ 0 = 7 3. Write + or ×. 4. Rico has 1 nickel, 5 dimes, and 7 pennies. How much money does Rico have? Show your work. ________________________________________________________________ ________________________________________________________________ Stretch Your Thinking Which is greater, the product of your age times 0 or the product of your age times 1? Explain. ___________________________________________________________________ ___________________________________________________________________ ___________________________________________________________________ 39 TU Using Skip Counting to Multiply T D E N B OO 3 K S UNIT 3 LESSO N Quick Review me At Sc At Ho l hoo You can use skip counting patterns to multiply mentally. ➤ To find 6 8, skip count by 8 six times. These numbers are multiples of 8. 8, 16, 24, 32, 40, 48 8 0 16 24 32 40 48 6 steps of 8 is 48. 6 8 = 48 ➤ Another way to find 6 8 is to skip count by 6 eight times. 6, 12, 18, 24, 30, 36, 42, 48 0 6 12 18 24 30 36 These numbers are multiples of 6. 42 48 8 steps of 6 is 48. 6 8 = 48 Try These 1. Skip count to find the missing numbers. a) 4, 8, 12, _____, _____, _____, _____ b) 9, 18, 27, _____, _____, _____, _____ c) 7, 14, 21, _____, _____, _____, _____ 2. Skip count to find each product. a) 5 4 = _____ b) 3 8 = _____ e) 7 5 = _____ 40 f) 3 7 = _____ c) 4 3 = _____ d) 9 2 = _____ g) 6 8 = _____ h) 8 8 = _____ Practice 1. a) Use the hundred chart. Hundred Chart Colour all the numbers in which the ones digit and the tens digit add up to 9. b) What multiples have you coloured? _________________________ _________________________ _________________________ 2. Play this game with 2 or 3 friends. You will need: 2 sets of cards numbered 2 to 10 3 counters for each player a small container ➤ ➤ ➤ ➤ Take 3 counters each. Shuffle the cards and put them in a pile face down. Turn over the top card. This is the number you will start with. Go around the group. Say one number each, counting on by the number on the card. The player who says 100 or a number over 100 puts a counter in the container. The next player turns over a new card and starts the counting. ➤ The first person to get rid of all 3 counters wins. Stretch Your Thinking 1. a) In the game above, which start numbers will result in a player saying 100? _______________________________________________________________ b) Which start numbers will result in a player going over 100? _______________________________________________________________ 41 TU T D E N B OO 4 K S UNIT 3 Other Strategies for Multiplying LESSO N Quick Review me At Sc At Ho l hoo You can multiply by adding groups to the facts you know. ➤ Use facts with 2 to multiply by 3. ➤ Use facts with 5 to multiply by 6. To find 3 9: To find 6 8: 2 9 = 18 5 8 = 40 18 + 9 = 27 40 + 8 = 48 19= 9 18= 8 So, 3 9 = 27 So, 6 8 = 48 ➤ Use facts with 5 and 2 to multiply by 7. To find 7 6: 5 6 = 30 30 + 12 = 42 2 6 = 12 So, 7 6 = 42 ➤ Use facts with 10 to multiply by 9. To find 9 8: 10 8 = 80 80 – 8 = 72 18= 8 So, 9 8 = 72 ➤ To multiply by an even factor, use a half, and then double. To find 8 7: Half of 8 is 4. 4 7 = 28 28 2 = 56 So, 8 7 = 56 Try These a) 3 7 = ____ b) 3 5 = ____ c) 3 8 = ____ 2. a) 6 9 = ____ b) 6 5 = ____ c) 6 7 = ____ 3. a) 7 7 = ____ b) 7 9 = ____ c) 7 8 = ____ 4. a) 9 9 = ____ b) 9 7 = ____ c) 9 4 = ____ 5. a) 6 3 = ____ b) 8 6 = ____ c) 4 9 = ____ 1. 42 Practice 1. Name two facts that help you find each product. a) 4 9 ______________________________________________________ b) 7 6 ______________________________________________________ c) 6 8 ______________________________________________________ d) 9 6 ______________________________________________________ e) 4 8 ______________________________________________________ f) 8 7 ______________________________________________________ 2. Show how you could use the product of 4 × 6 to find the product of 8 × 6. ________________________________________________________________ 3. Play this game with a partner. You will need: 3 number cubes labelled 1 to 6 2 calculators 6 2 3 5 1 4 5 1 3 ➤ Take turns to roll all 3 number cubes. Put the one with the greatest number aside. If you roll more than one greatest number, put only one aside. Roll the other 2 number cubes. Put the one with the greater number aside. Roll the last number cube. ➤ Add the numbers on your first 2 cubes. Multiply the total by the number on your third cube. The product is your score. ➤ Keep playing until one player reaches a total of 200. Stretch Your Thinking Show how you could use a half, than double to find the product 6 9. ___________________________________________________________________ 43 TU T D E N B OO 5 K S UNIT 3 Using Patterns in a Multiplication Chart LESSO N Quick Review me At Sc At Ho l hoo You can use patterns to remember multiplication facts. ➤ In a multiplication chart, there are matching numbers on each side of the diagonal from 1 to 81. If you know... then you know: 5 7 = 35 7 5 = 35 9 8 = 72 8 9 = 72 ➤ There are patterns in the multiplication facts with 9. • • The digits in the product always add to 9. 5 9 = 45 4+5=9 1 2 3 4 5 6 7 8 9 1 1 2 3 4 5 6 7 8 9 2 2 4 6 8 10 12 14 16 18 3 3 6 9 12 15 18 21 24 27 4 4 8 12 16 20 24 28 32 36 5 5 10 15 20 25 30 35 40 45 6 6 12 18 24 30 36 42 48 54 7 7 14 21 28 35 42 49 56 63 8 8 16 24 32 40 48 56 64 72 9 9 18 27 36 45 54 63 72 81 8 9 = 72 7+2=9 The number multiplied by 9 is always 1 more than the tens digit in the product. 6 9 = 54 6 is 1 more than 5. 4 9 = 36 4 is 1 more than 3. Try These 1. Complete. a) 8 9 = ___ 8 b) 3 7 = 7 ___ c) 6 4 = ___ 6 2. Multiply. 44 a) 9 6 = ____ b) 5 9 = ____ c) 2 9 = _____ d) 9 8 = ____ e) 7 9 = ____ f) 4 9 = _____ g) 8 9 = ____ h) 9 7 = ____ i) 9 4 = _____ Practice 1. Play this game with a partner. You will need: 25 counters 2 calculators paper and pencils ➤ Decide on a number from 2 to 9. This number will be the game factor. ➤ Player A: Place a counter on any number on the board and multiply by the game factor. Record the product as your score. ➤ Player B: Place a counter on a number When something is adjacent to Player A’s number. Multiply by adjacent to something the game factor and record your score. else, it is next to it. ➤ Continue playing. On each turn, place a counter next to the last one played. If an adjacent square is not empty, place the counter in any empty square. ➤ When the board is filled, the winner is the player with the highest total score. 1 5 0 2 9 7 8 3 7 1 8 3 4 2 6 4 6 7 9 3 2 4 1 5 0 Stretch Your Thinking Suppose you are Player A. Where will you place the first counter? Explain. ____________________________________________________________________ ____________________________________________________________________ 45 TU T D E N B OO 7 K S UNIT 3 Using Arrays to Divide LESSO N Quick Review You can make an array to show each way. 2 rows of 3 stools 62=3 3 rows of 2 3 rows of 2 stools 63=2 1 row of 6 6 rows of 1 1 row of 6 stools 61=6 6 rows of 1 stool 66=1 Try These 1. Use the array to complete the sentence. a) 18 6 = _______ 46 b) 14 2 = _______ c) 15 3 = _______ l hoo There are 6 stools. They will be put into equal rows. How many stools could be in each row? 2 rows of 3 me At Sc At Ho Practice 1. Write a division sentence for each array. a) b) _______________ c) _______________ _______________ 2. Draw an array for each division sentence. a) 15 5 = _______ b) 12 2 = ______ c) 24 6 = _______ 3. Use counters. Make an array to find each answer. a) 20 4 = _______ b) 16 2 = _______ c) 6 1 = _______ d) 18 9 = _______ e) 30 5 = _______ f) 28 7 = _______ Stretch Your Thinking There are 24 members in the Boy Scout troop. They will march in the parade in equal rows. How many Boy Scouts could be in each row? Find as many answers as you can. ___________________________________________________________________ 47 TU T D E N B OO 8 K S UNIT 3 Relating Multiplication and Division LESSO N Quick Review me At Sc At Ho l hoo There are 42 students who want to play hockey. There are 6 players on a team. How many teams can there be? To find out, divide: 42 6 Here are two ways to find 42 6: ➤ Make an array of 42 counters with 6 counters in each row. There are 7 rows. So: 42 6 = 7 There can be 7 teams. Think: ➤ You can think about multiplication to divide. Every division fact has a related multiplication fact. 6 times which number is 42? You know 6 7= 42. So, 42 6 = 7 Try These 1. Write a multiplication fact and a division fact for each array. a) b) _________________________ _________________________ 2. Use a related multiplication fact to help you divide. Write the related fact. a) 20 4 = _______ b) 30 5 = _______ c) 14 7 = _______ _______________ 48 _______________ _______________ Practice 1. Divide. Draw a picture to show your work. 24 3 = _______ 30 5 = _______ 18 2 = _______ 5 5 = _______ 2. Use a related multiplication fact to divide. a) 18 6 = _____ b) 45 5 = _____ c) 56 7 = _____ d) 35 5 = _____ e) 24 4 = _____ f) 27 3 = _____ g) 12 2 = _____ h) 9 1 = _____ 3. Write a division fact to solve each question. a) 24 children b) 18 cookies c) 42 cans 6 children on a team How many teams? 9 cookies on a plate How many plates? 7 cans in each row How many rows? _______________ _______________ _______________ Stretch Your Thinking Find all the ways of dividing 36 students into equal teams. Write a division fact to show each way. ___________________________________________________________________ ___________________________________________________________________ ___________________________________________________________________ ___________________________________________________________________ 49 TU T D E N B OO 9 K S UNIT 3 Dividing by Numbers from 1 to 9 LESSO N Quick Review l hoo Here’s how to divide by 8 and 9. 48 8 8× = 48 Think 8 × 6 = 48 multiplication. So, 48 8 = 6 Also, 48 6 = 8 63 9 9× = 63 9 × 7 = 63 So, 63 9 = 7 Also, 63 7 = 9 me At Sc At Ho Related Facts 48 8 = 6 48 6 = 8 6 8 = 48 8 6 = 48 Related Facts 63 9 = 7 63 7 = 9 7 9 = 63 9 7 = 63 Think multiplication. Try These 1. Write two multiplication facts and two division facts for each array. a) __________ __________ __________ __________ __________ __________ a) 27 9 = _______ b) 16 8 = _______ c) 45 9 = _______ d) 64 8 = _______ 50 __________ __________ 2. Divide. e) 36 9 = _______ b) f) 32 8 = _______ Practice 1. Find the product. Then write a related multiplication fact and two related division facts. a) 3 9 = _______ b) 8 5 = _______ c) 9 7 = _______ ______________ ______________ ______________ ______________ ______________ ______________ ______________ ______________ ______________ 2. Divide. a) 49 7 = _______ b) 81 9 = _______ c) 45 5 = _______ d) 27 3 = _______ e) 56 8 = _______ f) 36 6 = _______ 3. Write a division sentence to show each answer. a) There are 28 days in February. How many weeks is that? _____________________________________________________________ b) There are 3 tennis balls in a carton. How many cartons are needed for 27 balls? _____________________________________________________________ c) There are 54 students in the band. They march in 6 equal rows. How many students are in each row? _____________________________________________________________ d) There are 9 kiwi fruit in a small basket. A box contains 72 kiwi fruit in a single layer. How many small baskets of kiwi fruit can be filled? _____________________________________________________________ Stretch Your Thinking Complete this division sentence in as many ways as you can. =8 _____________________________________________________________________ ____________________________________________________________________ 51 UNIT 3 TU T D E N B OO S K 10 Pose and Solve Problems LESSO N Thirty-two students signed up for swimming lessons. The classes are taught in groups of 8. How many classes will there be? Here are 2 ways to find out. ➤ Use a model. Use 32 counters. Put them into groups of 8. So, there