Nathalie Fortier Annie Leblanc - Amazon Web Services · 2020-03-20 · Electronic Publishing Interscript Illustrator Michel Rouleau (p. 47, 96) ENGLISH VERSION Pedagogical Reviewer

Elementary – Grade 6

Nathalie FortierAnnie Leblanc

WORKBOOK

M A T H E M A T I C S

B

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Registration of copyright – Bibliothèque et Archives nationales du Québec, 2014 Registration of copyright – Library and Archives Canada, 2014

Printed in Canada 67890 HLN 20 19 ISBN 978-2-7613-6136-1 13328 ABCD OF10

© ÉDITIONS DU RENOUVEAU PÉDAGOGIQUE INC., 2014 Member of Pearson Education since 1989

1611 Crémazie Boulevard East, 10th Floor Montréal, Québec H2M 2P2 Canada Telephone: 514 334-2690 Fax: 514 334-4720 [email protected] pearsonerpi.com

ENGLISH VERSION

Project Editor and TranslatorAmy Paradis

ProofreaderBrian Parsons

Art DirectorHélène Cousineau

Graphic Design CoordinatorSylvie Piotte

CoverFrédérique Bouvier

Electronic PublishingCatherine Boily

ORIGINAL VERSION

Managing EditorMonique Daigle

Project Editor and Linguistic ReviewerLina Binet

Project Editor and Photo Research Marie-Claude Rioux

ProofreaderLucie Lefebvre

Coordinator, Rights and PermissionsPierre Richard Bernier

Art DirectorHélène Cousineau

Graphic Design CoordinatorSylvie Piotte

Graphic Design and CoverFrédérique Bouvier

Electronic PublishingInterscript

IllustratorMichel Rouleau (p. 47, 96)

ENGLISH VERSION

Pedagogical ReviewerPaul Lamarche

Pedagogical ConsultantBrenda Raymond, Cycle 3 Teacher, Pierre Elliott Trudeau

Elementary School, Western Québec School Board

ORIGINAL VERSION

Science Content ReviewerPhilippe Bazinet, Mathematics Pedagogical Consultant,

Western Québec School Board

ConsultantsAnn-France Couture, Teacher, École Auclair,

commission scolaire des Trois-LacsAntoine Leblanc, Teacher, École Sainte-Anne,

commission scolaire des Hautes-RivièresAmélie Turmel, Teacher, École Notre-Dame-des-Bois-Francs,

commission scolaire des Bois-Francs

Stock Illustrationsshutterstock

Meaning of Pictograms

Student constructs knowledge with teacher guidance.

Student applies knowledge by the end of the school year.

Problem-solving steps are presented on the inside cover of the workbook.

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TABLE OF CONTENTS

THEME

Freestyle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

4.1 Arithmetic Following the Order of Operations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

4.2 Arithmetic Associative, Commutative and Distributive Properties . . . . . . . . . . . . . . . . . . . . . 5

4.3 Arithmetic Multiplying Decimals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

4.4 Arithmetic Dividing Natural Numbers with a Decimal Remainder . . . . . . . . . . . . . . . . . . . . . . 12Dividing by 10, 100 and 1000 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

4.5 Statistics Creating Questions for a Survey, Collecting and Organizing Data . . . . . . . . . . . 17

4.6 Statistics Understanding and Calculating the Arithmetic Mean . . . . . . . . . . . . . . . . . . . . . . . 20

4.7 Arithmetic Dividing a Decimal by a Natural Number Less than 11 . . . . . . . . . . . . . . . . . . . . 24

4.8 Measurement Estimating and Measuring Surface Area . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

MAKING CHOICES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

REVIEW . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

PROBLEM SOLVING . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

THEME

Underwater World . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

5.1 Arithmetic Reading and Writing Integers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44Locating Integers on a Number Line . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44Comparing Integers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

5.2 Measurement Estimating and Measuring Temperature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

5.3 Geometry Locating Points in a Cartesian Plane . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52

5.4 Geometry Observing and Producing Frieze Patterns Using Translations . . . . . . . . . . . . . . . 57Tessellations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59

5.5 Measurement Estimating and Measuring Mass . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61Establishing Relationships Between Units of Measure . . . . . . . . . . . . . . . . . . . . . 61

B-IIIIII


5.6 Measurement Establishing Relationships Between Units of Measure for Time . . . . . . . . . . 65

5.7 Measurement Estimating and Measuring Volume . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68

MAKING CHOICES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72

REVIEW . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74

PROBLEM SOLVING . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82

THEME Job Fair . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83

6.1 Probability Enumerating Possible Outcomes of a Random Experiment Using a Table and a Tree Diagram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84

6.2 Probability Comparing the Outcomes of a Random Experiment with Known Theoretical Probabilities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87

6.3 Geometry Describing and Classifying Prisms and Pyramids Using Faces, Vertices and Edges . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90

6.4 Geometry Nets of Solids or Convex Polyhedrons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93

6.5 Geometry Testing Euler’s Theorem on Convex Polyhedrons . . . . . . . . . . . . . . . . . . . . . . . . . . . 97

MAKING CHOICES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100

REVIEW . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102

PROBLEM SOLVING . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110

Final Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111

Glossary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129

IV IV


TH

EM

E

Freestyle

A Useful Concept

Arithmetic mean is an essential tool for evaluating and comparing the performance of an athlete or a sports team. A figure skater’s overall score is determined by the average number of points earned for each routine.

4.1 Following the Order of Operations

4.2 Associative, Commutative and Distributive Properties

4.3 Multiplying Decimals

4.4 Dividing Natural Numbers with a Decimal RemainderDividing by 10, 100 and 1000

4.5 Creating Questions for a Survey, Collecting and Organizing Data

4.6 Understanding and Calculating the Arithmetic Mean

4.7 Dividing a Decimal by a Natural Number Less than 11

4.8 Estimating and Measuring Surface Area

WHAT I’LL LEARN

There are many polling firms in Canada. Their role is to investigate the preferences or opinions of people on a specific subject matter. They use surveys to collect and analyze data, then present their results to the companies or media outlets that requested their services.

Statistical Investigations

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LEARN ABOUT IT

SECTION 4.1 ARITHMETIC Chain of Operations

Following the Order of OperationsThe order of operations is the order you must follow when making calculations in a chain of operations.

To avoid getting an incorrect result from a chain of operations, it is important to follow the order of operations.

Here is the order to follow.

1. Operations in brackets.

2. Exponentiation (exponents).

3. Multiplication and division, from left to right.

4. Addition and subtraction, from left to right.

Here are the steps for solving the following chain of operations: 4 × 6 ÷ 8 + 32 − (2 + 3) × 2 = ?

Steps Example

1. Do all operations in brackets. 4 × 6 ÷ 8 + 32 − (2 + 3) × 2 = ?

4 × 6 ÷ 8 + 32 − 5 × 2 = ?

2. Do the exponentiation (exponents). 4 × 6 ÷ 8 + 32 − 5 × 2 = ?

4 × 6 ÷ 8 + 9 − 5 × 2 = ?

3. Do the multiplication and division, from left to right.

4 × 6 ÷ 8 + 9 − 5 × 2 = ?

3 + 9 − 10 = ?

4. Do the addition and subtraction, from left to right.

3 + 9 − 10 = ?

