Let's Do Mathematics 4 – Worktext A by Regal Education

Workt ext

for learners 9 - 10 years old

2 km 25 min hike

Aligned to the US Common Core State Standards

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Workt ext

for learners 9 - 10 years old

2 km 25 min hike

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First edition 2021 This edition is published by Regal Education Inc. ISBN 978-1-953591-08-1

This book or parts thereof may not be reproduced in any form, stored in any retrieval system, or transmitted in any form by any means – electronic, mechanical, photocopy, recording, or otherwise – without prior written permission of the copyright owner.

Regal Education Inc. 10 Pienza, Irvine, CA 92606, United States www.regaleducation.org

Let’s Go! Mathematics

Let’s Go! Mathematics is a series covering levels K-6 and fully aligned to the United States Common Core State Standards (USCCSS). Each level consists of 2 books (Book A and Book B) and combines textbook-style presentation of concepts as well as workbook practice.

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Central to the USCCSS are the promotion of problem-solving skills and reasoning. Let’s Go! Mathematics achieves this by teaching and presenting concepts through problem-solving based pedagogy and the concrete-pictorial-abstract (CPA) approach. Learners acquire knowledge and understanding of concepts through a guided progression beginning with concrete examples and experiences which then flow into pictorial representations and finally mastery at the abstract and symbolic level. This approach ensures that learners develop a fundamental understanding of concepts rather than answering questions by learned procedures and algorithms. Key features of the series include:

Anchor Task

Line Plots and Line Graphs

Length of Pencils Total Tally

Length

Anchor Task

Open-ended activities serve as the starting point for understanding new concepts. Learners engage in activities and discussions to form concrete experiences before the concept is formalized.

209

208

Let’s Learn

Numbers to

+1,000

5,000

1,000,000

thousands

Find the num from 5,000.

+1,000

6,000

Ten Thousands Thousand s

+1,000

7,000

8,000 1,000 more than 9,000 is 10,0 We read 10,0 00 as ten thou 00. sand. ten thousand s from 50,0 00.

+1,000

9,000

We say: We write:

10,000 (b)

Count on in

+10,000

50,000

+10,000

60,000

+10,000

70,000

+10,000

80,000

90,000 10,000 mor e than 90,0 00 is 100,000 We read 100, . 000 as one hundred thou sand. Count on in one hundred thousands from 500,000 . +100,000

500,000

+100,000

600,000

+100,000

700,000

+100,000

800,000

100,000 mor e than 900 ,000 We read 1,00 0,000 as one is 1,000,000. million.

ber represen ted in the plac e value cha

(a)

+1,000

We write: (c)

900,000

1,000,000

(d)

Hundreds

Tens

Ones

Hundreds

Tens

Ones

Five hundred one thousand 501,062. , sixty-two.

Hundred Ten Thousands Thousands Thousand s

We say: We write:

Ones

Three hundred hundred thirt forty-two thousand, eight y-three. 342,833.

Hundred Ten Thousands Thousands Thousand s

We say: We write:

+100,000

Tens

Twenty-five thousand, one 25,170. hundred seve nty.

Hundred Ten Thousands Thousands Thousand s

We say:

100,000

rt.

Hundreds

Tens

Nine hundred thirty thousand 930,107. , one hundred

Ones

seven.

Concepts are presented in a clear and colorful manner. Worked problems provide learners with guided step-by-step progression through examples. Series mascots provide guidance through helpful comments and observations when new concepts are introduced.

Let’s Learn

Count on in

iii

Let’s Practice 1.

(b) 1:15

3:30

(d)

(c)

Morning:

(f)

(e)

Afternoon:

(d)

(c)

11:50

9:25

Complete the table.

t International Airpor Flight Departures JFK Departure Departure (24-hour time) (12-hour)

Morning:

City

Night:

07 35

Miami

9:05

7:45

3:40 p.m.

Dallas

Night:

(b) Home At Write the equivalent (a)

fractions.

20 20

Washington

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Morning:

Use multiplication

(a)

to find equivalent

4 7

At Home

1:45 a.m.

Los Angeles

(f)

(e)

(b)

2 9

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2 9

2 = 9

2 9

1 3

4 = 7

fractions.

4 7

1 2 (b)

Further practice designed to be completed without the guidance of a teacher. Exercises and problems in this section follow on from those completed under Let’s Practice.

p.m.

(b)

r time.

Write the times in 24-hou

time using a.m. and

(a)

Learners demonstrate their understanding of concepts through a range of exercises and problems to be completed in a classroom environment. Questions provide a varying degree of guidance and scaffolding as learners progress to mastery of the concepts.

Write the times in 12-hour

Let’s Practice

(c)

Use division to find

(a)

3 4

(b)

3 6

Learners are encouraged to ‘learn by doing’ through the use of group activities and the use of mathematical manipulatives.

7 kg (g)

÷4

÷6

18 42

÷6

153

36 cm (mm)

22,000 g (kg)

11 km (m)

182 dm (cm)

START

÷4

÷3

18 = 42

the dice. shown on Hands On kets. the number dice. Move shown in brac in rolling a to the unit Take turns surement metric mea Convert the t. s: k to the star Some rule tly, go bac ard 3 spaces. wer incorrec • If you ans pot, leap forw on a honey ces. back 3 spa • If you land on a bee, fly • If you land the winner! is hive er to the bee The first play

÷2

÷3

18 42

equivalent fractio ns.

12 20

12 = 20

(d)

152

Hands On

÷2

12 20

10 cm (dm)

4,000 m (km)

6,000 ml (l)

14 kg (g)

Solve It!

5l (ml)

Solve it!

What is Sophie’s favorite fruit? Match the mixed numbe rs and improper fractions to find out.

10 km (m)

Looking Back

Consolidated practice where learners demonstrate their understanding on a range of concepts taught within a unit.

Activities that require learners to apply logical reasoning and problem-solving. Problems are often posed which do not have a routine strategy for solving them. Learners are encouraged to think creatively and apply a range of problem-solving heuristics.

1 = 8

(e)

3 = 7

22 3

(f)

2 = 9

5 = 20

(d)

18 = 36

(f)

form.

12 = 16

(c)

3 4

9 8

(d)

4 3

5 2

12 5

Write the improper fraction represented of the shapes.

Write the mixed number represented the shapes in its simplest form.

by the colored parts

15 = 45

by the colored parts of

(a)

(b)

on 6. Draw a point to show the fraction

the number line.

(a) 2 3

by writing = or ≠. 3. Tell whether the fractions are equivalent (b) 12 2 (a) 6

7 4

(b)

2 = 5

1 3

(d)

(e)

4 3

166

(a)

2. Find the equivalent fraction in its simplest (b) 9 (a) 2 = = (c)

(c)

Looking Back 1. Find the first 2 equivalent fractions. (b) 3 (a) 1 = = =

220

FINISH

11 33

1 3

(b) 6 0

2 221

Contents 2 4 14 24 40 48

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Whole Numbers Numbers to 1,000,000 Place Value Comparing and Ordering Numbers Rounding and Estimation Factors and Multiples

2 Operations on Whole Numbers Addition and Subtraction Multiplying by a 1-digit Number Multiplying by a 2-digit Number Dividing by a 1-digit Number Word Problems

3 Fractions Equivalent Fractions Mixed Numbers and Improper Fractions Comparing and Ordering Fractions Adding and Subtracting Fractions Multiplying Fraction Word Problems

4 Decimals Tenths Hundredths Comparing Decimals 6

66 66 66 79 92 107 122 140 140 155 170 185 203 212 146 226 226 248 269 v

Whole Numbers

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Anchor Task

City

Population

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Numbers to 1,000,000 Let’s Learn

5,000

+1,000

6,000

+1,000

7,000

+1,000

8,000

9,000

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1,000 more than 9,000 is 10,000. We read 10,000 as ten thousand.

+1,000

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+1,000

Count on in thousands from 5,000.

10,000

Count on in ten thousands from 50,000. +10,000

50,000

+10,000

60,000

+10,000

70,000

+10,000

80,000

+10,000

90,000

100,000

10,000 more than 90,000 is 100,000. We read 100,000 as one hundred thousand.

Count on in one hundred thousands from 500,000.

+100,000

500,000

+100,000

600,000

+100,000

700,000

+100,000

800,000

100,000 more than 900,000 is 1,000,000. We read 1,000,000 as one million.

+100,000

900,000 1,000,000

Find the number represented in the place value chart. (a)

Hundreds

Tens

Ones

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Ten Thousands Thousands

We say: Twenty-five thousand, one hundred seventy. We write: 25,170. (b)

Hundreds

Tens

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Hundred Ten Thousands Thousands Thousands

Ones

We say: Three hundred forty-two thousand, eight hundred thirty-three. We write: 342,833. (c)

Hundreds

Tens

Ones

Hundred Ten Thousands Thousands Thousands

We say: Five hundred one thousand, sixty-two. We write: 501,062.

(d)

Hundred Ten Thousands Thousands Thousands

Hundreds

Tens

Ones

We say: Nine hundred thirty thousand, one hundred seven. We write: 930,107.

Count on in tens. +10

42,088

+10

42,098

(b)

42,108

+10

42,118

+10

206,984

+10

206,994

42,128 +10

207,004

207,014

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206,974

+10

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(a)

Count on in hundreds. (a)

+100

97,563 (b)

+100

97,663

+100

115,850

+100

97,763

+100

115,950

+100

97,863

+100

116,050

97,963

+100

116,150

116,250

+1,000

(a)

Count on in thousands.

66,400

(b)

67,400

+1,000

397,800

+1,000

68,400

+1,000

398,800

+1,000

69,400

+1,000

399,800

+1,000

70,400

+1,000

400,800

401,800

Count on in ten thousands.

530 (b)

+10,000

10,530 +10,000

20,530

+10,000

190,020

30,530

+10,000

200,020

+10,000

40,530

+10,000

210,020

220,020

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180,020

+10,000

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(a)

Count on in hundred thousands. (a)

+100,000

72,400 (b)

172,400

+100,000

543,210 (c)

+100,000

272,400

+100,000

643,210

+100,000

(d)

100,022

401,064

501,064

+100,000

300,022

+100,000

943,210

400,022

+100,000

601,064

701,064

301,064

+100,000

472,400

+100,000

843,210

+100,000

200,022

+100,000

372,400

+100,000

743,210

+100,000

Let’s Practice

Ten Thousands Hundreds Thousands

Tens

Ones

(b)

Ten Thousands Hundreds Thousands

Tens

Hundred Ten Thousands Hundreds Thousands Thousands

Ones

Tens

Ones

Tens

Ones

(c)

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(a)

1. Write as numerals and words.

(d)

Hundred Ten Thousands Hundreds Thousands Thousands

2. Write the numbers. (a) Ten thousand, five hundred six. (b) Seventeen thousand, six hundred ninety.

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(d) Seven hundred twelve thousand, one hundred eighteen. (e) Thirteen thousand, four hundred forty-nine.

(f) One hundred six thousand, two hundred eighty-one.

3. Write in words.

(a) 16,933

(b) 104,338

(d) 711,652 9

4. Count on in 100s.

(d) 9,820,

5. Count on in 1,000s. (a) 51,200,

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(b) 368,

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(a) 1,860,

(b) 16,152,

(d) 167,680,

6. Count on in 10,000s. (a) 270,

(b) 93,150,

(d) 331,705,

7. Count on in 100,000s.

(a) 1,899,

(b) 153,151, (c) 360,

(d) 600,000,

, ,

Hands On

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Form circles of 4 to 6 students. Each group receives a bean bag or ball. Your teacher will write a number on the whiteboard and say a count-on number.

Count on in 10,000s!

32,500!

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The student with the bean bag counts on from the number on the whiteboard and throws the bean bag to the next person in the group. Continue passing the bean bag and counting on until the teacher says 'Stop!'

At Home

68,020

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six hundred eighty thousand, twenty-seven

1. Match.

6,827

six hundred eight thousand, two hundred seven

680,027

sixty-eight thousand, two hundred seventy

608,207

six thousand, eight hundred twenty seven

68,270

sixty-eight thousand, twenty

2. Write as numerals and words. Hundred Ten Thousands Hundreds Thousands Thousands

Tens

Ones

Hundred Ten Thousands Hundreds Thousands Thousands

Tens

Ones

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(b)

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(a)

3. Count on in 10,000s. (a) 85,010,

(b) 107,290,

(d) 272,000,

4. Count on in 100,000s. (a) 11,100,

(b) 480,350,

(d) 599,500,

, ,

Place Value

(a)

Tens

The digit in the hundred thousands place is 2. It represents 200,000. The digit in the ten thousands place is 5. It represents 50,000. The digit in the thousands place is 1. It represents 1,000. The digit in the hundreds place is 6. It represents 600. The digit in the tens place is 9. It represents 90. The digit in the ones place is 3. It represents 3.

200,000 + 50,000 + 1,000 + 600 + 90 + 3 = 251,693

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Hundred Ten Thousands Hundreds Thousands Thousands

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Find the value of each digit in the numbers shown.

Let’s Learn

The number can be found by adding the values of each digit.

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(b)

The digit in the hundred thousands place is 6. It represents 600,000. The digit in the ten thousands place is 8. It represents 80,000. The digit in the thousands place is 9. It represents 9,000. The digit in the hundreds place is 4. It represents 400. The digit in the tens place is 2. It represents 20. The digit in the ones place is 5. It represents 5.

What is the value of the digit in the thousands place?

600,000 + 80,000 + 9,000 + 400 + 20 + 5 = 689,425

Let's find the value of each digit in the number. 6

4 0

R 16

The value of the digit 5 is 50,000. The value of the digit 6 is 6,000. The value of the digit 9 is 900. The value of the digit 8 is 80. The value of the digit 3 is 3. 50,000 + 6,000 + 900 + 80 + 3 = 56,983

(b)

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(a)

The value of the digit 4 is 400,000. The value of the digit 6 is 60,000. The value of the digit 5 is 5,000. The value of the digit 9 is 900. The value of the digit 2 is 20. The value of the digit 7 is 7. 400,000 + 60,000 + 5,000 + 900 + 20 + 7 = 465,927

Let’s Practice 1. Write the numbers shown in the place value abacus.

