Matholia Mathematics Primary 4B

M AT H E M AT I C S Workt ext

4B

for learners 9 - 10 years old

2 km 25 min hike

Aligned to the US Common Core State Standards

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

Central to the USCCSS is the promotion of problem-solving skills and reasoning.

Matholia Mathematics achieves this by teaching and presenting concepts through a problem-solving based pedagogy and using 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

9

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 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.

Numbers to Let’s Learn

Count on in

+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

+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

4

+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

Hundreds

Tens

Nine hundred thirty thousand 930,107. , one hundred

Ones

seven.

5

ii

Let’s Practice

2.

Let’s Practice 1.

(b) 1:15

3:30

(d)

(c)

Morning:

Morning:

(f)

(e)

Afternoon:

Afternoon:

(d)

(c)

11:50

9:25

Complete the table.

3.

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

Morning:

Morning:

City

Night:

Night:

1:45 a.m.

Los Angeles

(f)

(e)

07 35

Miami

9:05

7:45

3:40 p.m.

Dallas Morning:

Morning:

20 20

Washington

23

Night:

Night:

(b) Home At

1.

Write the equivalent (a)

2.

fractions.

Use multiplication (a)

At Home

to find equivalent

x2

4 7 =

=

(b)

x2

2 9 =

(c)

3.

=

Use division to find (a)

÷2

12 20

3 4

=

=

12 = 20

(d) (b)

3 6

=

÷4 = ÷4

=

18 42

= ÷3

18 = 42

152

equivalent fractio ns.

÷3

18 42 =

÷2

= x4

=

12 20

=

x4

2 9

= x3

2 = 9

=

x3

2 9

= x2

1 3

= x3

4 = 7

=

fractions.

x3

4 7

= x2

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

22

time using a.m. and

(a)

(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

÷6 = ÷6

=

153

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

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 winner! the is hive er to the bee The first play

36 cm (mm)

22,000 g (kg)

11 km (m)

182 dm (cm)

START

7 kg (g)

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)

N

FINISH

81

R

80

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.

M

D

22 3

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

4

(e)

3 = 7

=

=

=

(f)

2 = 9

=

5 = 20

(d)

18 = 36

(f)

form.

12 = 16

(c)

3 4

9 8

(d)

21

4

5 2

12 5

Write the improper fraction represented of the shapes.

5.

by the colored parts

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

(b)

on 6. Draw a point to show the fraction

15 = 45

the number line.

1

(a) 2 3

by writing = or ≠.

3. Tell whether the fractions are equivalent (b) 12 2 (a) 6

9

4 3

(b)

2 = 5

15

1 3

7 4

5

=

(d)

4

(e)

12

(a)

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

4 3

4.

7

1 = 8

I

166

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

A

14

7

11 33

1 3

0

2

1

3

9

(b) 6 0

1

2 221

220

iii

Contents 5 Time Converting Units of Time Expressing 12-hour and 24-hour Time Duration of Time Word Problems 6 Measurement, Perimeter and Area Benchmarks and Relative Sizes Converting Customary Units Converting Metric Units Perimeter Area Word Problems

42 43 58 72 84 100 120

7

134 135 140 150 160 170 179

Angles Identifying and Naming Angles Comparing Angles Measuring Angles Drawing Angles Properties of Angles Word Problems

8 Symmetry Identifying Symmetric Figures Drawing Symmetric Figures 6 iv

2 2 20 25 34

190 192 200

9 Line Plots and Line Graphs Interpreting and Creating Line Plots Interpreting and Creating Line Graphs

208 210 230

10 Problem Solving Act It Out Draw a Model Guess-and-Check Make a List Look for Patterns Work Backwards Before-After Concept Simplify the Problem

248 248 253 258 263 268 274 278 282

v

5

Time

Converting Units of Time Anchor Task

Activity

2

Time (s)

Time (min and s)

Let’s Learn The analog clock below has an hour hand, minute hand and second hand.

second hand

hour hand

minute hand

The hour hand moves the slowest. It takes the hour hand one hour to move from one number to the next. It takes the hour hand 12 hours to move once around the clock. There are 24 hours in one day. So, the hour hand moves around the clock 2 times in one day.

The minute hand moves faster than the hour hand. It takes the minute hand 5 minutes to move from one number to the next.

It takes the minute hand 60 minutes, or one hour, to move once around the clock. There are 60 minutes in one hour.

The second hand moves the fastest. It takes the second hand 5 seconds to move from one number to the next. It takes the second hand 60 seconds, or one minute, to move once around the clock. There are 60 seconds in one minute.

3

We know that in 1 minute there are 60 seconds.

How many seconds are there in 2 minutes?

2 min = 2 x 60 s = 120 s There are 120 s in 2 min.

1 min = 60 s 2 min = 120 s 3 min = 180 s 4 min = 240 s 5 min = 300 s

Use this chart to convert between minutes and seconds.

Blake finished a running race in 3 min 13 s.

Express the time in seconds.

3 min 13 s

3 min = 180 s 13 s

3 min 13 s = 180 s + 13 s = 193 s Blake finished the running race in 193 seconds.

Express 255 seconds in minutes and seconds.

255 s = 240 s + 15 s = 4 min 15 s

4

We know that in 1 hour there are 60 minutes.

How many minutes are there in 4 hours?

4 h = 4 x 60 min = 240 min There are 240 min in 4 hours.

1 h = 60 min 2 h = 120 min 3 h = 180 min 4 h = 240 min 5 h = 300 min

Use this chart to convert between hours and minutes.

Sophie went on a hike for 4 h 35 min.

Express the time Sophie hiked in minutes.

4 h 35 min

4 h = 240 min 35 min

4 h 35 min = 240 min + 35 min = 275 min Sophie hiked for 275 min.

Express 282 minutes in hours and minutes.

282 min = 240 min + 42 min = 4 h 42 s

5

Let’s Practice 1. Convert the times to seconds. (a) Riley talked on the phone for 2 minutes 21 seconds.

How long did Riley talk on the phone in seconds? min =

2 min 21 s

s

s 2 min 21 s =

=

s+

s

s

Riley talked on the phone for

seconds.

(b) Wyatt heated his dinner for 3 minutes 47 seconds.

How long did Wyatt heat his dinner for in seconds? min =

3 min 47 s

s

s 3 min 47 s =

=

s+ s

Wyatt heated his dinner for

6

s

seconds.

(c) Halle sang a song for 4 minutes 12 seconds.

How long did Halle sing for in seconds? min =

4 min 12 s

s

s 4 min 12 s =

=

s+

s

s

Halle sang for

seconds.

(d) A news update lasted 3 minutes 38 seconds.

How long was the news update in seconds? min =

3 min 38 s

s

s 3 min 38 s =

=

s+

s

s

The news update went for

seconds.

2. Write the time in seconds. (a) 3 min 18 s =

s (b) 1 min 50 s =

s

(c) 4 min 42 s =

s (d) 2 min 46 s =

s

(e) 1 min 23 s =

s (f) 4 min 17 s

s

=

7

3. Convert the times to minutes and seconds. (a) Chelsea danced for 95 seconds.

How long did Chelsea dance for in minutes and seconds?

95 s = s+ s

= min s

Chelsea danced for min

(b) A train takes 124 seconds to travel from one stop to the next.

How long does the train take in minutes and seconds?

124 s =

=

s+

s

min

s

The train takes min

(c) Sophie ran 1 km in 265 seconds.

How long did she take to run 1 km in minutes and seconds?

265 s =

=

s+ min

Sophie ran 1 km in

8

s.

s.

s s min

s.

(d) Ethan completed a mathematics quiz in 410 seconds. How long did it take Ethan to finish the quiz in minutes and seconds?

410 s =

=

s+

s

min

s

Ethan completed the quiz in

min

s.

(e) It took Halle 278 seconds to make her bed. How long did it take her in minutes and seconds?

278 s =

=

s+ min

s s

Halle made her bed in

min

s.

4. Write the time in minutes and seconds. (a) 68 s =

(b) 101 s =

min

s

min

s

(c) 317 s =

min

s

(d) 299 s =

min

s

(e) 138 s =

min

s

9

5. Convert the times to minutes. (a) Jordan took a nap for 2 hours 15 minutes.

How long did Jordan nap in minutes? h=

2 h 15 min

min

min 2 h 15 min =

=

min +

min

min

Jordan took a nap for

minutes.

(b) Wyatt played tennis for 3 hours 46 minutes.

How long did Wyatt play tennis for in minutes? h=

3 h 46 min

min

min 3 h 46 min =

=

min + min

Wyatt played tennis for

10

min

minutes.

(c) Mrs. Lee worked in her garden for 4 hours 21 minutes.

How long did Mrs. Lee work in her garden in minutes? min =

4 h 21 min

min

min 4 h 21 min =

=

min +

min

min

Mrs. Lee worked in her garden for minutes.

(d) Riley watched a movie that went for 2 hours 7 minutes.

How long was the movie in minutes? min =

2 h 7 min

min

min 2 h 7 min =

=

min +

min

min

The movie was

minutes long.

6. Write the time in minutes. (a) 3 h 8 min =

min (b) 3 h 33 min =

min

(c) 1 h 45 min =

min (d) 4 h 15 min =

min

min (f) 2 h 56 min =

min

(e) 4 h 28 min =

11

7. Convert the times to hours and minutes. (a) A car ride to the beach takes 95 minutes.

How long is the trip in hours and minutes?

95 min =

=

min + h

min min

The car ride to the beach takes

(b) A flight from Los Angles to Seattle takes 192 minutes. How long does the flight take in hours and minutes?

192 min =

=

min + h

h

min min

The flight takes h min.

(c) Blake played golf for 425 minutes.

How long did Blake play golf for in hours and minutes?

425 min =

=

min + h

Blake played golf for

12

min min h

min.

min.

(d) Chelsea read a book for 152 minutes.

How long did she read for in hours and minutes?

152 min =

=

min + h

min min

Chelsea read for h min.

(e) Mr. Jones took 395 minutes to milk all of his cows. How long did he take in hours and minutes?

395 min =

=

min + h

min min

Mr. Jones milked all of his cows in

h

min.

8. Write the time in hours and minutes. (a) 168 min =

(b) 109 min =

h

min

h

min

(c) 377 min =

h

min

(d) 218 min =

h

min

(e) 405 min =

h

min 13

Solve It! Complete each table to help find the answer.

1. Sophie finished a mathematics quiz in 222 seconds.

Riley finished the same quiz in 3 minutes 40 seconds.

Who finished the mathematics quiz in the shorter time?

Minutes

Seconds

1 2 3 4

finished the mathematics quiz in a shorter time

than

.

2. Jordan and Ethan hiked from the camping site to a waterfall.

Jordan reached the waterfall in 4 hours 7 minutes. Ethan reached the waterfall in 219 minutes. Who was hiking for the longer time?

Hours

Minutes

1 2 3 4

14

hiked for a longer time than

.

Hands On 1. Take turns in rolling the dice. Move your counter forward the number of spaces shown on the dice.

2. Say the time in minutes and seconds. If you say the incorrect time, go back to the start.

3. The first player to the finish is the winner.

60 s

144 s 20 0

s 89

s

7s 0 1

188 s

420 s

29 5s

s

10

374 s

195 s

315

9s

134 s

30 1s

34 7s 20 9

s

15

At Home 1. Convert the times to seconds. (a) It takes Chelsea 4 minutes 35 seconds to ride to school.

How long does it take Chelsea to ride to school in seconds? min =

4 min 35 s

s

s 4 min 35 s =

=

s+

s

s

It takes Chelsea

seconds to ride to school.

(b) In a game of basketball, Wyatt scored the first goal in 3 minutes 14 seconds. How long did it take for Wyatt to score the first goal in seconds? min =

3 min 14 s

s

s 3 min 14 s =

=

s+ s

Wyatt scored the first goal in

16

s

seconds.

2. Convert the times to minutes and seconds. (a) Blake chatted with his friends for 173 seconds. How long did Blake chat for in minutes and seconds?

173 s =

=

s+

s

min

s

Blake chatted with his friends for

min

s.

(b) Jordan finished a science quiz in 311 seconds. How long did he take in minutes and seconds?

311 s =

=

s+

s

min

s

Jordan finished the science quiz in

(c) Sophie took 287 seconds to row across the lake.

How long did she take in minutes and seconds?

287 s =

= Sophie took

s+

min

s.

s

min

s min

s to row across the lake.

17

3. Convert the times to minutes. (a) Students have 1 hour 35 minutes to finish a science exam. How many minutes do they have to finish the exam? h=

1 h 35 min

min

min 1 h 35 min =

=

min +

min

min

Students have

minutes to finish the science exam.

(b) Wyatt went fishing for 4 hours 26 minutes.