12 − 10 = 2

4 × 6 ÷ 8 + 32 − (2 + 3) × 2 = 2

WORK IT OUT

1 Add brackets to each chain of operations to get 24 as a result.

a) 3 + 5 × 2 + 2 × 4 = 24 b) 30 − 2 + 6 × 3 + 2 × 9 = 24

c) 100 ÷ 4 − 12 − 11 = 24 d) 6 × 8 − 2 − 12 = 24

A series of mathematical

operations is called a “chain of operations.”

B-2 Section 4.1


2 Calculate these chains of operations by following the order of operations.

a) (30 − 15) + 13 − 10 + 6 × 7 − 6 = b) 80 ÷ 4 + 12 × 3 − 40 + 6 × 3 =

c) 6 − 3 + 42 − 7 + 12 × 2 = d) (4 × 8) − 3 + (2 × 32) − (2 × 21) =

e) 42 × (4 + 2) − 32 + 101 + 102 = f) 4 × 10 ÷ 8 + (60 ÷ 6) × 4 − 22 =

3 Add the symbols (+, –, × or ÷) to each chain of operations to get the correct result.

My Calculations

Theme 4 B-3


a) 2 × 4 6 × 5 9 = 29 b) 7 + 8 2 + 4 6 = 35

c) 3 + 9 5 + 6 5 = 78 d) 8 × 9 6 ÷ 2 5 = 70

USE REASONING

1 Beth puts away 35 pairs of children’s skis, 65 pairs of junior skis and 130 pairs of adult skis in a warehouse. In all, how many skis does Beth put away? Use a chain of operations to help you calculate.

Solution:

2 Alex is 12 years old. His parents, his 5-year-old sister and his 16-year-old twin brothers go to the indoor skatepark. The entry fee is $7.00 for children up to 5 years old, $10.00 for children ages 6 to 11, $15.50 for children ages 12 to 17 and $21.25 for people 18 years and older. Each family member must also rent equipment for $5.00. What is the total cost of their outing? Use a chain of operations to help you calculate.

Solution:

B-4 Section 4.1


LEARN ABOUT IT

ARITHMETIC Determining Numerical Equivalencies

Using Relationships Between Operations SECTION 4.2

Associative, Commutative and Distributive PropertiesAssociative, commutative and distributive properties make calculating mathematical operations easier.

• The associative property applies to addition and multiplication. It groups the numbers in an equation in different ways without changing the result.

Examples:

Associative Property of Addition Associative Property of Multiplication

3 + 6 + (2 + 8) = 3 + (6 + 2) + 8

3 + 6 + 10 = 3 + 8 + 8

19 = 19

2 × (4 × 5) × 6 = (2 × 4) × 5 × 6

2 × 20 × 6 = 8 × 5 × 6

240 = 240

• The commutative property also applies to addition and multiplication. It moves around the numbers in an equation in different ways without changing the result.

Examples:

Commutative Property of Addition Commutative Property of Multiplication

20 + 35 + 7 + 3 = 35 + 3 + 20 + 7

65 = 656 × 4 × 2 × 3 = 4 × 6 × 3 × 2

144 = 144

• The distributive property applies to multiplication. It distributes multiplication over addition or subtraction.

Examples:

Distributive Property of Addition Distributive Property of Subtraction

1. 8 × (4 + 5) = (8 × 4) + (8 × 5)

2. = 32 + 40

= 72

1. Distribute 8 over 4 and 5.

2. Add the 2 products.

1. 10 × (16 − 9) = (10 × 16) − (10 × 9)

2. = 160 − 90

= 70

1. Distribute 10 over 16 and 9.

2. Subtract the 2 products.

Theme 4 B-5


WORK IT OUT

1 Use the associative property to do these operations.

example 15 + 11 + 4 + 8 = (15 + 11) + 4 + 8 = 38 or 15 + (11 + 4) + 8 = 38

26 + 4 + 8 = 38 or 15 + 15 + 8 = 38

a) 30 + 60 + 40 + 20 =

b) 20 × 3 × 4 × 5 =

c) 12 × 4 × 2 × 10 =

d) 5 × 9 × 8 =

2 Write 2 equivalent chains of operations for each equation by applying the commutative property. Then, calculate the result.

example 3 + 5 + 6 + 7 = (3 + 7) + (6 + 5) or (3 + 6) + (5 + 7) = 21

10 + 11 or 9 + 12 = 21

a) 4 + 12 + 25 + 3 =

b) 6 × 2 × 3 × 5 =

c) 7 × 2 × 3 × 10 =

d) 10 × 6 × 4 =

B-6 Section 4.2


3 Use the distributive property to do these operations.

a) 8 × (6 + 5) =

b) 6 × (6 + 2 + 4) =

c) (8 − 5) × 15 =

d) (9 + 12) × 7 =

e) 11 × (12 – 8) =

4 Use the distributive property to simplify each operation. Then, calculate the result of each chain of operations.

example 3 × 4 + 3 × 8 + 3 × 5 = a) 12 × 6 − 12 × 3 − 12 × 2 =

3 × (4 + 8 + 5) =

3 × 17 = 51

b) 6 × 5 + 6 × 3 + 6 × 4 = c) 15 × 7 − 15 × 1 − 15 × 2 =

5 Use the symbol = or ≠ to indicate whether or not these operations are equivalent.

a) 3 × 4 × 2 × 7 3 × (4 × 2) × 7

b) 5 + 8 × 2 + 7 5 + 8 × (2 + 7)

c) 6 × 12 × 4 × 2 4 × 12 × 2 × 6

d) 3 + 4 × 2 + 5 3 × 4 + 2 × 5

e) 7 × 5 + 4 × 6 7 × (5 + 4) × 6

My Calculations

Theme 4 B-7


LEARN ABOUT IT

ARITHMETIC Multiplying Decimals SECTION 4.3

Multiplying DecimalsDecimals are multiplied in the same way that natural numbers are multiplied. The decimal point is then added based on the number of decimal places in the 2 factors.

Here are the steps for multiplying one decimal by another decimal.

Steps Example: 236.5 × 5.7

1. Align the 2 numbers to be multiplied into columns.

2 3 6.5× 5.7

2. Multiply the 2 numbers. Ignore the decimals points.

1 3 22 4 3

2 3 6 5× 5 7

1 1

1 6 5 5 5+ 1 1 8 2 5 0

1 3 4 8 0 5

3. Count the total number of digits after the decimal point in both factors. (In this case, there are 2.)

236.5 There is 1 digit after the decimal point.

5.7 There is 1 digit after the decimal point.

4. Add a decimal point to the product before the last 2 digits.

2 3 6.5× 5.7 There are 2 digits after

the decimal point.1 3 4 8.0 5

1 3 22 4 3 2 4

2 3 6.5 2 3 7× 5.7 × 6

1 1 1 4 2 21 6 5 5 5

+ 1 1 8 2 5 0

1 3 4 8 0 5

The product is therefore close to 1400, not 14 000.

.

When multiplying the 1st factor by the digit in the tens position in the 2nd factor, start by placing a 0.

Think about it!

To make sure the decimal point is placed correctly, round

the 2 factors to make an approximation of the product.

Then, multiply.

B-8 Section 4.3


WORK IT OUT

1 Make an approximation of the product, then calculate it.

a) Approximation b)

Approximation

2 Fill in the table.

×0.7 2.6 3.4 45.3

12.5

289.3

45.9

My Calculations

3 Find the product of each multiplication.

a) b) c)

1 2 5.8× 3.6

4 7 8.3× 7.2

1 8 2.3× 5.8

3 4 1.5× 9.6

7 5.7× 2 1.3

Theme 4 B-9


4 Solve these problems.

a) One 125 ml glass of chocolate milk

contains 14.3 g of sugar. Emma drinks

1 1

2 glasses of chocolate milk after her

snowboarding lesson. How many

grams of sugar does Emma consume?