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TTh

HTh

TTh

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HTh

(a) (b)

HTh TTh

(e) (f)

HTh TTh

2. Write the number represented by the place value disks. 100,000

10,000

1,000

100

100,000

10,000

1,000

100

100,000

10,000

1,000

100

100,000

10,000

1,000

100

100,000

10,000

100,000

10,000

100

100,000

10,000

100

10,000 10,000

3. Write the value of the digit.

(a) (b)

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1 1

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100

4. Write the value of each digit. Then add the values. 4

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(a)

(b)

(c)

Solve It!

The code has 6 digits. The code is greater than 200 000 less than 400 000. The code is an odd number that is not divisible by 5. The sum of the digits in the hundreds, tens and ones place is 10. The digit in the thousands place is 3. All digits are less than 6 and no 2 digits are the same.

• • • • • •

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Read the clues to find the combination to the safe!

Safe combination 20

At Home 1. Match the numbers in two ways.

20,000 + 5,000 + 600 + 20

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258,602

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two hundred eighty-five thousand, sixty

twenty-five thousand, six hundred twenty

25,620

285,060

260,285

200,000 + 50,000 + 8,000 + 600 + 2 two hundred sixty thousand, two-hundred eighty five two hundred fifty-eight thousand, six hundred two 200,000 + 60,000 + 200 + 80 + 5 200,000 + 80,000 + 5,000 + 60

2. Write the numbers shown in the place value abacus.

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(a) (b)

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(a)

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3. Write the numbers represented by the place value disks. 100,000 100,000 10,000 10,000

1,000 1,000 100

100

100,000 100,000 10,000 10,000

1,000

100

100,000 100,000 10,000 10,000

1,000

100

10,000

1,000

100

10,000

1,000

100

100,000

(b)

1,000 1,000 100

100,000

100

1 1

100,000

1,000

100

100,000

1,000

100

100,000

1,000

100

100,000

1,000

100

4. Write the value of each digit. Then add the values. 1

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(a)

(b)

5. Add the place values.

(a) 400,000 + 10,000 + 600 + 80 + 2 = (b) 200,000 + 20,000 + 2,000 =

Comparing and Ordering Numbers Let’s Learn

Let's compare the numbers.

3 3

Tens

Ones

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Hundred Ten Thousands Hundreds Thousands Thousands

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(a) Compare the numbers 352,189 and 351,667. Which number is greater?

First, compare the values in the hundred thousands place. The values in the hundred thousands place are the same. Compare the values in the next place – ten thousands. The values in the ten thousands place are the same. Compare the values in the thousands place. 2 thousands is greater than 1 thousand.

So, 352,189 is greater than 351,667.

(b) Compare the numbers 522,165 and 522,775.

Hundred Ten Thousands Hundreds Thousands Thousands

Tens

Ones

The values in the hundred thousands, ten thousands and thousands place are the same. Compare the values in the hundreds place. 1 hundred is smaller than 7 hundreds. 522,165 < 522,775 522,775 > 522,165

Ones

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Tens

Hundred Ten Thousands Hundreds Thousands Thousands

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First, compare the values in the hundred thousands place. 85,580 does not have any digits in the hundred thousands place. So, it is the smallest number. The remaining numbers both have 2 hundred thousands. Compare the values in the ten thousands place. 5 ten thousands is greater than 4 ten thousands. So, it is the greatest number. 256,027

85,580

smallest

Always start by comparing the digits in the highest place value.

greatest

245,831

Let’s Practice

(a) 1,000 100

1,000 1,000 1,000 1,000

100

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100

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100,000 100,000 10,000

100

(b) 100,000 100,000 100,000 100,000 100,000 10,000 10,000

1,000

100,000 100,000 100,000 100,000 100,000 10,000 10,000

1,000

1,000 1,000 1,000 1,000

1,000 1,000 100

100

al 100

100 10

1,000

100,000 100,000 10,000 10,000

1. Write the number represented by the place value disks. Check the smaller number.

100

100 10

2. Write the numbers in the place value chart and compare. (a) Compare 704,561 and 703,761.

Ones

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Tens

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Hundred Ten Thousands Hundreds Thousands Thousands

(b) Compare 185,119 and 185,102.

Hundred Ten Thousands Hundreds Thousands Thousands

Tens

Ones

3. Use the symbols >, < and = to fill in the blanks. 11,505 (b) 135,509

135,509

80,219 (d) 959,934

959,349

(e) 746,450

746,399 (f) 478,012

478,120

(g) 347,822

743,822 (h) 870,338

870,338

(a) 11,055

12,993

16,033

(b)

512,533

510,838

(c)

770,809

770,688

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(a)

4. Check the smaller number.

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5. Check the greatest number. (a)

31,533

7,543

4,573

(b)

192,606

193,000

192,506

(c)

742,167

742,176

742,168

6. Arrange the numbers from the greatest to the smallest. (a) 109,558 105,558 110,598, ,

(b) 753,186 119,060 401,306

(d) 29,158 19,414 9,455

At Home

1. Write the number represented by the place value disks. Check the greater number.

(b)

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(a)

HTh TTh

2. Compare 104,070 and 104,101.

Hundred Ten Thousands Hundreds Thousands Thousands

Tens

Ones

> 29

3. Check the numbers greater than 234,567.

234,560

243,650

335,707

48,589

500,367

234,558

243,006

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35,675

234,580

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4. Use the words is greater than, is smaller than and is equal to to fill in the blanks. (a) 103,520 (b) 18,544

103,920

18,655

202,113

(d) 999,478

999,666

(e) 234,980

234,980

(f) 567,010

576,010

5. Arrange the numbers from the greatest to the smallest.

(a) 6,488 65,489 64,000

(b) 18,227 80,228 8,048

(d) 698,123 698,114 697,199

Number Patterns Let’s Learn

What is the next number in the pattern? 65,400

65,900

66,400

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(a)

66,900

66,900 + 500 = 67,400

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In each step the numbers increase by 500.

+500

67,400

The next number in the pattern is 67,400. (b) 131,570

128,570

In each step the numbers decrease by 3,000.

125,570

-3,000

122,570

122,570 – 3,000 = 119,570

119,570

The next number in the pattern is 119,570. Can you see a pattern with the digits in the thousands place?

1, 8, 5, 2, 9... They alternate between odd and even numbers!

284,900

304,900

(d) 577,090

572,090

567,090

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582,090

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The numbers increase by 20,000 in each step. 304,900 + 20,000 = 324,900 The next number in the pattern is 324,900.

244,900

The numbers decrease by 5,000 in each step. 567,090 – 5,000 = 562,090 The next number in the pattern is 562,090. (e) 782

50,782

100,782

150,782

(f)

The numbers increase by 50,000 in each step. 150,782 + 50,000 = 200,782 The next number in the pattern is 200,782.

907,900

910,400

905,400

902,900

The numbers decrease by 2,500 in each step. 902,900 – 2,500 = 900,400 The next number in the pattern is 900,400.

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? (a) 20,578, 20,573, 20,568, , 20,558, 20,553 The numbers decrease by 5 in each step. 20,568 – 5 = 20,563 The missing number is 20,563.

What is the missing number?

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? (b) , 98,700, 94,700, 90,700, 86,700, 82,700 The numbers decrease by 4,000 in each step. 98,700 + 4,000 = 102,700 The missing number is 102,700. What are the missing numbers? ?

, 608,351,

, 622,351, 629,351, 636,351, 643,351

Subtract 7,000 from 608,351 and add 7,000 to 608,351.

In each step the numbers increase by 7,000.

608,351 – 7,000 = 601,351 608,351 + 7,000 = 615,351 The missing numbers are 601,351 and 615,351.

Let’s Practice

Hundred Ten Thousands Hundreds Thousands Thousands

5,000 less

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Hundred Ten Thousands Hundreds Thousands Thousands

40,000 less

30,000 less

(d)

Ones

Tens

Ones

30,000 more

Hundred Ten Thousands Hundreds Thousands Thousands

25,000 less

Tens

40,000 more

Hundred Ten Thousands Hundreds Thousands Thousands

(c)

Ones

5,000 more

558,340

(b)

Tens

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(a)

1. Fill in the blanks.

Tens

25,000 more

Ones

2. Fill in the blanks. 5,000 less

60,510

5,000 more

(b)

20,000 less

135,180

20,000 more

(c)

4,000 less

447,990

(d)

2,000 less

4,000 more 2,000 more

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625,250

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(a)

(e) (f)

250,000 less

385,100

250,000 more

7,500 less

335,707

7,500 more

3. Find the number that comes next in the pattern. 3,050

5,050

7,050

(b) 20,500

15,500

10,500

5,500

217,490

197,490

177,490

354,800

304,800

254,800

12,536

25,036

37,536

708,223

508,223

308,223

(a) 1,050

(d) 404,800

(e)

(f) 908,223

(a)

+5,000

4. Write the rule for the number pattern. The first one has been done for you.

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9,311, 14,311, 19,311, 24,311

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(b)

216,678, 191,678, 166,678, 141,678 (c)

70,

60,070,

120,070,

180,070

950,800,

920,800,

890,800,

860,800

(d)

5. Find the missing numbers in the number pattern.

(a)

, 173,120, 198,120, 223,120, 248,120,

(b) 940,375,

, 640,375, 490,375, 340,375,

(d)

(e) 40,910, (f)

, 365,090,

, 468,096, 476,096, 484,096, ,

, 16,910, 8,910, 910

, 664,944, 656,944, 648,944, 640,944,

, 500,096

Hands On

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3. Flick the paper clip to spin it.

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2. Place a paper clip on the center of the circle and hold it in place with a pencil as shown.

1. Work in pairs. Write a 6-digit number in your notebook.

4. Have your friend add or subtract to find the next number.

+800 +10,0 00 –1 00

5. Write the number in your notebook and repeat steps 2 to 4 with the a new 6-digit number.

0 00 0, +2 00 –10,0 +500

0 +7,50 –100 , 0 0 0

–

0 0 0

4 0 ,

00 0 , 5 + –1,00 0

At Home

Hundred Ten Thousands Hundreds Thousands Thousands

Tens

50,000 less

50,000 more

600 less

17,507

600 more

114,950

8,000 more

320,146

12,000 more

2. Fill in the blanks.

(a)

(b)

8,000 less

12,000 less

(d)

100,000 less

888,225

100,000 more

(e)

30,000 less

700,900

30,000 more

(c)

Ones

5,000 more

Ed uc a

5,000 less

(b)

Tens

tio

(a)

1. Fill in the blanks.

Ones

3. Fill in the missing numbers. (a) 10 more than 13,590 is

. .

(d) 40 less than 14,506 is

. .

(e) 100 more than 153,100 is

(f) 1,500 less than 43,400 is

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(g) 1,500 more than 161,980 is

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(b) 200 less than 100,700 is

(h) 2,500 less than 76,800 is

(i) 2,500 more than 19,300 is

(j) 200,000 more than 51,200 is

4. Find the missing numbers in the number pattern. (a) 12,700,

, 11,650, 11,300, 10,950

(b) 205,448, 206,198, 206,948,

, 446,197, 452,197, 458,197, 464,197,

(c)

, 208,448,

(d) 38,500,

, 30,500, 26,500, 22,500,

, 50,123, 100,123, 150,123,

(f)

, 189,210, 188,410, 187,610, 186,810,

, 250,123

(e)

Rounding and Estimation Let’s Learn

Round off 105,998 to the nearest ten.

When rounding, remember 5 or more – round up!

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When rounding, remember 4 or less – round down!

105,998

105,995

105,990

106,000

When rounding to the nearest ten, we look at the digit in the ones place. The digit in the ones place is 8, so we round up. 105,998 rounded off to the nearest ten is 106,000.

Round 26,575 to the nearest hundred.

26,500

26,575

26,550

26,600

When rounding to the nearest hundred, we look at the digit in the tens place. The digit in the tens place is 7, so we round up. 26,575 rounded off to the nearest hundred is 26,600.

Round 162,450 to the nearest thousand.

162,500

163,000

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162,000

162,450

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hen rounding to the nearest thousand, we look at the W digit in the hundreds place. The digit in the hundreds place is 4, so we round down. 162,450 rounded off to the nearest thousand is 162,000. We write: 162,450 ≈ 162,000 We read: 162,450 is approximately equal to 162,000 The population of San Francisco is 883,305. Find the population when rounded to the nearest thousand. The digit in the hundreds place is 3. So we round down.

Rounded off to the nearest thousand, the population of San Francisco is 883,000. 883,305 ≈ 883,000 We need to look at the digit in the 10,000s place.

Find the population rounded to the nearest 100,000.

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A new sports car costs $274,800. Round the cost of the sports car to the nearest ten thousand dollars.

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In 274,800 the digit in the thousands place is 4. So, we round down.

274,800 ≈ 270,000 Rounded to the nearest ten thousand dollars, the sports car costs approximately $270,000.

384,400 km

The distance from Earth to the moon is 384,400 km. Find the distance to the nearest hundred thousand kilometers.

The digit in the ten thousands place is 8. So, we round the hundred thousands up. 384,800 ≈ 400,000 Rounded to the nearest hundred thousand kilometers, the distance from the Earth to the moon is approximately 400,000 km.

Let’s Practice 1. Fill in the missing numbers. (a)

tio

14,355

14,350

14,356

14,360

rounded off to the nearest ten is

≈

(b)

231,910

231,950

231,900

≈

(c)

471,000

rounded off to the nearest

thousand is

470,800

470,500

470,000

232,000

rounded off to the nearest

hundred is

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≈

(d)

84,960

85,000

ten thousand is

≈

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962,111

950,000

900,000

1,000,000

rounded off to the nearest

hundred thousand is

tio

rounded off to the nearest

(e)

90,000

80,000

≈

2. A factory produces 23,875 paper clips per day. Round the number of paper clips to the nearest ten thousand.

≈

The factory produces about

paper clips per day.