will be 4 classes. ➤ Guess, then test. Suppose you guess 5 classes. Test: 5 × 8 = 40; that is too many students. Guess again: 4 × 8 = 32; that is the correct number. So, there will be 4 classes. Try These Use counters or guess, then test. Show your work. 1. Twenty-three students go on a camping trip. Each tent holds 4 students. How many tents will be needed? __________________________________ 2. Ramzi has 4 cages of gerbils. There are 5 gerbils in each cage. How many gerbils does Ramzi have? __________________________________ 52 me hoo l Quick Review At Sc At Ho Practice 1. Suri picked 72 apples. Each basket holds 9 apples. How many baskets did she need? ____________________________________________________________ 2. Enrico saw 16 bicycles and tricycles in the playground. He counted a total of 36 wheels. How many bicycles were there? How many tricycles? _____________________________________________________________ _____________________________________________________________ _____________________________________________________________ _____________________________________________________________ _____________________________________________________________ 3. Use the data in the table. Write a story problem you can solve using multiplication or division. Solve your problem. Product Tennis balls Baseballs Hockey pucks Number in a Box 3 6 4 _____________________________________________________________ _____________________________________________________________ Stretch Your Thinking Chase had 81 chickens. He sold an equal number of chickens to each of 3 customers and had 54 chickens left. How many chickens did Chase sell to each customer? _________________________________________________________________ _________________________________________________________________ 53 TU T D E N B OO 1 Xxx Calendar Time K S UNIT 4 LESSO N Quick Review me At Sc At Ho l hoo Gillian’s cat was born on May 15th, 2004. We can write this date in different ways: ➤ We use 2 digits for the month and 2 digits for the day. 2004 05 15 Year 5th month This date is written in metric notation. 15th day ➤ This way of writing the date uses two 2 digits for the year too. 04 05 Year Month 15 05 15 04 15 05 04 Day Month Day Year Day Month Year Try These 1. Write each date in metric notation. a) November 30th, 2005 ___________ b) March 17th, 1998 _____________ c) April 7, 2000 ___________________ d) June 26, 1959 ________________ 2. Write each date using words and numbers. a) 1976 10 14 b) 2007 12 01 Year Month Day Year Month Day c) 01 03 95 Month Day Year e) 05 06 00 Day Month Year 54 d) 08 04 06 Month Day f) 09 Year 05 12 Day Month Year Practice 1. Write each date using words and numbers. a) 2001 09 08 ___________________ b) 1989 12 11 ___________________ c) 2009 10 02 ___________________ d) 2004 04 03 __________________ 2. Use words and numbers to record the date of birth of 2 classmates. Then write each date in metric notation. a) _____________________________________________________________ b) _____________________________________________________________ 3. Write each date in metric notation. a) the seventh day of last month _______________________________ b) the first day of this year _______________________________ c) the date of your fifth birthday _______________________________ d) the last day of next month _______________________________ e) the day after April 19th, 2008 _______________________________ f) the day before June 1st, 1987 _______________________________ g) the day after December 31st, 2010 _______________________________ 4. In what ways can the date 03 04 79 be interpreted? ________________________________________________________________ Stretch Your Thinking Benito turned 10 on the 3rd day of the 11th month of 2005. Write this date in as many ways as you can. ___________________________________________________________________ 55 TU T D E N B OO 2 Exploring Time K S UNIT 4 LESSO N Quick Review quarter after 5 5:15 half past 5 5:30 quarter to 6 5:45 ➤ A clock with numbers and no hands is a digital clock. The clock shows 45 minutes after 10 o’ clock. 10 45 We say: “Ten forty-five.” Try These 1. Write each time two different ways. a) b) ____________ ____________ c) ____________ ____________ ____________ ____________ 2. Write each time in a different way. 56 a) 2:00 _______________ b) quarter after 9 ____________ c) 8:30 _______________ d) twelve forty-five ____________ l hoo ➤ A clock with numbers and hands is an analog clock. 5 o’ clock 5:00 me At Sc At Ho Practice 1. Read the time on each analog clock. Write the same time on the digital clock. a) b) 3 45 c) 11 30 d) 2 15 11 00 2. Write each time in a different way. a) quarter after 12 __________ b) 7:45 ___________________ c) nine o’clock _____________ d) three thirty _____________ e) 7:15 ___________________ f) half past one ____________ g) six forty-five ____________ h) quarter to four __________ 3. Caleb did push-ups for 15 minutes. He started at 4:30. At what time did he finish? ____________________________________ Stretch Your Thinking Millie started baking at 3:45. She finished at 5:00. How long did Millie spend baking? Explain how you know. _______________________________________________________________ _______________________________________________________________ _______________________________________________________________ 57 TU T D E N B OO 3 K S UNIT 4 Telling Time LESSO N Quick Review 8 o’clock 8:00 5 minutes after 8 o’clock 8:05 5 35 This analog clock shows 50 minutes after 12 o’clock or 10 minutes before 1 o’clock 12:50 This digital clock shows 35 minutes after 5 o’clock 5:35 It is twelve fifty or ten to one. It is five thirty-five. Try These Write the time shown on each analog clock. a) b) _______ 58 c) _______ _______ l hoo It takes 5 minutes for the minute hand to move from one number to the next number. 1. me At Sc At Ho Practice 1. Write each time two different ways. a) b) c) _______ _______ _______ __________________ __________________ __________________ 2. Skip count to find how many minutes are between each pair of times. a) 6:15 and 6:20 _______________ b) 8:10 and 8:40 _______________ c) 2:40 and 2:55 _______________ d) 12:00 and 12:30 _____________ 3. Read the time on the analog clock. Write the same time on the digital clock. 3 45 4. What is another way you could write twenty-five to seven? ________________________________________________________________ Stretch Your Thinking Lester left the library at 20 minutes before 5:00. Show the time on the digital clock. 4:40 4 40 59 TU T D E N B OO 4 K S UNIT 4 Elapsed Time LESSO N Quick Review me At Sc At Ho l hoo The amount of time from the start to the end of an activity is the elapsed time. Oscar practised on his drums from 2:30 P.M. to 3:05 P.M. To find the elapsed time in minutes, count on by 5s. Oscar practised for 35 minutes. 30 25 20 11 35 12 End 1 10 2 3 9 15 4 8 7 10 5 6 5 Start Try These Use a clock to help you. 1. Find each elapsed time. Write the answer in minutes. a) 2:40 P.M. to 2:55 P.M. ___________________________________________ b) 6:05 A.M. to 6:40 A.M. ___________________________________________ c) 7:55 P.M. to 8:35 P.M. ___________________________________________ d) 11:45 A.M. to 12:25 P.M. _________________________________________ 2. Tell what time it will be 25 minutes later. 60 a) It’s 4:30 P.M. __________ b) It’s 1:25 P.M. __________ c) It’s 8:20 A.M. __________ d) It’s 5:15 A.M. __________ Practice 1. Play this game with a partner. You will need: 2 play clocks 2 markers 1 number cube labelled 1 to 6 Go ahead 15 minutes Go back 5 minutes Time Time Start Finish Go ahead 10 minutes Time Go back 10 minutes Time ➤ Show 4:00 on your play clock. Go ahead ➤ Put your markers on Start. 30 minutes ➤ Take turns: • Roll the number cube. Time Move your marker that many spaces. • If you land on a Time space, change the time on your clock. Read the new time. ➤ Keep playing until you reach Finish. ➤ Find the elapsed time between 4:00 and the new time on your clock. Go ahead ➤ The player with the greater elapsed 25 minutes time wins. Time Go back 15 minutes Go ahead 20 minutes Time Time Stretch Your Thinking It is 11:20 P.M. What time will it be in 2 hours 25 minutes? __________ 61 TU T D E N B OO 5 K S UNIT 4 Telling Time to the Minute LESSO N Quick Review 9:25 9:26 5 You can read times after the half-hour in different ways. 12 52 minutes after 4 o'clock or 4:52 1 2 10 3 9 4 8 7 6 8 minutes before 5 o'clock or 8 minutes to 5 5 Try These Write the time shown on each clock. a) b) ____________ c) ____________ ____________ 2. Show the time on each clock. a) b) 9:58 62 c) 3:39 10:21 l hoo When the minute hand moves from one mark on the clock to the next mark, it takes 1 minute of time. 1. me At Sc At Ho Practice 1. Write each time two different ways. a) b) _______________________ _______________________ _______________________ _______________________ 2. Show the time on each digital clock. a) quarter to five b) half past eleven 4:45 4 45 11:30 11 30 c) quarter past six 6:15 6 15 3. Write something you might be doing at each time. a) 12:04 P.M. ____________________________________________________ b) 3:58 A.M. _____________________________________________________ c) 9:25 P.M. _____________________________________________________ Stretch Your Thinking The sum of the digits on this digital clock is 15. At what other times will the digits add up to 15? Give at least 2 answers. 5 37 ___________________________________________________________________ 63 TU T D E N B OO 6 The 24-Hour Clock K S UNIT 4 LESSO N This is a 24-h clock. There are 24 h in one day. From midnight to noon, the hours are from 0 to 12. From 1 P.M. to midnight, the hours are from 13 to 24. 24 13 11 12 1 22 14 10 2 21 9 3 15 8 4 20 7 6 5 16 19 18 hoo l 23 me Quick Review At Sc At Ho 17 When we use the 24-h clock, we use 4 digits to write the time. 10:15 A.M. is written 10:15. 23 24 13 11 12 1 14 10 2 21 9 3 15 8 4 20 7 6 5 16 22 19 18 6:30 A.M. is written 06:30. 24 23 11 12 1 14 10 2 21 9 3 15 8 4 16 20 7 6 5 19 18 23 13 22 17 6:30 P.M. is written 18:30. 24 13 11 12 1 14 10 2 21 9 3 15 8 4 16 20 7 6 5 17 22 19 18 17 Try These 1. Write each time using a 24-h clock. a) 8:10 A.M. b) 12:00 noon c) 10:20 P.M. 2. Write each time using A.M. or P.M. a) b) 6 12 ________________ 64 c) 10 55 __________________ 13 43 ________________ Practice 1. Write each time using a 24-h clock. Assume it is past noon. a) 23 24 13 b) 11 12 1 14 22 10 2 21 9 3 15 8 4 16 20 7 6 5 19 18 23 24 13 c) 11 12 1 22 14 10 2 21 9 3 15 8 4 20 16 7 6 5 19 17 18 23 24 13 d) 11 12 1 22 14 10 2 21 9 3 15 8 4 20 7 6 5 16 19 17 18 23 24 13 11 12 1 14 10 2 21 9 3 15 8 4 20 7 6 5 16 22 19 17 18 17 2. Write each time using A.M. or P.M. a) 07:14 b) 11:47 c) 15:58 d) 04:44 3. What time is it? a) 2 h after 17:25 b) 7 h after 18:45 c) 6 h before 14:30 d) 12 h before 07:21 e) 20 min after 11:55 f) 45 min after 23:00 4. Gerald arrived at school at 09:03. School starts at 09:00. How late was Gerald? 