My Calculation

b) On Monday, Tim takes his mountain bike along a 1.4 km trail. On Tuesday, he takes a trail that is 2.7 times longer. In all, how many kilometres does Tim bike on Monday and Tuesday?

My Calculation

c) A boat uses 33.4 L of gasoline during a water ski competition. One litre of gasoline costs $1.30. What is the total cost of the gasoline used during the competition?

My Calculation

d) Matteo skates 1.8 km to make one complete lap of an in-line skate track. How many kilometres does Matteo skate after 4.5 laps?

My Calculation

B-10 Section 4.3


USE REASONING

1 At the rock-climbing gym, the 1st wall is 3.4 m high. The 2nd wall is 1.8 times higher than the 1st and the 3rd wall is 3.6 times higher than the 1st. Chloe climbs the 1st wall, her mother climbs the 2nd wall and her father climbs the 3rd wall. How many metres does each parent climb?

Solution:

2 The town mayor wants to have a fence installed around the skatepark. The park is 24.6 m wide and 1.9 times longer than it is wide. The fence the mayor chooses costs $36.00 per metre. It will take 3 hours and 30 minutes to install. The employees’ rate is $70.50 per hour. How much will it cost to buy and install the fence?

Solution:

Theme 4 B-11


LEARN ABOUT IT

Dividing Natural Numbers with a Decimal RemainderDivision is an operation for finding how many times a divisor goes into a dividend. If the quotient is not an integer (whole number), the remainder is expressed with decimals.

Here are the steps for expressing the remainder of a division with decimals.

Steps Example: 32 32401. The divisor 32 does not go into 3 thousands,

the 1st digit of the dividend. So, use 32 hundreds. • 32 goes into 32 one time. Write the number 1

above 2 hundreds.• Multiply 1 × 32 = 32 and write 32 below 32 hundreds. • Subtract 32 – 32 = 0.

2. Bring down the 4 tens. • 32 goes into 4 zero times.

Write the number 0 above 4 tens.• Multiply 0 × 32 = 0 and write 0 below 4 tens. • Subtract 4 – 0 = 4.

3. Bring down the 0 units. • 32 goes into 40 one time. Write the number 1 above 0 units.• Multiply 1 × 32 = 32 and write 32 below 40 units. • Subtract 40 – 32 = 8.

4. Since the difference is not equal to 0, there is a remainder. • Add a decimal point and 2 zeroes to the dividend

and a decimal point to the quotient.

5. Bring down the 1st 0. • 32 goes into 80 two times. Write the number 2 above 0 tenths. • Multiply 2 × 32 = 64 and write 64 below 80. • Subtract 80 – 64 = 16.

6. Bring down the 2nd 0. • 32 goes into 160 five times. Write the number 5 above 0 hundredths.• Multiply 5 × 32 = 160 and write 160 below 160. • Subtract 160 – 160 = 0.

Do the inverse operation to check your answer: 101.25 × 32 = 3240

ARITHMETIC Dividing Natural Numbers with a Decimal Remainder

Dividing by 10, 100 and 1000 SECTION 4.4

Divisor Dividend Quotient

25 263 = 10.52

Decimals

Th H T U

3 2 4 0 . 0 0 − 3 2 0 4 − 0 3

1 4 0 − 3 2 7

1 8 0 − 6 4 1 6 0 − 1 6 0 0

1 0 1 . 2 532

B-12 Section 4.4


WORK IT OUT

Do these divisions. Then, arrange the quotients in increasing order by letter to discover Tommy’s favourite sport.

a) b) c)

d) e) f)

g) h) Tommy’s favourite sport:

Do the inverse operation to check your answers.

Think about it!

25

15

32 16

30 24

20 201 4 5 6 2 8 9 0 3 2 7 6

2 7 9 3 6 9 8 3 4

3 4 6 4 4 1 8 8

Th H T U

3 2 4 0 . 0 0 − 3 2 0 4 − 0 3

1 4 0 − 3 2 7

1 8 0 − 6 4 1 6 0 − 1 6 0 0

M I N

L C I

B G

Theme 4 B-13


LEARN ABOUT IT

Dividing by 10, 100 and 1000Look at these examples for dividing integers.

86 ÷ 10 = 8.6 86 ÷ 100 = 0.86 86 ÷ 1000 = 0.086

524 ÷ 10 = 52.4 524 ÷ 100 = 5.24 524 ÷ 1000 = 0.524

2689 ÷ 10 = 268.9 2689 ÷ 100 = 26.89 2689 ÷ 1000 = 2.689

When dividing an integer by a multiple of 10 (10, 100, 1000, etc.), move the decimal point one or more places to the left. Add a decimal point and one or more zeroes if needed.

524 ÷ 10 = 52.4 524 ÷ 100 = 5.24 524 ÷ 1000 = 0.524

Look at these examples for dividing decimals.

23.9 ÷ 10 = 2.39 23.9 ÷ 100 = 0.239

625.8 ÷ 10 = 62.58 625.8 ÷ 100 = 6.258

2647.3 ÷ 10 = 264.73 2647.3 ÷ 100 = 26.473

When dividing a decimal by a multiple of 10 (10, 100, 1000, etc.), move the decimal point one or more places to the left. Add one or more zeroes if needed.

For example, to calculate 625.8 ÷ 100, move the decimal point 2 places to the left to get 6.258.

To divide by 10, move the decimal point one place to the left. To divide by 100, move the decimal point two places to the left. To divide by 1000, move the decimal point three places to the left.

WORK IT OUT

1 Complete each equation.

a) 41 ÷ = 4.1 b) 65.23 ÷ = 6.523

c) 256.8 ÷ = 25.68 d) 1257.5 ÷ = 12.575

e) 8974 ÷ = 89.74 f) 5896.1 ÷ = 589.61

= 6.258625.8 ÷ 100

B-14 Section 4.4



a) The total length of the ski slopes at Snow Mountain is 186 km. The total length at Mount Snowflake is 4 times smaller. What is the total length of the ski slopes at Mount Snowflake?

My Calculation

b) 20 people pay $195.00 to go on a snowboard simulator. What is the cost per person?

My Calculation

c) 153 children have signed up for snowboarding lessons at a ski centre. They are put into groups of 15 children. How many groups are there?

My Calculation

d) William rode his mountain bike 1264 km over 2 summers. He rode 10 times more kilometres than Lucas. How many kilometres did Lucas ride?

My Calculation

Theme 4 B-15


USE REASONING

1 Bruno wants to climb Mount Washington in the United States, which is 1916 m high. He plans to stop 10 times from the base to the summit. There is an equal distance between each stop. How many metres will Bruno have travelled at each stop?

Stop Number of Metres Travelled

1st

2nd

3rd

4th

5th

6th

7th

8th

9th

10th

2 Workers are installing 60 lampposts and 20 benches along a bicycle path that is 225 km long. Both the lampposts and the benches are evenly spaced along the path. What is the distance between each lamppost? What is the distance between each bench?

Solution:

B-16 Section 4.4


LEARN ABOUT IT

STATISTICS Creating Questions for a Survey,

Collecting, Describing and Organizing Data SECTION 4.5

Creating Questions for a Survey, Collecting and Organizing DataAn investigation or survey is a means to gather information for obtaining statistics.