3. A swimming pool contains 660,430 gallons of water. Round the volume to the nearest thousand gallons.

≈

There are about pool.

gallons gallons of water in the swimming

4. A house is for sale for $543,000. Round the price to the nearest one hundred thousand dollars. .

tio

The price of the house is about $

≈

5. Round the numbers to the nearest hundred. (a) 5,649 ≈

(d) 95,045 ≈

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(b) 60,153 ≈

6. Round the numbers to the nearest thousand. (a) 12,466 ≈

(b) 701,709 ≈

(d) 33,187 ≈

7. Round the numbers to the nearest ten thousand. (a) 8,335 ≈

(b) 54,750 ≈

(d) 865,630 ≈

8. Round the numbers to the nearest hundred thousand. (a) 91,700 ≈

(d) 763,016 ≈

(b) 222,550 ≈

At Home 1. Fill in the missing numbers. (a)

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(b)

≈

660,200

650,000

600,000

700,000

rounded off to the nearest

hundred thousand

84,000

rounded off to the nearest

thousand is

tio

83,500

83,000

83,395

≈

2. Round the numbers to different places values.

(a)

324,617

≈

when rounded to the nearest hundred.

≈

when rounded to the nearest ten thousand.

≈

when rounded to the nearest thousand.

≈

(b)

when rounded to the nearest hundred thousand.

≈

tio

≈

when rounded to the nearest ten thousand.

675,390

Ed uc a

when rounded to the nearest thousand.

3. Round the numbers to the nearest hundred. (a) 1,840 ≈

(b) 45,454 ≈

(d) 263,977 ≈

4. Round the numbers to the nearest thousand. (a) 3,560 ≈

(d) 599,429 ≈

(b) 45,800 ≈

5. Round the numbers to the nearest ten thousand. (b) 225,000 ≈

(d) 805,200 ≈

(a) 14,630 ≈

6. Round the numbers to the nearest hundred thousand. (a) 287,444 ≈

(b) 56,399 ≈

(d) 748,522 ≈

Factors and Multiples

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Anchor Task

Let’s Learn

Multiples Look at the products of 3 we can make with the cherries.

3x3=9

3 x 4 = 12

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3x2=6

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3x1=3

The product of 3 and any number is called a multiple of 3.

3, 6, 9 and 12 are multiples of 3.

Can you find the 6th multiple of 3?

6 x 3 = 18 The 6th multiple of 3 is 18!

Let's look at the first 10 multiples of 3 and 4. 3 4

6 8

9 12

12 16

15 20

18 24

21 28

24 32

Notice that 12 and 24 are multiples of both 3 and 4. 3 4

6 8

9 12

12 16

15 20

18 24

21 28

24 32

27 30 36 40

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Multiples of 3 Multiples of 4

27 30 36 40

Multiples of 3 Multiples of 4

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We say 12 and 24 are common multiples of 3 and 4. As 12 is the first common multiple of 3 and 4, we say 12 is the lowest common multiple of 3 and 4. Let's find the lowest common multiple of 2 and 3. Multiples of 2: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24 Multiples of 3: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30 6, 12 and 24 are common multiples of 2 and 3. 6 is the lowest common multiple of 2 and 3.

Factors How many ways can we arrange 12 cubes into equal rows?

1 x 12

2x6

3x4

12 = 1 x 12 12 = 2 x 6 12 = 3 x 4

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The numbers that we multiply to make 12 are called factors. 1, 2, 3, 4, 6 and 12 are all of the factors of 12. Let's find the factors of 20.

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1 x 20

2 x 10

4x5

The factors of 20 are 1, 2, 4, 5, 10 and 20.

We can use division to find factors. Is 5 a factor of 15? Let's divide. 15 ÷ 5 = 3 5 divides 15 with no remainder. So, 5 is a factor of 15.

Is 4 a factor of 15? 15 ÷ 4 = 3 R 3 There is a remainder of 3. So, 4 is not a factor of 15.

The factors of 20 are 1, 2, 4, 5 and 20. Let's compare the factors of 12 and 20.

tio

Factors of 12: 1, 2, 3, 4, 6 and 12. Factors of 20: 1, 2, 4, 5, 10 and 20. Both 12 and 20 share the factors 1, 2 and 4. We say 1, 2 and 4 are common factors of 12 and 20.

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The greatest factor shared by 12 and 20 is 4. We say 4 is the greatest common factor of 12 and 20. Look at the numbers and their factors in the table. Number 18 30 45 56 60

Factors

1, 2, 3, 6, 9, 18 1, 2, 3, 5, 6, 10, 15, 30 1, 3, 5, 9, 15, 45 1, 2, 4, 7, 8, 14, 28, 56 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60

(a) Let's list the common factors of 18 and 45. 1, 3 and 9.

(b) What is the greatest common factor of 30 and 56? The common factors of 30 and 56 are 1 and 2. So, 2 is the greatest common factor.

(c) What are the common factors of 30 and 60? 1, 2, 3, 5, 6, 10, 15 and 30. (d) What is the greatest common factor of 30 and 60? From (c), we can see the greatest common factor is 30.

Prime and Composite Numbers Let's find the factors of 7.

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7 can only be arranged in 1 row of 7. The only factors of 7 are 1 and 7.

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I can only make 1 row of 7 dots!

A number that is greater than 1 and only has factors of 1 and itself is called a prime number. Numbers that have more than 2 factors are called composite numbers. We can identify the numbers 2 to 12 as prime or composite in the table. Factors

1, 2 1, 3 1, 2, 4 1, 5 1, 2, 3, 6 1, 7 1, 2, 4, 8 1, 3, 9 1, 2, 5, 10 1, 11 1, 2, 3, 4, 6, 12

Number 2 3 4 5 6 7 8 9 10 11 12

Prime or Composite

Prime Prime Composite Prime Composite Prime Composite Composite Composite Prime Composite 53

Let’s Practice 2

99 100

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1. (a) Color the multiples of 3 and 5 in the 100-square.

(b) What is the lowest common multiple of 3 and 5?

2. Complete the following.

(a) List the first six multiples of 8. ,

(b) List the first four multiples of 12.

(d) List the third multiple of 9. 54

3. Complete the following. (a) Find two common multiples of 3 and 7. and

(b) What is the lowest common multiple of 4 and 6?

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(a) Multiples of 6.

, 18, 24,

(b) Multiples of 7. 7,

14, 21,

, 16,

(d) Multiples of 9.

, 32,

, 36, 45,

, 42

, 49,

, 48,

, 64

, 63,

5. Find out if 4 is a factor of 18.

(a) Circle to make groups of 4 boats.

(b) Are there any boats remaining?

6. Is 3 a factor of 20? Show your working.

7. Is 6 a factor of 42? Show your working.

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8. List the factors of each number. (a) 12: (b) 18: (c) 36: (d) 59: (e) 62: (f) 100:

9. Find the common factors. Show your working.

(a) Common factors of 24 and 42:

(b) Common factors of 60 and 15:

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10. Find the greatest common factor. Show your working.

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(a) The greatest common factor of 20 and 50 is

(b) The greatest common factor of 54 and 24 is

11. Circle the prime numbers.

23 11

74 39

7 87

47 63 57

Solve It!

99 100

Multiples of prime numbers cannot be prime numbers themselves!

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Michelle is looking for prime numbers between 2 and 100. She knows 2 is a prime number. She colors it green and then crosses out all of the multiples of 2.

(a) Continue the process to find the prime numbers between 2 and 100. List them here.

(b) 792 is a composite number. Look at the digit in the ones place and explain how you know 792 is not a prime number.

At Home 1. The table shows the first 20 multiple of 3, 4, 5 and 6. Multiples of 4

Multiples of 5

Multiples of 6

3 6 9 12 15 18 21 24 27 30 33 36 39 42 45 48 51 54 57 60

4 8 12 16 20 24 28 32 36 40 44 48 52 56 60 64 68 72 76 80

5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100

6 12 18 24 30 36 42 48 54 60 66 72 78 84 90 96 102 108 114 120

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Multiples of 3

(b) Find two common multiples of 4 and 5.

(a) Find two common multiples of 3 and 4. (c) Find two common multiples of 5 and 6.

(d) What is the first common multiple of 3 and 5?

2. Complete the following. (a) Find two common multiples of 2 and 8. and

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(b) What is the lowest common multiple of 3 and 12? (c) What is the lowest common multiple of 8 and 12?

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3. Fill in the blanks.

(a) Multiples of 4. 4,

(b) Multiples of 10.

, 16, 20,

, 30, 40,

, 24,

, 48,

4. Find out if 13 is a factor of 39.

(a) Circle to make groups of 13 dots.

(b) Are there any dots remaining? (c) Is 13 a factor of 39?

, 28,

, 72,

, 70

, 96

of 4.

(b) 36 is a

of 9.

of 60.

(d) 7 is a

of 49.

(a) 21: (b) 47: (c) 48: (d) 80:

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6. List the factors of each number.

tio

(a) 12 is a

5. Complete the sentences with the word factor or multiple.

7. Find the four prime numbers between 100 and 110. Show your working.

, 61

Looking Back 1. Write the numbers.

(a) Fifty-eight thousand, two hundred forty-one.

tio

(b) Six hundred thirty-four thousand, nine hundred seven.

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2. Write in words. (a) 256,915

(b) 42,003

3. Count on in 1,000s. (a) 8,710,

(b) 496,800,

4. Count on in 10,000s.

(a) 1,121,

(d) 695,500,

5. Count on in 100,000s. (a) 600, (b) 125,780,

, ,

6. Write the value of each digit. Then add the values. 7

(b)

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(a)

7. Use the symbols >, < and = to fill in the blanks. 31,700 (b) 125,844

125,844

945,608 (d) 733,012

733,021

(a) 30,765

8. Arrange the numbers from the greatest to the smallest.

(a) 79,754 79,761 70,988

(b) 205,126 205,121 205,120

, 63

9. Fill in the blanks. 2,000 less

20,830

2,000 more

(b)

50,000 less

251,200

50,000 more

(c)

100,000 less

103,660

(d)

10,000 less

tio 100,000 more 10,000 more

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307,500

(a)

10. Find the missing numbers in the number pattern. (a)

(b) 254,500,

, 3,600, 4,600, 5,600, 6,600,

, 234,500, 224,500, 214,500,

, 410,355,

, 80,250, 130,250, 180,250,

, 280,250

11. Round the numbers to the nearest ten thousand. (b) 54,750 ≈

(a) 8,335 ≈

(d) 865,630 ≈

12. Round the numbers to the nearest hundred thousand. (a) 99,700 ≈

(b) 222,550 ≈

(d) 763,016 ≈

of 7.

(b) 3 is a

of 18.

of 24.

(d) 42 is a

of 6.

14. Fill in the blanks. 5, 10,

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(a) Multiples of 5.

tio

(a) 14 is a

13. Complete the sentences with the word factor or multiple.

, 30, 35,

(b) Multiples of 8. 8,

, 40,

, 56

15. List the factors of each number. (a) 21: (b) 47:

16. Find the two prime numbers between 20 and 30. Show your working.

, 65

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Anchor Task

Addition and Subtraction

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Operations on Whole Numbers

Let’s Learn

25,650

Keira scored 25,650 points in a computer game. Sophie scored 5,380 more points than Keira. How many points did Sophie score? 5,380

tio

Keira Sophie

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To find Sophie's score, we add. Step 1

Step 2

Add the ones.

Add the tens.

2 5 6 5 0

2 5 16 5 0

5 3 8 0

5 3 8 0 3 0

Thousands

Hundreds

Tens

Ones

Ten Thousands

We can regroup 13 tens into 1 hundred and 3 tens.

Step 3 Add the hundreds. 2 15 16 5 0 5 3 8 0

0 3 0

Step 4

Thousands

Hundreds

Add the thousands. 1

2 15 1 6 5 0 5 3 8 0

1 0 3 0

Ten Thousands

Tens

Ones

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Ten Thousands

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We can regroup 10 hundreds into 1 thousand.

Thousands

Hundreds

Regroup 11 thousands into 1 ten thousand and 1 thousand.

Tens

Ones

Step 5 Add the ten thousands. 2 15 16 5 0

5 3 8 0

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3 1 0 3 0

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25,650 + 5,380 = 31,030. Sophie scored 31,030 points.

Mr. Begg bought a boat and a trailer for a total price of $52,350. The trailer cost $4,750. Find the cost of the boat.

$52,350

$4,750

To find the cost of the boat, we subtract. Step 1

Step 2 Subtract the tens.

5 2 3 5 0

Subtract the ones. –

4 7 5 0 0

–

4 7 5 0 0 0 69

Step 3 Subtract the hundreds. 5 1 2 133 5 0

Regroup 1 thousand into 10 hundreds.

6 0 0

Step 4

Thousands

Hundreds

Subtract the thousands. 4 7 5 0

–

Ones

Regroup 1 ten thousand into 10 thousands.

5 11 2 133 5 0

Tens

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Ten Thousands

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4 7 5 0

–

7 6 0 0

Thousands

Ten Thousands

Hundreds

Tens

Ones

Step 5 Subtract the ten thousands. 5 11 2 133 5 0

4 7 5 0 4 7 6 0 0

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52,350 – 4,750 = 47,600. Mr. Begg’s boat cost $47,600.

tio

–

Find the sum and difference of 73,892 and 14,266.

To find the sum of 2 numbers, we add them together. 7 +

The sum of 73,892 and 14,266 is 88,158.

To find the difference between 2 numbers, we subtract the smaller number from the greater number. 6

–

The difference between 73,892 and 14,266 is 59,626.

Let’s Practice 1. Add.