How long did Wyatt go fishing for in minutes? h=

4 h 26 min

min

min 4 h 26 min =

=

min + min

Wyatt went fishing for

18

min

minutes.

4. Convert the times to hours and minutes. (a) It takes 155 minutes to travel from San Francisco to Sacramento by train. How long is the train ride in hours and minutes?

155 min =

=

min + h

min min

The train ride is h min.

(b) A flight from Miami to Denver takes 192 minutes.

How long does the flight take in hours and minutes?

192 min =

=

min + h

min min

The flight takes h min.

(c) Wyatt did his homework for 205 minutes. How long did he do his homework for in hours and minutes?

205 min =

=

min + h

Wyatt did his homework for

min min h

min.

19

Expressing 12-hour and 24-hour Time Let’s Learn The times on the departure board are shown in 24-hour time.

When we use 24-hour time, we do not need to use a.m. or p.m.

When using 24-hour time, midnight is expressed as 00 00.

12:00 a.m.

6:00 a.m.

00 00

06 00

In 24-hour time you normally don’t say o’clock.

20

12:00 noon 12 00

6:00 p.m.

18 00

12:00 a.m.

00 00

For 18 00, we say eighteen hundred hours.

To convert times between noon and midnight into 24-hour time, you add 12 to the hours. To convert times between noon and midnight from 24-hour time to 12-hour time, you subtract 12 from the hours and add p.m.

Chelsea arrives home from school at 4:15 p.m.

Express the time Chelsea arrives home in 24-hour time.

4 + 12 = 16

12-hour time: 4:15 p.m. four fifteen p.m.

24-hour time: 16 15 sixteen fifteen

Chelsea goes to bed at 21 35.

Express the time Chelsea goes to bed in 12-hour time.

21 – 12 = 9

24-hour time: 21 35 twenty-one thirty-five 12-hour time: 9:35 p.m. nine thirty-five p.m.

21

Let’s Practice 1. Write the times in 24-hour time. (a) (b) 3:30

1:15

Morning:

Morning:

Afternoon:

Afternoon:

(c) (d) 9:25

11:50

Morning:

Morning:

Night:

Night:

(e) (f) 7:45

22

9:05

Morning:

Morning:

Night:

Night:

2. Write the times in 12-hour time using a.m. and p.m. (a) (b)

(c) (d)

(e) (f)

3. Complete the table.

Flight Departures JFK International Airport City Los Angeles

Departure

Departure

(12-hour)

(24-hour time)

1:45 a.m.

07 35

Miami Dallas Washington

3:40 p.m.

20 20 23

At Home Complete the table.

School Camp Activities Program Activity

12-hour Time

Breakfast

7:45 a.m.

Hike to Waterfall Swimming

24-hour Time

10 10 11:50 a.m.

Lunch

12 30

Hike to Caves

1:35 p.m.

Cave Exploration

2:25 p.m.

Dinner

18 45

Campfire Songs

20 05

24

Duration of Time Let’s Learn Blake and Ethan went to the beach at 12 20. They left at 14 45.

How long were Blake and Ethan at the beach?

2h

25 min

12 20

14 20

14 45

2 h + 25 min = 2 h 25 min Ethan and Blake were at the beach for 2 h 25 min.

Chelsea and Halle arrived at the mall at 13 30. They shopped until 15 15, then they went home. How long were Chelsea and Halle at the mall?

30 min 13 30

1h 14 00

15 min 15 00

15 15

1 h + 30 min + 15 min = 1 h 45 min Chelsea and Halle were at the mall for 1 h 45 min.

25

Riley and her family left for the beach at 12 20. They arrived at the beach 4 hours 25 minutes later. What time did they arrive at the beach?

4h

25 min

12 20

16 20 16 45

4 hours after 12 20 is 16 20.

25 min after 16 20 is 16 45.

Riley and her family arrived at the beach at 16 45.

On Saturday, Ethan played tennis for 2 hours 50 minutes. He finished playing at 16 30. What time did Ethan start playing tennis?

20 min 13 40

30 min

14 00

14 30

2 hours before 16 30 is 14 30.

30 minutes before 14 30 is 14 00.

20 minutes before 14 00 is 13 40.

Ethan started playing tennis at 13 40.

26

2h 16 30

Let’s Practice Complete the word problems.

Use a timeline to show your working.

1. Mrs. Jackson started cooking dinner at 17 20. Dinner was ready at 18 45. How long did Mrs. Jackson spend cooking dinner?

2. A flight left Dallas airport at 05 50. It arrived in Kansas City at 07 15. How long was the flight from Dallas to Kansas City?

3. Halle visited her grandmother at 11 25. She left her grandmother’s house at 14 50. How long did Halle spend visiting her grandmother?

27

4. Riley and her sister arrived at the zoo at 10 25. They stayed at the zoo for 3 hours 35 minutes. What time did they leave the zoo?

5. Jordan arrived at school at 08 25. His English class started 2 hours 40 minutes after he arrived. What time did Jordan’s English class start?

6. Wyatt washed the car with his father for 1 hour 45 minutes.

They started washing the car at 11 30. What time did they finish washing the car?

28

7. On Saturday, Ethan played in the park for 2 hours 35 minutes. He left the park at 17 10. What time did Ethan arrive at the park?

8. A tennis match lasted 5 hours 5 minutes. The match finished at 21 25. What time did the tennis match start?

9. On Sunday, Sophie did housework for 3 hours 45 minutes.

She finished the housework at 15 15. What time did Sophie start doing housework?

29

Solve It! Use the map on the next page to answer the questions.

Show your working.

1. Riley hiked from the mountains, past the campsite, to the pond. She arrived at the pond at 14 40. What time did Riley leave the mountains?

2. Wyatt left the mountains at 10 25. He hiked past the waterfall to the forest. What time did Wyatt arrive at the forest?

30

Mountains 25 min

35 min 15 min

40 min

45 min 50 min

35 min

55 min

31

At Home Complete the word problems.

Use a timeline to show your working.

1. Mr. Woods started playing golf at 06 30. He finished playing golf at 11 15. How long did Mr. Woods spend playing golf?

2. Mrs. Robinson opened her pet store at 10 35. She stayed open for 5 hours 50 minutes. What time did Mrs. Robinson close her pet store?

3. A school play goes for 3 hours 45 minutes. The play finishes at 20 35. What time did the school play start?

32

4. Blake’s family arrived at the lake at 12 50. They stayed at the lake for 4 hours 25 minutes. What time did Blake’s family leave the lake?

5. Mr. Arlo opened his pizza shop at 15 45. He closed the shop at 23 30. How long was Mr. Arlo’s pizza shop open?

6. Mr. Whyte raced his car for 3 hours 55 minutes. He finished the race at 16 45. What time did the car race start?

33

Word Problems Let’s Learn Halle did her mathematics homework for 2 hours 15 minutes.

She then did her science homework for 1 hour 35 minutes.

How long did Halle spend doing her mathematics and science homework altogether?

2 h 15 min

1 h 35 min

mathematics

science ?

2 h 15 min + 1 h 35 min = 3 h + 15 min + 35 min

= 3 h 50 min Halle spent 3 hours 50 minutes doing her mathematics and science homework altogether.

Blake spent 1 hour 25 minutes gardening. Blake’s father spent 3 hours 30 minutes gardening. How much longer did Blake’s father spend gardening?

1 h 25

?

Blake Blake’s father 3 h 30

3 h 30 min – 1 h 25 min = 2 h + 30 min – 25 min = 2 h 5 min Blake’s father spent 2 hours 5 minutes longer gardening than Blake.

34

Lola rides her horse every day for 45 minutes.

How long does Lola spend riding her horse in 5 days?

45 min

?

2

4 5

x

5

2 2 5 225 min = 3 h 45 min In 5 days, Lola rides her horse for 3 hours 45 minutes.

Mr. Whyte buys a package of 8 golf lessons for a total of 4 hours.

How long is one golf lesson?

First, convert the hours into minutes.

?

240 min

240 min ÷ 8 = 30 min Each golf lesson is 30 minutes long.

35

Let’s Practice Complete the word problems. Show your working.

1. Sophie ran for 1 hour 45 minutes. She then cycled for 3 hours 23 minutes. How long did Sophie spend exercising in all?

2. It took Jordan 3 hours 20 minutes to reach the top of a mountain. Blake reached the mountain top 1 hour 50 minutes faster than Jordan. How long did it take Blake to reach the mountain top?

3. Riley spent 1 hour 48 minutes doing her homework. Halle spent 3 hours 15 minutes doing her homework. How much longer did Halle spend doing her homework?

36

4. Riley takes 4 minutes 40 seconds to walk once around the school oval. How long will it take Riley to walk around the school oval 6 times?

5. On a hike, Halle and Sophie stopped for a break 6 times. Each break was the same number of minutes. The total break time was 1 hour 30 minutes. How long was each break?

6. It takes Mrs. Whyte 26 minutes to bake a cake. How long will it take Mrs. Whyte to bake 8 cakes?

37

At Home Complete the word problems. Show your working.

1. Wyatt took 2 hours 15 minutes to revise for his English test.

He took 3 hours 55 minutes to revise for his science test. How much longer did he take to revise for his science test than his English test?

2. Riley swims one lap of a swimming pool in 3 minutes 35 seconds. How long does it take for Riley to swim 9 laps of the swimming pool?

3. Chelsea watched a series of 10 short stories. Each short story goes for the same length of time. The whole series went for 3 hours 20 minutes. How long was each short story?

38

Solve It! Complete the word problems. Show your working.

1. Halle took 35 minutes to walk from her house to the library.

She read in the library for 1 hour 45 minutes and left at 16 50.

What time did Halle leave her house?

2. A chef takes 12 minutes to cook a pizza and 6 minutes to prepare a salad. He needs to cook 8 pizzas and prepare 6 salads by 19 45. What is the latest time that the chef should start cooking?

39

Looking Back 1. A news brief went for 4 minutes 43 seconds.

How long was the news brief in seconds? min =

4 min 43 s

s

s 4 min 43 s =

=

s+

s

s

The news brief lasted for

seconds.

2. Blake cycled 2 kilometers in 269 seconds.

How long did it take in minutes and seconds?

269 s =

=

s+

s

min

s

Blake cycled 2 kilometers in

min

3. Convert the times. (a) 168 min =

(b) 109 min =

h

min

h

min

(c) 3 h 22 min =

min

(d) 4 h 41 min =

min

40

s.

4. Complete the table.

Departures – Eastern Bus Terminal City

Departure (12-hour)

Hawthorne

6:45 a.m.

09 25

Inglewood Santa Monica Malibu

Departure (24-hour time)

6:40 p.m.

21 55

5. A chef takes 16 minutes to prepare a meal. How long will it take the chef to prepare 9 such meals?

6. It took Wyatt 3 hours 12 minutes to jog around the lake 8 times.

How long does it Wyatt to jog once around the lake?

41

6

Measurement, Perimeter and Area

Anchor Task

42

Benchmarks and Relative Sizes Let’s Learn These objects and distances can be used as benchmarks for customary units of measurement.

Benchmarks for Customary Units of Length 4 laps

about 1 inch (in)

about 1 foot (ft)

about 1 yard (yd)

about 1 mile (mi)

Benchmarks for Customary Units of Volume

1 cup (c) (8 fluid ounces)

1 pint (pt)

1 quart (qt)

1 half gallon

1 gallon (gal)

Benchmarks for Customary Units of Weight

about 1 ounce (oz)

about 1 pound (lb)

about 1 ton (T)

43

Let’s Practice 1. Write the customary benchmark unit of measurement. (a) length of a paper clip (b) volume of tea in a cup

about 1

about 1

(c) weight of a loaf of bread (d) volume of juice in carton

about 1

about 1

(e) width of a tablet computer (f) weight of a small car

about 1

about 1

(g) length of a baseball bat (h) weight of a cookie

about 1 44

about 1

2. Circle an appropriate customary unit of measurement. (a) weight of an apple (b) weight of a bicycle

pounds tons ounces ounces pounds tons (c) height of a palm tree (d) length of a marker

inches miles feet inches feet yards (e) length of a tennis court (f) volume of water in a tub

inches yards miles gallons cups pints (g) weight of a tiger cub (h) distance from home to school

ounces pounds tons inches feet miles 45

3. Circle the appropriate measurement. (a) punch in a punch bowl (b) weight of a full schoolbag

4 cups 4 quarts 4 ounces 4 pounds (c) length of a snake (d) weight of a truck

2 inches 2 feet 5 pounds 5 tons (e) volume of milk in a bowl (f) distance ran in 1 hour

1 gallon 1 pint 6 miles 6 yards (g) weight of a cell phone (h) length of a violin

6 ounces 46

6 pounds 14 feet 14 inches

At Home 1. Find an object or distance to represent these benchmark units of measurement around your home or school. (a)

Benchmarks for Customary Units of Length about 1 inch about 1 foot about 1 yard about 1 mile

(b)

Benchmarks for Customary Units of Volume about 1 cup about 1 pint about 1 quart about 1 gallon

(c)

Benchmarks for Customary Units of Weight about 1 ounce about 1 pound about 1 ton

47

2. Write 'more than', 'less than' or 'about'. (a) weight of a kitten (b) volume of milk in small carton

1 ounce

1 half gallon

(c) weight of a bowling ball (d) weight of a basketball

1 pound

1 pound

(e) volume of milk in a cup (f) height of an armchair

1 pint

1 foot

(g) volume of soda in a can (h) weight of a skateboard

48

1 gallon

1 pound

3. Write an appropriate customary unit of measurement. (a) width of a TV cabinet (b) weight of a stapler

about 6

about 4

(c) length of bed (d) distance ran in 30 min

about 3

about 3

(e) volume of water in bucket (f) weight of a small truck

about 2

about 6

(g) height of a door (h) volume of milk in a milkshake

about 6

about 3 49

Let’s Learn These objects and distances can be used as benchmarks for metric units of measurement.