5. Shu Ying started running on the treadmill at 07:45. She stopped at 08:02. How long did Shu Ying run? 6. Mr. Albert fell asleep at 23:30 and slept for seven and one-quarter hours. At what time did he wake up? Stretch Your Thinking Amanjeet left Winnipeg, MB, at 16:55 on Oct. 26. When she arrived in Edmonton, AB, her watch showed 08:05, Oct. 27. How long was the trip? 65 TU T D E N B OO 7 K S UNIT 4 Covering Shapes LESSO N Quick Review Try These 1. a) Use yellow Pattern Blocks to find the area of this shape. Record the area in the table. b) Repeat using red, blue, and green Pattern Blocks. Area in Pattern Blocks 3 Yellow Pattern Block Red Pattern Block 6 Blue Pattern Block 9 Green Pattern Block 18 Unit 66 The unit is 1 blue Pattern Block. The area is 3 blue Pattern Blocks. l hoo The number of units needed to cover a shape is the area of the shape. The units must be the same size. The units must be congruent. To find the area of a shape, count how many units cover it. The unit is 1 green Pattern Block. The area is 4 green Pattern Blocks. me At Sc At Ho Practice 1. a) Estimate the area of the hexagon in red Pattern Blocks. Then find the area in red Pattern Blocks and record it in the table. b) Repeat the activity with blue and green Pattern Blocks. Pattern Area in Block Estimate Pattern Unit Blocks red 10 8 blue 14 12 green 30 24 2. Use this grid. Draw a shape with area 3 red Pattern Blocks. Stretch Your Thinking Suppose a shape has an area of 5 yellow Pattern Blocks. What is its area in red Pattern Blocks? ____________________________________ In blue Pattern Blocks? ________________________________________________ 67 TU T D E N B OO 8 K S UNIT 4 Exploring Area LESSO N Quick Review me At Sc At Ho l hoo To find the area of a shape, count the number of square units needed to cover it. The area of this shape is 5 square units. To find the area of a rectangle, you can count the number of square units or you can multiply. There are 2 rows of 5 squares. 2 5 = 10 The area of this rectangle is 10 square units. Try These Find the area of each shape in square units. 1. a) b) _______ square units c) _______ square units _______ square units 2. Write a multiplication fact to find the area of each rectangle. a) b) _______________ 68 c) _______________ _______________ Practice 1. Play this game with a partner. You will need: 2 number cubes 2 pencil crayons of different colours Take turns: ➤ Roll the cubes. Add the numbers to get an area in square units. ➤ Colour a shape with that area on the grid. ➤ No shape can overlap another shape. ➤ If there is no room left for your shape, you lose your turn. ➤ Continue until there is no more room on the grid. Stretch Your Thinking Find the total area you coloured on the grid. Then find the total area your partner coloured. Who coloured the greater area? ___________________________________________________________________ ___________________________________________________________________ ___________________________________________________________________ 69 TU T D E N B OO 9 K S UNIT 4 Measuring Area in Square Centimetres LESSO N Quick Review Every square has an area of one square centimetre (1 cm2). You can use square centimetres to measure area. The area of this shape is 3 cm2. Try These Find the area of each rectangle in square centimetres. a) b) Area = _______ 70 c) Area = _______ Area = _______ l hoo Each side of every square on this grid paper is 1 cm long. 1. me At Sc At Ho Practice 1. Write the area inside each shape in square centimetres. C A B D E F 2. Draw three different rectangles with area 12 cm2. Stretch Your Thinking The area of a square is 25 cm2. What are its length and width? ___________________________________________________________________ 71 UNIT 4 TU T D E N B OO S K 10 Estimating and Measuring Area LESSO N Quick Review * * Try These Find the approximate area of each polygon. a) b) Area = about _______ Area = about _______ 72 l hoo This is one way to find the approximate area of a triangle. ➤ Count each whole square. X There are 8 whole squares. ➤ Count each half square. X X X There are 4 half squares. This equals 2 whole squares. X X X X ➤ Count each part greater than 12 a square as 1 square. This triangle has an area There are 2 parts of about 12 cm2. 1 greater than 2 a square. ➤ Ignore each part less than 12 a square. ➤ Add to find the total number of squares: 8 + 2 + 2 = 12 1. me At Sc At Ho Practice 1. Draw a large clown’s head on the grid. Use as many different polygons as you can. Find the approximate area of each part of the head. Nose Mouth One Eye Whole Head Approximate Area Stretch Your Thinking Explain how you would find the approximate area of a leaf. ___________________________________________________________________ ___________________________________________________________________ 73 UNIT 4 TU T D E N B OO S K 11 Finding Area in Square Metres LESSO N Quick Review me At Sc At Ho l hoo A square with side lengths of 1 m has an area of one square metre (1 m2). You can use grid paper to model a large area. Each square represents 1 m2. 8m represents 1 square metre This is a model of a strawberry patch. It is 7 m wide and 8 m long. The model has 7 rows of 8 squares. 7 × 8 = 56 7m The area of the strawberry patch is 56 m2. Try These 1. Find the area of each garden. Each square has an area of 1 m2. 1m 2m 4m a) Area = _______ 2m 6m 2m b) Area = _______ c) Area = _______ 2. Put the rectangles in question 1 in order from least to greatest area. _______________________________________________________________ 74 Practice 1. Here are the dimensions of each of Sheila’s rectangular gardens. Model each of the gardens on the grid. ➤ Find the area of each garden. ➤ On each model, record the area and the type of flowers. Sheila’s Gardens Flowers Width Length Roses 7m 3m Wildflowers 5m 4m Pansies 1m 8m Petunias 6m 4m 10 m 2m Daisies represents 1 m2 Stretch Your Thinking Sheila has a rectangular pumpkin patch with area 36 m2. The patch is 4 m wide. How long is it? ___________________________________________________________________ 75 UNIT 4 TU T D E N B OO S K 13 Exploring Rectangles with Equal Areas LESSO N Quick Review = 1 m2 Try These Find the area of each rectangle. a) b) c) = 1 cm2 1 cm2 1 cm2 Area = _______ Area = _______ 2. Draw all rectangles with an area of 12 cm2. 76 Area = _______ l hoo Different rectangles can have equal areas. Each rectangle below has an area of 10 m2. 1. me At Sc At Ho Practice 1. Work with a partner. ➤ Draw a rectangle on the grid. ➤ Record the area on the rectangle. Your partner draws a different rectangle with the same area, and records the area. ➤ Switch roles and repeat. Continue the game until the grid is full. = 1 cm2 Stretch Your Thinking Draw two rectangles on the grid, each with an area of 1 cm2. 77 TU T D E N B OO 1 K S UNIT 5 Xxx Fractions of a Whole LESSO N Quick Review me At Sc At Ho l hoo ➤ Fractions describe equal parts of a whole. 3 equal parts are thirds. 1 is shaded. 3 5 equal parts are fifths. 4 are shaded. 5 The denominator tells how many equal parts are in 1 whole. 8 equal parts are eighths. 5 are shaded. 8 The numerator tells how many equal parts are counted. 5 8 ➤ A proper fraction represents an amount less than 1 whole. 5 is a proper fraction. 8 Try These 1. Write a fraction to tell what part of each shape is shaded. a) b) c) _______ _______ 2. Colour some of the equal parts of each shape. Write a fraction to describe the coloured parts. a) b) ____ c) d) _______ 78 _______ _______ Practice Play this game with a partner. You will need: 2 number cubes labelled 1 to 6 2 pencil crayons or crayons of different colours Take turns making fractions. ➤ Roll the number cubes. Use the greater number as the denominator. ➤ Find a shape on the game board that can be used to show your fraction. Colour the shape. Write the fraction. ➤ If there is no shape that can be used, you lose your turn. ➤ Keep playing until all the shapes are coloured. Stretch Your Thinking This shape represents 53 of one whole. Show what the whole might look like. 79 TU T D E N B OO 2 K S UNIT 5 Fraction Benchmarks LESSO N Quick Review me At Sc At Ho l hoo This number line shows the benchmarks 0, 12, and 1. 0 1 1 2 You can use number lines to find which benchmark a fraction is closer to. 7 is 8 closer to 1. 5 12 is closer to 12. It is a little less than 21. 1 6 is closer to 0. 0 1 2 0 0 5 12 1 6 7 8 1 1 2 1 1 2 1 Try These 1. Colour each strip to show a fraction. Write whether the fraction is closer to 0, 12, or 1. a) 0 1 2 1 Closer to ________ b) 0 1 2 Closer to ________ 2. A trash can is not quite full. Write a fraction that might tell how full it is. ___________________________________________________________ 80 1 Practice Play this game with a partner. You will need: index cards with these fractions written on them: 1 2 1 2 3 4 1 2 4 5 1 2 3 5 6 7 1 2 4 5 7 8 10 11 , , , , , , , , , , , , , , , , , , , , , , , 3 3 5 5 5 5 6 6 6 6 8 8 8 8 8 8 12 12 12 12 12 12 12 12 a paper bag strips of paper 15 cm long crayons Put the fraction cards in the bag. Take turns. ➤ Draw a card from the bag. ➤ Estimate whether the fraction is closer to 0, 12, or 1. ➤ Fold and colour a paper strip to show the fraction. ➤ Line up your strip with this number line to check your estimate. 0 1 2 1 ➤ You get a point if your estimate was right. ➤ Your partner gets a point if your estimate was wrong. ➤ Keep playing until one player has 10 points. Stretch Your Thinking 1. Name a fraction between 0 and 21 that is neither closer to 0 nor closer to 21. _______________________________________________________________ 1 1 2. Name a fraction that is between 2 and 1 that is neither closer to 2 nor closer to 1. ________________________________________________________________ 81 TU T D E N B OO 3 K S UNIT 5 Exploring Fractions of a Set LESSO N Quick Review ➤ There are 8 buttons. 6 of the 8 buttons are white. 6 of the buttons are white. 8 2 of the buttons are black. 8 ➤ There are 9 fish bowls. 7 of the 9 fish bowls have a fish. 7 of the fish bowls have a fish. 9 2 of the fish bowls are empty. 9 Try These What fraction of each set is shaded? a) b) _________ c) _________ d) __________ __________ 2. Here are the children who signed up for the chess club. What fraction are boys? __________ What fraction of the children are girls? __________ 82 l hoo To find a fraction of a set, start by counting. 1. me At Sc At Ho Practice 1. Colour some of the fish in each set. Write to tell what fraction you coloured. a) b) ___________ c) ___________ d) ___________ ___________ 2. a) Marvin has 8 pets. 2 of the pets are cats. 8 3 of the pets are dogs. 8 The rest are hamsters. Draw Marvin’s pets. b) Suppose Marvin gets 1 more cat. What fraction of his pets will be cats? ______________________________ Stretch Your Thinking Three of Sally’s pencils are broken. That’s 1 quarter of Sally’s pencils. How many pencils does Sally have? Use pictures, words, and numbers to show your answer. ________________________________ 83 TU T D E N B OO 4 K S UNIT 5 Finding a Fraction of a Set LESSO N Quick Review 1 4 of 8 = 2 4 4 3 4 of 8 = 6 1 6 1 6 of 8 = 8 5 Here is a way to find 6 of 18. 1 6 1 6 1 6 of 18 = 3 5 6 1 6 1 6 of 18 = 15 Try These Draw a picture to show the fraction of each set. 1. 2. 1 of 10 = _______ 2 3. 4. 4 of 15 = _______ 5 84 2 of 9 = _______ 3 1 of 12 = _______ 4 l hoo You can use fractions to show equal parts of a set. The denominator lets us know we are counting sixths. Divide 18 counters into 6 equal groups to show sixths. me At Sc At Ho Practice 1. Write a fraction for the shaded part of each set. a) b) ______________ c) _______________ ______________ 2. Use counters to find the fraction of each set. 1 a) 2 of 14 = _______ 2 b) 6 of 18 = _______ 3 c) 5 of 15 = _______ 3 d) 8 of 16 = _______ 3 e) 4 of 12 = _______ 6 f) 1 0 of 20 = _______ 7 g) 7 of 14 = _______ 7 h) 8 of 24 = _______ 2 i) 3 of 15 = _______ 3. On Pet Day, 18 children brought a pet to school. Two-thirds of the pets were dogs. One-ninth of the pets were cats. a) How many dogs were there? _______ b) How many cats were there? _______ c) How many animals were neither dogs nor cats? _______ Stretch Your Thinking 1. Choose letters from the box. 1 a) Write a word that uses 2 of the letters. ____________________________________________ 3 b) Write a word that uses 5 of the letters. ____________________________________________ T A I L U M R O E S 85 T E N T B OO UD 5 K S UNIT 5 LESSO N Relating Fractional Parts of Different Wholes and Sets Quick Review 3 Three-quarters of the big circle is greater than 4 of the small circle. ➤ 3 3 of 15 counters are greater than of 10 counters. 5 5 3 3 of 15 counters of 10 counters 5 5 are 9 counters. are 6 counters. Try These 1. Draw a picture to show that: 1 1 a) 2 of one pizza is less than 2 of another pizza. 