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(a) (b) 2 4 6 8

(e) (f) 5 2 3 9 3 7

(g) (h) 9 1 8 6 7

2. Subtract.

–

(e) (f) 5 2 3 9 3 –

–

(g) (h) 9 9 4 6 4 7

–

(i) (j) 2 2 5 4 3 –

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–

tio

–

(a) (b) 5 9 7 2

–

3. Use the column method to add or subtract. (b) 14,603 – 10,735 =

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(a) 63,210 + 18,824 =

(e) 43,855 + 7,054 =

(d) 70,656 – 8,779 =

(f) 64,003 – 8,325 =

Solve It!

E –

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It’s Blake’s birthday! What flavor is his cake? Match the letters to the correct answers to find out!

–

A +

–

70,208

87,070

70,802

87,070

17,820

82,017

82,710 75

(b) Home At 1. Add.

(e) (f) 4 2 1 6 8 7

(g) 3,679 + 27,052 =

6 4

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(a) (b) 9 3 2 7

(h) 44,080 + 9,326 =

2. Subtract.

–

(e) (f) 5 2 6 4 4 –

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–

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–

(a) (b) 6 2 0 3

–

(h) 70,925 – 38,716 =

(g) 23,207 – 9,416 =

3. Find the sum and difference of each pair of numbers.

sum =

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(a) 3,827 and 7,294

difference =

(b) 56,845 and 12,033

difference =

sum =

difference =

Multiplying by a 1-digit Number

Tens

Ones

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Hundreds

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Anchor Task

Let’s Learn

The Paradise Hotel has rooms for $132 per night. How much does it cost to stay at the hotel for 3 nights?

Tens

Each row represents the cost of 1 night’s stay.

Ones

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Hundreds

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We need to multiply $132 by 3 to find out. Let’s use a place value chart to help find the answer.

$132

3x2=6

Step 1

Multiply the ones. 1 3 2

Tens

Ones

Hundreds

3 x 30 = 90

Step 2

Multiply the tens. x

1 3 2

3 9 6

Hundreds

Tens

Ones

Step 3

3 x 100 = 300

Multiply the hundreds. 3

Hundreds

Tens

Ones

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3 9 6

1 3 2

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132 x 3 = 396 So, 3 nights at the Paradise Hotel costs $396. Find 403 x 2 using the column method. 4 0 3

4 0 3

0 6

403 x 2 = 806

8 0 6

Find 2,130 x 3 using the column method. x

2 1 3 0

2 1 3 0 3

9 0

2 1 3 0 x

3 3 9 0

2 1 3 0 x

3 6 3 9 0

2,130 x 3 = 6,390

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tio

A new car has a mass of 1,275 kg. 3 identical cars are loaded onto a truck to be transported to a dealership. Find the total mass of the 3 cars.

1,275 kg

We need to multiply 1,275 kg by 3 to find the total mass of the cars. Let’s use a place value chart to help find the answer.

5 x 3 = 15. Regroup 15 into 1 ten and 5 ones.

Step 1

Multiply the ones. 1

Thousands

Hundreds

Tens

2 17 5

3 5

5 x 3 = 15 Regroup 10 ones into 1 ten and write 5 in the ones column.

Ones

Step 2 Multiply the tens. 1

2 7 5

Thousands

Hundreds

Tens

Ones

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2 5

Step 3

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7 tens x 3 = 21 tens. 21 tens + 1 ten = 22 tens. Regroup 20 tens into 2 hundreds and write 2 in the tens column.

Multiply the hundreds. 2

1 2 7 5

Thousands

Hundreds

Tens

Ones

8 2 5

2 hundreds x 3 = 6 hundreds. 6 hundreds + 2 hundreds = 8 hundreds. Step 4

5 x 3 = 15. Regroup into 1 ten and 5 ones.

Multiply the thousands. 1 22 1 7 5

Thousands

Hundreds

Tens

Ones

3 8 2 5

1 thousand x 3 = 3 thousands. 1,275 x 3 = 3,825 So, the total mass of the 3 cars is 3,825 kg. 83

Find 48 x 6 using the column method. 4

4 8

2 8 8

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4 8

48 x 6 = 288

5 27 7 4

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Find 577 x 4 using the column method. 5 27 7

5 27 7

0 8

2 3 0 8

577 x 4 = 2,308

Find 1,392 x 5 using the column method. 1 43 1 9 2

1 3 19 2

1,392 x 5 = 6,960

6 0

1 43 1 9 2 5 9 6 0

1 43 1 9 2 5 6 9 6 0

Let’s Practice 1. Multiply.

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(a) (b) 3 4

(e) (f) 1 3 5 7 7

(g) (h) 4 5 9 0

3 x

1 6

6 8

2. Use the column method to multiply. (b) 738 x 8 =

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(a) 95 x 6 =

(d) 456 x 5 =

(e) 6,782 x 7 =

(f) 9,813 x 4 =

Solve It! The shapes represent digits.

•

+2=

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x 12 =

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•

Here are some clues about the digits and the numbers they form.

Can you work out what numbers the shapes represent?

= 87

H 9

1 5

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Sophie is having ice cream for dessert. What fruit does she like on her ice cream? Match the letters to the correct answers to find out!

7 x

22,806

18,160

9,963

926

24,655

9,963

3,458

(b) Home At 1. Multiply.

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(a) (b) 2 9

(e) (f) 1 0 9 8 7

(g) (h) 5 2 4 8

7 x

2 5

0 4

2. Multiply using the column method. (b) 837 x 4 =

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(a) 173 x 6 =

(d) 5,389 x 3 =

(e) 6,841 x 8 =

(f) 9,409 x 7 =

Hands On

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3 9 4 x 4 8 3 8

tio

Ethan, Dominic and Jordan are having problems with multiplication. Work in pairs to identify the errors each child has made. Explain the error and how they can fix it.

2 10 5 x 3 6 4 5

1 7 6 x 3 3 2 1 1 8

Multiplying by a 2-digit Number

Anchor Task

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x 10

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Dice 1

Dice 2

Let’s Learn Let’s use place value disks to help multiply numbers by ten.

x 10

10 10 10

x 10

100

62 x 10 = 620 1

100

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23 x 10 = 230

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4 x 10 = 40

x 10

100 100

100

Do you see a pattern?

Let’s use place value disks to help multiply numbers by tens. We know that when we multiply a number by ten, we shift the values to the left one place and put a zero in the ones place.

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When multiplying a number by a multiple of ten, we can separate the tens and ones and multiply in 2 steps. Find 32 x 20.

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Method 1 Multiply by 10 first. Then multiply by 2. x 10

100

Method 2 Multiply by 2 first. Then multiply by 10.

32 x 20 = 640

x 10

100

200

Now, add the products together!

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2 0 8 6 + 2 3 6

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Add the products. 1

Multiply 26 and 14. We can regroup these numbers into tens and ones, then place them in a table and multiply each column and row.

0 0 0 4 4

So, 26 multiplied by 14 is 364.

Find the product of 48 and 17 using the column method.

Step 1

Multiply by the ones. 1

4 8 1

3 3 6

7 x 8 = 56 Regroup into 5 tens and 6 ones. 7 x 4 tens = 28 tens 28 tens + 5 tens = 33 tens.

4 8

Step 2 Multiply by the tens. 1

3 3 6

8 0

4 8 0

Step 3

1 ten x 8 = 8 tens

1 ten x 40 = 40 tens 40 tens = 4 hundreds

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3 3 6

4 8

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4 8

Add the products. 4 8 x

3 3 6 4 8 0 6 48 x 17 = 816

4 8

3 3 6

4 8 0 1

3 3 6

4 8 0

Find 56 x 27 using the column method.

Multiply by 7. Multiply by 20. Add the products. 4

5 6

2 7

3 9 2

56 x 27 = 1,512 96

5 6 2 7

3 9 2 1 1 2 0

5 6 x

2 7 1

3 9 2

1 1 2 0 1 5 1 2

Let’s Practice

1 1

3 x 10 10

22 x (c)

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(b)

1 1

100

10 100

al 10

(d)

100

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(a)

1. Fill in the blanks.

100

2. Find the products. (b) 4 x 7 =

6 x 50 =

12 x 30 =

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30 x 8 =

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(d) 12 x 3 =

(e) 9 x 2 =

4 x 70 =

(a) 6 x 5 =

(f) 5 x 8 =

90 x 2 =

5 x 80 =

3. Work out 17 x 36 by multiplying rows and columns in a table. Then add the products. x 30

17 x 36 =

4. Multiply using the column method.

(e) (f) 6 4

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(a) (b) 1 9

5. Multiply using the column method. (b) 28 x 14 =

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(a) 13 x 36 =

(d) 54 x 39 =

(e) 73 x 25 =

100

(f) 96 x 23 =

Solve It!

Can you work out what numbers the shapes represent?

Try and solve this using Guess and Check.

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1 01

At Home 1. Fill in the blanks. 10

100

(b)

100

102

100

(c)

100

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(a)

100

2. Find the products. (b) 5 x 9 =

3 x 40 =

100 x 6 = (f) 8 x 7 =

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70 x 7 =

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(d) 10 x 6 =

(e) 9 x 4 =

5 x 90 =

(a) 3 x 4 =

90 x 4 =

80 x 7 =

3. Multiply. Show your working.

(b) 30 x 80 =

(d) 50 x 6 =

(a) 4 x 70 =

(f) 70 x 8 =

(e) 40 x 4 =

103

4. Work out the following by multiplying rows and columns in a table. Then add the products.

20 7

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(b) 58 x 46 = x

104

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(a) 33 x 27 =

5. Multiply using the column method.

(e) (f) 8 4

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(a) (b) 1 3

105

6. Multiply using the column method. Show your working. (b) 28 x 15 =

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(a) 14 x 16 =

(d) 53 x 34 =

(e) 82 x 62 =

106

(f) 93 x 76 =

Dividing by a 1-digit Number

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Anchor Task

48 60 720 840 107

Let’s Learn Let’s use place value disks to divide 164 by 4.

10 10 10 10 10

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100

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Regroup 1 hundred into 10 tens. Now we can make equal groups!

There are 4 equal groups of 41. 164 ÷ 4 = 41

The parts of a division equation have special names.

164 ÷ 4 = 41 dividend

108

divisor

quotient

100 100

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100

Let’s use place value disks to divide 368 by 3.

100

We can make 3 equal groups of 122 with 2 ones remaining.

We say: 368 divide 3 is 122 remainder 2. We write: 368 ÷ 3 = 122 R 2

The remainder is 2!

The quotient is 122!

109

Step 1 2 4

Divide 9 tens by 4. 9 tens ÷ 4 = 2 tens remainder 1 ten. 9 tens – 8 tens = 1 ten.

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8 1

6 0

Divide 16 ones by 4. 16 ones ÷ 4 = 4 ones. 16 ones – 16 ones = 0.

quotient

96 ÷ 4 = 24

Bring the 6 ones down. 1 ten and 6 ones is 16.

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Step 2 2 4

The quotient is 24 and there is no remainder!

110

Divide 96 by 4.

divisor

dividend

8 1

6 0

remainder

Find 742 ÷ 6. Step 1 1 4

7 6 1

14 tens ÷ 6 = 2 tens remainder 2 tens. 14 tens – 12 tens = 2 tens.

6 1

2 2

Step 3 1 2

Bring down the 2 ones. Now there are 22 ones.

Bring the 4 tens down. Now there are 14 tens.

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Step 2 1 2

22 ÷ 6 = 3 R 4 22 – 18 = 4

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Divide 7 hundreds by 6. 7 hundreds ÷ 6 = 1 hundred remainder 1 hundred. 7 hundreds – 6 hundreds = 1 hundred.

2 2

The remainder is 4!

742 ÷ 6 = 123 R 4

111

Find 1,813 ÷ 7.

4 4

5 6

Step 3 5

41 tens ÷ 7 = 5 tens remainder 6 tens. 41 tens – 35 tens = 6 tens.

63 ÷ 7 = 9 63 – 63 = 0

5 6

1,813 ÷ 7 = 259

112

Bring down the 3 ones. Now there are 63 ones.

Bring down the 1 ten. Now there are 41 tens.

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Step 2

Divide 1 thousand by 7. Regroup into 10 hundreds and add 8 hundreds. 18 hundreds ÷ 7 = 2 hundreds remainder 4 hundreds. 18 hundreds – 14 hundreds = 4 hundreds.

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Step 1

Let’s Practice 1. Find the quotient and remainder.

(a) 6 ÷ 3 (b) 8 ÷ 2 Quotient: Quotient: Remainder: Remainder:

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(c) 7 ÷ 2 (d) 12 ÷ 5 Quotient: Quotient: Remainder: Remainder: (e) 21 ÷ 3 (f) 35 ÷ 8 Quotient: Quotient: Remainder: Remainder: 2. Divide.

(b) 9 ÷ 3 =

(d) 22 ÷ 6 =

(e) 27 ÷ 3 =

(f) 31 ÷ 3 =

(g) 28 ÷ 9 =

(h) 36 ÷ 6 =

(i) 52 ÷ 8 =

(j) 42 ÷ 6 =

(a) 5 ÷ 2 =

113

3. Divide. (a) (b) (c) 4

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(d) (e) (f) 8

114

(g) (h) 3

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(i) (j) 5

115

3. Complete the following.

4 9 6

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3 9 3

(a) (b)

3 2 6 4

(e) (f)

4 3 1 0 8

116

7 6 5 3 9

Hands On

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Work in pairs. Take turns choosing a 3 or 4-digit number. Show the number using place value disks. Roll a dice and divide your number by the number on the dice. Work together to show the quotient and remainder with the place value disks.

117

At Home

100

(b) 100

(c)

118

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(a)

1. Write the division equation represented by the place value disks.

100

1 1

(d)

100 100 100

100

100 100 100

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1,000

100

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100 100 100

(e)

1,000

119

2. Divide. (a) (b) (c) 4

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(d) (e) 6

1 20

3. Complete the following.

5 9 4

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3 8 1

(a) (b)

6 7 8 0

(e) (f)

9 7 0 3 8

4 1 2 2 7

121

Word Problems

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Mr. Wong bought a new dining set which included a dining table and 6 chairs. The table cost $488 and one chair cost $136. Find the total cost of the dining set. Use rounding and estimation to check if your answer is reasonable.