Benchmarks for Metric Units of Length width of nail

10-minute walk

about 1 millimeter about 1 centimeter

about 1 meter

Benchmarks for Metric Units of Volume

5 drops

about 1 milliliter

about 1 liter

sa m

pl

e

Benchmarks for Metric Units of Weight

about 1 gram

50

about 1 kilogram

about 1 kilometer

Let’s Practice 1. Write the metric benchmark unit of measurement. (a) water in a drink bottle (b) weight of a feather

about 1

about 1

(c) weight of a pineapple (d) thickness of a coin

about 1

about 1

(e) width of a television (f) width of a marker

about 1

about 1

(g) height of a mountain (h) liquid in an eye dropper

about 1

about 1 51

2. Circle an appropriate metric unit of measurement. (a) weight of a strawberry (b) weight of a bicycle

grams kilograms kilograms grams (c) volume of water in a tub (d) length of an ant

liters milliliters centimeters millimeters (e) length of a jogging track (f) length of a pencil

centimeters kilometers centimeters meters (g) weight of a hippopotamus (h) weight of a gold ring

grams 52

kilograms kilograms grams

3. Circle the appropriate metric measurement. (a) weight of a grasshopper (b) volume of coffee in a cup

5 grams 5 kilograms 250 milliliters 250 liters (c) height of a slide (d) volume of water in a bottle

2 centimeters 2 meters 20 milliliters 20 liters (e) bottle of nail polish (f) weight of a calculator

50 milliliters 50 liters 50 kilograms 50 grams (g) weight of a pot plant (h) length of a ukulele

3 grams 3 kilograms 35 centimeters 35 meters 53

At Home 1. Find an object or distance to represent these benchmark units of measurement around your home or school. (a)

Benchmarks for Metric Units of Length about 1 millimeter about 10 millimeters about 10 centimeters about 1 meter about 10 meters

(b)

Benchmarks for Metric Units of Volume about 1 milliliter about 10 milliliters about 1 liter

(c)

Benchmarks for Metric Units of Weight about 1 gram about 10 grams about 1 kilogram

54

2. Write 'more than', 'less than' or 'about'. (a) weight of a chair (b) height of the classroom door

1 kilogram

1 meter

(c) liquid in a soap dispenser (d) volume of a kitchen sink

1 liter

1 liter

(e) carton of milk (f) height of an armchair

1 liter

1 meter

(g) weight of a soda can (h) weight of a hamster

10 grams

1 kilogram 55

3. Write an appropriate metric unit of measurement. (a) height of a giraffe (b) weight of a baby

about 3 (c) medicine in a teaspoon

about 5

about 10 (d) distance walked in 15 min

about 2

(e) weight of a motorbike (f) length of a truck

about 200

about 8

(g) paint in a large paint tin (h) length of a football field

about 6 56

about 100

Solve It! 1. Jordan has 10 dimes. He stacks them in a pile. Which metric units should Jordan use to measure the weight and height of the pile of coins?

2. Halle wants to measure her own weight and height.

Which metric units should she use?

3. A truck driver needs to fill in the form below. Complete the form using appropriate customary units of measurement.

57

Converting Customary Units Let’s Learn Use this table to help convert different units of length!

Customary Units of Length 1 foot 1 yard

1 mile

12 inches (in) 36 inches (in) 3 feet (ft) 5,280 feet (ft) 1,760 yards (yd)

In 1 foot, there are 12 inches. So to convert feet to inches, we multiply the number of feet by 12.

Chelsea cuts a piece of ribbon that is 3 feet in length.

How long is the ribbon in inches?

3 x 12 = 36 The ribbon is 36 inches in length.

To convert inches to feet, we divide the number of inches by 12.

Ethan needs an electrical cable that is 60 inches long.

What length of electrical cable does Ethan need in feet?

60 ÷ 12 = 5 Ethan needs an electrical cable that is 5 feet in length.

58

Use this table to help convert different units of volume!

Customary Units of Volume 4 quarts (qt) 1 gallon

8 pints (pt) 16 cups (c)

1 quart

1 pint 1 cup

4 cups (c) 2 pints (pt) 2 cups (c) 16 fluid ounces (fl oz) 8 fluid ounces (fl oz)

In 1 gallon, there are 4 quarts. So to convert gallons to quarts, we multiply the number of gallons by 4.

Ethan has a container with 3 gallons of fruit punch.

How many quarts of fruit punch are in the container?

3 x 4 = 12 There are 12 quarts of fruit punch in the container.

To convert quarts to gallons, we divide the number of quarts by 4.

Halle buys 16 quarts of milk from a mini-mart. How many gallons of milk does she buy?

16 ÷ 4 = 4 Halle buys 4 gallons of milk from the mini-mart.

59

Use this table to help convert different units of weight!

Customary Units of Weight 1 pound (lb) 1 ton (T)

16 ounces (oz) 2,000 pounds (lb)

In 1 pound, there are 16 ounces. So to convert pounds to ounces, we multiply the number of pounds by 16.

A baker needs 3 pounds of butter to bake some cakes.

How many ounces of butter does he need?

3 x 16 = 48 The baker needs 48 ounces of butter.

To convert ounces to pounds, we divide the number of ounces by 16.

Sophie's pet cat weighs 64 ounces. What is the weight of the cat in pounds?

64 ÷ 16 = 4 The weight of Sophie's pet cat is 4 pounds.

60

Let’s Practice 1. Convert the customary units to complete the tables. (a)

(b)

(c)

Feet

1

Inches

12

Yards

1

Feet

3

9

Miles

1

3

Yards (d)

Pints

2

3 48

2

4

1

2

Quarts

8,800

3

Quarts Cups

5 8

1

Pints (f)

5

4

3,520

Cups (e)

5

3

4

5

4

1

2

3

5 16 61

(g)

(h)

Gallons

1

Pints

8

Gallons

1

Quarts

(i)

(j)

(k)

5 32

3

4

8

Feet

1

Inches

12

Pounds

1

2

20

3

5 48

2

Ounces

32

Tons

2

Pounds 2,000

62

3

3

5 64

3

5 8,000

2. Convert the units. Show your working. (a) 2 ft =

(c) 4 gal =

in (b) 4 ft =

qt (d) 5 yd =

in

ft

(e) 3 lb =

oz (f) 2 c =

fl oz

(g) 5 T =

lb (h) 2 mi =

yd

(i) 3 pt =

c (j) 6 qt =

(k) 2 yd =

in (l) 2 gal =

pt

c

63

3. Convert the units. Show your working. (a) 72 in =

(c) 3,520 yd =

ft (b) 18 ft =

yd

mi (d) 8,000 lb =

T

(e) 32 c =

qt (f) 3 gal =

c

(g) 60 ft =

yd (h) 64 oz =

lb

(i) 48 in =

ft (j) 24 qt =

gal

(k) 72 in =

yd (l) 2 pt =

fl oz

64

4. Write >, < or = to fill in the blanks. Show your working. (a) 48 oz

(c) 4,000 yd

4 lb (b) 12 ft

4 yd

2 mi (d) 5,000 lb

6T

(e) 62 in

2 yd (f) 22 c

14 pt

(g) 5 gal

20 pt (h) 6 qt

16 c

(i) 4 lb

66 oz (j) 15 pt

9 qt

(k) 3 c

24 fl oz (l) 2 mi

4,000 yd

65

Hands On Take turns in rolling a dice. Move forward the number shown on the dice. Convert the measurement to the unit shown in brackets.

Some rules: • If you answer incorrectly, go back to the start.

• If you land on a lotus, leap forward 3 spaces.

• If you land on a dragonfly, fly back 3 spaces.

START

2 lb (oz)

6 yd (ft)

12 ft (yd)

1T (lb)

5 qt (pt)

66

8 yd (ft)

16 pt (gal)

1c (fl oz)

7T (lb)

10 pt (c) 56 fl oz (c)

2 gal (pt)

FINISH 67

Solve It! 1. Mrs. Jones needs 4 pounds of apples to bake some apple pies. She has 52 ounces of apples. How many more ounces of apples does Mrs. Jones need to bake the apple pies? Complete the table to help you find the answer.

Pounds

Ounces

1

16

2 3 4 5 Mrs. Jones needs

more ounces of apples.

2. Mr. Williams sells his milk for $1 per pint. He has 5 gallons of milk. If Mr. Williams sells all of his milk, how much money will he make? Complete the table to help you find the answer.

Gallons

Pints

1

8

2 3 4 5 If he sells all his milk, Mr. Williams will make $ 68

.

3. A hardware store sells garden hoses for $6 per yard. The distance from Jordan's tap to his garden is 14 feet. How much will Jordan pay for a hose that can reach his garden?

Complete the table to help you find the answer.

Yards

Feet

1 2 3 4 5 6 Jordan will pay $

for a hose to reach his garden.

4. There are 9 players on a basketball team. During a game, each player drinks 6 cups of sports drink. Coach Davis has 4 gallons of sports drink. How many cups of sports drink will be left after the game? Complete the table to help you find the answer.

Gallons

Cups

1 2 3 4 There will be

cups of sports drink left after the game.

69

At Home 1. Convert the units. Show your working. (a) 4 lb =

oz (b) 30 ft =

(c) 3 yd =

in (d) 7 T =

(e) 64 c =

gal (f) 10 gal =

qt

(g) 24 pt =

c (h) 40 yd =

ft

(i) 150 ft =

yd (j) 3 mi =

(k) 80 oz =

lb (l) 32 fl oz =

70

yd

lb

yd

pt

2. Write >, < or = to fill in the blanks. Show your working. (a) 9 c

(c) 2,700 yd

2 qt (b) 21 ft

8 yd

2 mi (d) 5,000 lb

(e) 3 yd

108 in (f) 40 fl oz

(g) 4 gal

32 c (h) 6 qt

(i) 6 lb

100 oz (j) 48 fl oz

(k) 4 mi

10,000 ft (l) 100 in

5T

3 pt

20 c

3 pt

3 yd

71

Converting Metric Units Let’s Learn Use this table to help convert different units of length!

Metric Units of Length 1 centimeter 1 decimeter (dm)

1 meter 1 kilometer (km)

10 millimeters (mm) 100 millimeters (mm) 10 centimeters (cm) 100 centimeters (cm) 1,000 millimeters (mm) 1,000 meters (m)

In 1 meter, there are 100 centimeters. So to convert meters to centimeters, we multiply the number of meters by 100.

The length of Chelsea's school bus is 7 meters.

How long is the school bus in centimeters?

7 x 100 = 700 The length of the school bus is 700 centimeters.

72

To convert centimeters to meters, we divide the number of centimeters by 100.

The height of a giraffe is 300 cm.

What is the height of the giraffe in meters?

300 ÷ 100 = 3 The height of the giraffe is 3 meters.

The chart below shows how to convert between metric units of length. ÷ 100 ÷ 10

millimeters (mm)

x 10

÷ 10

centimeters (cm)

÷ 10

decimeters (dm)

x 10

÷ 1,000

meters (m)

x 10

kilometers (km)

x 1,000

x 100

73

Metric Units of Volume 1 liter ( l )

1,000 milliliters (ml)

In 1 liter, there are 1,000 milliliters. So to convert liters to milliliters, we multiply the number of liters by 1,000.

A drink cooler contains 5 liters of sports drink. How many milliliters of sports drink are in the drink cooler?

5 x 1,000 = 5,000 There are 5,000 milliliters of sports drink in the cooler.

To convert milliliters to liters, we divide the number of milliliters by 1,000.

Riley fills the kitchen sink with 8,000 milliliters of water.

How many liters of water are in the kitchen sink?

8,000 ÷ 1,000 = 8 There are 8 liters of water in the kitchen sink.