• Survey questions are designed to collect data. Here are 3 characteristics of an effective survey question:

Examples1. A clear question linked to the subject

of the survey.• Which season is your favourite for

doing sports? a) Spring b) Summer c) Fall d) Winter

2. A question, often multiple choice, that is easy to read and simple to answer.

• Which sport impresses you the most: snowboarding, skateboarding or surfing?

3. A question that leads to an answer that is easy to process.

• Between skiing, snowboarding and skating, which winter sport do you like best?

• A data table can help you to organize survey data and compile your answers.

Example:

A data table has 4 elements.1. A survey title.2. Answer categories.3. A tally of answers (each answer is represented by ).4. Results (the total number of answers in each category).

1 Favourite Season for Doing Sports

2 Spring Summer Fall Winter

3

4 4 10 4 12

WORK IT OUT

1 Design a survey question that could produce the following results. Cake

Ice cream

Apple pie

Chocolate mousse25%

35%30%

10%

Cake

Ice cream

Apple pie

Chocolate mousse25%

35%30%

10%

Theme 4 B-17


2 Use the following data to fill in the table below.

• 13 boys and 12 girls are participating in winter carnival activities.

• Sledding is the least popular activity.

• There are just as many children signed up for dogsledding as there are for snowboarding.

• 8 children are signed up for downhill skiing.

Winter Carnival Activity Participation

Dogsledding

6

3 Use the data in Exercise 2 to create a bar graph.

B-18 Section 4.5


4 The students on the skateboarding team spent the day training for a competition. Here are the number of kilometres travelled.

Distance Travelled by the Girls (km)

Distance Travelled by the Boys (km)

2 2.25 5 1.5

3.75 3.25 2.8 4.5

3.4 5.25 4 2.3

6 1 2.75 3

4.75 3.5 3.6 2.5

Use this data to fill in the table below.

Number of Kilometres Travelled

Number of Kilometres Less than 2 km From 2 to 4 km More than 4 km

Tally

Result

Use the information in the data table to add labels to this circle graph.

Less than 2 km

From 2 to 4 km

More than 4 km

5 Look at the data in Exercise 4, then answer these true or false questions.

True False

a) 25 students travelled more than 4 km.

b) The majority of the students travelled less than 2 km.

c) There are twice as many students who travelled 2 to 4 km as there are students who travelled more than 4 km.

d) All of the students on the team trained for the competition.

10%

25%

65%

Theme 4 B-19


LEARN ABOUT IT

STATISTICS Understanding and Calculating the Arithmetic Mean SECTION 4.6

Understanding and Calculating the Arithmetic MeanThe arithmetic mean is the sum of a set of numbers divided by the total number of parts in the set.

In statistics, it is used for analyzing a group of data and for finding an average value, which can then replace the individual data to redistribute it evenly.

To calculate the arithmetic mean:

1) add all of the data within a group;

2) divide the sum by the total number of data values.

Example 1 : Example 2 :

Calculate the average amount of snow accumulated at Flurry Mountain each month of the ski season:

• December: 15 cm

• January: 46 cm

• February: 72 cm

• March: 34 cm

• April: 19 cm

1. Add 15 + 46 + 72 + 34 + 19 = 186

2. Divide by the number of pieces of data (5): 186 ÷ 5 = 37.2

The average amount of snow accumulated each month is 37.2 cm. If this amount of snow were to be evenly distributed over the 5 months of the ski season, the average would be 37.2 cm per month.

Calculate the average amount of time Collin spends snowboarding each week:

• 1st week: 180 min

• 2nd week: 196 min

• 3rd week: 265 min

• 4th week: 0 min

• 5th week: 324 min

1. Add 180 + 196 + 265 + 0 + 324 = 965 minutes

2. Divide by the number of pieces of data (5): 965 ÷ 5 = 193 minutes

The average amount of time Collin spends snowboarding is 965 minutes per week. If this amount of time were to be evenly distributed over his 5-week training period, the average would be 193 minutes per week.

B-20 Section 4.6


WORK IT OUT

1 Calculate the arithmetic mean of each group of data.

a) Ski slope lengths.

231 m 427 m 621 m 348 m

Arithmetic mean:

My Calculation

b) Number of students per class who do winter sports.

18 14 7 8 11 15 17 6

Arithmetic mean:

My Calculation

c) Number of participants in a competition.

50 76 55 89 70

Arithmetic mean:

My Calculation

2 Add a number to each group of data to get the arithmetic mean indicated.

Arithmetic Mean

Number Added

My Calculations

example 10, 6, 8, 12, 9, 7 8 4

a) 23, 20, 18, 24 21

b) 112, 118, 129 116

c) 50, 75, 67, 32 55

d) 89, 95, 80, 110, 99 96

e) 315, 328, 317, 309, 321, 301

321

Theme 4 B-21


3 Natasha is making hot chocolate for her friends after a day of skiing.

Nancy Salomé Julia Katie Bianca

32 ml 25 ml45 ml 50 ml 0 ml

32 ml 25 ml45 ml 50 ml 0 ml

32 ml 25 ml45 ml 50 ml 0 ml

32 ml 25 ml45 ml 50 ml 0 ml

32 ml 25 ml45 ml 50 ml 0 ml

If Natasha distributes equal portions of hot chocolate, how much does each friend get?

My Calculation

4 This bar graph shows the temperature in Mont-Tremblant during the first week of April.

Days

Temperature from April 1 to 7 in Mont-Tremblant (°C)

Tem

pera

ture

(°

C)

16

14

12

10

8

6

4

2

0

MondayTuesday

WednesdayFrid

aySaturday

SundayThursday

What is the average temperature for the first week of April in Mont-Tremblant?

My Calculation

B-22 Section 4.6


USE REASONING

1 Leah is analyzing data on the people who use the snowboarding park.

Percentage of People Using the Snowboarding Park

Age Group Friday Saturday Sunday

Ages 12–18 32% 56% 65%Ages 19–25 68% 44% 35%

What is the average percentage of people in each age group who go to the snowboarding park during these 3 days?

Age Group Average Number of People

Ages 12–18

Ages 19–25

Solution:

2 Here are the number of motorcycles and snowmobiles sold at SpeedyMoto from 2010 to 2014.

2010 2011 2012 2013 2014 2015

Motorcycles 23 20 25 31 21 ?Snowmobiles 15 10 19 21 15 ?

In 2015, the shop owner wants to sell 3 more motorcycles and 2 more snowmobiles than the average over the last 5 years. How many motorcycles and snowmobiles does he hope to sell in 2015?

Solution:

Theme 4 B-23


LEARN ABOUT IT

ARITHMETIC Dividing a Decimal by

a Natural Number Less than 11 SECTION 4.7

Dividing a Decimal by a Natural Number Less than 11Division calculates the number of times a divisor fits into a dividend. The dividend is not always an integer.

Decimals are divided in the same way that natural numbers are divided. Simply add one more step: the decimal point.

Steps Example: 6 271.62

1. Write the numbers in the division by placing the divisor to the left of the bracket.

2. Divide the whole part as you would normally do.

• The divisor 6 does not go into 2 hundreds. Use 27 tens.6 goes into 27 four times: 6 × 4 = 24. There are 3 tens left.

• Bring down the 1 unit. There are now 31 units to divide.6 goes into 31 five times: 6 × 5 = 30. There is 1 unit left.

3. When you have finished dividing the whole part, move on to the decimal part.

• Add a decimal point to the quotient before bringing down the tenths.