Step 1 First, let’s find the total cost of the 6 chairs.

$136 chairs

To find the total cost of the 6 chairs, we multiply.

1 33 6 6

8 1 6

136 x 6 = 816 The total cost of the chairs is $816.

1 22

$488

$816

table

6 chairs ?

4 8

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To find the total cost of the dining set, we add.

Step 2

488 + 816 = 1,303 The total cost of the dining set is $1,304.

Check Let’s use rounding and estimation to check that the answer is reasonable.

Cost of 6 chairs = $816 ≈ $800 Cost of table = $488 ≈ $500

$800 + $500 = $1,300 1,300 is approximately equal to 1,304. So, the answer is reasonable.

123

A clothing factory makes shirts that have 8 buttons. The factory orders 715 buttons and uses them to make shirts.

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(a) Find the total number of shirts that can be made with the buttons. Check that your answer is reasonable.

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Let’s use a bar model to help find the answer. 8 buttons shirts

4 7

715 ÷ 8 = 89 R 3 The clothing factory can make 89 shirts with 3 buttons left over. Check Let’s check that the answer is reasonable.

70 ÷ 8 ≈ 9 700 ÷ 8 ≈ 90

90 is close to 89 so our answer is reasonable. 124

(b) The shirts are sold for $28 each. How much money does the clothing factory receive if all of the shirts are sold? Check that your answer is reasonable. 1 shirt

89 shirts

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1 shirt

$28

To find the total amount of money, we multiply.

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2 8

8 9 2 5 2

2 2 4 0 2 4 9 2

The clothing factory will receive $2,492.

Check Let’s use rounding and estimation to check that the answer is reasonable.

Round 28 and 89 to the nearest 10. 28 ≈ 30 and 89 ≈ 90 3 x 9 = 27 3 x 90 = 270 30 x 90 = 2,700 2,700 is close to 2,492 so our answer is reasonable.

125

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Farmer Joe picks 1,758 apples from his orchard in the morning. He picks 4 times as many apples in the afternoon. The apples are placed in small baskets to be sold at the market. Each basket holds 6 apples. Find the total number of baskets of apples. Check that your answer is reasonable.

Step 1 First, we need to find the total number of apples picked.

morning

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1,758

afternoon

Multiply 1,758 by 4 to find the number of apples picked in the afternoon. 3

1 27 35 8

7 0 3 2

7,032 apples were picked in the afternoon. 7,032

morning

afternoon

1,758

1 7 15 8

+ 7 0 3 2 8 7 9 0

126

8,790 apples were picked in all.

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Step 2

Check 1,758 ≈ 1,800 7,032 ≈ 7,000 1,800 + 7,000 = 8,800 8,800 is close to 8,790, so the answer is reasonable.

6 apples

8,790 apples

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apples ?

Now we can divide.

4 6 5 7 9 0 7 4 3 9 3 6 3 0 3 0 0

1 6 8 6 2 2

A total of 1,465 baskets are used to pack the apples.

Check 8790 ≈ 9000 90 ÷ 6 = 15 900 ÷ 6 = 150 9000 ÷ 6 = 1,500 1,500 is close to 1,465, so the answer is reasonable. 127

Step 1 Find the cost of a computer. $ printer computer

A computer cost $

Check

1 28

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1. A computer costs 3 times as much as a printer. Summer Bay Primary School bought a printer and 5 computers for the IT center. The printer cost $476, find the total cost of all the items. Check that your answer is reasonable.

Let’s Practice

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Step 2 Find the cost of 5 computers.

$ printer

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Step 3 Find the total cost of the items.

computers

The total cost of the items is $

Check

129

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2. Halle buys gifts for the 23 pupils in her class. Each gift box is tied with a piece of ribbon that is 36 cm long. She bought 1,000 cm of ribbon. How much ribbon does she have left? Check that your answer is reasonable.

1 30

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3. Mrs. Cooper orders 3,192 kg of soil for her new garden. She puts half of the soil on the front lawn. She puts equal amounts of the remaining soil into 7 big pots. Find the mass of the soil in each pot. Check that your answer is reasonable.

131

At Home

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1. 78 people in an office each donate $63 for a charity fundraiser. The money is collected and shared equally between 4 charities. How much money does each charity receive? Check that your answer is reasonable.

Step 1 Find the total amount of money raised. $63

78 people

A total of $

Check

1 32

was raised.

Step 2 Find the amount of money each charity received.

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charities

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Each charity received $

Check

133

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2. A bakery bakes 3,310 rolls. It sells 1,014 rolls in bags of 6. The remaining rolls are sold in bags of 8. Find the total number of bags to be sold. Check that your answer is reasonable.

1 34

Looking Back 1. Add or subtract.

–

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(a) (b) 1 3 3 6

(e) 1,068 + 7,951 =

(f) 2,106 – 955 =

(h) 46,040 – 18,565 =

(g) 23,840 + 27,291 =

–

135

2. Work out the following by multiplying rows and columns in a table. Then add the products. (a) 18 x 39 =

30 9

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(b) 24 x 26 = x 20

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3. Multiply using the column method. (a) (b) 1 7

136

(d) 52 x 13 =

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(f) 25 x 77 =

(e) 44 x 43 =

(h) 39 x 64 =

(g) 16 x 82 =

137

4. Divide. (a) (b) 4

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4 7 8 3 9

138

8 6 2 2 4

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5. A factory produces 1,366 tins of pears and 4 times as many tins of peaches. They are placed into 4 storage containers in equal numbers. Find the number of tins in each storage container. Check that your answer is reasonable.

139

Equivalent Fractions

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Anchor Task

Fractions

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140

Let’s Learn

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Halle, Sophie and Chelsea each have a paper strip of the same size. Halle divides her paper strip into 3 equal parts. She colors 1 part. 1 of the paper 3 strip is colored.

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Sophie divides her paper strip into 6 equal parts. She colors 2 parts.

Chelsea divides her paper strip into 9 equal parts. She colors 3 parts.

2 6

of the paper strip is colored.

3 9

of the paper strip is colored.

Let’s compare each strip of paper.

1 3 2 6 3 9

and 39 are equal. Equal fractions are called equivalent fractions. The fractions

1 2 3, 6

1 2 3 = = 3 6 9

1 41

Find equivalent fractions of 1 using multiplication. 4

1 4

= x2

2 8

1 4

3 12

1 4

4 16

1 4

2 3 4 , , and 5 are equivalent fractions of 1 . 8 12 16 4 20 1 4

2 8

1 = 2 = 3 = 4 = 5 4 8 12 16 20

142

= 20

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1 4

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2 8

Multiply the numerator and denominator by the same number.

3 12

4 16 5 20

Find the first 4 equivalent fractions of 1 . 5

2 10

1 5

3 15

1 5

= 20

= 25

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2 3 4 , , and 5 are equivalent fractions of 1 . 10 15 20 25 5

1 5

1 = 2 = 3 = 4 = 5 5 10 15 25 25

Find the first 4 equivalent fractions of 2 . 3

2 3

= 6 x2

2 3

6 9

2 3

= 12

2 3

= 15

4 6 8 , , and 10 are equivalent fractions of 2 . 6 9 12 15 3

4 = 6 = 8 = 10 = 2 6 9 12 15 3

143

We can find equivalent fractions by multiplying the numerator and denominator by the same number.

÷3

6 = 18

2 6

1 3

÷2

6 18

2 6

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÷3

2 6

÷2

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We can also find equivalent fractions by dividing the numerator and denominator by the same number.

We cannot divide the numerator and denominator of 1 3 further.

1 3

When a fraction cannot be divided further by the same number, we say it is in its simplest form. 1 is the simplest form of 6 . 3 18

Find the simplest form of 8 .

The numerator and denominator are both divisible by 4.

÷4

8 = 12

2 3

÷4

2 is the simplest form of 8 . 3 12

144

8 12 2 3

Let’s Practice 1. Use the fraction chart to find equivalent fractions.

1 5

1 4

1 5

1 3

1 6

1 5

1 6

1 4

1 5

1 6 1 1 1 7 7 7 1 1 1 8 8 8 1 1 1 1 9 9 9 9 1 1 1 1 10 10 10 10 1 1 1 1 1 11 11 11 11 11 1 1 1 1 1 12 12 12 12 12

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1 1 1 6 6 6 1 1 1 7 7 7 1 1 1 1 8 8 8 8 1 1 1 1 9 9 9 9 1 1 1 1 1 10 10 10 10 10 1 1 1 1 1 11 11 11 11 11 1 1 1 1 1 1 12 12 12 12 12 12

1 2

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1 5

1 4

1 3

1 2

1 7

1 9

1 10

1 12

1 11

1 8

(a) (b) 1 = = =

4 5

2 3

145

2. Use multiplication to find equivalent fractions.

3 4 3 4

3 4

= x2 =

(b)

2 5

x2 =

(c)

1 4

(d)

146

3 7

x2 =

1 4

3 7

2 5

1 4

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2 5

= x2

2 5

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(a)

= x3

3 7

= x4

3. Use division to find equivalent fractions.

8 20

÷4

8 20

= ÷2

8 20

÷4 =

18 27

÷9

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÷3

(b)

18 27

÷3

18 27

(c)

÷3

6 18

÷3

÷2

(d)

8 32

÷2

8 32

6 18

÷3

÷6

÷4

÷8

= ÷4

÷6

6 18

÷9

÷2

6 18

÷2

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(a)

8 32

= ÷8

= 147

4. Fill in the blanks.

8 10

1 3

3 5

2 7

4 12

10 35

7 10

42 60

3 8

12 32

12 16

3 4

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9 15

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4 5

(a) (b)

(e) (f)

12 32

3 8

(g) (h) =

2 7

10 35

(i) (j)

1 48

42 60

7 10

1 4

1 9

(e) (f) 5 = =

7 12

(a) (b) 1 =

1 2

2 3

8 16

12 18

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(a) (b) 3 = =

5. Find the first 2 equivalent fractions.

6. Write an equivalent fraction.

(e) (f) =

6 8

(g) (h) 5 10 =

4 2

149

7. Check the fraction that is in its simplest form.

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(a)

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(b)

(c)

8. Circle the fractions that are in their simplest form.

150

1 3

4 8

2 5

3 6

5 15

3 12

4 7

3 11

10 16

6 18

7 10

6 8

12 22

8 24

4 9

Solve It!

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We both have 1 4 of a pizza left!

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Ethan and Jordan bought pizza for lunch. Their pizzas were cut into 4 equal slices. They each ate 3 slices of pizza. Ethan said that they have an equal amount of pizza left, but Jordan disagrees. Look at their pizzas below and decide who is correct. Explain your answer.

What about the size and shape of the slices?

1 51

(b) Home At 1. Write the equivalent fractions.

(b)

1 3

(c)

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1 2

3 6

3 4

(d)

152

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(a)

2. Use multiplication to find equivalent fractions.

4 7 4 7

4 7

= x2 =

(b)

2 9

x2 =

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2 9

= x2

2 9

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(a)

2 9

3. Use division to find equivalent fractions. (a)

÷2

12 20

÷4

12 20

÷2

12 20

÷4

÷3

(b)

18 42

÷6

18 42

÷3

18 42

= ÷6

= 1 53

4. Write an equivalent fraction. =

4 5

2 3

5. Find the first 2 equivalent fractions.

1 3

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(a) (b)

5 6

4 11

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(a) (b) 2 = =

(a) (b) 4 =

9 12

6. Find the equivalent fraction in its simplest form.

15 35

7. Tell whether the fractions are equivalent by writing = or ≠.

(a) (b) 3 6

154

10 14

5 6

24 32

3 4

Mixed Numbers and Improper Fractions Let’s Learn

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How many pizzas are there?

1 whole

1 half

There are 2 whole pizzas and 1 half pizza. 2+ 1 =2 1 2

There are two and a half pizzas.

There are 2 1 pizzas. 2

2 1 is a mixed number.

Adding a whole number and a fraction gives a mixed number.

155

1 whole

1 quarter

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1 whole

How many limes are there?

There are 3 whole limes and 1 quarter of a lime. 4

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3+ 1 =3 1

There are 3 1 limes. 4

Write a mixed number that represents the colored parts of the shapes. (a)

2+ 1 =2 1

(b)

2+ 3 =23 5

(c)

156

3+ 5 =35 8

Let’s look at mixed numbers on a number line. (a) 2 3

(b)

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1 2

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The arrow is pointing at 1 2 .

1 3

The arrow is pointing at 2 1 . 2

1 4

2 4

3 4

22 23 4

The arrow is pointing at 2 3 . (d)

1 5

2 5

3 5

4 5

13 5

The arrow is pointing at 1 3 .

1 57

1 whole

1 quarter

When the numerator is greater than or equal to the denominator, we get an improper fraction. Improper fractions are greater than or equal to one. Five quarters is an improper fraction.

When the numerator is less than the denominator, we get a proper fraction. Proper fractions are less than one. One-half is a proper fraction.

158

4 quarters

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1 1 1 1 1 1 = + + + + 4 4 4 4 4 4 5 = 4 There are 5 of a cake. 4 5 is an improper fraction. 4

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Express the amount of cake in quarters.

1 quarter

There are five quarters of cake.