74

Metric Units of Weight 1 kilogram (kg)

1,000 grams (g)

In 1 kilogram, there are 1,000 grams. So to convert kilograms to grams, we multiply the number of kilograms by 1,000.

A bag of oranges has a mass of 8 kilograms.

Find the mass of oranges in grams.

8 x 1,000 = 8,000 There are 8,000 grams of oranges.

To convert grams to kilograms, we divide the number of grams by 1,000.

A tin of beans has a mass of 4,000 grams. Find the mass of the tin of beans in kilograms.

4,000 ÷ 1,000 = 4 The tin of beans has a mass of 4 kilograms.

75

Let’s Practice 1. Convert the metric units to complete the tables. (a)

(b)

Centimeters

1

Millimeters

10

Decimeters

1

2

Meters

2

Meters

4

1

3

Kilometers Meters

76

4

20

1

2

50

3

Centimeters

(e)

5

30

Decimeters

(d)

5 40

Centimeters

(c)

3

5 400

1

4 2,000 3,000

5

(f)

Liters

1

2

3

Milliliters (g)

4,000

Kilograms Grams

5

2 1,000

3

5

3,000

2. Convert the units. Show your working. (a) 2 m =

cm (b) 4 dm =

cm

(c) 5 kg =

g (d) 2 km =

dm

(e) 900 ml =

(g) 9 m =

l (f) 5,210 cm =

cm (h) 7,000 ml =

dm

l

77

(i) 11 kg =

g (j) 52 km =

(k) 190 cm =

dm (l) 233 m =

(m) 8,000 g =

kg (n) 320 dm =

m

cm

m

3. Write >, < or = to fill in the blanks. Show your working. (a) 12 m

1,200 cm (b) 4,500 ml

(c) 6,000 g

5 kg (d) 120 cm

(e) 32 dm

320 cm (f) 290 dm

78

4l

10 m

3,800 mm

At Home 1. Convert the units. Show your working. (a) 6,000 g =

(c) 5 kg =

(e) 900 ml =

kg (b) 4 dm =

cm

g (d) 2 km =

dm

l (f) 5,210 cm =

dm

2. Write >, < or = to fill in the blanks. Show your working. (a) 5 km

(c) 1,200 g

(e) 5,990 mm

1,200 cm (b) 980 ml

12 kg (d) 96 dm

4,000 cm (f) 12 km

9l

9,600 cm

12,000 m

79

Hands On Take turns in rolling a dice. Move forward the number shown on the dice. Convert the metric measurement to the unit shown in brackets.

Some rules: • If you answer incorrectly, go back to the start.

• If you land on a honey pot, leap forward 3 spaces.

• If you land on a bee, fly back 3 spaces.

The first player to the beehive is the winner!

START

7 kg (g)

5l (ml)

80

4,000 m (km)

10 km (m)

22,000 g (kg)

36 cm (mm)

11 km (m) 182 dm (cm) 10 cm (dm) 6,000 ml (l) 14 kg (g)

FINISH 81

Solve It! 1. The distance from the camp ground to the waterfall is 5 kilometers. Ethan has hiked for 3,200 meters. How many more meters does Ethan need to hike to reach the waterfall?

Complete the table to help you find the answer.

Show your working.

Kilometers

Meters

1 2 3 4 5 Ethan needs to hike another

meters.

2. Mrs. Jenkins needs 625 centimeters of ribbon to make a dress.

She buys a ribbon that is 7 meters in length. After making the dress, how much ribbon will Mrs. Jenkins have left? Complete the table to help you find the answer. Show your working.

Meters

Centimeters

3 4 5 6 7 Mrs. Jenkins will have 82

centimeters of ribbon left.

3. Mrs. Watkins made 9 liters of fruit punch for a party of 15 people. Each person drank 500 milliliters of fruit punch.

How much fruit punch was left after the party? Complete the table to help you find the answer. Show your working.

Liters

Milliliters

5 6 7 8 9 10 There was

milliliters of fruit punch left.

4. A baker needs to make 20 cakes. For each cake, he needs 250 grams of flour. He has 3 kilograms of flour. How many more kilograms of flour does the baker need?

Kilograms

Grams

1 2 3 4 5 6 The baker needs another

kilograms of flour.

83

Perimeter Let’s Learn The total distance around an object or figure is called its perimeter. We can find the perimeter of figures and objects in different ways.

The figure below is an irregular shape. We can find the perimeter by adding the lengths of each side.

8 in

4 in

A

5 in

4 in

Perimeter A = 4 + 8 + 5 + 4 = 21 The perimeter of Figure A is 21 in.

Find the perimeter of Figure B. 6 cm

4 cm

2 cm

B

6 cm

8 cm

Perimeter B = 4 + 6 + 2 + 6 + 8 = 26 The perimeter of Figure B is 26 cm.

84

Remember to include the correct unit of measurement when writing the perimeter.

We can use mathematical formulae to find the perimeter of rectangles and squares.

A square has four sides of equal length.

C

12 yd

Perimeter C = 4 x Length = 4 x 12 = 48

The perimeter of Figure C is 48 yd.

How can you find the side lengths of a square if you know the perimeter?

The perimeter of the square is 52 in. Find the length of each side.

Perimeter = 52 in

?

Side length = Perimeter ÷ 4 = 52 ÷ 4 = 13

The square has side lengths of 13 in.

85

Riley wants to measure the perimeter of her swimming pool.

The swimming pool is in the shape of a rectangle.

What formula can she use to find the perimeter?

A rectangle has opposite sides of equal length.

5m

10 m

Perimeter = (2 x Length) + (2 x Breadth) = (2 x 10) + (2 x 5) = 20 + 10 = 30 The perimeter of Riley's swimming pool is 30 meters.

How can you find the breadth of a rectangle if you know the perimeter?

Find the breadth of the rectangle.

?

Perimeter = 20 ft

7 ft

The breadth of the rectangle is 3 ft.

86

Breadth + Breadth = Perimeter – 7 – 7 = 20 – 7 – 7 = 6 ft Breadth = 6 ÷ 2 = 3 ft

We can also find the perimeter of objects and figures by adding or subtracting to find unknown sides.

A farmer needs to put a fence around his paddock.

How much fencing does he need?

First find the lengths of side BC and side EF. 90 m

A

B

?

60 m

BC = AF – DE = 60 – 25 = 35 m

D 45 m 25 F

?

E

C

Now that we know all the side lengths, we can add to find the perimeter!

EF = AB – CD = 90 – 45 = 45 m

Perimeter = AB + BC + CD + DE + EF + FA = 90 + 35 + 25 + 45 + 45 + 60 = 300 m The farmer needs 300 m of fencing.

87

Let’s Practice 1. Find the perimeter of each figure. (a) 5 in

3 in A

6 in

Perimeter A =

+

=

in

(b)

+

14 m 4m

4m

B

6m 18 m

Perimeter B =

+

=

m

(c)

+

8 yd

+

+

8 yd C

6 yd

6 yd 5 yd

11 yd

Perimeter C =

+

=

yd

88

+

+

+

+

2. Find the perimeter of the squares. (a) 22 ft

Perimeter of square =

x

=

(b)

ft

16 yd

Perimeter of square =

x

=

(c)

yd

35 mm

Perimeter of square =

x

=

mm

89

3. Find the perimeter of the rectangles. (a) 4 ft 7 ft

Perimeter of rectangle = (2 x =

+

=

(b)

ft

) + (2 x

)

) + (2 x

)

9m

24 m

Perimeter of rectangle = (2 x =

+

=

(c)

m 20 in

120 in

Perimeter of rectangle = (

x

=

+

=

in

90

)+(

x

)

4. Find the side lengths of the squares. (a)

Perimeter = 88 m

Side length of square =

÷4

=

(b)

m

Perimeter = 36 in

Side length of square =

÷

=

(c)

in

Perimeter = 144 cm

Side length of square =

÷

=

cm 91

5. Find the length or breadth of the rectangles. (a) Perimeter = 30 in

5 in

Length + Length = 30 –

–

=

–

=

in

Length =

÷2

=

in

(b) Perimeter = 50 yd

?

18 yd

Breadth + Breadth =

–

=

–

=

yd

Breadth =

÷

=

yd

92

–

6. Find the lengths of the unknown sides. Find the perimeter. (a)

71 yd

A

B 23 yd

?

D 13 yd 17 yd

F

=

m

E

58 yd

Perimeter =

C

AF = BC + DE

= +

+

+

+

+

+

= (b)

?

R

S

?

74 m

P

Q

55 m

32 m

U

T

120 m

QR = ST – PU

RS = TU – PQ

=

–

=

–

=

m

=

m

Perimeter =

+

+

+

+

+

= 93

At Home 1. Find the perimeter of each figure. Show your working. (a)

54 yd

22 yd

45 yd 32 yd

Perimeter = (b)

54 m

68 m

32 m

30 m 71 m

Perimeter = 94

38 m

2. Find the perimeter of the squares. Show your working. (a) 15 ft

Perimeter =

(b)

Perimeter =

55 yd

(c) 42 mm

Perimeter =

95

3. Find the perimeter of the rectangles. Show your working. (a) 6 in 21 in

Perimeter = (b)

60 m

Perimeter =

30 m

(c)

15 cm 95 cm

Perimeter = 96

4. Find the length or breadth of the rectangles. (a) Perimeter = 250 yd

15 yd

Length = (b)

Perimeter = 240 in

78 in

Breadth =

97

5. Find the perimeter of the figures. Show your working. (a)

A

15 m

B

19 m 30 m

D C

F

?

?

E

42 m

Perimeter = (b)

?

10 yd

10 yd

26 yd

18 yd 14 yd

?

53 yd

Perimeter = 98

Solve It! Halle's desk at home can be represented by the figure below.

The figure is composed of 2 rectangles. Read the clues and complete the table.

Clues: • AB has a length of 140 cm.

• AF and DC are of equal length.

• EF has a length of 100 cm.

• The perimeter of the desk is 480 cm.

A

F

B

E

C

D

Side

Length

AB BC CD DE EF FA 99

Area Let’s Learn The amount of space occupied by a shape or surface is called its area. Area is measured in square units. A square unit is a square that has a side length of 1 unit.

We can use customary and metric units of length as a measurement for area.

The grid below is made up of squares with side lengths of 1 cm.

We can measure the area of the shapes in square centimeters.

1 cm 1 cm

A C B

Shape

Length (cm)

Breadth (cm)

Area

A

7

1

7 cm2

B

6

3

18 cm2

C

5

5

25 cm2

What pattern do you notice about the length, breadth and area of the shapes? What formula can we use to calculate the area of rectangles and squares?

100

We can calculate the area of a square using the formula: Area of square = Side length x Side length We can calculate the area of a rectangle using the formula: Area of rectangle = Length x Breadth Let's use the formulae above to measure the area of the squares and rectangles below.

S

T

12 ft

50 yd

50 yd

9 ft

Area S = 50 x 50 = 250 yd2

Area T = 12 x 9 = 108 ft2

V U 32 m

Area U = 32 x 8 = 256 m2

15 mi

8m 15 mi

Area V = 15 x 15 = 225 mi2

101

We can find the unknown side of a rectangle if we know one side length and the area.

The football field has a length of 100 m and an area of 3,000 m2.

Find the breadth of the football field.

100 m

Area = 3,000 m2

?

Breadth = Area ÷ 100 = 30 m We can find the unknown side lengths of a square if we know the area.

A square tile has an area of 81 cm. Find its side lengths.

Area = 81 cm2

?

Area of square = Side length x Side length 81 = 9 x 9 The tile has a side length of 9 cm.

102

A composite figure is a shape that is made of two or more shapes joined together.

The composite figure below is made of 2 rectangles.

How can you calculate the area?

12 m 5m

12 m

13 m 8m

To find the area of the composite figure, we can find the area of each rectangle and add them together.

12 m 5m 13 m

12 m

A B

Area A = 13 x 12 = 156 m2

8m

Area B = 12 x 8 = 96 m2

Area of Figure = Area of Figure A + Area of Figure B = 156 + 96 = 252 m2 103

We can also divide the figure another way.

12 m 5m

C

12 m

13 m 8m

D

Area C = 12 x 5 = 60 m2

Area D = 24 x 8 = 192 m2

Area of Figure = Area of Figure C + Area of Figure D = 60 + 192 = 252 m2 We can also make the composite figure into a rectangle and subtract the unshaded figure from the shaded figure.

12 m 5m

12 m

13 m 8m

Area shaded = 24 x 13 Area unshaded = 12 x 5 2 = 312 m = 60 m2 Area of Figure = Area shaded – Area unshaded = 312 – 60 = 252 m2 104

Let’s Practice 1. Find the area of each figure. Complete the table.

1 in 1 in

A B

C E D

Shape

Length

Breadth

Area

A B C D E 105

2.