5 5 b) 6 of one group of birds is greater than 6 of another group of birds. 86 l hoo When 2 wholes have different sizes, the same fraction of the whole is different for each whole. ➤ me At Sc At Ho Practice 1. 1 Colour each strip to show 4 . 1 Circle the strip that shows a shorter length to represent 4 . 4 2. Colour 5 of each set of balloons. 4 Circle the set in which 5 represents a greater amount. 2 3. Draw a picture to show that 3 of one set of counters is greater than 2 of another set of counters. 3 Stretch Your Thinking Use 2 strips of paper of different lengths. 5 Fold and colour each strip to show 8. Paste the strips below. 5 Circle the one in which 8 represents a lesser amount. 87 TU Comparing and Ordering Unit Fractions T D E N B OO 7 K S UNIT 5 LESSO N Quick Review ➤ With different unit fractions, the equal parts of the whole have different sizes. 1 5 5 equal parts in the whole 1 8 8 equal parts in the whole Fifths are greater than eighths. 1 1 So, 5 > 8 1 1 1 ➤ Order these unit fractions from greatest to least: 7, 1 0, 2 1 is the greatest because halves are greater than sevenths and tenths. 2 1 is the least because tenths are smaller than sevenths. 10 1 1 1 From the greatest to least: 2, 7, 1 0 Try These Use > or < to compare each pair of fractions. a) 1 3 1 6 b) 1 9 1 4 2. Order these fractions from least to greatest. 88 a) 1, 1, 1 6 3 8 b) 1, 1, 1 4 2 5 c) 1, 1, 1 7 12 10 d) 1, 1, 1 9 3 7 c) 1 5 1 2 l hoo A fraction with a numerator of 1 is a unit fraction. 1 1 1 , , and are unit fractions. 3 8 1 1. me At Sc At Ho Practice 1. Work with a partner. You will need crayons and four strips of paper of the same length for each person. ➤ Each of you folds a strip into any number of equal parts. Colour one of the parts to show a unit fraction. ➤ Show your strip to your partner and name the fraction. ➤ Compare the fractions by lining the strips up one below the other. ➤ On the lines below, record a fraction sentence using >, <, or =. ➤ Repeat with three more pairs of strips. a) ________________ b) ________________ c) ________________ d) ________________ 2. Order these numbers from least to greatest. 1 a) 81, 11 4, 3 1 1 1 b) 1 0, 4, 6 c) 1, 1, 1 3 4 2 d) 1, 1, 1 6 7 4 3. Stivi and Zach each ordered a medium pizza. 1 1 Stivi ate 3 of the pizza and Zach ate 4 of his pizza. Who ate more? Explain. ________________________________________________________________ Stretch Your Thinking 1. Write a unit fraction to make each statement true. a) 1 > 9 e) ___ ____ < 1 5 b) 1 < 3 f) ____ > ____ 1 9 c) ___ > g) 1 < 10 1 8 ____ d) 1 > 7 h) ____ > 41 ____ 89 Comparing and Ordering Fractions with the Same Numerator or Denominator T E N T B OO UD 8 K S UNIT 5 LESSO N Quick Review 2 4 1 1 has the fewest parts, so it is the least. 5 4 2 1 From greatest to least: 5, 5, 5 2 2 2 ➤ Here are two ways to order 5, 3, and 6 from least to greatest. The fractions have the same numerator but different denominators, so the parts being counted have different sizes. ● Use number lines. ● Use strips. 2 5 2 3 0 0 1 5 1 1 3 1 2 6 1 5 1 5 1 6 1 1 5 1 5 1 3 1 6 1 6 1 3 1 6 1 6 1 6 2 2 2 From least to greatest: 6, 5, 3 Try These 1. 3 3 0 1 0 1 0 1 From greatest to least: 90 3 Use the number lines to order 8, 4, and 6. l hoo ➤ Here is one way to order 5, 5, and 5 from greatest to least. The fractions have the same denominator, so the parts being counted have the same size. 4 has the most parts, so it is the greatest. 5 0 me At Sc At Ho Practice 1. Colour the strips to show the fractions. Use > or < to compare the fractions. a) 3 5 3 4 b) 4 10 2 3 10 2 2. Estimate to place 8 and 4 on the number line. 0 1 Which fraction is greater? 4 4 4 3. Use the 3 number lines to order 8, 6, 5. 0 1 0 1 0 1 From least to greatest: Stretch Your Thinking Fold and colour paper strips to show each pair of fractions. Use < or > to compare the fractions. a) 4 8 __ 4 6 b) 53 __ 3 4 2 c) 3 __ 2 5 91 TU T D E N B OO 9 Exploring Tenths K S UNIT 5 LESSO N Quick Review ➤ ➤ You can write the fraction as a decimal using a symbol, the decimal point. 3 is the same as 0.3. We say 0.3 as “zero and three-tenths.” 10 This is the decimal point. 3 Since 1 0 , or 0.3, is less than 1 whole, we write 0 before the decimal point to show there is no whole number part. ➤ You can also use a place-value chart to show a decimal. Tenths 0 3 The decimal point is between the ones place and the tenths place. Try These 1. Write a fraction and a decimal for each group of Base Ten Blocks shown. a) _________ b) _________ c) _________ 2. Write each fraction as a decimal. 7 a) 1 0 _______ 92 2 b) 1 0 _______ 8 c) 1 0 _______ l hoo 3 You can use Base Ten Blocks to model 1 0. Ones me At Sc At Ho Practice 1. Play this game with a partner. You will need: 24 small counters 1 number cube 0.1 9 10 8 10 0.3 7 10 6 10 5 10 4 10 0.6 0.7 0.1 3 10 2 10 1 10 Player A 0.4 0.2 2 game markers 0.2 0.4 0.9 0.8 Each player selects a strip to the right or the left of the game board. The object of the game is to play until one of you covers all the numbers on your strip. ➤ Put your markers on Start. ➤ Take turns rolling the number cube. Move that number of spaces in either direction. ➤ Put a counter on your strip on the fraction that names the same amount as the decimal you landed on. ➤ The first one to cover a full strip wins. 0.5 START 0.5 9 10 0.7 8 10 7 10 0.4 0.8 0.9 6 10 5 10 4 10 3 10 0.6 2 10 1 10 0.3 Player B Stretch Your Thinking Place each decimal on the number line. 0.4 0.7 0.1 0.9 0.2 0 1 93 UNIT 5 TU T D E N B OO S K 10 Exploring Hundredths LESSO N Quick Review ➤ We can use decimals to write parts of one dollar. 1 dollar = 100 cents 1 So, 1 cent = 100 dollar, or 0.01 dollar. Here are 23 cents. 2 3 23 cents = 100 dollar We write this as 23¢ or $0.23. Try These Write a fraction and a decimal for the shaded part of each picture. a) b) c) 2. Write each fraction as a decimal. 94 4 8 a) 100 _______ 7 b) 100 _______ 6 c) 100 _______ 17 d) 100 _______ 67 e) 100 _______ 5 f) 100 _______ l hoo ➤ This grid is divided into 100 equal squares. Each square is one-hundredth of the grid. Three-hundredths of the grid are shaded. 3 We can write this as 100 or 0.03. 1. me At Sc At Ho Practice 1. Colour the grids to show the numbers. a) 0.09 b) 0.43 c) 0.02 70 d) 100 2. Write each decimal as a fraction. a) 0.24 __________ b) 0.93 __________ c) 0.80 __________ d) 0.27 __________ e) 0.01 __________ f) 0.4 __________ 3. Draw pictures of dimes and pennies to show each amount. $0.33 4. Write each amount as a decimal. a) 84¢ b) 7 cents $0.19 c) 15¢ Stretch Your Thinking Carlos said that 0.30 is greater than 0.3 because 30 is greater than 3. Is he correct? Use pictures to support your answer. _________________________________ _________________________________ _________________________________ _________________________________ 95 UNIT 5 TU T D E N B OO Equivalent Decimals S K 11 LESSO N Quick Review me At Sc At Ho One row of this hundredths grid is one-tenth of the grid. Each small square is one-hundredth of the grid. l hoo =1 70 squares are 70 hundredths. 7 rows are 7 tenths. 0.7 0.70 Both 0.7 and 0.70 name the shaded part of the grid. So, 0.7 = 0.70 Decimals that name the same amount are called equivalent decimals. Try These 1. Write two equivalent decimals that name each shaded part. a) b) _____ _____ c) _____ _____ d) _____ _____ _____ _____ 2. Write an equivalent decimal for each number. a) 0.6 ________ b) 0.70 _______ c) 0.90 _______ d) 0.5 ________ e) 0.80 _______ f) 0.1 ________ g) 0.30 _______ h) 0.60 _______ 0.40 _______ j) 0.2 ________ k) 0.50 _______ l) i) 96 0.10 _______ Practice 1. Colour the grid to show each decimal. Write an equivalent decimal. a) 0.3 ____________ b) 0.80 ____________ c) 0.6 ____________ 2. Play this game with a partner. You will need: 9 pairs of cards with 2 equivalent decimals (0.1 and 0.10 to 0.9 and 0.90). ➤ Shuffle the cards and turn them face down on a table in 3 rows of 6. ➤ Take turns to turn over 2 cards. If the cards name equivalent decimals, keep the cards and play again. If the cards do not name equivalent decimals, turn them face down again. ➤ Play until there are no cards left on the table. ➤ The player with the most cards wins. Stretch Your Thinking Gabriel is making a design on a hundredths grid. He says he will colour 0.6 of the grid red, and 0.6 black. Will Gabriel’s plan work? Explain. ___________________________________________________________________ ___________________________________________________________________ ___________________________________________________________________ 97 UNIT 5 TU Adding Decimals to Tenths T D E N B OO S K 12 LESSO N Quick Review ➤ To estimate 3.6 + 1.9, find a whole number close to each decimal. 3.6 is close to 4. 1.9 is close to 2. 4+2=6 So 3.6 + 1.9 is about 6. ➤ Use Base Ten Blocks to add. Tenths Ones Tenths 3.6 10 tenths equal 1 whole. 1.9 3.6 + 1.9 = 5.5 ➤ Use place value to add. Add the tenths: 10 tenths equal 1 whole. 15 tenths That’s 1 and 5 tenths. 3.6 + 1.9 1 3.6 + 1.9 .5 Add the ones. 1 3.6 + 1.9 5.5 Try These Estimate each sum. 1. a) 2.8 + 3.4 _________ b) 5.9 + 2.8 ________ c) 4.3 + 5.2 ________ 2. Add. Use Base Ten Blocks to help you. a) 3.2 + 4.5 = _______ b) 6.6 + 2.4 = _______ c) 3.5 + 8.7 = _______ 98 l hoo You can use whole number strategies to add decimals. Ones me At Sc At Ho Practice 1. Add. Use Base Ten Blocks or pictures of the blocks to help you. a) 1.7 + 4.9 = _______ b) 6.5 + 2.7 = _______ c) 3.9 + 8.6 = _______ d) 3.8 + 2.7 = _______ e) 2.4 + 6.3 = _______ f) 4.1 + 6.4 = _______ 2. Use place value to find each sum. a) 4.2 + 2.3 b) 1.7 + 5.6 c) 7.3 + 2.8 d) 2.3 + 1.6 e) 6.4 + 9.7 f) 7.4 + 8.6 g) 3.7 + 1.9 h) 8.2 + 3.8 i) 5.7 + 6.7 j) 3.2 + 9.8 3. Kruti jogged 2.8 km on Saturday and 1.9 km on Sunday. How far did she jog altogether? ________________________________________________________________ 4. Alexander grew two pumpkins in his garden. One had a mass of 4.7 kg. The other had a mass of 3.6 kg. What was the total mass of both pumpkins? ________________________________________________________________ 5. Sally had 3.4 L of orange juice and 2.7 L of grape juice. How much juice did she have altogether? ________________________________________________________________ Stretch Your Thinking 1. a) Write two decimals whose sum is approximately 5. _____________________________________________________________ b) Write two decimals whose sum is closer to 1 than 2. _____________________________________________________________ 99 UNIT 5 TU Subtracting Decimals to Tenths T D E N B OO S K 13 LESSO N Quick Review 4.2 is close to 4. 1.7 is close to 2. 4–2=2 So 4.2 – 1.7 is about 2. ➤ Use Base Ten Blocks to subtract. Tenths Ones Tenths Trade 1 whole for 10 tenths. 4.2 – 1.7 = 2.5 ➤ Use place value to subtract. Try to subtract the tenths. You cannot take 7 tenths from 2 tenths. 