• Bring down the 6 tenths. There are now 16 tenths.6 goes into 16 two times: 6 × 2 = 12. There are 4 tenths left.

• Bring down the 2 hundredths. There are now 42 hundredths.6 goes into 42 seven times.

H T U4 5

2 7 1 . 6 2− 2 4

3 1

− 3 0

1

6

6

H T U4 5 . 2 7

2 7 1 . 6 2− 2 4

3 1

− 3 0

1 6

− 1 2

4 2

− 4 2

0

Do the inverse operation to check your answer: 45.27 × 6 = 271.62

Divisor Dividend

Decimals6 271.62

B-24 Section 4.7


WORK IT OUT

1 Calculate the quotient of each division.

a) b) c)

d) e) f)

g) h) i)

3 5 7.24

7

8

3

4 6

5

9 65 4 1 8.9 2 3 4.24

6 8 3.06 4 1 9.64 3 8 9.3

3 9 4.56 2 9 2.8 4 0 2.54

Theme 4 B-25



a) Lucy is given 395.2 L of paint to repaint 8 identically sized rooms at the ski resort. If she plans on using all of the paint, how many litres of paint does she use in each room?

My Calculation

b) Kelly and her 5 friends pay a total of $94.20 to go to the skateboarding festival. How much does one entry fee cost?

My Calculation

c) Cedric is ordering supplies for an in-line skating competition. These items are sold in packs. Calculate the individual price of each item ordered.

My Calculations

Items Ordered Individual Price

Elbow pads: $92.75 for a pack of 7Spare wheels: $26.95 for a pack of 11Protective helmets: $162.45 for a pack of 5Knee pads: $102.24 for a pack of 8Shirts: $159.90 for a pack of 6

B-26 Section 4.7


USE REASONING

1 During a family ski trip, Mia buys an 8 L jar of ski wax for $26.32 and 5 L of sealant for $28.25. Calculate the price per litre of ski wax and sealant.

Solution:

2 Lucas sells lemonade to the competitors and spectators at a surfing contest. He sells a total of 99.6 L of lemonade at 8 different booths. What is the average number of litres of lemonade sold at each booth?

Solution:

Theme 4 B-27


LEARN ABOUT IT

MEASUREMENT Estimating and Measuring Surface Area SECTION 4.8

Estimating and Measuring Surface AreaArea is the measurement of a figure’s surface.

Measure the area to calculate the surface of a skatepark, a ski slope, a floor, etc.

Use the international system of units (SI) to measure surface area. This conversion table displays the most common units of measure for area.

Square Centimetres (cm2) Square Decimetres (dm2) Square Metres (m2)

1 cm × 1 cm = 1 cm2 1 dm × 1 dm = 1 dm2

10 cm × 10 cm = 100 cm21 m × 1 m = 1 m2

10 dm × 10 dm = 100 dm2

100 cm × 100 cm = 10 000 cm2

Unit of Measure

1 cm

square unit The area of a square or a rectangle can be rapidly calculated with a mathematical formula.

Area of a Square Area of a Rectangle

Multiply the measurement of one side by itself.

Formula: Area = side × side

Area = 4 cm × 4 cm

Area = 16 cm2, which reads, “16 square centimetres.”

Multiply the measurement of its length by its width.

Formula: Area = length × width

Area = 4.5 cm × 3 cm

Area = 13.5 cm2, which reads, “13.5 square centimetres.”

4 cm

4 c

m

4 c

m

4 cm

4.5 cm

3 c

m

3 c

m

4.5 cm

WORK IT OUT

1 Write the best unit of measure for calculating the area of each surface.

a) A ski. b) The area of Canada.

c) A door. d) A ski pass.

B-28 Section 4.8


2 Estimate the area of each object in square metres.

a) A blackboard.

b) The classroom floor.

c) A classroom window.

d) An object of your choice in the classroom.

3 Estimate the area of each polygon in square centimetres. Then, use your ruler to calculate the exact area.

a)

Estimate:

Area:

b)

Estimate:

Area:

4 Find the missing measurement for each rectangle.

a)

14 dm

Area: 84 dm2

Length:

b)

0.5 dm

Area: 3500 cm2

Length:

Theme 4 B-29


5 The length of a rectangle is 12 dm.

Its width is equivalent to 1

3 its length.

What is the area of the rectangle

in square decimetres and square

centimetres?

My Calculation

6 Joshua says that his square property with 100 m sides has the same area as Myong’s rectangular property measuring 200 dm long and 500 dm wide. Is Joshua correct?

My Calculation

7 Calculate the area of this property in square metres and square decimetres.

130 m

400 dm

15 000 cm

60

00

cm900 dm

50 m

50 m 50 m

My CalculationDivide the figure into squares or rectangles.

Think about it!

130 m

40 m

150 m

60 m

90 m

50 m 50 m

50 m

130 m

40 m

150 m

60 m

90 m

50 m 50 m

50 m

B-30 Section 4.8


USE REASONING

1 The owner of Super Slopes ski resort is repaving the parking lot. It is 125.5 m long by 55.7 m wide. The resort’s welcome centre is also located on this piece of land. It is a square with sides that are 20 m. It costs $36.00 per square metre to pave the area. What is the total cost of paving the parking lot?

Solution:

2 The employees at a skatepark would like to install new obstacles

and a ramp. The park is 40 m long and its width is 3

5 its length.

The table indicates the dimensions of the ramp and the obstacles

they wish to install.

If the employees want to install more equipment in the future, what area of the skatepark is still available?

Length Width

Ramp 4 m 0.5 mSquare obstacle 30 dm 30 dmRectangular obstacle 2.2 m 1.5 m

Solution:

Theme 4 B-31


Circle the correct answer(s) to each question below.

Show your calculations.

MAKING CHOICES

1 Calculate the result of this chain of operations by following the order of operations.

4 + 6 × 22 + 4 × 5 − 2 = ?

a) 58 b) 46

c) 153 d) 218

My Calculation

2 Which operation represents the commutative property?

8 + 4 + 12 + 10 = ?

a) (8 + 4) + (12 + 10)

b) 8 × (4 + 12 + 10)

c) 8 + 4 × 12 + 10

d) 4 + 10 + 8 + 12

My Calculation

3 What is the product of 29.8 × 3.3?

a) 98.14 b) 98.34

c) 983.4 d) 97.34

My Calculation

4 What is the quotient of 2349 ÷ 18?

a) 130.5 b) 13.05

c) 1305 d) 13.5

My Calculation

B-32 Making Choice


5 Which of these questions is an effective survey question?

a) What do cats like?

b) Which type of pet is your favourite: dogs, cats or rabbits?

c) What are you thinking?

d) Do you own a lot of sporting equipment?