(a) (b) (c) (d)

Draw a square with an area of 4 cm2. Label it 'A'.

Draw a square with an area of 9 cm2. Label it 'B'.

Draw a rectangle with an area of 14 cm2. Label it 'C'.

Draw a rectangle with an area of 21 cm2. Label it 'D'.

1 cm

1 cm

106

3. Find the area of each figure. (a) M

90 yd

Area square M =

x

=

yd2

(b) 6 ft

N 21 ft

Area N =

x

=

ft2

(c)

O

40 m

110 m

Area O =

x

=

m2 107

(d) 25 in

P

Area square P =

x

=

in2

(e) 4 ft

Q 26 ft

Area Q =

x

=

ft2

(f)

R

26 m

Area R =

x

=

m2

108

12 m

4. Find the length or breadth of the rectangles and squares. (a) Area = 30 in2

5 in

=

?

(b)

Length = 30 ÷ in

9m

Area = 63 m2

?

Breadth =

÷

=

m

(c) Area of square = Side length x Side length Area = 144 yd

2

144 = ?

Side length =

x yd

(d) Area of square = Side length x Side length Area = 400 mm2

?

Side length =

=

x mm

109

5. Find the area of the composite figures. Show your working. (a)

10 m

3m 6m

6m 3m

4m

Area = (b)

14 ft

7 ft

4 ft

4 ft 7 ft

Area = 110

2 ft

4m

(c)

8m

7m

6m

7m

10 m 5m

6m

4m

23 m

Area = (d)

33 ft 7 ft 13 ft 10 ft

5 ft

3 ft

17 ft

Area = 111

Hands On Work in pairs to find 4 rectangle-shaped objects inside your classroom and in the schoolyard. Find the area and perimeter of each object and record your findings in the table on the next page.

112

113

Object

Appropriate unit of length Picture

Perimeter

Area

At Home 1. Find the area of the squares. Show your working. (a) 12 in

A

Area =

(b)

B

21 ft

Area =

(c) C

35 mm

Area =

114

2. Find the area of the rectangles. Show your working. (a) 15 yd

Q 70 yd

Area = (b) 32 cm

R

16 cm

(c)

Area =

12 cm

S

22 cm

Area = 115

3. Find the length or breadth of the rectangles and squares. (a) Area = 35 in2

?

(b)

5 in

=

15 m

?

Area = 120 m2

=

(c)

Area = 64 yd2 ?

=

116

4. Find the perimeter and area of the composite figures.

Show your working. (a)

16 in

6 in

7 in

3 in

Perimeter =

14 in 7 in

7 in

Area = 117

(b)

23 yd 5 yd

5 yd 4 yd

14 yd 7 yd

5 yd

Perimeter = 118

Area =

(c)

64 m 15 m 12 m

44 m

29 m

20 m

38 m

90 m

Perimeter =

Area = 119

Word Problems Use the chart below to help you answer the word problems.

Length Metric

Customary

1 centimeter = 10 millimeters 1 decimeter = 10 centimeters 1 meter = 100 centimeters

1 foot = 12 inches 1 yard = 3 feet 1 mile = 1,760 yards

1 kilometer = 1,000 meters

Mass Metric

Customary 1 pound = 16 ounces 1 ton = 2,000 pounds

1 kilogram = 1,000 grams

Volume Metric

Customary 1 cup = 8 fluid ounces 1 pint = 2 cups 1 quart = 2 pints

1 liter = 1,000 milliliters

1 gallon = 8 pints

Time 1 minute = 60 seconds 1 hour = 60 minutes 1 day = 24 hours 1 week = 7 days 1 year = 52 weeks

120

Let’s Practice 1. Blake chooses a bowling ball with a weight of 9 kilograms.

How many grams does the bowling ball weigh?

grams 2. The cost to send a parcel at Truck Express depends on the weight of the parcel. How much will it cost Sophie to send a parcel that weighs 40 ounces?

Price List

Up to 1 lb – $25 1 lb to 2 lb – $30 2 lb to 3 lb – $34 3lb to 4 lb – $38 Please contact us for packages over 4 lb.

$

3. Ethan practices tennis for 45 minutes every evening. How many hours and minutes does Ethan practice for in 1 week?

h

min

121

4. A chef made 5 gallons of soup. A serving of soup is 1 cup.

How many servings did the chef make?

cups 5. Mr. Patel wants to build a fence around his square vegetable patch. The vegetable patch has an area of 36 m2.

What length of fencing does Mr. Patel need?

m 6. A flight from Dallas to Tallahassee takes 2 hours 45 minutes.

How long is the flight in minutes?

min

122

7. Ethan arrived at the snowfields at 11:15 a.m.

He skied for 1 hour and 40 minutes before having lunch.

What time did Ethan have lunch?

8. Blake is building a wooden frame around his favourite photograph. The length of the photograph is 8 inches.

The breadth of the photograph is 6 inches.

How much wood does Blake need?

in 123

9. Mr. Roberts has a rectangular garden that is 12 m by 7 m.

He installs a square hot tub within the garden area that has a side length of 3 m. Find the remaining area of his garden

m2 10. A shoebox lid has a perimeter of 120 cm and a length of 38 cm. What is the breadth of the shoebox lid?

Breadth = 124

11. Mrs. Windfield's kitchen is 5 yards long and 3 yards wide. Tiles cost $4 per square foot. How much will it cost Mrs. Windfield to buy enough tiles to cover her kitchen floor?

$

12. Mr. Martinez needs 7,800 ml of cooking oil for his restaurant.

The oil is sold in 2 l bottles which are $6 each. How much money does Mr. Martinez need to buy the oil?

$ 125

At Home 1. Sophie finished a running race in 240 seconds.

How many minutes did she take to finish the race?

min 2. Mr. Jackson needs 13 quarts of paint to paint his living room.

The paint comes in 1-gallon tins and cost $22 each. How many tins of paint does Mr. Jackson need? How much will he spend?

tins

$

3. An alligator has a length of 4 meters. What is the length of the alligator in decimeters?

dm

126

4. Ethan threw a 32-ounce discus a distance of 63 feet. What was the weight of the discus in pounds? What was the distance he threw the discus in yards?

lb 5. The base of a square gazebo has a side length of 14 feet.

What is the area of the base of the gazebo?

yd

ft2 6. A rectangular birthday card has a perimeter of 30 inches.

The height of the card is 10 inches. Find the breadth.

in 127

7. Chelsea's family is building a new house. What is the area of the house? What is the area of the lawn?

10 m

5m

6m 2m

3m

3m 4m

8m

4m 7m

10 m

128

Solve It! Mr. Rossi is building a fence to make a rectangular paddock on his farm. He bought 96 yards of fencing. What length and width should he build the fence in order to get a paddock with the largest area? Draw a diagram and show your working.

length =

width = 129

Looking Back 1. Circle the appropriate measurement. (a) weight of a pencil case (b) volume of water in a large bottle

1 ounce 1 pound 5 gallons 5 pints (c) length of a bench (d) volume of perfume in a bottle

5 inches 5 feet 50 milliliters 50 liters (e) height of a mountain

(f) weight of a doll house

2 kilometers 2 meters 3 grams 3 kilograms 130

2. Convert the units. Show your working. (a) 60 in =

(c) 1,760 yd =

(e) 32 c =

(g) 20 cm =

(i) 4,000 g =

(k) 3,000 ml =

ft (b) 30 ft =

yd

mi (d) 3,000 lb =

pt (f) 2 gal =

mm (h) 4 l =

kg (j) 7 km =

l (l) 2 dm =

T

c

ml

m

cm

131

3. Find the perimeter of the rectangle. Show your working.

12 yd 42 yd

Perimeter = 4. Find the area and perimeter of the composite figure.

Show your working.

8 cm

3 cm 6 cm

4 cm

1 cm

Perimeter = 132

Area =

5. Sophie makes a basket as a gift for her grandmother.

She also bakes 6 cupcakes and puts them into the basket.

The total mass of the basket and cupcakes is 1 kg.

The mass of 1 cupcake is 140 g. Find the mass of the basket.

Mass of basket =

g

6. A cleaning company charges $5 per square meter to clean carpets. Jordan's living room is square in shape with a side length of 6 m. How much would it cost to clean the carpet in Jordan's living room?

$ 133

7

Angles

Anchor Task

1 34

Identifying and Naming Angles Let’s Learn An angle is formed by two rays with a common endpoint.

The common endpoint where the rays meet is called a vertex.

A

We use the symbol to name angles.

x C

B

Rays AC and BC meet at vertex C to form an angle.

We can name the angle ACB or BCA. We can also name the angle x.

Angles are also formed within shapes.

A triangle has 3 sides and 3 angles.

A rectangle has 4 sides and 4 angles.

D

P

x y

E x= y= z =

z EDF = DEF = EFD =

FDE FED DFE

F

a

b

c

d

S

Q

R a= b= c = d=

SPQ = PQR = PSR = SRQ =

QPS RQP RSP QRS 135

Let’s Practice 1. Circle the diagrams that show angles. (a) (b)

(c) (d)

(e) (f)

2. Circle the angles in each shape. Fill in the blanks. (a) (b)

sides

angles

sides

angles

sides

angles

(c) (d)

136

sides

angles

3. Name the angles. (a) (b) F T

G

S

U

E

(c) (d) B

X

A

Y C W

4. Name the angles in other ways. (a) (b) C D a

V

b

h k

d

l

c

F

E

a=

i

W j

Y

X

Z

i = =

CFE

c =

=

VZY

=

WXY

k= =

CDE

137

At Home 1. Name the angles.

N

G (a) (b) H

x

q I

x =

O

M

q =

R (c) (d)

P

m

z Q

P

z =

Q

O

m =

2. Name the angles. (a) (b) S T n

m

p

Y e

U

c

X a

o

V

d b

V

U

a=

p = =

VUT

m =

=

WXY

=

UYX

e = =

138

W

UTS

3. Name the angles in other ways. (a)

N

e

M

f

d g i

O

h

P

d=

= =

NPO

e = (b) Z n

ONM

i = g= r

m

o Y

p

W

q X

=

p = = r =

XZW

XYZ

q = n = 139

Comparing Angles Anchor Task

140

Let’s Learn Compare the angles made by the popsicle sticks.

Which angle is bigger? Which angle is smaller?

a

b

Angle a is bigger than angle b.

Angle b is smaller than angle a.

Compare the angles made by the popsicle sticks.

Which angle is the biggest? Which angle is the smallest? x y

z

Angle x is bigger than angle y and angle z. Angle x is the biggest.

Angle y is smaller than angle x and angle z. Angle y is the smallest.

1 41

Take a piece of paper and fold it two times as shown.

The angle formed at the corner of the paper is called a right angle.

We show a right angle by drawing 2 perpendicular lines.

Use your folded piece of paper to compare the angles below.

s

Angle s is bigger than a right angle.

142

t

Angle t is a right angle.

u

Angle u is smaller than a right angle.

Let’s Practice 1. Check the bigger angle. (a)

(b)

2. Check the smaller angle. (a)

(b)

143

3. Check the biggest angle. Cross the smallest angle. (a)

(b)

144

4. Circle the right angles. Use a piece of paper to help you.

145

5. Circle the right angle in each shape.

146

6. Check the angles smaller than a right angle.

7. Check the angles bigger than a right angle.

147

At Home 1. Check the biggest angle. Cross the smallest angle. (a)

(b)

1 48

2. Check the box that applies to each angle. Use a piece of paper to help you.

Angle

Smaller than a right angle

Right angle

Bigger than a right angle

149

Measuring Angles Let’s Learn A protractor is used to measure and draw angles in degrees.

Let's look at the different parts of a protractor.

outer scale

inner scale center point

base line

Angle ABC below is a right angle. A right angle is 90 degrees.

We write 90 degrees as 90o.

C

A

150

B

We use straight lines to show right angles.

Let's look at how to measure an angle using a protractor.

Step 2

Step 1

Align the base line of the protractor with the ray DE.

Align the center point of the protractor on vertex E. Step 3 Measure

F

DEF.

D

E

Line EF aligns with the 50o mark on the protractor. DEF = 50o Angles that are less than 90 degrees are called acute angles.

Find

XYZ.

X

Z

Y

Line YZ aligns with the 125o mark on the protractor. XYZ = 125o Angles that are more than 90 degrees are called obtuse angles.