4.2 – 1.7 Trade 1 whole for 10 tenths. Subtract the tenths. Subtract the ones. 3 12 3 12 3 12 4.2 – 1.7 4.2 – 1.7 .5 4.2 – 1.7 2.5 Try These 1. Estimate each difference. a) 5.8 – 2.9 ________ b) 8.1 – 3.2 ________ c) 2.1 – 0.9 ________ 2. Subtract. a) 8.4 – 3.2 = _______ b) 7.9 – 4.2 = _______ c) 6.4 – 2.5 = _______ 100 l hoo You can use whole number strategies to subtract decimals. ➤ To estimate 4.2 – 1.7, find a whole number close to each decimal. Ones me At Sc At Ho Practice 1. Subtract. Use Base Ten Blocks or pictures of the blocks to help you. a) 7.4 – 2.3 = _______ b) 2.7 – 0.8 = _______ c) 4.2 – 3.8 = _______ d) 4.9 – 2.6 = _______ e) 5.2 – 3.7 = _______ f) 0.9 – 0.2 = _______ g) 4.8 – 3.7 = _______ h) 6.4 – 5.8 = _______ i) 3.6 – 0.7 = _______ 2. Use place value to find each difference. a) 9.3 b) 10.2 c) 14.8 – 6.4 f) 8.4 – 0.9 – 3.6 g) 3.8 – 1.2 d) 8.5 – 0.7 e) 6.4 – 2.8 i) 12.6 – 9.9 j) 10.4 – 3.7 – 6.9 h) 7.5 – 2.8 3. When Baily planted a new evergreen tree, the tree was 1.3 m tall. Now it is 2.1 m tall. How much has the tree grown? _____________________________________ 4. Symron lives 2.4 km from the movie theatre. Sofia lives 3.1 km from the theatre. How much farther away does Sofia live? ______________________________ 5. Stephanie had 1.8 L of water. After she drank some water, she had 1.3 L of water left. How much water did she drink? __________________ Stretch Your Thinking 1. a) Name two decimals whose difference is approximately 2. _____________________________________________________________ b) Name two decimals whose difference is between 2 and 3, but closer to 3. _____________________________________________________________ 101 UNIT 5 TU T D E N B OO S K 14 Adding and Subtracting Decimals to Hundredths LESSO N Quick Review me At Sc At Ho l hoo You can use different methods to add and subtract decimals to hundredths. ➤ You can use a place-value mat. ➤ You can count on. ➤ You can use place value. What is the change from $5 when you spend $3.52? Use place value and subtraction to find out. Line up the decimal points. Trade $1 for 10 dimes. Trade 1 dime for 10 pennies. Subtract the cents. 9 41010 $5.00 – 3.52 $5.00 – 3.52 Subtract the dollars. 4 9 10 4 9 10 $5.00 – 3.52 .48 $5.00 – 3.52 $1.48 The change from $5 is $1.48. Try These 1. Add or subtract. a) $2.49 +1.30 b) $4.26 +3.49 c) $9.32 – 4.50 d) $7.27 – 4.88 2. Find each sum or difference. a) $5.39 + $2.20 = _______ b) $1.49 + $7.37 = _______ c) $14.55 – $8.32 = _______ d) $10.00 – $8.23 = _______ 102 Practice 1. Find each sum. a) $6.70 + 2.85 b) $2.57 c) $6.85 d) $1.99 + 5.84 + 1.78 + 0.67 a) $6.74 b) $5.75 c) $7.00 d) $3.49 – 2.54 – 2.83 – 2.51 – 0.58 2. Find each difference. 3. Use the prices in the table to solve the problems. a) Yvonne bought a sun hat and beach towel. How much did she spend? ____________________________ Beach Supplies Sun Hat Sunglasses Beach Towel Beach Ball Flippers Sun Umbrella $5.79 $8.95 $9.85 $1.59 $4.67 $12.84 b) How much change did Yvonne get from $20? _______________ c) Sandy bought two items. She spent $13.62. Which two items did she buy? _____________________________________________________________ d) How much more does a sun umbrella cost than a beach towel? ________ e) How much do a beach ball and a sun umbrella cost altogether? _______ Stretch Your Thinking Malio bought two items listed on the Beach Supplies table. He got $2.62 change from $10. Which two items did he buy? __________________________________________ ___________________________________________________________________ 103 TU T D E N B OO 1 Xxx Objects in Our World K S UNIT 6 LESSO N Quick Review me At Sc At Ho Rectangular face Rectangular base l hoo Rectangular face Triangular base ➤ You can sort objects by the shapes of the bases. Rectangular bases Triangular bases ➤ You can sort objects by the shapes of the faces. Triangular faces All congruent faces Try These 1. Sort these objects. Use the letters to record your sorting. A B C E F G D Rectangular faces 104 Triangular faces Practice 1. Write the name of a prism to answer each riddle. a) I have 6 congruent faces. b) I have 3 rectangular faces and 2 triangular faces. c) I have 2 square bases and 4 square faces. 2. Look through old magazines or catalogues for 3 small pictures of objects that look like prisms. Cut them out and paste them here. Name the prism each object resembles. 3. Sort these objects. Use these attributes: “Has square bases” and “Has all congruent faces” Record your sorting. A B D E C Stretch Your Thinking Complete each sentence. a) All triangular prisms have b) All cubes have c) No rectangular prisms have 105 TU T D E N B OO 2 K S UNIT 6 Constructing Prisms LESSO N You can use modelling clay to build prisms. ➤ Rectangular prisms ➤ Triangular prisms Try These 1. Use modelling clay. Make a prism with each set of faces. Identify each prism. a) b) 106 me hoo l Quick Review At Sc At Ho Practice 1. Identify the object that has each set of faces. a) b) c) 2. Use modelling clay. Make a prism for each description. Identify the prism. a) It has 2 congruent triangle faces and 3 congruent rectangle faces. b) It has 2 congruent square faces and 4 congruent rectangle faces. c) It has 3 pairs of congruent rectangle faces. Stretch Your Thinking Make a prism with modelling clay. Describe the prism in as many ways as you can. 107 TU T D E N B OO 3 K S UNIT 6 Exploring Nets LESSO N Quick Review ➤ A triangular prism can also be made from a net. Try These Name the prism you could make with each net. a) 108 b) c) l hoo A pattern that can be folded to form an object is called a net. ➤ A rectangular prism can be made from a net. 1. me At Sc At Ho Practice 1. Circle the picture that shows a net for the prism named. a) cube b) rectangular prism c) triangular prism 2. Trace this net on paper, then cut it out. Decorate the net to look like a package for a product. Then fold and tape your package. Stretch Your Thinking Draw a net for a cube on the grid paper. Write the letters T and B on 2 faces of the net so that when the net is folded, the T will be on the top and the B on the bottom. 109 TU T D E N B OO 5 K S UNIT 6 Symmetrical Shapes LESSO N Quick Review A line of symmetry divides a shape into 2 congruent parts. You can fold along the line and the 2 parts match. You can use a Mira to check a line of symmetry. Some shapes have more than 1 line of symmetry. Some shapes have no line of symmetry. A rectangle has 2 lines of symmetry. This shape is non-symmetrical. Try These Colour the pictures that have 1 or more lines of symmetry. 110 l hoo Line of symmetry 1. me At Sc At Ho Practice 1. Label the shapes below as follows: A – no lines of symmetry C – 2 lines of symmetry B – 1 line of symmetry D – more than 2 lines of symmetry 2. Look at these numbers. a) Which numbers have no lines of symmetry? _______________ b) Which numbers have 1 line of symmetry? _______ c) Which numbers have more than 1 line of symmetry? _______ Stretch Your Thinking 1. Does a circle have more than 1 line of symmetry? Explain. ________________________________________________________________ ________________________________________________________________ 111 TU T D E N B OO 6 K S UNIT 6 Line Symmetry LESSO N Quick Review ➤ Draw a line of symmetry on dot paper. Draw one-half of a shape on one side of the line. ➤ Draw the other half of the shape on the other side of the line. Try These One-half of a symmetrical shape is shown. Complete the shape. a) 112 b) l hoo A symmetrical shape has one or more lines of symmetry. Here is one way to make a symmetrical shape. 1. me At Sc At Ho Practice 1. Work with a partner. One person draws one-half of a symmetrical shape on one side of the line. The other person completes the shape. 2. Find the shapes that are symmetrical. Draw the lines of symmetry. a) b) c) Stretch Your Thinking One-quarter of a symmetrical shape is shown. Complete the shape. 113 TU T D E N B OO 7 K S UNIT 6 Sorting by Lines of Symmetry LESSO N Quick Review When a line of symmetry can be drawn on a shape, it has symmetry. Some shapes have no lines of symmetry. Some shapes have more than one line of symmetry. 1 line of symmetry 4 lines of symmetry Try These 1. Is each broken line a line of symmetry? Write Yes or No. a) b) _______ 114 c) _______ _______ l hoo A line of symmetry divides a shape into two parts that are congruent. 0 lines of symmetry me At Sc At Ho Practice 1. Draw as many lines of symmetry on each shape as you can. a) b) c) 2. Work with a partner. Each of you draw one-half of a design on one side of the line of symmetry on your grid. Switch places and complete your partner’s design. Your Grid Your Partner’s Grid Line of symmetry Line of symmetry Stretch Your Thinking Complete the shape to make it symmetrical. 115 TU T D E N B OO 1 K S UNIT 7 Reading Pictographs and Bar Graphs LESSO N Quick Review Pictograph Symbols are used to show data in a pictograph. The key shows what each symbol stands for. Bar Graph Bars are used to show data in a bar graph. Numbers on the axis show the scale. Tickets Sold for Each Performance of the Fourth Grade Play vertical axis Tuesday Tuesday Wednesday Wednesday Thursday Friday Thursday Saturday Friday = 10 tickets Saturday horizontal axis 0 10 20 30 40 50 60 70 80 90 100 Number of Tickets For this pictograph, the key is represents 10 tickets. So, represents 5 tickets. In this bar graph, 1 square represents 10 tickets. So, 12 square represents 5 tickets. Try These Favourite Drinks Use the pictograph to answer these questions. 1. Which drink had the most votes? 2. Which drink had 12 votes? 3. How many votes did lemonade have? 116 Milk Juice Lemonade Water = 6 votes l hoo The title of a graph tells you what the graph is about. The labels on the axes tell you what data are shown in the graph. Tickets Sold for Each Performance of the Fourth Grade Play me At Sc At Ho Practice Pet Owners 1. This graph shows the number of pet owners Grade 1 in each grade at Parkdale School. a) Which grade has the most Grade 2 Grade 3 pet owners? _____________ Grade 4 Grade 5 b) Which grade has one-half as many Grade 6 pet owners as Grade 2? _____________ = 4 students c) How many pet owners did Grade 6 have? ___ 2. This graph shows the types of dwellings Types of Dwellings Number of Students the students in Enzo’s school live in. a) How many students live in condos? __________________ b) How many more students live in duplexes than condos? __________________ c) How many students live in condos and townhouses altogether? __________________ d) 26 girls live in apartments. How many boys live in apartments? __________________ 70 60 50 40 30 20 10 0 Ap t en tm ar o ily ex se nd pl ou am u h F Co D le wn ng To Si Dwellings Stretch Your Thinking How many students attend Enzo’s school? Show how you know. ___________________________________________________________________ ___________________________________________________________________ ___________________________________________________________________ 117 TU T D E N B OO 2 Drawing Pictographs K S UNIT 7 LESSO N Quick Review me At Sc At Ho l hoo Here are the results of a survey showing the favourite subjects of students in Kim’s class. Math Science Social Gym Writing Studies Number of Students 6 7 4 5 6 title Students' Favourite Subjects Here’s how Kim made a pictograph to display these data. To make sure her graph was not too large, Kim chose to represent 2 students. Kim completed the pictograph with a key, a label on the axis, and a title. Math Science vertical axis label Subjects Subject Social Studies Gym Writing = 2 students key symbol Try These 1. Suppose you drew a pictograph to represent the data in each table. What key would you use for each graph? a) Favourite Fruit Orange Number of Students 12 Eye Colour 25 40 6 Brown Banana 8 Grey 10 Key: _________________________ Number of People Blue Apple Grape 118 b) Green 5 15 Key: ____________________ Practice 1. Draw a pictograph to display these data. Names for Our Fish Bubbles Spotty Precious Ralph 20 10 5 10 Number of students 2. Finish the pictograph to display the data in the table. Birds Seen in the Park Birds Seen in the Park Bird Number Crow 4 Robin 12 Chickadee 14 Duck 20 Crow Robin Chickadee Duck = 4 birds Stretch Your Thinking Suppose the key on a pictograph is = 40 votes. What symbol would you draw to represent: 10 votes? _______________ 20 votes? _______________ 119 TU T D E N B OO 3 K S UNIT 7 Drawing Bar Graphs LESSO N Quick Review Student Votes Brown bear Cougar Eagle Coyote 40 60 75 35 Favourite Mascots for the Hockey Team 80 75 70 65 60 55 Student Votes Here’s how to draw a vertical bar graph to display the data in Arnie’s table. 1. Draw 2 axes. Label them “Animal” and “Student Votes”. 2. Count by 5s for the scale. The scale is 1 square represents 5 votes. 3. Draw a vertical bar for each animal in the table. 4. Write a title for the graph. Try These Use the data in this table to complete the graph. Ice-Cream Flavour Vanilla Chocolate Strawberry Number of People 40 75 50 a) Label the axes. b) Number the scale. c) Give the graph a title. 