My Calculation

6 What is the arithmetic mean of this group of data?

42 35.5 65 75.3 56

a) 57.6 b) 547.6

c) 54.76 d) 50.76

My Calculation

7 What is the quotient of 398.24 ÷ 8?

a) 49.78 b) 49.88

c) 497.8 d) 48.78

My Calculation

8 What is the area of a rectangle measuring 32 m by 5.6 m?

a) 1792 m2 b) 178.2 m2

c) 179.2 m2 d) 169.2 m2

My Calculation

Theme 4 B-33


TH

EM

E

REVIEW SECTIONS 4.1 TO 4.8

ARITHMETIC


a) (4 × 8) − 3 + 2 × 32 − (2 × 21) = b) 6 − 3 + 42 − 7 + 12 × 2 =

2 Add brackets to each chain of operations, then follow the order of operations to get the correct result.

a) 2 + 3 × 4 + 5 − 3 = 22 b) 13 + 7 − 2 + 8 × 6 ÷ 4 + 6 = 11

c) 5 × 4 + 3 × 2 = 70 d) 8 + 4 + 3 × 5 − 15 = 28

3 Use the associative property to do these operations.

a) 4 + 19 + 21 + 16 =

b) 10 × 4 × 8 × 2 =

4 Use the distributive property to do these operations.

a) 12 × (7 + 3) =

b) 7 × (7 − 3 − 2) =

B-34 Review


5 Calculate the product of each multiplication.

a) b) c)

d) e) f)


a) b)

30.2× 16.4

24.7× 0.8

164.5× 7.3

78.6× 9.4

100.9× 12.7

6 7 6× 4.8

7 7 2 0 2 9 1 216 20

Theme 4 B-35


7 Calculate the quotient of each division. Use mental calculation strategies.

a) 56.98 ÷ 10 = b) 286.34 ÷ 10 =

c) 8654 ÷ 100 = d) 8654 ÷ 1000 =

e) 89.2 ÷ 100 = f) 25 050 ÷ 100 =

g) 84.91 ÷ 10 = h) 32 983 ÷ 1000 =

8 Mark sold 60 skateboards over the summer for a total of $2535.00. What is the average cost of one of the skateboards sold?

My Calculation


a) b)

2 5 6.2 8 3 6.686 4

B-36 Review


STATISTICS

10 Fill in the data table based on the following information.

Registration for Women’s Ski Competition

Rose: Moguls Tamara: Downhill

Zoe: Downhill Katie: Moguls

Emma: Downhill Juliette: Downhill

Flavia: Aerials Nina: Aerials

Anna: Ski jumping Laura: Downhill

Leanne: Downhill Chrissy: Moguls

Data Table

Type

Tally

Result

11 Use the data table in Exercise 10 to answer these questions.

a) Which type of sport is the most popular?

b) Which type of sport counts for 25% of the participants?

c) Which type of sport is the least popular?

d) Which type of sport counts for half of the participants?

e) What fraction represents participants registered for aerials?

Theme 4 B-37



a) 34 45 67 14 0

Arithmetic mean:

b) 26.5 23.7 35.4 20 12.8 16.6

Arithmetic mean:

c) 17 23 68 72 18 45

Arithmetic mean:

13 Liam is slated to waterski 10 times during a competition. Here are the scores that the judges give him for his first 8 passes: 6, 8, 9, 7, 8, 9, 7 and 10. What scores must Liam get on his last 2 passes if he wants to keep his current average?

My Calculation

MEASUREMENT

14 Here is a diagram of 2 playgrounds. Estimate and measure the area of each playground.

a)

45 m

82.5 m

Estimate:

Measurement:

b)

32 m

91.25 m

Estimate:

Measurement:

My Calculations

B-38 Review


15 Answer these questions.

a) What is the area of a square with 42.5 cm sides?

My Calculation

b) What is the length of a rectangle with a width of 24 dm and a total area of 1248 dm2?

My Calculation

16 The owners of the Mountain Pass Arena are installing new flooring in 3 rooms.

• The 1st room is 5.8 m long and 3.2 m wide.

• The 2nd room is 4.9 m long and 3.7 m wide.

• The 3rd room is 6.4 m long and 4.5 m wide.

If the ceramic tiles cost $8.00 per square metre, what is the total cost for all 3 rooms?

My Calculation

Theme 4 B-39


PROBLEM SOLVING

What I’m Looking ForWhat I Know

Ski DayThe school is organizing a ski day for Cycle 3 students. A fleet of buses will take them to the ski hill. The cost of the outing includes bus transportation and a ski pass for the day.

Use the following information to calculate the cost of the outing per student, as well as the average number of students per bus.

• There are 48 Grade 5 students and 42 Grade 6 students.

• A ski pass for the day costs $31.00 per person.

• The school gets a 20% discount on the price of a ski pass.

• One bus can transport 48 students.

• It costs $495.00 to rent one bus.

PROBLEM SOLVING

B-40 Problem Solving


My Solution

Validation

Solution:

Theme 4 B-41


Starting from the top, map out the route that Florence takes down Evergreen Mountain by connecting each equation with the correct answer.

The Ski Hill

350.05 350.5

125

15 225

2240

2280

22 800

22.8

134 1342.413 422 1342.2 1342

2453.5 ÷ 7 =

53 =

285 × 8 =

5360 ÷ 40 = 6712 ÷ 5 = 2684.4 × 5 = 4026.6 ÷ 3 =

142.5 × 16 = 228 × 10 =

52 + 20 × 5 =

B-42 Game Time


Underwater WorldT

HE

ME

5.1 Reading and Writing Integers Locating Integers on a

Number Line Comparing Integers

5.2 Estimating and Measuring Temperature

5.3 Locating Points in a Cartesian Plane

5.4 Observing and Producing Frieze Patterns Using Translations

Tessellations

5.5 Estimating and Measuring Mass

Establishing Relationships Between Units of Measure

5.6 Establishing Relationships Between Units of Measure for Time

5.7 Estimating and Measuring Volume

WHAT I’LL LEARN

Art Meets Mathematics

In mathematics, frieze patterns and tessellations are linked to the study of geometric transformations. In art, they can be found in embellishments adorning all types of creations. Stained glass windows in churches and cathedrals often have patterns that are repeated through reflection and translation.

Sailors have relied on Cartesian planes for years to locate objects and animals at sea. For example, the precise coordinates of a small island in the Pacific Ocean can be determined by overlapping a sea chart with a Cartesian plane.

Cartesian Markers


LEARN ABOUT IT

SECTION 5.1 ARITHMETIC Estimating and Measuring Volume Locating Integers on a Number Line Comparing Integers

Reading and Writing IntegersIntegers are whole numbers that are part of a set {…, –3, –2, –1, 0, 1, 2, 3, …} represented by the symbol . This set contains positive integers (greater than 0) and negative integers (less than 0).

–4 –3 –2 –1 0 1 2 3 4

Negative integers Positive integers

Positive and negative integers are used every day to express such things as:

• temperature (–15 °C, 22 °C);

• money (–$10 is a loss, while $10 is a gain).

Locating Integers on a Number LineIntegers can be represented on a horizontal axis or a vertical axis.

• On a horizontal axis, negative integers are to the left of 0 and positive integers are to the right of 0.

–14–20 –12–18 –10–16 –8 4–6 6–4 8–2 10 160 12 182 14 20

Negative integers Positive integers

• On a vertical axis, negative integers are below 0 and positive integers are above 0.

–6–5–4

2

–3

3

–2

4

–1

5

0

6

1

Positive integers

Negative integers

The number 0 is both a positive

integer and a negative integer.

B-44 Section 5.1


Calculate the difference between 2 integers by counting the spaces that separate them on a number line.

–4 2–3 3–2 4–1 0 1

On this number line, there are 8 spaces between –4 and 4: 4 spaces on the negative integer side and 4 spaces on the positive integer side. Therefore, there is a difference of 8 between –4 and 4.

WORK IT OUT

1 Arrange the integers correctly on each number line.

a) –18 3 –24 21 –9

0 9–6

b) 60 –15 –90 45 –60

0 30–45

2 Indicate the value of each letter on the number line.

D

0

AB

12–18

C

a) D: b) B: c) A: d) C:

e) What is the difference between A and B?