1 51

Let’s Practice 1. Write the angle. Check if the angle is acute or obtuse. (a) C

A

B

ABC = acute obtuse

(b)

O

M

N

(c)

W

V

152

MNO = acute obtuse

U

UVW = acute obtuse

(d)

G

EFG = acute obtuse

E F

(e) J H

HIJ = acute obtuse

I

(f) K

L

KLM = acute obtuse

M

1 53

2. Measure the angle. Check if the angle is acute or obtuse. (a)

A

ABC = acute obtuse

C

B

(b) D

F

E O

(c)

M

(d)

N

MNO = acute obtuse

X

Y

154

DEF = acute obtuse

Z

XYZ = acute obtuse

3. Estimate then measure the angles. (a) (b)

t s (c) (d)

v

u

(e) (f)

x

w (g) (h)

z y

Angle

s

t

u

v

w

x

y

z

Estimate Measure 155

Hands On 1. With a partner, use your popsicle angle-maker to make an angle.

2. Trace the inside of the angle-maker to draw an angle on a sheet of paper. Label the rays, vertex and angle.

3. Estimate and measure the angle.

4. Make different angles and complete the table below.

Angle Estimate Measure 156

At Home 1. Measure the angle. Check if the angle is acute or obtuse. (a)

O

M

(b)

N

MNO = acute obtuse

D

DEF = acute obtuse F

E

(c)

A

ABC = acute obtuse C

B

(d)

X

XYZ = acute obtuse Y

Z

1 57

2. Estimate then measure the angles. (a) (b)

a b

(c) (d)

c d

(e) (f)

f e

Angle Estimate Measure 158

a

b

c

d

e

f

Solve It! Measure the angles Halle turns as she walks to the waterfall.

A

B

ABC =

C

BCD =

E

DEF =

D

CDE =

F

159

Drawing Angles Let’s Learn We can use a protractor and ruler to draw angles.

Let's draw an acute angle of 60o.

Step 1 Use a ruler to draw a straight line. Label the line AB.

A

B

Step 2 Align line AB to the base line of the protractor. Align point A to the center point.

A

B C

Step 3 Draw a dot at the 60o mark on the inner scale of the protractor. Label it point C. A C

Step 4 Use a ruler to draw a line to connect point A to point C. Label the angle.

60o A

160

B

B

Let's draw an obtuse angle of 142o.

Step 1 Use a ruler to draw a straight line. Label the line YZ.

Y

Z

Step 2 Align line YZ to the base line of the protractor. Align point Z to the center point.

Y

Z

Step 3

X

Draw a dot at the 142o mark on the outer scale of the protractor. Label it point X. Y

Z

Step 4 Use a ruler to draw a line to connect point Z to point X. Label the angle.

X 142o Y

Z

161

Let’s Practice 1. Draw a line from the center point to make each angle. (a) 30o

(b) 72o

(c) 144o

1 62

2. Draw and label the angles. (a)

ABC = 50o

B

(b)

A

DEF = 114o

D

(c)

E

GHI = 158o

H

G

163

3. Draw and label the angles. (a)

ABC = 50o

(b)

MNO = 129o

(c)

PQR = 95o

164

Hands On Draw and label an angle. Have your friend use a protractor to measure your angle.

Angle 1:

Friend's measurement: =

o

Angle 2:

=

o

Friend's measurement: =

o

Angle 3:

=

o

Friend's measurement: =

o

=

o

165

At Home 1. Draw a line from the center point to make each angle. (a) 76o

(b) 124o

(c) 156o

166

2. Draw and label the angles. (a)

ABC = 34o

B

(b)

A

DEF = 148o

D

(c)

E

GHI = 28o

H

G

1 67

3. Draw and label the angles. (a)

JKL = 121o

(b)

XYZ = 162o

(c)

DEF = 77o

168

Solve It! Draw the times on the clocks. Measure the angle between the hour hand and the minute hand. (a) 3:00

=

(b) 1:20

=

(c) 5:00

=

(d) 4:20

=

(e) 5:10

=

(f) 2:30

=

169

Properties of Angles Let’s Learn When an angle is comprised of non-overlapping parts, the angle measure is the sum of the angles of the smaller parts.

Let's find

ABC.

A

ABC = ABD + DBC = 30o + 75o = 105o

D 75o 30o

C

B

ABC = 105o When an angle is comprised of non-overlapping parts, we can subtract the smaller parts to find the unknown angle measure.

WOZ = 160o Let's find x.

Y

W

108o O

x = 52o 170

x = WOZ – WOY = 160o – 108o = 52o x Z

Line ST is a straight line.

Add SVU and UVT.

The sum of the angles on a straight line is 180o.

U

S

T

V

180o

SVU + UVT = 126o + 54o = 180o

Line AB is a straight line.

Find y. o

46

A

126o

B O

y

61o

D

C

y = 180o – AOC – = 180o – 46o – 61o

= 73o

54o

180o

BOD

61o

46o

y

171

Lines OA, OB and OC meet at point O. Find the sum of the angles.

A

The sum of the angles at a point is 360o.

155o 65o

O B

140o C

360o 155o

140o

65o

AOB + BOC + COA = 155o + 140o + 65o = 360o Lines OP, OQ, OR and OS meet at point O. Find x.

S

P 76o

x

59o O

Q

140o

R 360o

76o

59o o

140o

x = 360 – SOP – POQ – QOR = 360o – 76o – 59o – 140o = 85o 172

x ?

Let’s Practice 1. Find the unknown angle. Show your working.

LON = 100o a=

(a)

L

M

a 22o

N

O

AOD = 129o AOB =

(b)

B

C

A

50o 64o

D

O

P (c) POR =

42

Q

o

O

12o

R

173

2. Find the unknown angle. Show your working. (a) PS is a straight line. x = R

Q

x 102o

64o

P

S

O

(b) EH is a straight line. w = F G 60o E

w

H

O

(c) LP is a straight line. r = N

M L

174

13o

49o

r O

O 16o

P

3. Find the unknown angle. Show your working. (a) All straight lines meet at point F. m = C B 59o 44o

A

82o

m

F

15o D

E

(b) All straight lines meet at point N. JK is a straight line.

J

I

a=

50o N

84o

a

34o

M L

K

175

Solve It! Read the clues and find the unknown angles. (a) AB is a straight line. a is half the size of c. b is 3 times the size of a.

b

c

a

A

a=

B

b=

c=

(b) PQ and RS are straight lines.

ROQ = 130º P

n

m

O

R

n

S

m

Q

176

m=

n=

At Home Find the unknown angle. Show your working.

AOC = 139º

(a)

AOB =

C O

67o

B

A

(b)

S

R

y=

y 50o

Q

T

(c) LP is a straight line.

M N

MQN =

O 11o

87o

75o L

Q

P

177

(d) All straight lines meet at point Y.

UYV =

U T 37o

148o Y 83

o

V 74o

X

W

(e) All straight lines meet at point E. A

E

32o

B

C D

178

AED =

Word Problems Let’s Practice 1. Sophie tries to perform a 360º spin while ice skating.

She manages to spin 327º. How much more does she need to turn to complete a full spin?

2. How many degrees does the minute hand of a clock turn in 15 minutes?

179

3. Ethan and his friends are erecting a flag pole. How much more do they have to turn the pole to make it upright?

38º

4. A wrecking ball is pulled back by an angle of 28º and released.

It swings to an angle that is 5º less than the release angle.

Find the total angle that the wrecking ball swings.

28º

180

?

At Home 1. The Leaning Tower of Pisa forms an angle of 86º to the ground as shown below. How many degrees must it turn to become fully upright?

86o

2. A Ferris wheel turns 42º in 1 minute.

How much does it turn in 5 minutes?

181

3. Look at the time shown on the clock below to answer the questions.

(a) How many degrees has the minute hand turned since 1 o'clock?

(b) The minute hand turns another 60º. What is the time now?

182

Looking Back 1. Name the angles.

B v

C

w x

y z

u

A

D

v=

= =

BCD

z=

BAD

y= w=

2. Check the bigger angle. (a)

(b)

183

3. Check the box that applies to each angle. Use a piece of paper to help you.

Angle

184

Smaller than a right angle

Right angle

Bigger than a right angle

4. Draw and label the angles. (a)

WXY = 115o

(b)

p = 64o

(c)

PQR = 90o

185

(d)

t = 120o

(e)

ABC = 160o

5. Find the unknown angle. Show your working.

SOU = 135º

(a)

T U

S

186

O

TOU =

ROQ =

(b) QT is a straight line and

SOT.

ROS =

S

R

50o

Q

T

O

(c) HK is a straight line.

HOI =

I

J 15o

H

O

K

(d) AE is a straight line.

AOB =

A

B O

52o 28o C

20o E

D

1 87

(e) All straight lines meet at a point.

k=

R

120o

S

k

83o Q

T

(f) All straight lines meet at point E. A B 7o 34o E

95o

D

1 88

C

AED =

6. The roof of a school building is the shape of a triangle and has a flag on top. Find the angle formed between the flag pole and the roof.

?

75o

7. When the minute hand on a clock is pointing at 10, how many degrees must it turn to point at 12?

189

8

Symmetry

Anchor Task

190

191

Identifying Symmetric Figures Let’s Learn Take a sheet of paper and fold it in half as shown.

When the paper is folded along the dotted line, the halves formed are exactly the same shape. The dotted line is a line of symmetry.

Fold the paper again as shown.

A figure can have more than one line of symmetry.

This dotted line is also a line of symmetry.

192

Now fold the paper as shown.

When folded along the dotted line, the two shapes formed are not exactly the same shape. The dotted line is not a line of symmetry.

A symmetric figure has at least one line of symmetry.

The figures below are symmetric figures.

The figures below do not have any lines of symmetry.

They are not symmetric figures.

193

Let’s Practice 1. (a) Check the lines of symmetry.

Cross the lines that are not lines of symmetry.

(b) Is a hexagon a symmetric figure? Explain your answer.

2. (a) Check the lines of symmetry. Cross the lines that are not lines of symmetry.

(b) How many lines of symmetry does the heart have?

194

3. Use a ruler to draw a line of symmetry through each figure. (a) (b)

(c) (d)

(e) (f)

(g) (h)

195

4. Shade the symmetric figures and draw a line of symmetry. (a) (b)

(c) (d)

(e) (f)

(g) (h)

196

Hands On 1. In small groups, walk around your schoolyard and search for symmetric figures.

2. Draw four symmetric figures in the space below. Draw a line of symmetry through each figure.

197

At Home 1. Check the lines of symmetry. Cross the lines that are not lines of symmetry.

(a) (b)

(c) (d)

(e) (f)

1 98

2. Put a cross through the figures that are not symmetric.

Shade and use a ruler to draw a line of symmetry through the symmetric figures. (a) (b)

(c) (d)

(e) (f)

199

Drawing Symmetric Figures Let’s Learn Trace this shape on a folded sheet of paper.

Cut out the shape and unfold the paper.

The figure made has two identical halves.

It is a symmetrical figure.

We can also draw symmetric figures using square grid paper.

2 00

Hands On 1. Fold a sheet of paper in half.

Trace and cut out a symmetric figure.

2. Trace or paste the figure in the space below. Draw a line of symmetry.

2 01

Let’s Practice I n each grid, the dotted line is a line of symmetry.

Draw lines to form the symmetric figure. (a) (b)

(c) (d)

(e)

202

Hands On 1. Draw half of a symmetric figure on each square grid.

Draw the line of symmetry.

2. Swap books with a partner and have them complete each symmetric figure.

(a) (b)

(c) (d)

203

At Home 1. In each grid, the dotted line is a line of symmetry.

Draw lines to form the symmetric figure. (a) (b)

(c) (d)

(e)

2 04

Solve It! We can use square grid paper to make symmetric patterns.

Complete these symmetric patterns. (a) (b)

(c) (d)

205

Looking Back 1. Check the lines of symmetry. Cross the lines that are not lines of symmetry. (a) (b)

(c) (d)

2. Use a ruler to draw a line of symmetry through each figure. (a) (b)

206

3. In each grid, the dotted line is a line of symmetry.

Draw lines to form the symmetric figure. (a) (b)

(c) (d)

4. Draw a symmetric figure on each square grid.

Draw the line of symmetry. (a) (b)

207

9

Line Plots and Line Graphs

Anchor Task

208

Length of Pencils Length

Tally

Total

209

Interpreting and Creating Line Plots Let’s Learn A line plot shows how frequently data occurs along a number line.

An 'X' is placed above a number each time it occurs in the data set.

Length of Pencils Length Tally Total 3 in

3

1 in 4 1 3 in 2 3 3 in 4

4 5

4 in

2

3

Blake and Wyatt measured the length of all of the pencils in their pencil cases. They first recorded the data in a tally and then into a line plot.

7 7 7 3 in Most of the pencils 1 were 3 2 in.

21 0

2

7 7 7 7

7 7 7 7 7

7 7

7 7

1 3 in 4

1 3 2 in

3 3 4 in

4 in

The shortest pencils were 3 in The longest were 4 in.

The City Zoo measured the heights of the giraffes in the African Animals enclosure. The data is shown in the line plot below.