120 50 45 40 35 30 25 20 15 10 5 0 Brown bear Cougar Eagle Animal Coyote l hoo The students in Arnie’s school voted on a mascot for their school hockey team. Here is a table Arnie made to show how they voted. Animal me At Sc At Ho Practice 1. The students in Peter’s school voted for their favourite type of music. The results are displayed in this table. a) Draw a vertical bar graph to display these data. Type of Music Number of Students Rock Rap Hip Hop Pop 65 70 40 55 b) Write two things you know from looking at your graph. _____________________________________________________________ _____________________________________________________________ Stretch Your Thinking Your grid paper has 20 squares along one side. The greatest value you have to display on the graph is 150. What scale will you use? Explain. ___________________________________________________________________ ___________________________________________________________________ 121 D TU Comparing Pictographs and Bar Graphs E N T B OO 4 K S UNIT 7 LESSO N Quick Review Trees Planted in Victory Park Trees Planted in Victory Park Hickory Species Hickory Species Oak Willow Birch Willow 0 10 20 30 40 50 60 70 80 Number of Trees Birch represents 20 trees In the pictograph, symbols show the data. In the bar graph, bars show the data. From the pictograph, we use the key to determine the number of trees. From the bar graph, we use the scale to determine the number. Try These Use the data displayed in the graphs above. a) How many oak trees were planted in Victory Park? __________ b) What does on the pictograph represent? ___________ c) How many birch trees were planted? ___________ d) What is the scale on the bar graph? ________________________ e) How many more oak trees were planted than willow trees? _________ 122 l hoo These two graphs show the same data. Oak me At Sc At Ho Practice 1. Use the data in the bar graph. Walk-A-Thon Participants 26 24 22 20 18 16 14 12 10 8 6 4 2 0 b) Which group had the most people? ________________ Number of People a) How many people took part in the walk-a-thon? _____ c) How many more Brownies took part than Cubs? ____ __ d) Suppose you wanted to display these data as a pictograph. What key would you use? s de ui G s irl G ts es ni ou ow y Sc r B Bo bs Cu Groups ___________________________________ How many symbols would you need for the Girl Guides? ___________________ 2. This bar graph shows how long five of Canada’s Prime Ministers of Canada were in office. Prime Ministers' Time in Office 22 20 18 16 14 12 10 8 6 4 2 0 __________________________________ Who was in office the shortest time? ___________________________________ Number of Years a) Who was in office the longest time? b) Who was in office about 7 years longer than St. Laurent? __________________________________ r d al n do ac M A. . rJ Si __________________________________ ilfr S W ir rie u La ng zie Ki nt re u La n t. e ke is S ierr ac u P M Lo id u ea ud Tr Names Stretch Your Thinking Lester B. Pearson was Prime Minister from April, 1963 to April, 1968. How long was he in office?______________ Add this information to the graph in question 2 above. 123 TU T D E N B OO 1 K S UNIT 8 Exploring Multiplication Patterns LESSO N Quick Review You know 5 × 1 = 5. Use mental math to find 5 10 and 5 100. 5 × 1 ten = 5 tens 5 × 10 = 50 5 × 1 hundred = 5 hundreds 5 × 100 = 500 ➤ Use basic multiplication facts and place value to multiply by multiples of 10 and 100. You know 3 × 3 = 9. Use mental math to find 3 30 and 3 300. 3 × 3 tens = 9 tens 3 × 30 = 90 3 × 3 hundreds = 9 hundreds 3 × 300 = 900 Try These Multiply. Use Base Ten Blocks when they help. 1. a) 6 × 1 = _______ b) 8 × 1 = _______ 6 × 10 = _______ 8 × 10 = _______ 9 × 10 = _______ 6 × 100 = _______ 8 × 100 = _______ 9 × 100 = _______ b) 5 × 2 = _______ c) 4 × 2 = _______ 3 × 20 = _______ 5 × 20 = _______ 4 × 20 = _______ 3 × 200 = _______ 5 × 200 = _______ 4 × 200 = _______ 3. a) 8 × 4 = _______ 124 c) 9 × 1 = _______ b) 3 × 4 = _______ c) 5 × 4 = _______ 8 × 40 = _______ 3 × 40 = _______ 5 × 40 = _______ 8 × 400 = _______ 3 × 400 = _______ 5 × 400 = _______ l hoo ➤ Use place value to multiply by 10 and by 100. 2. a) 3 × 2 = _______ me At Sc At Ho Practice Find each product. Then fill in the boxes below with the letters that match the products. The words in the boxes will answer this riddle: Why do rabbits make good mathematicians? A 6 × 100 = _______ J 200 × 5 = _______ S 8 × 20 = _______ B 8 × 10 = _______ K 5 × 100 = _______ T 3 × 80 = _______ C 3 × 50 = _______ L D 80 × 7 = _______ M 9 × 10 = _______ V 5 × 10 = ______ U 7 × 50 = _______ 4 × 30 = _______ E 6 × 80 = _______ N 2 × 9 = _______ W 7 × 300 = _______ F 3 × 300 = _______ O 2 × 100 = _______ X 8 × 90 = _______ G 6 × 400 = _______ P 6 × 30 = _______ Y 4 × 200 = _______ H 5 × 60 = _______ Q 7 × 700 = _______ Z 9 × 50 = _______ 7 × 100 = _______ I R 3 × 10 = _______ ← ← ← ← ← ← ← ← ← ← ← 80 480 150 600 350 160 480 240 300 480 800 ← ← ← ← ← ← ← ← 90 350 120 240 700 180 120 800 Stretch Your Thinking There are 40 quarters in a roll. How many quarters are there in 10 rolls? ___________________________________________________________________ How many quarters are there in 100 rolls? ___________________________________________________________________ 125 TU T D E N B OO 2 K S UNIT 8 Estimating Products LESSO N Quick Review me At Sc At Ho l hoo Estimate to solve multiplication problems. ➤ A basket holds 23 apples. About how many apples do 5 baskets hold? To estimate 5 × 23 5 × 20 = 100 Think: 23 is close to 20. There are about 100 apples in 5 baskets. ➤ A bucket holds 28 tennis balls. About how many tennis balls do 7 buckets hold? To estimate 7 × 28 7 × 30 = 210 Think: 28 is close to 30. There are about 210 tennis balls in 7 buckets. Try These 1. Estimate each product. a) 4 × 29 b) 6 × 52 Estimate: __________ Estimate: __________ c) 5 × 81 Estimate: __________ 2. There are 48 crayons in a box. About how many crayons are there in 8 boxes? _________________________ 3. There are 9 chairs in each row. About how many chairs are there in 18 rows? __________________________ 4. Kara bought 27 packs of stickers. There are 8 stickers in each pack. About how many stickers does Kara have? _____________________________ 126 Practice 1. Estimate each product. a) 6 × 78 __________ b) 4 × 93 __________ c) 9 × 42 __________ d) 5 × 69 __________ e) 7 × 21 __________ f) 52 × 7 __________ g) 38 × 8 __________ h) 47 × 6 __________ i) 84 × 5 __________ 2. About how many gel pens would you have if you bought: a) 3 boxes? __________ b) 7 boxes? __________ c) 5 boxes? __________ d) 8 boxes? __________ 3. Bertha types 58 words a minute. About how many words can she type in: a) 5 minutes? ____________ b) 8 minutes? ____________ c) 30 minutes? ___________ 4. Estimate how many treats you would get from: a) 6 piñatas __________ b) 4 piñatas __________ c) 9 piñatas __________ d) 8 piñatas __________ Stretch Your Thinking Jack collects superhero trading cards. He has 5 collections with 22 cards each and 7 collections with 27 cards each. About how many cards does Jack have altogether? ___________________________________________________________________ ___________________________________________________________________ 127 TU T D E N B OO 3 K S UNIT 8 Using Models to Multiply LESSO N Quick Review ➤ Show an array on grid paper. 2 20 5 ← ← 5 rows of 20 = 100 5 rows of 2 = 10 Add. 100 + 10 = 110 Try These Use the models to multiply. b) 4 × 16 = _____ 3 × 15 = _____ 4 × 10 = _____ 3 rows of 10 = _____ ______________ __________________ ______________ __________________ 128 l hoo Here are two ways to use models to multiply 5 × 22. ➤ Use Base Ten Blocks. Arrange 5 groups of 22. Multiply the tens. 5 × 20 = 100 Multiply the ones. 5 × 2 = 10 Add. 100 + 10 = 110 1. a) me At Sc At Ho Practice 1. Multiply. Use grid paper or Base Ten Blocks when they help. a) 32 b) 42 c) 84 d) 71 e) ×4 f) 56 ×3 ×4 g) 19 ×5 ×2 h) 57 ×6 65 ×3 ×8 i) 48 ×4 j) 56 ×9 2. Play this game with a partner. You will need: 10 small pieces of paper with one of these numbers written on each piece: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 a small paper bag paper and pencil ➤ ➤ ➤ ➤ ➤ × Draw a multiplication grid like this on your paper. Put the numbered pieces of paper in a bag. Pull out 3 numbered pieces each. Record each digit in one of the boxes in your multiplication grid. Find your products. The player with the greater product wins a point. ➤ Play 5 rounds. ➤ Then, change the rules to make a new game. Record your digits in the boxes of your partner’s multiplication grid. Play 5 more rounds. Stretch Your Thinking The box to the right represents the game you just played. The digit boxes are represented by A, B, and C. Which digit box is the best place to write your highest number? Explain. A B × C _________________________________________________________________ _________________________________________________________________ 129 TU T D E N B OO 5 K S UNIT 8 Other Strategies for Multiplication LESSO N Quick Review Add. 360 24 = 384 ← ← ← ← ➤ Write the number in expanded form: 64 = 60 + 4 Multiply the tens and multiply the ones. Then add. 6 64 = (6 60) + (6 4) 24 = 384 ➤ Break the number apart. Multiply the ones: 6 4 Multiply the tens: 6 60 Add. So, 64 6 = 384 64 6 24 360 384 Try These Find each product. Show your work. 1. a) 27 8 = ______ b) 58 3 = ______ 2. a) 51 b) 8 130 35 6 c) 77 7 = ______ c) 6 3 2 l hoo Here are 3 ways to multiply: 64 6. ➤ Multiply the tens. Multiply the ones. 60 6 = 360 4 6 = 24 So, 64 6 = 384 360 + So, 64 6 = 384 me At Sc At Ho Practice Play this game with a partner. You will need: paper and pencils counters of 2 colours ➤ Take turns to choose one number from each number box. Multiply your 2 numbers and cover the product on the game board with a counter. ➤ Continue playing until one player covers 4 products in a vertical, horizontal, or diagonal line. 117 216 304 504 135 54 252 424 380 159 273 336 234 532 2 3 4 5 6 7 8 78 456 608 106 162 371 212 189 228 312 265 672 108 318 156 168 195 588 81 53 76 420 152 84 27 39 Stretch Your Thinking Which product is greater, 98 6 or 76 9? How much greater? ___________________________________________________________________ ___________________________________________________________________ ___________________________________________________________________ 131 TU T D E N B OO 6 Using Patterns to Multiply K S UNIT 8 LESSO N Quick Review ➤ Multiply: 6 52 Think: 89 is 1 less than 90. So, 7 89 is 7 less than 7 90. 7 90 = 630 Subtract 7. 630 – 7 = 623 So, 7 89 = 623 Think: 52 is 2 more than 50. So, 6 52 is 6 50 plus 6 2. 6 50 = 300 Add 6 2, or 12. 300 + 12 = 312 So, 6 52 = 312 Try These Use patterns to multiply. 