5 4

1 2

Write an improper fraction to represent the shapes. (a)

17 6

(b)

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13 3

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(c)

17 5

3 x 5 = 15

(d)

21 8

(e)

2 x 8 = 16

27 9

3 x 9 = 27

(f)

19 2

9 x 2 = 18

1 159

Let’s Practice

1 2

3 4

1 4

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3 8

1. Match.

1 4

3 4

eg 1

160

2. Write the mixed number represented by the colored parts of the shapes.

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(a)

(c)

(d)

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(b)

(e)

(f)

161

3. Fill in the blanks. (a) 1 1 is represented by point

(b) 2 2 is represented by point

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1 2

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S 2

4. Draw a point to show the fraction on the number line. (a) 1 3

(b) 1 4

1 62

5. Match.

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5 2

8 4

7 5

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5 3

10 3

12 7

163

6. Write the improper fraction represented by the colored parts of the shapes.

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(a)

(c)

(d)

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(b)

(e)

(f)

164

7. Check the improper fractions.

5 2

(b)

6 7

(c)

2 3

1 2

4 5

5 2

1 2

9 3

12 5

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1 2

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(a)

2 2

7 4

6 8

3 4

3 10

8. Check to name each fraction.

5 2

(a)

1 2

(b)

proper improper mixed number

(c)

(d)

proper improper mixed number

4 7

proper improper mixed number

7 8

proper improper mixed number

165

Solve It!

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hat is Sophie’s favorite fruit? W Match the mixed numbers and improper fractions to find out.

166

4 3

7 4

4 3

5 2

At Home 1. Write the mixed number represented by the colored parts of the shapes.

(b)

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(a)

2. Write the improper fraction represented by the colored parts of the shapes.

(a)

(b)

1 67

3. Match.

1 2

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1 3

6 2

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8 3

1 2

168

12 7

4. Write the mixed number shown on the number line. (a)

(b) 1

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(c)

(d)

5. Label each fraction as proper, improper or mixed number.

4 3

(a)

1 2

(b)

(c)

(d)

8 9

12 5 169

Comparing and Ordering Fractions Let’s Learn

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Ethan and Dominic each bought a pumpkin pie of the same size. They compared how much pie they had left. I have 2 of 3

the pie left.

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2 3

I have 3 of 4

the pie left.

3 4

Dominic has more pie left than Ethan.

We say:

3 is greater than 2 . 4 3

We write: 3 > 2 We say:

2 is smaller than 3 . 3 4

We write: 2 < 3 170

2 3

3 4

How else can you compare these fractions?

Compare the fractions. Which is greater 1 or 3 ? 2

3 > 1 5

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Compare the fractions. Which is smaller 3 or 3 ? 4

3 4

3 < 3 7

3 5

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1 2

3 7

Arrange the fractions 7 , 1 and 1 in order from the smallest to 8 6 2 the greatest.

1 6

7 8

1 2 greatest

smallest

Arrange the fractions 3 , 5 and 6 in order from the greatest to 4 9 7 the smallest. 6 7 greatest

3 4

5 9 smallest

171

Riley has 3 of an apple pie. Halle has 5 of an apple pie of 4

the same size.

5 8 Halle’s apple pie

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Riley’s apple pie

tio

3 4

Which child has the larger portion of apple pie?

Let’s find an equivalent fraction of 3 that has the same 4 denominator as 5 .

3 4

and 6 are 8 equivalent fractions.

6 8

3 4

5 8

Riley’s apple pie

Halle’s apple pie

When comparing fractions with the same denominator, the greater the numerator, the greater the fraction. So, 6 is greater than 5 .

8 3 > 5. 4 8

Riley has the larger portion of apple pie.

172

Compare 5 and 5 . Which fraction is greater? 6

5 9

tio

5 6

So, 5 > 5 . 6

Ed uc a

hen comparing fractions with the same numerator, the smaller W the denominator, the greater the fraction.

First, let’s find equivalent fractions with a common denominator.

Compare 3 and 5 . 4

Which fraction is smaller?

3 4

9 12

5 6

10 12

3 4

9 12

5 6

10 12

9 is smaller than 10 . 12 12 3 5 So, < . 4 6

173

Let’s Practice 1. Compare the fractions.

1 4 1 5

(b)

3 5 3 7

Ed uc a

> 1 6 1 8

(c)

(d)

174

tio

(a)

5 9 4 7

2. Label the fractions on the number line and compare.

tio

(a)

(b)

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(c)

175

3. Write the fractions. Arrange the fractions from the smallest to the greatest.

Ed uc a

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(a)

smallest

(b)

greatest

smallest

176

greatest

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(c)

smallest

(d)

greatest

smallest

177

4. Make equivalent fractions, then compare. The first one has been done for you. (a) Compare 1 and 3 . 4

x2 2

2 4

x2 3

2 3

3 4

1 2

3 4

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(b) Compare 2 and 4 .

tio

1 2

2 3

4 9

5 6

7 12

1 4

5 16

5 6

(d) Compare 1 and 5 .

178

1 4

5. Make equivalent fractions, then compare. (a) Compare 1 and 1 .

1 2

1 3

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1 2

tio

(b) Compare 2 and 2 . 5

2 5

2 3

5 9

2 3

2 5

4 6

5 9

179

Ed uc a

Draw and label the fractions in your notebook. Repeat the process until the bag of dominos is empty.

tio

Work in pairs. Take turns picking a domino from a bag. Your domino represents a proper fraction. Compare your fractions by placing them in the boxes below.

Hands On

180

At Home 1. Write and compare the fractions.

(a)

tio

(c)

(d)

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(b)

(e)

(f) < 181

2. Write the fractions. Arrange the fractions from the smallest to the greatest.

Ed uc a

tio

(a)

smallest

(b)

greatest

smallest

182

greatest

3. Arrange the fractions from the smallest to the greatest.

2 3

2 7

2 5

smallest

1 8

1 9

smallest

4 7

greatest

1 3

(c)

smallest

5 6

(d)

1 3

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(b)

greatest

tio

(a)

smallest

1 6

3 4

greatest

5 7

greatest

183

4. Make equivalent fractions then compare. (a) Compare 2 and 5 .

2 3

5 8

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2 3

tio

(b) Compare 4 and 5 . 5

4 5

5 7

1 6

5 7

4 5

184

3 4

1 6

Adding and Subtracting Fractions

Ed uc a

tio

Anchor Task

185

Let’s Learn Jordan folds a piece of paper into 9 equal parts. He colors 1 of the paper blue.

tio

Dominic colors 4 of the paper green.

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Find the total fraction of paper they colored.

older Jordan

1 9

4 9

5 9

1 + 4 = 5 9

When adding like fractions, we add the numerators and leave the denominator unchanged.

186

Find the sum of 5 and 3 . 12

Divide the numerator and the denominator by 4 to simplify.

Write the answer in its simplest form.

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5 + 3 = 8 12 12 12 = 2 3

Halle and Riley shared an orange. Halle ate 1 of the orange.

1 2

2 Riley ate 1 of the orange. 4

1 4

How much of the orange did Halle and Riley eat in all?

1 2

1 4

1 2

2 4

3 4

1 + 1 = 2 + 1 2 4 4 4 3 = 4

Halle and Riley ate 4 of the orange in all. 1 87

Find the sum of 1 and 3 . 10

1 5

2 10

3 10

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2 10

1 5

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3 10

Express the

1 + 3 = 2 + 3 answer in its 5 10 10 10 simplest form. 5 = 10 = 1 2

5 = 1 10 2

Find the sum of 2 and 2 . 3

6 9

2 3

2 + 2 = 6 + 2 3

9 = 8 9

1 88

6 9

2 9

5 10

1 2

Keira and Riley each have a similar shaped pancake for breakfast. 2

4 9

Riley

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Keira

tio

2 3

Keira eats 3 of her pancake. 4 Riley eats 9 of her pancake.

How much more pancake did Keira eat than Riley? Find an equivalent 2 fraction of that has the 3 same denominator as 4 .

2 3

6 – 9

2 3

and 6 are 9 equivalent fractions.

6 9

4 = 9

2 9

2 – 4 = 6 – 4

9 9 = 2 9 Keira ate 2 more pancake than Riley. 9 3

189

Find the difference between 3 and 5 . 3 4

–

5 12

9 12

–

9 12

3 4 x3

12 = 4 12 = 1 3

Express the answer in its simplest form.

4 = 1 12 3

Find the difference between 4 and 3 . 5

8 10

4 5

8 10

3 10

4 – 3 = 8 – 3 5

190

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3 – 5 = 9 – 5 4

5 12

tio

10 10 = 5 10 = 1 2

4 12

1 3

is blue.

tio

1. Add to find the fraction each shape is colored. (a) is green.

Let’s Practice

(b)

Ed uc a

of the shape is colored.

is pink. +

is orange.

of the shape is colored.

(c)

is yellow. +

is red.

of the shape is colored.

191

2. Use the models to help subtract the fractions. Give the answer in its simplest form. (a)

Ed uc a

tio

(b)

3 – 1 = 5

(c)

4 – 3 = 6

(d)

5 – 4 =

6 – 1 =

(f)

(e)

192

3 – 2 = 7

3 – 2 = 4

3. Find the equivalent fraction and add.

+ 1 12

3 (b) + 1 = 8

+ 1 8

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2 (c) + 1 = 2 + 9

(d) 1 + 5 = 12

(e) 4 + 2 = 5

+ 5

tio

1 (a) + 1 =

+ 2 10

+ 193

1 (a) + 1 = 4

Ed uc a

tio

4. Find the equivalent fraction and add. Use the space to draw a model and show your working. Write the answer in its simplest form.

1 (b) + 2 = 2

7 (c) + 1 = 4

3 3 (d) + =

194

5. Find the equivalent fraction and subtract.

– 1

9 (b) – 1 = 9 – 12

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tio

4 (a) – 1 =

11 (c) – 2 = 11 – 15

1 (d) – 3 = 14

3 14

–

(e) 5 – 5 = 12

5 12

–

195

5 (a) – 3 = 12

Ed uc a

tio

6. Find the equivalent fraction and subtract. Use the space to draw a model and show your working. Write the answer in its simplest form.

1 (b) – 3 = 2

12 (c) – 1 = 4

1 (d) – 7 =

196

Solve It!

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Ed uc a

Jordan spent the weekend at his grandmother's house. In which city does she live? Add or subtract the fractions and match the letters to find out.

3 5

7 12

3 5

1 2

1 7

1 197

1. Color and add. Write the answer in its simplest form. (a) 4 is green and 1 is blue. 6

tio

At Home

(b)

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of the shape is colored in total.

2 is yellow and 3 is red. 8 8

of the shape is colored in total.

3 is green and 11 is blue. 21 21

(c)

(d)

of the shape is colored in total.

1 is orange, 5 is blue and 4 is pink. 12 12 12

of the shape is colored in total. 1 98

2. Match. 4 – 1

1 3

7 – 2 8

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9 – 6 12

3 – 2

11 – 7 14

6 – 1 10

1 5

1 2

2 7

1 4

5 8

199

3. Find the equivalent fraction and add. Write the answer in its simplest form.

1 (d) + 1 = 1 +

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3 (c) + 1 = 3 + 8

+ 3

tio

2 + 1 (b) + 3 =

3 (a) + 1 =

4. Find the equivalent fraction and subtract. Write the answer in its simplest form. 5 (a) – 3 = 5 – 6

2 (c) – 2 =

–

(b) 3 – 1 =

2 00

–

3 (d) – 1 = 4

–

1 (a) + 1 = 4

Ed uc a

tio

5. Find the equivalent fraction and add. Use the space to draw a model and show your working. Write the answer in its simplest form.

1 (b) + 3 = 2

3 (c) + 2 = 9

3 (d) + 3 = 20

2 01

1 (a) – 1 = 12

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tio

6. Find the equivalent fraction and subtract. Use the space to draw a model and show your working. Write the answer in its simplest form.

4 (b) – 2 = 5

5 (c) – 3 = 24

2 (d) – 12 =

202

Multiplying Fractions

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Chocolate Lava Cake Recipe

tio

Anchor Task

Ingredients

1 teaspoon salt 3

5 3 ounces of chocolate

2 large eggs

1 cup flour 4

2 large egg yolks

1 cup unsalted butter 2

1 1 cup sugar

203

A pizza is cut into 8 equal slices. Sophie and her 4 friends each eat a slice. What fraction of the pizza did they eat in all? 1 8

1 8

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1 8

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1 8

Let’s Learn

5 8

1 1 1 1 1 5 + + + + = 8 8 8 8 8 8 5 1 = 5 x 8 8 5 They ate 8 of the pizza in all.

1 5

Multiply 5 by 4.

1 5

1 5 1 5

4x 5 = 5 2 04

4 5

5 8

is the same as 5 x the unit fraction 1 . 8

Riley is making lemonade for a school fundraiser. 1

The recipe requires a 3 cup of fresh lemon juice per jug. She plans on making 5 jugs of lemonade.

1 3

1 3 1 3 1 3

1 3

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How much lemon juice will she need in total?

Multiply the numerator by the whole number. Then simplify.

1 3 1 3

5 2 = 1 3 3

5x1

5x 3 = 3 5 2 = 3 = 1 3

When multiplying a fraction by a whole number, we multiply the numerator by the whole number. We simplify if the product is greater than or equal to 1. 2

Riley needs 1 3 cups of lemon juice in total. 205

The running track at Ethan's school is

1 mile around. 4

Find the total distance he ran.

6 = 1 42 4

1 2

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Let's skip count on a number line to find the answer.

Ethan runs 6 laps of the track.

1 2 3 4 5 6 , , , , , 4 4 4 4 4 4

2 3 4 5 , , , 4 4 4 4

and 6

are multiples of 1 . 4

Ethan ran a total distance of 1 2 miles. 2

Find 4 x 7 . 2 Use the number line to find the first 4 multiples of .

1 7

2 7

2 4 6 8 , , , 7 7 7 7 8 1 = 1 7 7 2 1 4x 7 =17

206

3 7

4 7

5 7

6 7

12 13 14 15 16 7

We can find the product using this method too!