7 7 7 7

7 1 14 ft 2

15 ft

7 7 7 7 7 1 15 ft 2

7 16 ft

7 7 1 16 ft 2

1 The line plot shows that most of the giraffes are 15 ft tall.

2 1 It shows that the shortest giraffe is 14 ft tall and the tallest giraffes 2 1 are 16 ft tall.

2 What is the difference in height between the shortest and tallest giraffes?

1 1 16 – 14 = 2 2 2 The difference in height between the shortest and the tallest giraffes is 2 ft.

211

Let’s Practice 1. The line plot shows the ages of children at Chelsea's birthday party.

Ages of Children

7 7 7

7 7 7

7

7 7 7 7 7

6

7

8

9

7 7 10

(a) How many children are 9 years old?

(b) How many children are 6 years old?

(c) How many children are 8 years or older?

(d) How many children are 6 or 7 years old?

(e) What is the age difference between the youngest and oldest children?

212

2. Sophie surveyed the children in her class to find out how many people live in their households. She recorded the data in a line plot.

Number of People in Household

7 7

7 7 7 7 7 7

7 7 7 7 7

7 7 7 7

7

3

4

5

6

7

(a) How many households have 6 people?

(b) How many households have 4 people?

(c) How many households have more than 4 people?

(d) How many households have fewer than 6 people?

(e) How many people did Sophie survey?

213

3. Jordan loves to collect rare coins. The line plot below shows the denominations of the coins in his collection.

Jordan's Rare Coins

7 7 7 7 7

7 7 7

7 7

pennies

nickels

dimes

7 7 7 7 7 7

7 7 7 7 7

quarters half dollars

(a) How many nickels does Jordan have?

(b) How many dimes and quarters does Jordan have?

(c) How many more quarters than dimes does Jordan have?

(d) How many fewer nickels than half dollars does Jordan have?

(e) How many of Jordan's coins are not quarters?

21 4

4. The line plot below shows the number of each item sold at the school cafeteria at lunch time.

Cafeteria Sales

7 7 7 7 7 7 pies

7 7

7 7 7 7 7

sandwiches hot dogs

7 7 7 7 7 7

7 7 7 7 7 7 7

salads

apples

(a) Which item sold the least?

(b) Which item sold the most?

(c) How many more apples were sold than sandwiches?

(d) How many items were sold in all?

(e) How many fewer pies and sandwiches were sold than salads and apples?

215

5. On a holiday to Mermaid Beach, Wyatt went fishing with his dad and brother every day. The table below shows the number of fish Wyatt caught each day.

Fish Caught at Mermaid Beach Day

Number of Fish Caught

Wed

4

Thurs

3

Fri

6

Sat

6

Sun

4

(a) Represent the data in the table in a line plot.

21 6

(b) On which two days did Wyatt catch the most fish?

(c ) On which day did Wyatt catch the fewest fish?

(d) On which days did Wyatt catch an equal number of fish?

(e) How many fish were caught on Wednesday to Friday?

(f) How many fish were caught on the weekend?

(g) How many more fish were caught on the weekend compared to Wednesday and Thursday?

(h) On Saturday, Wyatt's brother caught twice as many fish as Wyatt. How many fish did Wyatt's brother catch on Saturday?

(i) On Friday, Wyatt and his dad caught 20 fish in all.

How many fish did Wyatt's dad catch on Friday?

217

6. Ethan measured the length of the nails in his dad's toolbox.

He made a tally to record the data.

Length of Nails Length (in)

Tally

21 2 23 4 3 31 4 31 2 33 4 (a) Represent the data in the table in a line plot.

218

(b) What was the length of the longest nails?

(c ) What was the length of the shortest nails?

(d) What was the most common nail length?

(e) What was the least common nail length?

(f) How many nails were shorter than 3 inches?

(g) What was the difference in length between the shortest and longest nails?

(h) What is the total length of all the 3-inch nails?

(i) What is the total length of all the 2 1 -inch nails?

2

219

Hands On 1. Use a ruler to measure the animals.

Record your data in a tally on the next page.

22 0

Length of Animals Length (in)

Tally

221

2. Use the data in your tally to create a line plot.

3. (a) What is the most common animal length?

(b) What is the least common animal length?

(c) What was the longest animal? What was its length?

(d) What was the shortest animal? What was its length?

(e) What was the difference in length between the shortest and longest animals?

22 2

At Home 1. Blake surveyed his classmates about the time they spent doing homework on the weekend. He presented the data he collected in the line plot below.

Hours Doing Homework on Weekend

7 7

7 7 7 7

1 2

3 4

1

7 7 7

7 7 7 7 7 7

7 7 7 7

11 4

11 2

13 4

(a) How many students did homework for 45 minutes?

(b) How many students did homework for less than 1 hour?

(c) How many students did homework for 90 minutes or more?

(d) What was the most common amount of time spent doing homework?

223

2. Wyatt surveyed his friends about how many houses they visited on Halloween. He presented his data in a line plot.

Houses Visited on Halloween

7 7

7 7 7 7

7 7 7 7 7 7

7 7 7

7 7 7

7 7

0

5

10

15

20

20+

(a) How many students did not visit any houses?

(b) How many students visited 10 or fewer houses?

(c) How many students visited more than 20 houses?

(d) How many fewer students visited 20 houses than students who visited 10 houses?

(e) What was the most common number of houses visited by students on Halloween?

224

3. Ethan measured the length of the fishing gear in his tackle box.

He represented the data in a line plot.

Length of Fishing Gear (in)

7 7 1 2

7 7 7 7 1

7 7 7

7 7 7 7 7 7

7

11 4

11 2

13 4

7 7 7 7 7 2

(a) What length are the shortest items in the tackle box?

(b) What length are the longest items in the tackle box?

(c) What is the difference in length between the longest and shortest items?

(d) What is the total length of the items that are 1 1 in long?

4

(e) How many items in the tackle box are shorter than 2 in?

225

4. Sophie surveyed the students in her class to see how far each student ran during the school fun run.

She recorded her data in a tally.

School Fun Run Distance (mi)

Students

2 2

1 2

3 3

1 2

4 4

1 2

(a) Represent the data in the table in a line plot.

22 6

(b) How many students ran 4 1 mi?

2

(c) How many students ran 2 1 miles?

2

(d) How many students ran 3 miles or less?

(e) How many students ran 3 miles or more?

(f) What was the difference between the shortest and longest distance ran?

(g) Which distances were ran by at least 5 students?

(h) How many students ran more than 4 miles?

(i) What was the total distance ran by all students who ran more than 4 miles?

227

Hands On 1. Gather 15-20 objects from around your home that are more than 2 inches and less than 6 inches in length.

2. Use a ruler to measure the length of each object to the 1 nearest inch.

4 3. Record your data in a tally, then represent the data in a line plot.

Tally

228

Line Plot

4. Write four questions that can be answered by interpreting the data in your line plot. Ask the questions to your classmates and record their answers.

Questions

229

Interpreting and Creating Line Graphs Let’s Learn 1. Mr. Whyte recorded the amount of fuel he used every month for five months. He recorded the data in the table below.

Fuel Consumption Month

Fuel Used (l)

Jan

50

Feb

125

Mar

100

Apr

100

May

150

To help us interpret the data, we can represent the data in a line graph.

Mr. Whyte's Fuel Consumption

Fuel (l)

150 100 50 0

Jan

Feb

Mar

Apr

May

Month

What things can you interpret about Mr. Whyte's fuel consumption?

230

(a) In which month did Mr. Whyte consume the most fuel?

Mr. Whyte consumed the most fuel in May. (b) In which months did Mr. Whyte consume 100 l of fuel?

Mr. Whyte consumed 100 l of fuel in March and in April. (c) How much did the fuel consumption increase from

January to February?

From January to February, fuel consumption increased by 75 l.

2. The line graph below shows the number of visitors to a zoo for a period of one week.

Visitors

Zoo Visitors – Monday to Sunday 1,500 1,250 1,000 750 500 250 0

Mon

Tues

Wed

Thurs Day

Fri

Sat

Sun

(a) On which two days were there fewer than 700 visitors?

Tuesday and Wednesday had fewer than 700 visitors. (b) How many more visitors were there on Friday than on Wednesday?

There were 500 more visitors on Friday than on Wednesday. (c) How many visitors were there on the weekend?

There were 2,750 visitors on the weekend.

231

Let’s Practice 1. The line graph below shows bakery sales for one week.

Bakery Sales – Monday to Sunday

Sales ($)

3,000 2,000 1,000 0

Mon

Tues

Wed

Thurs Day

Fri

Sat

Sun

(a) What were the bakery sales on Saturday?

(b) What were the total sales on Monday and Tuesday?

(c) What was the difference between the lowest sales and the highest sales?

(d) On how many days were sales greater than $750?

(e) What was the difference in sales from Thursday to Friday?

232

2. The line graph below shows the number of visitors to Mermaid Beach in the morning.

Mermaid Beach Visitors

Visitors

150 100 50 0

06 00 06 30 07 00 07 30 08 00 08 30 09 00 Time

(a) At what time was the number of visitors the highest?

(b) At what time was the number of visitors the lowest?

(c) How many visitors were at Mermaid Beach at 07 00?

(d) What was the increase in visitors from 07 00 to 07 30?

(e) What was the difference in visitors from 08 30 to 09 00?

233

3. Riley planted a seedling. She measured the height of the plant every day for five days. She recorded her measurements in the table below.

Seedling Height Day

Height (cm)

Tues

1

Wed

2

1 2

Thur

3

Fri

4

Sat

5

(a) Represent the data from the table in a line graph below.

Seedling Height

5

Height (cm)

4 3 2 1 0

Tues

Wed

Thurs Day

23 4

Fri

Sat

(b) What was the height of the seedling when Riley planted it?

(c) How much did the plant grow from Tuesday to Wednesday?

(d) On which day was the seedling 3 cm tall?

1 (e) When did the seedling grow by 1 cm in one day?

2

(f) When did the seedling grow the least in one day?

(g) How many centimeters did the seedling grow in five days?

4. The table below shows the monthly shoe sales from a sporting goods store.

Shoe Sales (Jan to Jun) Month

Jan

Feb

Mar

Apr

May

Jun

Sales ($)

200

250

150

400

300

200

(a) Represent the data in a line graph on the next page.

235

Shoe Sales (Jan to Jun)

Sales ($)

500

100 0 Month

(b) What were the shoe sales for the month of March?

(c) What was the difference in shoe sales from April to May?

(d) In which month was shoe sales the greatest?

(e) In which months were shoe sales greater than $200?

(f) What was the total shoe sales for April, May and June?

236

Hands On Riley recorded the distances she jogged every day for one week.

She recorded the data in a table.

Distances Ran Day Distance (km)

Mon

Tues

Wed

Thur

1 2

4

4

6

2

Fri 4

1 2

Sat 3

1 2

Sun 4

1 2

1. Use a computer graphic tool to represent the data in a line graph. Give your graph a title and label the axes. Print and paste the graph in the space below.

2. With a classmate, talk about the things the line graph shows.

237

At Home 1. Blake and Wyatt counted the number of birds in the local wetlands every Saturday for six weeks.

Wetland Bird Population

Number of Birds

40 30 20 10 0

1

2

3

Week

4

5

6

(a) How many birds were at the wetlands in week 2?

(b) How many more birds were in the wetlands in week 5 than in week 4?

(c) In which weeks did they spot the fewest birds?

(d) In week 7, Blake and Wyatt spotted 15 fewer birds than in week 6. How many birds did they observe?

23 8

2. The line graph below shows the total number of enrolled students at Miami Primary School from 2015 to 2020.

Miami Primary School Enrolments Students Enrolled

500 400 300 200 0

2015

2016

2017 2018 Year

2019

2020

(a) How many more students enrolled in 2016 compared to 2015?

(b) What happened to enrollments from 2016 to 2019? .

(c) What is the total number of enrollments from 2018 to 2020?

(d) Miami Primary School predicts enrollments will increase by 150 students in 2021. If they are correct, how many students will enroll in 2021?

239

3. The table below shows the mass of meat sold each weekday at Peter's Fine Meats.

Meat Sold Day

Mass (kg)

Mon

225

Tue

250

Wed

175

Thur

200

Fri

150

(a) Represent the data from the table in a line graph.

Meat Sold (Mon – Fri)

Mass (kg)

250

50 0 Day

240

(b) On which day was the most meat sold?

(c) How much meat was sold on Friday?

(d) How much more meat was sold on Monday than Friday?

(e) How much meat was sold from Wednesday to Friday?

(f) On Saturday, Peter's Fine Meats sold twice as much meat as Friday. How much meat was sold on Saturday?

(g) On Sunday, Peter's Fine Meats had a sale. They sold three times as much meat as they did on Saturday. How much meat was sold on Sunday?

(h) What was the total mass of meat sold from Friday to Sunday?