1. a) 6 78 = _______ b) 4 29 = _______ c) 5 59 = _______ d) 7 68 = _______ e) 8 27 = _______ f) 9 79 = _______ 2. a) 8 31 = _______ b) 7 52 = _______ c) 6 42 = _______ d) 4 92 = _______ e) 9 71 = _______ f) 8 62 = _______ 3. a) 53 8 = _______ b) 79 7 = _______ c) 61 6 = _______ d) 82 5 = _______ e) 58 4 = _______ f) 32 9 = _______ g) 41 6 = _______ h) 9 82 = _______ i) 51 7 = _______ 132 l hoo You can use patterns and mental math to multiply. ➤ Multiply: 7 89 me At Sc At Ho Practice 1. Use patterns to complete each multiplication chart. a) b) 12 13 14 15 5 7 6 8 7 9 20 21 22 23 2. Hot dogs cost $2 each. How much do 7 hot dogs cost? _______________ 3. Marbles are sold in bags of 49. How many marbles are in 8 bags? _______________ 4. There are 52 cards in a deck. How many cards are in 7 decks? _______________ 5. There are 13 doughnuts in a baker’s dozen. How many doughnuts are there in 9 bakers’ dozens? _______________ 6. There are 24 pencil-tip erasers in a package. How many erasers are there in 6 packages? _______________ Stretch Your Thinking Explain how you could use patterns to find 7 699. ___________________________________________________________________ ___________________________________________________________________ ___________________________________________________________________ 133 TU T D E N B OO 7 K S UNIT 8 Multiplying a 3-Digit Number by a 1-Digit Number LESSO N Quick Review The total number of paper clips is 5 175. Here is one way to multiply: Break 175 apart. Multiply each part by 5. Then add. 175 5 25 350 + 500 875 Multiply the ones: 5 5 Multiply the tens: 5 70 Multiply the hundreds: 5 100 Add. Margaret got 875 paper clips. Try These 1. Multiply. b) 121 9 c) 517 8 d) 258 7 2. Lester has 3 books of stickers. Each book has 144 stickers. How many stickers does Lester have? _______________ 134 e) 409 6 l hoo Margaret bought 5 boxes of paper clips. Each box contains 175 paper clips. How many paper clips did she get? a) 340 2 me At Sc At Ho Practice 1. Multiply. a) 763 4 b) 495 8 c) 508 9 d) 659 5 e) 828 3 f) 614 7 = ________ g) 8 271 = ________ h) 366 6 = _______ 2. There are 125 balloons in a bag. How many balloons are there in 7 bags? _______________ 3. Play this game with a partner. You will need a set of 10 cards numbered 0 to 9. ➤ Each of you draw a multiplication grid like this: ➤ Shuffle the cards and lay them face side down. ➤ Take turns flipping over a card. Each time a card is turned over, both players write that number in any box on their grids. ➤ Continue until players have filled all the boxes on their grids. ➤ Multiply. The player with the greater product wins. Play 5 more games. Stretch Your Thinking Choose a 3-digit number to multiply by 8 so that the product is between 4000 and 5000, but closer to 4000. _____________________________________________ _____________________________________________ 8 135 TU T D E N B OO 8 K S UNIT 8 Estimating Quotients LESSO N Quick Review ← quotient Here are two ways to estimate 74 8. ➤ Use division. 74 is close to 72. 72 is a multiple of 8. 72 8 = 9. So, 74 8 is about 9. Think: Think ➤ Use multiplication. About how many groups of 8 are in 74? 9 8 is 72. 72 is close to 74. So, 74 8 is about 9. Think: Think Try These 1. Circle the quotient in each division fact. b) 32 4 = 8 c) 48 6 = 8 2. Write a division fact that helps you estimate each quotient. a) 37 6 __________ b) 48 7___________ c) 25 4 __________ 3. Write a multiplication fact that helps you estimate each quotient. a) 17 8 ___________ 136 b) 82 9 ___________ c) 34 7 __________ l hoo In a division fact, the answer is the quotient. 18 6 = 3 a) 24 8 = 3 me At Sc At Ho Practice 1. Write a division and a multiplication fact that help you estimate the quotient. a) 23 6 __________ ___________ b) 55 9 ___________ ___________ c) 36 5 __________ ___________ d) 39 8 ___________ ___________ 2. Estimate each quotient. a) 17 6 _________ b) 44 9 ________ c) 37 5 ________ d) 20 7 ________ e) 19 2 _________ f) 33 4 ________ g) 29 3 ________ h) 70 8 ________ 3. Joachim has 71 stickers. He wants to arrange them into 8 groups. About how many stickers will be in each group? ________________ 4. About how many weeks are there in 44 days? _________ __________ 5. Eighty-four students sign up for basketball. The coach puts them into 9 teams. About how many students are on each team? ________________ 6. Sarah shares 26 seashells among 8 friends. About how many seashells does each friend get? __________________ Stretch Your Thinking Is the quotient of 55 7 greater than or less than 8? Explain. ___________________________________________________________________ ___________________________________________________________________ 137 TU T D E N B OO 9 K S UNIT 8 Division with Remainders LESSO N Quick Review me At Sc At Ho l hoo ➤ Here’s how to share 17 pears equally among 5 boxes. Divide: 17 5 Put 3 pears in each box. There are 2 pears left over. Write: 17 5 = 3 R2 This is a division sentence. The “R” stands for remainder. ➤ Here’s how to decide how many tables are needed for 32 students eating in the lunchroom. Six students can fit at each table. Divide: 32 6 Think about the division fact that is closest to 32 6. You know that 30 6 = 5. So, 32 6 = 5 R2 But if 5 tables are used, then 2 students cannot sit at a table. So, 6 tables are needed. Try These 1. Write a division sentence for this picture. _______________ 2. Divide. a) 15 6 = _______ b) 27 5 = _______ c) 31 4 = _______ d) 19 6 = _______ e) 17 4 = _______ f) 138 37 8 = _______ Practice 1. Play this game with a partner. You will need: counters of two colours number cubes: one labelled 1, 1, 2, 2, 3, 3 and one labelled 4, 4, 5, 5, 6, 6 Take turns: ➤ Roll the number cubes to make a 2-digit number. (For example, with 6 and 3, you can make 63 or 36.) ➤ Place a counter on a circled number. Divide your 2-digit number by the number in your circle. ➤ Place a counter on a square containing your remainder if you can. ➤ Remove your counter from the circle. Continue playing until all the squares are covered. 7 6 1 2 0 5 3 5 4 5 2 6 0 8 3 4 8 3 7 1 1 6 0 2 4 2 6 3 7 4 8 5 9 Stretch Your Thinking 1. Write a division sentence with remainder 8. _______________________________________________________________ 2. Write a division sentence with remainder 4. ________________________________________________________________ 139 UNIT 8 TU T D E N B OO S K 10 Using Base Ten Blocks to Divide LESSO N Quick Review me At Sc At Ho l hoo ➤ Divide: 24 2 Divide the blocks into two equal groups. So, 24 2 = 12 12 in each group ➤ Divide: 63 5 Divide the blocks into 5 equal groups. There are 10 in each group and 13 left over. Trade the leftover ten rod for 10 unit cubes. Divide the 13 unit cubes among the 5 equal groups. So, 63 5 = 12 R3 Try These 1. Divide. Use Base Ten Blocks when they help. a) 88 4 = _______ b) 54 3 = _______ c) 37 2 = _______ d) 89 8 = _______ e) 25 2 = _______ f) 41 3 = _______ 2. Divide. Draw a picture to show how you got the answer. 27 7 = _______ 140 Practice 1. Divide. Use Base Ten Blocks when they help. a) 56 7 = _______ b) 81 9 = _______ c) 35 4 = _______ d) 27 6 = _______ e) 75 8 = _______ f) 24 6 = _______ 2. Write a division sentence to show each answer. a) Nine children want to share 36 stickers equally. How many stickers will each child get? _____________________________________________________________ b) It takes 2 cups of milk to make a milkshake. How many milkshakes can be made with 17 cups of milk? _____________________________________________________________ c) Emilio is putting 7 treats into each party bag. How many bags can he fill with 59 treats? _____________________________________________________________ 3. Three tennis balls fit into each carton. How many cartons are needed for 29 tennis balls? ________________________________________________________________ 4. Four children can fit into each seat on the carnival ride. How many seats are needed for 39 children? ________________________________________________________________ 5. Write 2 division sentences with remainders. ________________________________________________________________ Stretch Your Thinking Daniella divided a number between 45 and 50 by 5. The remainder was 4. What number did Daniella divide? Write the division sentence. ___________________________________________________________________ 141 UNIT 8 TU T D E N B OO S K 11 Another Strategy for Division LESSO N Quick Review me At Sc At Ho Divide: 55 2 l hoo You write: Arrange the 5 rods in 2 equal rows. 2 1 2 55 One ten rod remains. Trade the leftover ten rod for 10 ones. 2 7 R1 1 2 55 Now you have 15 unit cubes. Share the 15 cubes equally among the 2 groups. This is called short division. So, 55 2 = 27 R1 Try These 1. Divide. Use Base Ten Blocks when they help. a) 25 8 = _______ b) 42 5 = _______ c) 59 7 = _______ d) 29 4 = _______ e) 37 9 = _______ f) 34 6 = _______ g) 20 7 = _______ h) 52 8 = _______ i) 19 3 = _______ 2. Luis divided 43 marbles equally among his 6 friends. How many marbles did each friend get? Did Luis have any marbles left? Write a division sentence to show how you got the answer. ________________________________________________________________ 142 Practice 1. Play this game with a partner. Start 45 49 35 24 19 50 41 40 21 33 11 44 29 13 You will need: 1 marker per player 50 counters per player 1 number cube marked 2 to 7 36 Place your markers on Start. Take turns. 15 Roll the number cube. Move that many spaces in either direction. Divide the number you land on by the number you rolled. If you have a remainder, give that many counters to your partner. 28 Continue to take turns. On each turn, you may move your marker in either direction. Play until one player runs out of counters. That player is the winner. 31 20 25 39 42 48 32 38 Stretch Your Thinking Describe the strategy you used to try to win this game. ___________________________________________________________________ ___________________________________________________________________ ___________________________________________________________________ 143 8 Calendar Puzzles Copyright © 2008 Pearson Education Canada. Not to be copied. Fold Take a month from an old calendar. Cut out all the squares except the 1st and put them in a paper bag. Now, you can challenge a friend to help you put the month back together! ➤ Pull a square out of the bag. In your head, figure out where that day would lay using the first day as your starting point. ➤ Did you use a pattern to help? Share it with your partner! ➤ Take turns until the month is back in “tiptop” shape! Could you use the same pattern for another month? What did the girl octopus say to the Did You Know? boy octopus? Our number system was developed by mathematicians in India in the sixth century. What could a possible date be? Traders carried the system west to Baghdad. Arabs then took it to North Africa and Europe. See how a good idea spreads? The next 4 pages fold in half to make an 8-page booklet. I wanna hold your hand, hand, hand, hand, hand, hand, hand, hand Math at Home 1 Math at Home Math makes lots of sense to me Until my brain goes numb. But when I get confused, I remember the “rule of thumb.” I think about the problem As it happens day by day. I grab some stuff and act it out, Draw it a different way. Once I’ve got the picture, It’s time to make a plan. Now I’m ready to tackle it, ‘Cause now I know I can! Math at Home 1 2 Hey, here’s a really cool pattern! Take turns until someone gets 4 counters in a row. (The counters can run diagonally, vertically, and horizontally.) On your turn: ➤ Choose 2 cards from the top of the pile. ➤ Find the numbers on the top row and left side column of the multiplication chart. ➤ Find the product of the two numbers and put a counter on that square. ➤ If you draw a 10, you get to put your counter on any square. You’ll need: ➤ different counters for each player ➤ cards numbered 1–10 ➤ a multiplication table 4-In-A-Row Copyright © 2008 Pearson Education Canada. Not to be copied. 7 4 1 Switch the 8 and 1. 2 3 6 Switch the 9 and 2. 7 4 8 Then flipped tails ... 9 3 6 Figure out the sum of your two numbers. Show your numbers to your partner. The player with the highest sum earns a point. If the sums are within 1000 of each other, you both earn a point. ➤ The first player with 10 points wins! ➤ ➤ ➤ ➤ So, if you drew this: 1 2 You’d probably change it to this: 8 9 7 Switch the position of 4 cards. ➤ Both players may switch any 2 or 4 cards to make the largest sum. Flip the coin. Switch the position of 2 cards. To begin: Without peeking, each player draws 8 cards and lays them out one at a time, left to right in 2 rows of 4. You’ll need: ➤ 3 sets of cards numbered 1–9 (shuffled well) ➤ a coin ➤ a large book to use as a barrier Sum It Up! 6 How Many? Oh, no! I was on my way to pick up balls for a “Family Fun Day” when I accidentally spilled pop on my list. 36 s zzle n pu r ow you lve! e up so Mak hers to t for o ➤ Can you figure out how many of each ball I need? ➤ Is there more than one way to solve it? Make a list of all the choices. ➤ What if I could clean the spill enough to see that the first number had 2 digits, with a 0 in the ones place? How many of each ball would I need now? Think About It! 42 ? What is ? What is Copyright © 2008 Pearson Education Canada. Not to be copied. 