4x2

4 x 7 = 7 8 = 7 1

= 1 7

Let’s Practice

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(b) 5 x 1 =

tio

(a) 3 x 1 =

1. Color the unit fractions to multiply. Write the answer in its simplest form.

(d) 5 x 1 = 2

(e) 9 x 1 =

(f) 10 x 1 = 4

= 207

2. Use the number line to find the product. (a) 6 x 1 =

2 7

3 7

4 7

5 7

1 9

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(b) 5 x 1 = 9

6 7

tio

1 7

2 9

3 9

4 9

5 9

6 9

7 9

8 9

1 4

2 4

3 4

(d) 4 x 2 =

1 5

2 5

3 5

(e) 6 x 2 =

208

1 3

2 3

4 5

(a) 3 x 4 =

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tio

(b) 3 x 3 =

3. Multiply the fractions. Write the answer in its simplest form. Use the space provided to show your working.

(d) 8 x 1 =

(e) 5 x 5 =

(f) 3 x 7 =

209

At Home 1. Match.

5x 1

tio

3x 1

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18 x 1

7x 1

21 0

7x 1

15 6

13 4

11 x 1

2. Use the number line to find the products. (a) 7 x 1 =

(b) 6 x 2 =

1 5

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1 2

2 5

3 5

4 5

12 13 14 5

2 2 1 22 23 24 5

1 4

2 4

3 4

13 4

23 4

3. Multiply the fractions. Write the answer in its simplest form. Use the space provided to show your working. (a) 6 x 5 =

(b) 1 0 x 4 =

211

Word Problems Let’s Learn 1 of her pocket money on a present for her father and 3

tio

1 of her pocket money on some new pencils. 6

S ophie spent

What fraction of her pocket money did she spend in total?

Ed uc a

Express the answer in its simplest form.

1 2 = 3 6

1 6

1 1 2 1 + = + 3 6 6 6 3 = 6 1 = 2

Sophie spent

212

3 6

can be simplified to 1 . 2

1 of her pocket money. 2

Blake picked 48 strawberries at the farm. He ate 1 of the strawberries he picked. 6

How many strawberries did he eat?

tio

? 6

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48 x 1 = 48 x 1

If 6 units is 48 strawberries, then 1 unit is 48 ÷ 6 = 8 strawberries!

6 48 = =8 6

Blake ate 8 strawberries.

Mr. Hopkins has an empty field for planting corn and wheat. He plants corn in 1 of the field and wheat in 3 of the field. 2

What fraction of his field does he use in all?

3 8

1 2

1 = 4 8 2

Add. 3 + 4 = 7 8 8 8

Mr. Hopkins used 7 of his field in all. 8

213

Dominic bought a 3 kg pack of flour.

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How many kilograms of flour does he have left?

4 1 He used of the pack to bake some cookies. 3

3 kg 4

kg of flour

pack of flour

1 3

1– 1 = 2 3

Each unit in the model is 1 kg. 4

2x 1 = 2x1 4

= 2 = 1 4

Dominic has 1 kg flour left. 2

21 4

The units in the model represent 1 kg and 1 of 4 3 a pack.

Let’s Practice 1. Halle eats 1 of a health bar. 8

Her sister eats 3 of the health bar. 8

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tio

What fraction of the health bar did they eat in total?

They ate

of the health bar in total.

2. A baker bakes 28 pies.

She sells 2 of the pies before lunch time. 7

How many pies remain?

7 units =

1 unit =

5 units = 5 x

pies

pies =

pies

pies remain. 215

3. Jordan and Dominic shared a pizza. Together they ate 7 of the pizza.

8 3 If Jordan ate of the pizza, find the 8

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fraction of the pizza that Dominic ate.

–

Dominic ate

of the pizza.

4. Sophie has a piece of ribbon 4 m in length. 5

She uses 1 of the ribbon to tie a bow on a gift. 2

How much ribbon does she have left?

Sophie has 21 6

m of ribbon left.

5. Wyatt takes $42 to the mall. He spends 1 of his money on a movie ticket. 3

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How much money does he have left?

Wyatt has $

left.

6. Halle has a 5 m length of rope.

She uses 2 of the rope to make a swing. 3

How much rope does she have left?

Write your answer as a mixed number.

Halle has

m of rope left. 217

At Home 1. Michelle read 4 of a book on Saturday and the rest on Sunday. 9

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tio

What fraction of the book did she read on Sunday?

–

Michelle read

of the book on Sunday.

2. Ethan had 2 cakes.

He ate 2 of a cake. 5

How much cake does he have left?

Write your answer as a mixed number.

1 cake

Ethan has 218

1 cake

= cakes left.

3. Mrs. Taylor uses 1 of a tank of gas to drive to the beach.

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What fraction of the tank did she use in all?

4 2 She then uses of a tank to drive to her family's farm. 3

Mrs. Taylor used

of the tank of gas in all.

4. Keira saved $200 and spent 3 of her money on a new tennis

racket. Find the cost of the racket.

The racket cost $

. 219

Looking Back 3 4

2 5

(e) (f) 3 = =

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tio

(a) (b) 1 = =

2 9

(a) (b) 2 =

9 15

12 16

2. Write the equivalent fraction in its simplest form.

15 45

(e) (f) 18 =

3. Write = or ≠.

12 14

2 7

11 33

1 3

(a) (b) 1 6

22 0

1. Find the first 2 equivalent fractions.

4. Write the improper fraction represented by the colored parts of the shapes.

tio

(a)

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(b)

5. Write the mixed number represented by the colored parts of the shapes in its simplest form. (a)

(b)

6. Draw a point to show the fraction on the number line. (a) 2 1

(b) 9

2 221

7. Arrange the fractions from the smallest to the greatest.

1 3

1 7

1 2

smallest

6 10

3 4

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2 3

(b)

greatest

tio

(a)

smallest

greatest

8. Find the equivalent fraction and add. Write the answer in its simplest form. Use the space to draw a model and show your working.

3 3 (a) + = 15

6 (b) + 1 =

22 2

9. Find the equivalent fraction and subtract. Write the answer in its simplest form. Use the space provided to draw a model and show your working. 4 – 1 = (a) 15

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3 (b) – 2 = 7

10. Multiply the fractions. Write the answer in its simplest form. Use the space provided to show your working. (a) 3 x 5 =

(b) 7 x 3 =

223

11. Sophie went to the cinema. She spent 1

1 of her money on some snacks. What 5

Ed uc a

tio

fraction of her money did she have left?

of her money on the admission ticket and

Sophie had

of her money left.

12. There are 60 people in the cinema. 1 of the people are children. 4

How many adults are in the cinema?

224

adults are in the cinema.

13. Dominic has 4 m length of string. 5

Jordan gives him 3 m of string. 4

What is the total length of string Dominic has now?

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Express your answer as a mixed number in its simplest form.

Dominic has

m of string.

14. Halle drank 2 of a cup of fruit juice 5

and Riley drank 1 of a cup of fruit 3

juice of the same size.

How much more juice did Halle

drink than Riley?

Halle drank

cup more juice than Riley. 225

Decimals

Tenths

Ed uc a

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Anchor Task

22 6

Let’s Learn Halle counts the color of jelly beans in a packet. 3

She finds that 10 of the jelly beans are red. 3

tio

We can write the fraction 10 as the decimal 0.3.

A decimal is a number that has digits to the right of the

3 = 0.3 10

Ones

Tenths

Zero point three.

The digit to the right of the decimal point tells us the number of tenths.

Ed uc a

decimal point.

decimal point

We say: zero point three We write: 0.3

The number line shows tenths between 0 and 1 as fractions and decimals. 0 10

1 10

2 10

3 10

4 10

5 10

6 10

7 10

8 10

9 10

10 10

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

227

This is 1 whole divided into ten equal parts.

1 whole

= 1 10 = 0.1

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0.1

We say ‘zero point one’.

0.1 Ones 0

0.5

1 whole

0.4

. Tenths .

4 parts = 4 tenths

= 4 10 = 0.4

0.4

Ones

. Tenths

4 parts of the whole are coloured.

228

1 part = 1 tenth

tio

1 part of the whole is colored orange.

1 whole

We say ‘zero point four’.

0.5

0.1

tio

There are 10 tenths in 1 whole.

Write and say the decimal represented by the place value disks.

0.1

Ones 0

0.1

Ones 0

0.1

Ed uc a

0.1

. Tenths .

0.5 zero point five

0.8 zero point eight

1.3 one point three

0.1

Ones

. Tenths

0.1

Tens

Ones

. Tenths .

12.6 twelve point six

229

Let's find the value of each digit in the number. (a)

4 The value of the digit 4 is 4. The value of the digit 2 is 0.2. 4 + 0.2 = 4.2

(b)

Ed uc a

7.3

0.3 7

The value of the digit 1 is 10. The value of the digit 7 is 7. The value of the digit 3 is 0.3. 10 + 7 + 0.3 = 17.3 4

2.8

(c)

230

tio

0.2

4.2

0.8 2

4 0

The value of the digit 4 is 40. The value of the digit 2 is 2. The value of the digit 8 is 0.8. 40 + 2 + 0.8 = 42.8

Ed uc a

width of button = 9 tenths of a centimeter

tio

What is the width of the button?

= 9 cm 10 = 0.9 cm

Ones 0

. Tenths .

The width of the button is 0.9 cm.

What is the length of the crayon?

length of crayon = 7 cm + 5 tenths cm

= 7 5 cm 10 = 7.5 cm

Ones 7

. Tenths .

The length of the crayon is 7.5 cm. 231

What is the mass of the pineapple?

0 4 kg

1 kg

= 1 3 kg 10 = 1.3 kg

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3 kg

tio

mass of pineapple = 1 kg + 3 tenths kg

2 kg

Ones 1

. Tenths .

The mass of the pineapple is 1.3 kg.

What is the volume of water in the container?

volume = 1 liter + 2 tenths liters = 1 2 l 10 = 1.2 l Ones 1

. Tenths .

The volume of water in the container is 1.2 l.

232

Let’s Practice

tio

0.5

1. Match.

Ed uc a

0.1

0.8

0.6

0.9

0.3 233

2. Draw an arrow to show the decimal on the number line.

0.5

tio

(a) 0.2

(b) 0.7 0.5

Ed uc a

0 (c) 1.1 0

(d) 1.6 0

0.5

1.5

(e) 14.3

14.5

15.5

(f) 11.8

234

3. Write the decimal represented by the place value disks.

(c)

(d)

0.1

(g)

0.1

(f)

0.1

(e)

tio

(b)

Ed uc a

(a)

(h)

235

3.6

(d)

215.6

12.7

0.5

Ed uc a

(c)

(b)

tio

(a)

4. Write the value of the digit.

5. Read and write the numbers in the place value chart. (a) The four is in the ones place. The seven is in the tenths place. The two is in the tens place. Ones

. Tenths

Tens

(b) The six is in the tenths place. The one is in the tens place. The zero is in the ones place.

236

Tens

Ones

. Tenths

6. Find the length of the lines.

0 cm

(c)

0 cm

(d)

Ed uc a

(b)

tio

(a)

0 cm

(e)

0 cm

237

7. Find the mass of the boxes. (a)

1 kg

0 4 kg 3 kg

2 kg

1 kg

tio

3 kg

0 4 kg

Ed uc a

2 kg

(b)

0 4 kg

3 kg

1 kg

0 4 kg 3 kg

2 kg

1 kg

2 kg

(c)

23 8

0 4 kg 3 kg

1 kg

0 4 kg 3 kg

1 kg 2 kg

2 kg

8. Find the volume of liquid in the beakers. (a)

2 l

1 l

(b)

Ed uc a

1 l

tio

2 l

1 l

(c)

2 l

1 l

1 l 239

9. Write as words. (a) 0.2

(b) 1.1

tio

(e) 4.0 (f) 10.1 (g) 8.5 (h) 23.4

Ed uc a

(d) 3.9

10. Write as decimals.

(a) four tenths

(b) one and two tenths

(e) 2 1

(f) 5 6

(g) 1 3

(h) 3 7

(d) twenty-one tenths

240

10 10

Hands On

Ed uc a

tio

In small groups, visit each of the measuring stations your teacher has prepared. Record the lengths, masses and volumes to the nearest tenth in the table below.

Mass Station

Object

Mass (kg)

A B

Length Station

Length (cm)

Object A

Liquid

Volume Station Volume (liters)

A B 2 41

At Home

0.1

1 1

0.1

2 42

1.7

tio

0.1

Ed uc a

0.1

1. Match.

16.1

10.7

2.6

1.4

6.2

2. Fill in the blanks. (a)

28.1

place. It has a value of

The 8 is in the

place. It has a value of

The 1 is in the

place. It has a value of

tio

34.9

Ed uc a

(b)

The 2 is in the

The 3 is in the

place. It has a value of

The 4 is in the

place. It has a value of

The 9 is in the

place. It has a value of

The 6 is in the

place. It has a value of

The 9 is in the

place. It has a value of

The 3 is in the

place. It has a value of

The 7 is in the

place. It has a value of

(c)

5,693.7

The 5 is in the

243

3. Write the decimal that represents the colored part of the shapes.

tio

(a)

(c)

(d)

Ed uc a

(b)

(e)

(f)

2 44

4. Fill in the blanks on the number line. (a) 0.5

0.5

1.5

Ed uc a

tio

(b)

4.5

5.5

5. Find the length of the lines. (a)

0 cm

(b)

0 cm

245

6. Draw arrows on the scales to show the mass of the boxes. (a) (b)

0 4 kg

1 kg

3 kg

1 kg

Ed uc a

3 kg

tio

0 4 kg

2.4 kg

3.2 kg

2 kg

7. Draw a line to show the level of liquid in the beakers. (a) 0.4 l (b) 1.6 l

2 l

1 l

2 46

2 l

1 l

8. Write as words. (a) 0.1

(b) 2.6

tio

(e) 8.8

Ed uc a

(d) 5.9

(f) 100.2 (g) 40.4 (h) 20.0

9. Write as decimals.

(a) one and seven tenths (b) three and two tenths

(e) 2 2

(f) 7 1

(g) 1 5

(h) 13 6

(d) fifty and six tenths 10

10 10

247

Hundredths

Ed uc a

tio

Anchor Task

2 48

Let’s Learn

6 parts = 6 tenths = 6 10 = 0.6

tio

0.6 of the square is blue.