3 Use an integer to represent each situation.

example A whale swims 25 m below the water’s surface. –25

a) A boat is on the water’s surface.

b) A passenger is on the 4th deck of a cruise ship.

Pay attention to the intervals on a number line.

Think about it!

Theme 5 B-45


LEARN ABOUT IT

Comparing Integers Integers can be easily compared on a number line. Numbers are arranged in increasing order from left to right.

As the number line goes further to the left, the numbers are lesser in value.

Look at the numbers in red on the number line.

–7–10 –6–9 –5–8 –4 2–3 3–2 4–1 5 80 6 91 7 10

We see that: –9 < –5 –5 < 0 0 < 4 4 < 7

These numbers are arranged this way in increasing order: –9, –5, 0, 4, 7

As a vertical number line goes down, the numbers are lesser in value.

We see that: –5 < –3 –3 < 0 0 < 2 2 < 5

These numbers are arranged this way in increasing order: –5, –3, 0, 2, 5

WORK IT OUT

1 Compare these numbers using the < or > symbol.

a) –2 –20 b) 34 23 c) –8 0

d) 45 46 e) –12 –58 f) –76 76

g) –32 –24 h) 52 –63 i) 67 –68

2 Arrange these numbers in increasing order.

−12 −17 36 −45 −8 3 −39 0

–5–4

2

–3

3

–2

4

–1

5

01

B-46 Section 5.1


Rooms A

Rooms B

Kitchens

Captain’s cabin

Engine room

Main deck

25 m

0 m

3 Complete each number series.

a) 8 6 4 2

b) 15 10 5 0

c) 24 12 0 –12

d) –3 –8 –13 –18

0

4 Look at the oil platform, then answer the questions below.

a) Which integer represents the scuba diver’s position?

b) How deep is the ocean floor?

c) Which integer represents the water’s surface?

d) Which integer represents the height of the kitchens?

e) A scuba diver leaves the Rooms B area and dives 30 m deep. What is the difference between these 2 points?

To better understand the pattern in each number series, locate the position of the numbers on a number line.

Think about it!

Theme 5 B-47


USE REASONING

1 A submarine travels 45 m below the ocean’s surface. It locates a

shipwreck 15 m further below, then travels 20 m upwards to meet

another submarine. Finally, it dives 1

4 more than its actual depth.

What is the submarine’s final depth?

Solution:

2 A fishing company has a debt of $25 000.00. It manages

to earn 1

5 of this amount. It also sells parts, or shares, of the

company to 150 investors for $125.50 apiece. What integer

represents the company’s new financial situation?

Solution:

B-48 Section 5.1


LEARN ABOUT IT

MEASUREMENT Measuring and Estimating Temperature SECTION 5.2

Estimating and Measuring Temperature A thermometer is used to measure temperature.

The most common unit of measure is degree Celsius (°C).

A thermometer has a vertical scale.

• The temperature gets hotter as the numbers get closer to the top of the thermometer.

• The temperature gets colder as the numbers get closer to the bottom of the thermometer.

Examples:−7 °C is warmer than −24 °C.5 °C is colder than 14 °C.

Just like the numbers on a number line, all numbers below 0 °C represent negative temperatures, such as −10 °C. All numbers above 0 °C represent positive temperatures, such as 15 °C.

As with integers, you can calculate the difference between 2 temperatures.

Example: If it is −6 °C in the morning and 4 °C in the afternoon, the difference between the 2 temperatures is 10 degrees: 6 degrees between −6 and 0, and 4 degrees between 0 and 4.

Here are some important temperatures:

• Water freezes at a temperature of 0 °C.

• Water boils at a temperature of 100 °C.

• The normal body temperature of a human is 37 °C.

• The average temperature of a freezer is −18 °C.

• The average temperature of a refrigerator is 3 °C.

−30

−20

−40

−10

0

10

20

30

40

50

60

°C

0 °C

Glass tube

Positivetemperature

scale

ReservoirDegree

Celsius

Negativetemperature

scale

Morning: –6 °C

Difference

Afternoon: 4 °C

6

4+

−30

−20

−40

−10

0

10

20

30

40

°C

Theme 5 B-49


WORK IT OUT

1 Colour in the thermometers to indicate the following temperatures.

17 °C –13 °C 28 °C

a)

−30

−20

−10

0

10

20

30

°C

b)

−30

−20

−10

0

10

20

30

°C

c)

−30

−20

−10

0

10

20

30

°C

2 Determine the temperature on each thermometer.

a)

−30

−20

−10

0

10

20

30

°C

−30

−20

−10

0

10

20

30

°C

−30

−20

−10

0

10

20

30

°C

b)

−30

−20

−10

0

10

20

30

°C

−30

−20

−10

0

10

20

30

°C

−30

−20

−10

0

10

20

30

°C

c)

−30

−20

−10

0

10

20

30

°C

−30

−20

−10

0

10

20

30

°C

−30

−20

−10

0

10

20

30

°C

3 Arrange these temperatures from coldest to hottest.

–12 °C

6 °C

–32 °C

–15 °C

34 °C

45 °C

0 °C

B-50 Section 5.2


4 Look at the table, then answer the questions.

Ocean Temperatures at Various Locations

Los Angeles, Pacific Ocean 18 °C

Nunavut, Arctic Ocean 5 °C

Bordeaux, Atlantic Ocean 13 °C

New Zealand, Pacific Ocean 24 °C

Thailand, Indian Ocean 28 °C

Newfoundland, Atlantic Ocean 9 °C

Madagascar, Indian Ocean 22 °C

Other location ?

a) In which location is the water coldest?

b) In which location is the water warmest?

c) What is the difference between the warmest and coldest water temperatures?

d) What is the difference between the water temperature in Newfoundland and the water temperature in Los Angeles?

e) What is the average water temperature of the locations in the table?

f) If another location were to be added to the table, the average water temperature would be 16.5 °C. What is the water temperature at this location?

5 Gabriel and Sophie are going on a boating adventure.

They notice a temperature difference as they leave the shore.

It is 15 °C at the start. The temperature then gets 1

3 colder.

Further out, the temperature goes down another 3 degrees.

Finally, it warms up 6 degrees when they drift past an island.

What is the temperature near the island?

Theme 5 B-51


LEARN ABOUT IT

GEOMETRY Locating Points in a Cartesian Plane SECTION 5.3

Locating Points in a Cartesian Plane A 4-quadrant Cartesian plane is made up of 2 perpendicular number lines.

• The horizontal number line is called the x-axis.

• The vertical number line is called the y-axis.

• The point at which these 2 axes meet in the Cartesian plane is called the origin. The origin’s coordinates are (0, 0).

• A Cartesian plane is separated into 4 quadrants, which correspond to the 4 regions bordered by the axes.

• Each number line has a scale of negative and positive numbers. The negative numbers are to the left of 0 on the horizontal axis and below 0 on the vertical axis.

• A point’s position is indicated by a pair of numbers known as coordinates. These coordinates are shown between brackets and are separated by a comma, such as (−4, 5).

• The 1st number in a pair indicates the position of a point on the horizontal axis (x), while the 2nd number shows its position on the vertical axis (y).