8 7 6 5 4 3 2 1 X 9 8 7 6 5 4 3 2 1 1 18 27 36 45 54 63 72 81 16 24 32 40 48 56 64 72 14 21 28 35 42 49 56 63 12 18 24 30 36 42 48 54 10 15 20 25 30 35 40 45 8 6 4 2 2 12 16 20 24 28 32 36 9 6 3 3 12 15 18 21 24 27 8 4 4 10 12 14 16 18 5 5 6 6 7 7 8 8 9 9 Multiplication Table for 4-In-A-Row 9 3 4 “But that’s impossible! Each triangle has 3 sides. 7 3 = 21.” What if you changed the shape to squares? Would you need to build it all to find out? selgnairt eht fo lla oD • ?etarapes eb ot deen What do you think? Make a prediction, then try it out yourself. If you get stuck, use a mirror to read the hints below: “I built 7 triangles with only 13 toothpicks.” Powerful Patterns (Don’t give up! The more you try it, the faster you’ll get!) ➤ Can you estimate the distance between those places, before you drive past? ➤ Get everyone in on it. Who can make the best estimate? Do you find long car rides boring? Watch for a sign showing the number of kilometres to 2 or 3 places. On a Trip ... ni nrettap a ees uoy naC • skciphtoot fo rebmun eht ?emit hcae dda lliw uoy Copyright © 2008 Pearson Education Canada. Not to be copied. Hin out t: Tr e r u y g i t f o u buil using o y ? n s d th c Ca work e id ounter t i y e s a. wh Will it work with any number? Now tell your friend that the answer to his/her secret calculation is 3! 1. In your head, think of a secret number between 1 and 10. 2. Double that number. 3. Add 12. Now keep that total in your head. 4. Divide your total by 4 and remember the answer. 5. Now think of your original number. Take half of that and subtract it from the total in step 4. Master this trick and your friends will think you are a mind reader! Lead your friends carefully through the following steps: Mind Readers, Inc. 5 Math at Home 2 8 4 12 8 10 7 2 5 The next 4 pages fold in half to make an 8-page booklet. Copyright © 2008 Pearson Education Canada. Not to be copied. Fold Math at Home Math is all around my house. It shows up everywhere. How many eggs to bake a cake? How long to brush my hair? How many strokes will I need To sweep the upstairs hall? How many pop star posters Can I squeeze on my bedroom wall? How many of my sister’s toys Are scattered on the floor? Should I pick them up in groups of two Or grab a whole lot more? How much water fills the sink To scrub those dishes clean? How far can I blow the bubbles And still keep from being seen? How many minutes are left Until all these jobs are done? But wait! I guess it’s no big deal, ‘Cause “Mathy” chores are fun! Math at Home 2 2 Play until someone runs out of money! On your turn: ➤ Pull a “price tag” out of the bag. ➤ Print the price underneath the $20.00 and subtract. (Estimate first.) ➤ On your next turn, you’ll subtract the price from the money you had left from your turn before. Before you play: ➤ Cut out from a grocery store flyer about 20 items that cost less than $4.00. ➤ Place the pictures in a bag you can’t see through. ➤ Each take a pencil and paper and print $20.00 at the top of the page. Shopping Anyone? What is the perimeter of both shapes? Hmmm … interesting! Cut two pieces of string 30 cm long. Use one piece to design a dog pen with the greatest possible area. Use the other one to design a pen with the least possible area. String Shapes Copyright © 2008 Pearson Education Canada. Not to be copied. 1 3 5 Try it again – this time aim for a symmetrical design that is not a fish. How many different ways are there to make a fish with lines of symmetry? Can you design more than one? Use the pieces you’ve earned to begin building a fish design. You can make it any way you choose. The example on page 8 shows one way to do it. But, here’s the catch: every line of symmetry in your fish shape is worth 5 points if you can prove it! You might say, “5 1 is 5, and 5 + 3 is 8, so I get the shape with an 8 on it!” If you rolled: On your turn: ➤ Roll all three number cubes. ➤ Add, subtract, multiply, or divide the numbers to try to get an answer that matches a number on a tangram shape. The goal here is to earn each piece in order to make the fish on the next page! You’ll need: ➤ 3 number cubes labelled 1 to 6 ➤ 1 set of tangram pieces for each player (trace the pieces on the next page and cut apart) Terrific Tangrams 7 6 Chocolate Bar Surprise Willie Wonka is looking for a great new chocolate bar to make in his “Chocolate Factory.” Follow the clues below to create the perfect bar for Willie. ➤ 61 is mint (colour green) ➤ 41 is caramel filled (colour golden brown) ➤ 112 is dark chocolate (colour dark brown) ➤ 112 is white chocolate (colour white) ➤ 85 has rice crisps (colour speckled) Now, design your own! Tell a friend about each flavour using fractions. Is anyone hungry? Copyright © 2008 Pearson Education Canada. Not to be copied. Time Olympics With a friend, think of 10 “active events” to include in your “Time Olympics.” Print them on separate pieces of paper. Here are a few ideas to get you started: ➤ Do the “hokey-pokey” 2 times through. ➤ Run around the house 3 times (outside, please!). ➤ Push a cotton ball across the floor with your nose. ➤ Put the pieces of paper face down on the table. ➤ One person chooses one and reads it. ➤ Both players write down an estimate of how long it will take to do the event. ➤ The player who picked the activity begins, while the other person keeps track of the time. ➤ Whoever ends up with the closest estimate keeps the card. ➤ Take turns until all Olympic events are done. Whoever has the most cards wins GOLD! 3 4 Play until one player earns enough points! Hmmm … How are you going to decide how close is close enough? Is it harder to guess within 2 m or 2 cm? Why? On your turn: ➤ Choose a card and roll the number cube. ➤ Find something in your house that is about the same length as the card and number cube show. (If you rolled a 2 and picked a cm card, you’d look for something with a dimension of 2 cm.) ➤ Once you’ve found something, measure it. If you’re close: 1 point Exactly right: 2 points Before you begin, put the cards face down on the table. Decide how many points you’ll need to win the game. You’ll need: ➤ 3 of each card — cm, m ➤ a number cube labelled 1 to 6 How Long? How Wide? How Thick? Copyright © 2008 Pearson Education Canada. Not to be copied. Ralf Laue of Germany can toss a pancake 416 times in 2 minutes. How many times could he do it in 1 minute? 6 minutes? 10 seconds? Did You Know? How much do you think you’ll have by the end of the month? A calculator could be your friend on this one! ? If you start with 1¢ and double your savings each day, how long until you have about $5? Guess first, then try it! Savvy Saving Did anything surprise you? Check the mall layout sign and see if you’re right! ➤ Which stores do you think cover the greatest area? ➤ Which ones cover the least? ➤ Which ones are farthest away from each other? At the Mall 5 Math at Home 3 8 Pet Survey 12 six-year-olds were surveyed about their favourite pets. Dog /// Cat // Hamster / Goldfish / Bird Check the results below! //// 6 11 12 7 1 5 2 4 3 I guess 1:55 is the same as 5 minutes to 2! Now let’s make it a bit more interesting! Take the results from the survey and turn them into a circle graph. Need a hint? Figure out what fraction of kids liked each pet best. 9 8 10 Got a Minute? Look at a clock at your house and tell the time in two different ways. The next 4 pages fold in half to make an 8-page booklet. Copyright © 2008 Pearson Education Canada. Not to be copied. Fold Math at Home Visiting the supermarket Needn’t make you snore. Just take a look around And you’ll see Math galore! Numbers on the labels. Numbers on the tags. Numbers on the cash register. Numbers on the bags. There are shapes of every size Lining every aisle. Angles jumping out at you, Just browse a little while. Estimate the grocery bill. Count up change galore! But… Don’t ever let me hear you say, “Shopping’s just a BORE!” Math at Home 3 2 The product of my strip is somewhere between 300 and 400. Try making up your own number strips. Use division, multiplication or maybe a combination! 4. Player B tries to guess which strip Player A was thinking of. Could there be more than 1 answer? 5. Use the calculator to check! 6. Now switch roles. Example: 1. Place all of your strips on the table, face up. Mix them up so that they are not in any particular order. 2. Player A chooses a strip (in her mind). 3. She now gives the hint by telling 2 numbers that are close to the product of that strip. Here is a game you can play with 2 or more people. Before you begin, you will need to make number sentence strips. You can cut them from page 3 or make your own from cardstock. Guesstimate! Copyright © 2008 Pearson Education Canada. Not to be copied. What fraction will be left over? (Use the pizzas below to help you figure it out!) ➤ You estimate that each kid will eat 3 pieces. (Don’t forget yourself!) ➤ If each pizza is cut into 8 pieces, how many whole pizzas will you need to order? Imagine you’re having a pizza party and 5 kids have been invited over. Party Time Switch places and play again! Give the calculator to your friend and ask him to press the equal key 3 more times, watching the numbers change each time. Challenge him to try to figure out what you did! Enter a number in a calculator and show it to a friend. Secretly, either add or subtract a one-digit number from the first number and press the equal key. Calculator Patterns 7 6 Art Attack! Create an abstract sculpture using many 3-D objects, some tape, and your imagination. First, collect several empty boxes, toilet paper rolls, milk cartons, juice boxes, ice-cream cones, and any other interesting 3-D objects you can find. Think about how the shapes might fit together and then start taping. Each time you pick up a new object, count the faces and name them. 12 1 When you’re all done, tell someone about your masterpiece. (Be sure to point out lots of cool “attributes”!) 11 Crazy Clocks 10 What time could it be if 2 the minute hand and the hour hand made a square corner? 9 Smaller than a square corner? 3 Bigger than a square corner? 8 6 Is there more than one 4 choice? Use a real clock to find out! 5 7 Copyright © 2008 Pearson Education Canada. Not to be copied. 492 3 4 45 82 6 16 7 151 2 43 0 9 43 199 6 86 2 8 29 2 64 256 4 480 9 43 9 9 43 19 5 45 4 Guesstimate Number Strips 804 7 3 4 ➤ Draw in furniture where you would like it placed. (Pretend you’re looking down from the ceiling.) ➤ Estimate the actual size of real furniture and cover the right number of squares. (A queen-size bed would cover approximately 2 squares by 212 squares.) ➤ Colour your furniture. 5m What’s the area of the room? What’s the perimeter? 6m The grid below represents your new room. Each square stands for 1 square metre. Have you always wanted that dream room but never been allowed to design your own? Here’s your chance! Dream Design Copyright © 2008 Pearson Education Canada. Not to be copied. What area of floor space does your bed take up? Is it more or less than the dresser? What’s the area of the “empty” floor space? Find the perimeter of 3 different pieces of furniture. If your room was only 12 the size, would you still be able to fit all the furniture in? How could you test your prediction? Show your design to your family. Do you think they’ll go for it? 5m Great news! Now you get to design your floor! Use at least 3 different colours to create an interesting tile pattern on the grid below. 6m ➤ ➤ ➤ ➤ ➤ Let’s Take a Closer Look … 5

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