A square is divided into 10 equal parts. 6 of the parts are colored blue.

Ed uc a

0.6 of the square is blue.

The same square is then divided into 100 equal parts. 4 of the parts are colored yellow. 4 parts in 4 100 is . 100

4 parts = 4 hundredths

4 100 = 0.04 =

0.04 of the square is yellow.

Let's find the total amount the square has been colored.

6 + 4 = 60 + 4 10 100 100 100

= 64 = 0.64 100

6 10

= 100 They are equivalent fractions!

0.6 + 0.04 = 0.64

We say: zero point six four We write: 0.64 0.64 of the square is colored in total. 249

47 parts of the whole are colored orange. 1 whole =

47 100

tio

= 0.47

47 parts = 47 hundredths

0.40 Ones 0

Ed uc a

We say 0.47 as ‘zero point four seven’.

0.45

0.47

Tenths

Hundredths

0.50

82 parts of the whole are colored orange. 1 whole

82 parts = 82 hundredths

25 0

0.80

82 100

= 0.82 We say 0.82 as ‘zero point eight two’.

0.82

0.85

0.90

Ones

Tenths

Hundredths

0.01

0.01 0.1

0.01

tio

0.1 1

There are 10 hundredths in 1 tenth.

Write and say the decimal represented by the place value disks. 0.1

0.01

Ones

Tenths

Hundredths

Ed uc a

1.11 one point one one

1 0.1

0.01

0.1

0.01

0.1

0.01

0.1

0.01

Ones

Tenths

Hundredths

4.26 four point two six

Ones

Tenths

Hundredths

0.39 zero point three nine

2 51

Let's find the value of each digit in the number. 3 0. 0

2 . 5

0. 5 2

(b)

5 9. 2

Ed uc a

The value of the digit 2 is 2. The value of the digit 5 is 0.5. The value of the digit 3 is 0.03. 2 + 0.5 + 0.03 = 2.53

0. 0

0. 2 9

R 2 52

The value of the digit 5 is 50. The value of the digit 9 is 9. The value of the digit 2 is 0.2. The value of the digit 8 is 0.08. 50 + 9 + 0.2 + 0.08 = 59.28

tio

(a)

Write the amounts of money as decimals. When writing dollar amounts, we always include the hundredths.

$1 = 100¢ 10 100 = $0.1

0.1 = 0.10

= $0.10

10¢ = $0.10

Ed uc a

tio

10¢ = $

$1 = 100¢

7 100 = $0.07

7¢ = $

45 100 = $0.45

$1 = 100¢

sa m

45¢ = $

100¢ + 16¢ = 116¢ 116 100 = $1.16 = $

253

Let’s Practice

tio

0.81

1. Match.

Ed uc a

0.96

0.77

0.22

254

0.60

0.06

2. Draw an arrow to show the decimal on the number line.

0.05

(b) 0.08 0.05

(d) 1.67 1.5

0.10

Ed uc a

0.1

tio

(a) 0.03

2.35

2.4

2.45

2.5

1.55

1.6

1.65

1.7

(e) 3.19

3.05

3.1

3.15

3.2

3.25

3.3

5.4

5.45

5.5

5.55

5.6

5.65

5.7

(f) 5.42

2 55

3. Write the decimal represented by the place value disks. 1

0.1

(d)

0.1

0.1 0.01 0.01 0.01 0.01

0.1 0.01

(e)

0.1

Ed uc a

0.01 0.01 0.01 0.01 0.01

(c)

0.1 0.01 0.01

(b)

tio

(a)

0.1

0.1 0.01 0.01 0.01

0.01 0.01 0.01 0.01 0.01

(f)

2 56

10 0.01 0.01 0.01 0.01 0.01 0.01

4. Write the value of each digit. Then add the values. 1 . 6

(b)

4 9. 5

1 . 7

(c)

Ed uc a

tio

(a)

2 57

5. Check to show the amount of money.

tio

(a) $0.45

Ed uc a

(b) $0.26

(d) $0.37

(e) $0.20

258

6. Add the fractions. Then write as a decimal. 5

= 0.

tio

= 0.

(a) 100 + 100 = 100 (b) 100 + 100 = 100

= 0.

Ed uc a

= 0.

(e) 100 + 100 = 100 (f) 100 + 100 = 100 =

(g) 10 + 100 = 100 + 100 (h) 10 + 100 = 100 + 100

= 100 = 100 =

= 0.

(i)

7 38 50 9 + = 100 + 100 (j) + = 100 + 100 10 100 100 10

= 100 = 100 =

259

7. Write as words. (a) 0.02

(b) 0.53

tio

(e) 8.49

Ed uc a

(d) 10.01

(f) 20.08 8. Add.

(a) 5 + 0.3 + 0.05 = (c) 10 + 6 + 0.07 =

(b) 0.2 + 0.02 =

(d) 80 + 0.1 =

9. Write as decimals.

(a) three hundredths

(b) twenty-five hundredths

(d) 100

(e) 100

202

(g) 100

(f) 100 26 0

345

Ed uc a

(a)

tio

Color the circles to show each number. Color a circle green to show 0.01. Color a circle red to show 0.1. Color a circle blue to show 1. Color a circle yellow to show 10. The first one has been done for you.

Solve It!

21.4

(b)

seventeen point four six

261

(c)

Ed uc a

tio

fifty-eight point three one

(d)

forty point zero six

2 62

At Home

0.01 0.01 0.01 0.01 0.01

0.01 0.01 0.01

10 0.01

0.1

0.01 0.01 0.01 0.01

11.41

1.04

0.24

11.04

tio

0.1 0.01 0.01 0.01 0.01

Ed uc a

0.1

1. Match.

0.1

0.01 0.01 0.01 0.01

0.1

0.1 0.01

10.41

1.08

263

2. Write the value of each digit. Then add the values. 3. 2

(b)

8 . 9

4 2 . 7

(c)

Ed uc a

tio

(a)

264

3. Write the decimal that shows the colored part of the shapes.

tio

(a)

(c)

(d)

Ed uc a

(b)

(e)

(f)

265

4. Fill in the blanks on the number line. (a) 0.05

0.1

4.05

(d) 2.4

0.2

Ed uc a

(b)

tio

2.45

4.1

2.5

2.55

4.15

2.6

2.65

4.20

2.7

(e)

8.1

8.2

8.3

8.4

7.9

8.1

(f)

7.8

266

$0.76

tio $1.13

Ed uc a

sa m

pl e

5. Match.

$5.05

pl e

sa m sa m

$0.38

$1.25

$1.01

2 67

6. Add the fractions and write the sum as a decimal. 5

(a) 100 + 100 =

(b) 100 + 100 = 6

tio

Ed uc a

(d) 100 + 10 = 7. Write as words. (a) 2.04

(b) 1.56 (c) 0.29 (d) 10.70

8. Write as decimals.

(a) six hundredths

(b) fourteen hundredths 17 100

(d)

119

(f) 100

(c)

(e) 100

26 8

63 100 528

Comparing Decimals

$0.35

$0.24

$1.60

Ed uc a

$0.31

tio

Anchor Task

$1.08

$1.64

269

Let’s Learn

Tenths

Hundredths

Start by comparing the digits in the highest place.

Ed uc a

Ones

tio

Let's write the numbers in a place value chart.

Compare 1.4 and 1.63. Which number is smaller?

Compare the values from left to right. The values in the ones place are the same. Ones

Tenths

Hundredths

If the digits in the same place are the same, move on.

Move on to compare the digits in the tenths place. .

Tenths

Ones

Hundredths

4 tenths is smaller than 6 tenths. So, 1.4 is smaller than 1.63. We write: 1.4 < 1.63

2 70

Compare 4.17 and 4.13.

Tenths

Hundredths

tio

Ones

Let's write the numbers in a place value chart.

Ones

Ed uc a

The values in the ones place and the tenths place are the same. Move on to compare the digits in the hundredths place. Tenths

Hundredths

7 Hundredths is greater than 3 hundredths. 4.13 < 4.17

4.17 > 4.13

4.1

We can compare the decimals on a number line too!

4.13

4.17

4.2 271

Let's compare decimals on a number line. (a) Compare 0.01 and 0.09. 0.09

tio

0.01

0.05

0.1

0.09 > 0.01

0.01 < 0.09

0.09 is greater than 0.01

Ed uc a

0.01 is smaller than 0.09

(b) Compare 1.3 and 1.27.

1.27

1.2

1.3

1.4

1.3 > 1.27

1.27 < 1.3

1.3 is greater than 1.27

1.27 is smaller than 1.3

6.6

6.7

6.81 > 6.69 6.81 is greater than 6.69

27 2

6.81

6.8

6.9 6.69 < 6.81

6.69 is smaller than 6.81

Let’s Practice

(b)

0.1

10 0.1

0.1

(c)

0.1 0.01 0.01 0.01

(d)

0.1

0.01 0.01 0.01 0.01 0.01

0.1

tio

0.1

0.1 0.01

Ed uc a

(a)

1. Write the decimal represented by the place value disks. Check the greater number.

0.1

0.1 0.01

0.01 0.01 0.01 0.01

0.1 0.01 0.01 0.01 0.01

273

2. Write the numbers in the place value chart and compare.

Ones

Tenths

Hundredths

tio

. .

Ed uc a

(a) Compare 1.5 and 2.04

(b) Compare 6.49 and 6.94 Ones

Tenths

Hundredths

. .

Tens

2 74

. . .

Tenths

Hundredths

3. Write the numbers on the number line and compare.

0.05

is greater than

0.1

Ed uc a

tio

(a) Compare 0.04 and 0.06.

(b) Compare 4.25 and 4.5.

4.2

4.3

is smaller than

4.4

4.5

1.2

1.3

1.0

1.1

is smaller than

275

4. Circle the numbers that are greater than 2.6.

2.58

3.02

2.5

1.69

7.05

2.22

tio

2.67

5. Write the fractions as decimals and compare.

(b) 10 =

100 =

Ed uc a

(a) 100 =

100 =

6. Use the words is greater than, is smaller than and is equal to to fill in the blanks. (a) 0.5 (b) 13.03

1.2.

13.05.

10.61.

(d) 7.69

7.69.

(e) 0.04

(f) 105.38

0.06. 10.83.

(g) 30.11

30.11.

(h) 226.1

226.01.

276

Hands On

tio

Play Decimal Compare! in pairs. Roll a 10-sided dice 3 times to create a 3-digit decimal. Write the number in the box and have your partner repeat the steps to create their 3-digit decimal. Compare your numbers. The greater number wins! Play 5 games to determine the overall winner.

Game 1

Player 1

Player 2

Player 1

Player 2

Player 1

Player 2

. . .

Game 2

Ed uc a

Decimal Compare!

Game 3

Player 1

Player 2

Game 5

Player 1

Game 4

. .

277

At Home 1. Add the place values and compare.

tio

10 + 0.4 + 0.01 =

(a) 1 + 0.2 + 0.03 =

Ed uc a

(b) 30 + 5 + 0.6 + 0.07 =

30 + 5 + 0.8 + 0.06 =

(d) 300 + 80 + 2 + 0.7 + 0.01 =

300 + 80 + 2 + 0.7 + 0.04 =

278

2. Write the numbers in the place value chart and compare.

Tenths

Hundredths

. .

is greater than

Ed uc a

tio

Ones

(a) Compare 0.04 and 1.01

(b) Compare 12.5 and 12.48 Tens

Ones

Tenths

Hundredths

. .

is smaller than

Tens

Ones

Tenths

Hundredths

. .

is greater than

279

3. Draw an arrow to show the position of the numbers on the number line. Fill in the blanks.

3.1 >

Ed uc a

3.2

3.3

tio

(a) Compare 3.14 and 3.21.

(b) Compare 2.24 and 2.16.

2.1

2.2

2.3

9.7

9.8

7.5

7.6

9.5

9.6

(d) Compare 7.41 and 7.43.

2 80

7.3

7.4 >

4. Circle the numbers that are smaller than 0.8.

1.73

0.59

0.92

0.78

0.1

0.21

tio

0.09

(a) 100 = 1

(b) 10 = 130

(d) 10 =

Ed uc a

5. Write the fractions as decimals and compare. 179

195

100 =

100 = 100 =

100 =

6. Use the symbols >, < and = to fill in the blanks. (a) 1.1

2.02 (b) 14.5

6.74 (d) 10.88

1.98

(e) 3.15

3.15 (f) 12.01

1.28

(g) 5.31

8 (h) 6.48

281

1. Write the value of the digit.

12.78

95.16

6.05

Ed uc a

tio

3.64

(a) (b)

2. Write the value of each digit. Then add the values. 1 . 4

(a)

5. 9

(b)

+ 2 82

Looking Back

3. Find the length of the lines.

0 cm

Ed uc a

(b)

tio

(a)

4. Check to show the amount of money.

(a) $0.40

(b) $0.36

283

5. Write as words. (a) 0.71

(b) 2.06

tio

Ed uc a

(e) 1.58

(f) 16.87 (g) 3.03 (h) 10.21

6. Write as decimals.

(a) one and four tenths

(b) three and sixty-eight hundredths

(d) seventy and fifty-one hundredths

(e) 1 1

(g) 25 100

2 84

(f)

43 100 16

(h) 2 100

7. Draw an arrow to show the position of the numbers on the number line. Fill in the blanks.

1.1 >

1.3

Ed uc a

1.2

tio

(a) Compare 1.11 and 1.09.

(b) Compare 5.97 and 6.04.

5.8

5.9

6.1

8. Write the fractions as decimals and compare. 3

(a) 100 =

280

103

100 =

(b) 10 =

100 =

9. Use the symbols >, < and = to fill in the blanks. 2 (b) 1.5

4.15 (d) 0.18

(a) 0.3

(e) 55.55

55.55 (f) 16.01

1.06 0.45 16.09

285