2 41

Hands On 1. In small groups, use a thermometer to record the outdoor air temperature every hour from 9 a.m. until 1 p.m. Record your data in the table below.

Air Temperature Time

9 a.m. 10 a.m. 11 a.m. 12 p.m. 1 p.m.

Temperature (oC) 2. In the space below, represent the data in a line graph.

2 42

3. Interpret the data in your line graph. (a) What was the temperature at 9 a.m.?

(b) How did the temperature change in the first hour?

(c) What was the difference in temperature between 10 a.m. and 1 p.m.?

(d) At what time was the temperature the highest?

(e) At what time was the temperature the lowest?

(f) Based on the data in your graph, what do you predict the temperature will be at 5 p.m.? Explain your answer.

243

Looking Back 1. The line plot shows the number of questions students got correct in a 10-question math quiz.

Correct Answers in Math Quiz

7 7

7 7 7

7 7 7

7 7 7 7

6

7

8

9

7 10

(a) How many students answered all questions correctly?

(b) How many students answered 7 questions correctly?

(c) How many students answered less than 9 questions correctly?

(d) What was the difference between the lowest and highest scores?

(e) How many students took the quiz in all?

2 44

2. The table below shows the amount of sports drink children drank after a football match.

Sports Drink Consumption Amount (cups) Children

1 2

2

3

3

1

1 2

3

5

5

2

1 2

4

3

2

3

(a) Represent the data in a line plot.

(b) How many children drank less than 3 cups of sports drink?

(c) How many children drank more than 2 cups of sports drink?

(d) How much sports drink did the children drink in all?

245

3. The line graph below shows the temperature of water in a beaker over 1 hour.

Temperature (oC)

Water Temperature 100 80 60 40 20 0

1:00 p.m.

1:10 p.m.

1:20 p.m.

1:30 p.m.

1:40 p.m.

1:50 p.m. 2:00 p.m.

Time

(a) What was the temperature of the water at 1:10 p.m.?

(b) What was the increase in temperature from 1:10 p.m. to 1:20 p.m.?

(c) How did the temperature change from 1:40 p.m. to 2:00 p.m.?

(d) What was the increase in temperature from 1:00 p.m. to 1:30 p.m.?

2 46

4. The table below shows the amount of money Chelsea saved each month for 6 months.

Chelsea's Savings Month

Feb

Mar

Apr

May

Jun

Jul

Savings ($)

35

40

10

50

45

25

(a) Represent the data in a line graph.

(b) In which month did Chelsea save $40 more than the previous month?

(c) In which month did Chelsea save $20 less than the previous month?

(d) How much did Chelsea save from April to July?

247

10 Problem Solving Act It Out Example Two tennis teams are competing against each other. There are 4 players on each team. Each player must play each member of the opposing team. How many tennis matches are played in all?

There are a total of 12 pairs of players. So, 12 matches must be played in all.

2 48

1. 6 people attend a meeting. If everyone shakes hands with one another, how many handshakes occur?

249

2.

Use 9 toothpicks to make this shape.

(a) Take away 3 toothpicks to make 1 triangle. Cross out the toothpicks you removed. Draw the shapes formed.

(b) Take away 3 toothpicks to make 2 triangles.

Draw the shapes formed.

25 0

3.

Use 12 toothpicks to make this shape.

(a) Take away 2 toothpicks to make 2 squares.

Cross out the toothpicks you removed.

Draw the shapes formed.

(b) Take away 4 toothpicks to make 2 squares.

Cross out the toothpicks you removed.

Draw the shapes formed.

2 51

4. In small groups, sit in a circle. Take turns counting upward from 1. If the number is a multiple of 3, say 'fizz!' instead of the number. If the number is a multiple of 5, say 'buzz!' instead of the number. If the number is a multiple of both 3 and 5, say 'fizz buzz!' instead of the number. (a) At what number will 'fizz buzz!' be said for the 3rd time?

(b) At 50, how many times has 'fizz!', 'buzz!' and 'fizz buzz!' been called out?

252

Draw a Model Example A bicycle shop orders a scooter and a racer. The cost of a racer is 3 times the cost of a scooter. A scooter costs $354. Find the total cost of the shop’s order.

First, let’s find the cost of a racer. $354 1

scooter

x

3 15 4 3

1 0 6 2

racer ?

A racer costs $1,062. $354

$1,062

scooter

racer

1 10 6 2 +

3 5 4 1 4 1 6

?

1,062 + 354 = 1,416 So, the total cost of the shop’s order is $1,416.

253

1. 502 strawberries were picked at a strawberry farm. 46 of the strawberries were rotten and were put in the compost. The rest were packed into punnets of 8 strawberries. How many punnets were there in all?

254

2. Sophie buys 9 meters of ribbon to wrap presents and has $30 left over. If she bought 6 meters of ribbon, she would have $51 left. How much money did Sophie have originally?

2 55

3. 163 pupils each donate $12 for a charity fundraiser. The money is collected and shared equally between 3 charities.

How much money does each charity receive?

2 56

4. Halle loves to read. She reads 24 pages of a book per day for 3 weeks. In the 4th week, she had a lot of homework and read 10 pages less per day. Find the total number of pages she read in the 4 weeks.

2 57

Guess-and-Check Example An automotive factory produces motorcycles and cars. It produces 3 times as many cars than motorcycles. In one day it used a total of 168 wheels to produce the vehicles. How many motorcycles and cars were made?

Start with a guess on the number of motorcycles. Find the total wheels and then increase or decrease depending on the outcome.

Let's start with 3 motorcycles.

Motorcycles Motorcycle wheels

Cars

Car wheels

Total wheels

3

6

9

36

42

10

20

30

120

140

11

22

33

132

154

12

24

36

144

168

Our first guess was far too low. So we increased to 10 and got a result closer to 168. We then increased 1 motorcycle at a time until we found the correct answer.

The automotive factory produced 12 motorcycles and 36 cars in one day with 168 wheels.

258

1. 510 people attend a local soccer match. There are 66 more males at the soccer match than females. Find the total number of males and females at the soccer match.

Hint: There are more than 250 males at the match.

259

2. Mrs. Kim bought 5 movie tickets and 4 tubs of popcorn for $84. A tub of popcorn costs half as much as a movie ticket.

Find the cost of each item.

26 0

3. In art class, pupils made an equal number of spiders and ants with craft materials. A pipe cleaner was used to make each leg of the animals. The class used a total of 126 pipe cleaners. (a) Find the number of each animal made by the pupils.

(b) Each pupil made 1 animal. How many pupils are in the class?

261

4. Multiples of each coin are selected to give a total amount of $3.09. Twice as many quarters were selected than pennies.

Three times as many dimes were selected than nickels.

Find the number of each coin selected.

Hint: There are 8 quarters.

2 62

Make a List Example On vacation, Ethan packed the following clothing items: Tops Bottoms Footwear 1 x T-shirt 1 x pair of shorts 1 x pair flip flops 1 x singlet 1 x pair of jeans 1 x pair of runners How many different ways can Ethan dress on vacation?

T-shirt + shorts + flip flops T-shirt + shorts + runners T-shirt + jeans + flip flops T-shirt + jeans + runners singlet + shorts + flip flops singlet + shorts + runners singlet + jeans + flip flops singlet + jeans + runners There are 8 different ways Ethan can dress.

263

1. Michelle has forgotten the order of the combination to her bicycle lock. The lock requires 4 digits and she knows the digits are 2, 5, 6 and 8. Find the maximum number of combinations she must try to find the correct order.

264

2. Bongo the Clown has 3 hats – pink, yellow and purple.

He also has 3 pairs of shoes – orange, red and blue. How many different hat and shoe combinations can he wear?

265

3. Find 10 different ways to make $10 using the coins in the table below.

1 2 3 4 5 6 7 8 9 10

2 66

4. Find the sum of the digits from 1 to 20.

5. How many numbers between 100 and 200 contain the digit 2?

2 67

Look for Patterns Example The numbers in each triangle follow the same pattern. Identify the pattern and find the missing number.

3 9 5

7 13

27

25 6

4

17 5

Let's multiply the numbers at adjacent vertices on the left triangle 5 x 3 = 15 3 x 6 = 18 5 x 6 = 30 Notice that all of the products are greater than the number between the vertices of the triangle. Let's try subtracting the number on the opposite vertex from the product.

15 – 6 = 9 18 – 5 = 13 30 – 3 = 27 We have found the rule and can now find the missing number.

7 x 4 = 28 28 – ? = 25 The missing number is 3.

26 8

1. Look for the pattern and fill in the blanks. (a) (b)

3

1

3

3

10

2

9

10

10

15

4

8

(c) (d)

4

3

27

5

20

36

(e) (f)

4

2 12

5

5 6

32 50

40

40

15

9

180

36

80

269

2. The numbers in each triangle follow the same pattern.

Find the missing number. (a)

4 21 6

270

8 6

14

10 3

2

46 4

(b)

10 58 5

85 50

99 8

9

99 91

9

271

3. Study the numbers in the squares.

Find the missing number. (a)

(b)

2

4

3

7

5

6

20

1

10

35

5

9

12

8

3

3

7

2

2

15

27

3

40

9

4

1

7

3

27 2

5

8

4. Look for a pattern in the values and answer the questions.

Term

1

2

3

4

5

6

7

Value

8

16

24

32

40

48

56

(a) What is the value of the 10th term?

(b) What is the value of the 100th term?

5. Look for a pattern in the values and answer the questions.

Term

1

2

3

4

5

6

7

Value

11

22

33

44

55

66

77

(a) What is the value of the 10th term?

(b) What is the value of the 20th term?

273

Work Backwards Example Riley spent 45 minutes eating her lunch. She then attended her afternoon classes for 2 and 1/2 hours. After class, she spent 10 minutes talking with friends. She then took 15 minutes to walk home. She arrived home at 4:05 pm. What time did Riley start eating her lunch?

Let's work backwards and subtract the durations.

4:05 p.m. – 15 min = 3:50 p.m.

3:50 p.m. – 10 min = 3:40 p.m.

3:40 p.m. – 2 hr 30 min = 1:10 p.m.

1:10 p.m. – 45 min = 12:25 p.m.

She left school at 3:50 p.m.

She finished classes at 3:40 p.m.

She finished lunch at 1:10 p.m.

She started lunch at 12:25 p.m.

Riley started eating her lunch at 12:25 p.m.

2 74

1. Blake visits his father at work. They meet at the office and then take the lift up 12 floors to the observation deck. They then go down 16 floors to the cafeteria. After that, they take the lift up 7 floors to the fitness center. From there, Blake takes the lift down 21 floors to the ground floor and heads home.

On what floor is Blake's dad's office?

275

2. Keira takes her age in years and multiplies it by 6. She then subtracts 6 and divides by 2. She halves that result and adds 5.

Finally she divides that number by 5 and is left with 4.

Find Keira's age.

276

3. Halle is shopping at the local mall. She buys some guitar strings at the music shop and then goes up 5 floors to the cinema. After the movie, she goes up 3 floors to the chocolate shop. She then goes down 7 floors to the book shop. The book shop is on level 3. On what level is the music shop?

277

y

Before-After Concept Example There are 4 times as many girls playing in the park than boys.

4 more boys arrive at the park, and now there are 3 times as many girls. How many children were at the park in the beginning?

Before

girls boys

After

girls boys 4

1 unit = 4 Before girls: 12 units 12 x 4 = 48 boys: 3 units 3 x 4 = 12 48 + 12 = 60 So, there were 60 children at the park in the beginning.

278

1. Jordan had $260 more than Ethan. After Ethan received $80 for his birthday, Jordan had twice as much money as Ethan.

How much money did each person have at first?

279

2. 4 years ago, Ella was three times older than her brother Luke.

Today they have a combined age of 20 years. How old are Ella and Luke now?

280

3. McKenzie has 4 times the number of stickers than Robert.

Robert goes to the store and buys 21 more stickers. They now have an equal number of stickers. How many stickers do they each have?

281

Simplify the Problem Example The current month is November. What will the month be in 40 months?

Let's make a list of the months.

November – now December – 1 month later January – 2 months later February – 3 months later March – 4 months later April – 5 months later May – 6 months later June – 7 months later July – 8 months later August – 9 months later September – 10 months later October – 11 months later November – 12 months later We want to find the month in 40 month's time.

Let's divide by 12 and match the remainder to the months above.

40 ÷ 12 = 3 R 4 There is a remainder of 4, so the 40th month after November is March.

2 82

1. Today is Monday, what day will it be in 45 days?

2. Today is Wednesday, what day will it be in 288 days?

283

3. The current month is February. What month will it be in 175 month's time?

4. Look at the repeating pattern of 5 shapes. ...

If the pattern continues, what will the 12th shape be? What will the 184th shape be?

2 84