0 1 2 3 4 5

y

x

5

4

3

2

1

−1

−2

−3

−4

−5

−5 −4 −3 −2 −1

A

D

B

C

In this Cartesian plane, the coordinates of the points are:

A: (5, 2) B: (0, −4) C: (−2, −2) D: (3, 0)

X-Axis

Origin

Y-Axis

1st quadrant(+x, +y)

3rd quadrant(−x, −y)

4th quadrant(+x, −y)

0 1 2 3 4 5

y

x

5

4

3

2

1

−1

−2

−3

−4

−5

−5 −4 −3 −2 −1

2nd quadrant(−x, +y)

B-52 Section 5.3


WORK IT OUT

1 Find the coordinates of the following points.

0−1

−1 1 2 3 4 5 6 7 8−2−3−4−5−6−7−8

−2

−3

−4

−5

−6

−7

−8

8

7

6

5

4

3

2

1A

F

B

C

E

Dy

x

2 A team of scuba divers is searching for sunken treasure near a shipwreck. The search area is bordered by these points:

(–4, 3) (–4, –2)

(3, –2) (3, 3)

If one square of the Cartesian plane covers 5 m2, indicate the number of square metres that the scuba divers must search.

0−1

−1 1 2 3 4 5−2−3−4−5

−2

−3

−4

−5

y

x

5

4

3

2

1

A:

B:

C:

D:

E:

F:

Theme 5 B-53


3 A sea captain wants to navigate his boat close to the 4 animal species in this Cartesian plane without running into the iceberg. He can’t move more than 8 times before returning to his starting point.

Determine the captain’s route. Give the coordinates of each change of direction. He may move horizontally, vertically and diagonally.

70−1

−1 1 2 3 4 5 6−2−3−4−5−6

−2

−3

−4

−5

−6

6

5

4

3

2

1

7

8 9 10 11 12−7−8−9−10−11−12

y

x

−7

−8

−9

−10

−11

−12

12

11

10

9

8

Start/Finish

Seal

Whale

Walrus Polar bear

Iceberg

Coordinates of direction changes:

B-54 Section 5.3


4 Plot the following points in the Cartesian plane, then connect them in order.

A: (–2, 4) B: (–7, 4) C: (–10, 9) D: (–5, 9)

70−1

−1 1 2 3 4 5 6−2−3−4−5−6

−2

−3

−4

−5

−6

6

5

4

3

2

1

7

8 9 10−7−8−9−10

y

x

−7

−8

−9

−10

10

9

8

a) Using the horizontal axis as a line of reflection, draw a reflection of the figure. Indicate the new coordinates of this figure.

: : : :

b) Using the vertical axis as a line of reflection, draw a reflection of the figure you have just drawn. Indicate the new coordinates of this figure.

: : : :

c) Draw a hexagon in the empty quadrant. Give the coordinates of each vertex.

Theme 5 B-55


USE REASONING

This Cartesian plane shows a map of an ecological disaster in the ocean caused by an oil spill. The origin represents the starting point of the spill.

The rescue team leaves from point (11, –10) and takes this route: (−8, −7) (−10, 5) (7, 2) (9, 9) (11, –10).

The rescuers save the animals that they find along their route, except for those within a 1 km radius of the origin.

Draw the team’s route, then write the name and coordinates of each animal saved.

0−1

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

−2

−3

−4

−5

−6

−7

−8

−9

−10

−11

−12

8

9

10

11

12

7

6

5

4

3

2

1

y

x

Crab

Seaturtle

Shrimp

Eel

Jellyfish

Legend

Shark

Dolphin

Octopus

1 km

2 km

3 km

Oyster

Animal Saved Coordinates Animal Saved Coordinates Animal Saved Coordinates

B-56 Section 5.3


LEARN ABOUT IT

GEOMETRY Observing and Producing Frieze Patterns

and Tessellations Using Translations SECTION 5.4

Observing and Producing Frieze Patterns Using TranslationsA frieze pattern is a rectangular strip with a repeating pattern.

Use reflection or translation to create a frieze pattern from a starting pattern.

Figure 1Example of a frieze pattern created by reflecting a starting patternLine of reflection

Figure 2Example of a frieze pattern created by translating a starting pattern

Translation arrow

Translation is a geometric transformation that moves all of a figure’s points in the same direction and along the same distance. The figure keeps its shape, its orientation and its dimensions; it slides.

Translation is represented by a translation arrow. This arrow shows the translation’s direction and the length that it must move.

In Figure 2, the translation arrow indicates that the pattern must move 3 squares to the right. In Figure 3, the translation arrow shows that the pattern must move 4 squares to the right and 2 squares down.

Figure 3

A

BC

A

BC

Theme 5 B-57


WORK IT OUT

1 Complete the frieze patterns by following the translation arrows.

a)

b)

c)

2 Carry out the translation of the figure below by following the red translation arrow. Then, carry out the translation of the newly drawn figure by following the green translation arrow.

B-58 Section 5.4


LEARN ABOUT IT

TessellationsA tessellation is a collection of geometric figures that cover a surface.

• There is no empty space between the figures.

• The figures never overlap.

Reflection or translation, or a combination of both, can be used to create a tessellation from a starting pattern.

Example of a tessellation

WORK IT OUT

1 Carry out the translation of the figure below, then create a tessellation by adding 6 more figures.

Theme 5 B-59


2 Carry out the translation of the figure below, then create a tessellation by adding 4 more figures.

3 Henry chooses 2 pieces to make a tessellation. Look at the shape at the start of his tessellation. Arrange another set of pieces that cover the same area. Then, create a tessellation that fills in the entire grid by carrying out your choice of translations.

Pieces

4 Carry out the translation of the figure below, then complete the tessellation.

B-60 Section 5.4


LEARN ABOUT IT

MEASUREMENT Estimating and Measuring Mass

Establishing Relationships Between Units of Measure SECTION 5.5

Estimating and Measuring MassMass is the measure of the amount of matter in an object or living thing.

The international system of units (SI) is used to measure mass. Grams (g) and kilograms (kg) are the most common units of measure for mass.

1000 (g) = 1 kg, so 500 g = 1

2 kg.

A scale is used for finding the mass of an object, a product, a food item, etc.

A seashell has a mass of approximately 1 g while this fish has a mass of approximately 1 kg.

Establishing Relationships Between Units of MeasureThe following table compares units of measure for mass.

Unit of measure Kilogram Hectogram Decagram Gram Decigram Centigram Milligram

Symbol kg hg dag g dg cg mg

1st number 6

Equivalency 6 0 0 0

2nd number 4 2 5 0

Equivalency 4 2 5

3rd number 0 0 3 7

Equivalency 3 7

Note: Hectograms, decagrams, decigrams, centigrams and milligrams are not studied at the primary level, but it is useful to know their place in the table of units of measure.

The table demonstrates that:

1) 6 kg = 6000 g 2) 4250 g = 4.25 kg 3) 0.037 kg = 37 g (6 x 1000) (4250 ÷ 1000) (0.037 x 1000)

.

.

Theme 5 B-61


WORK IT OUT

1 Choose the most appropriate symbol to estimate the mass of each sea animal.

< 1 kg

> 1 kg

a) Dolphin b) Shrimp

c) Sea horse d) Clownfish

e) Whale f) Turtle

2 Convert these measurements.

a) 7.5 kg = g b) 0.407 kg = g

c) 462 g = kg d) 6 g = kg

e) 7460 g = kg f) 10.76 kg = g

3 Arrange these measures of mass in the correct order.

a) 740 g 4 kg 0.8 kg 2899 g 7.4 kg

Increasing order:

b) 6.05 kg 6055 g 65 kg 5065 g 650 g

Decreasing order:

4 Complete these equivalencies.

a) 1065 g = 1 kg +

b) 2.57 kg = 257 g +

c) 0.65 kg = 250 g +

My Calculations

B-62 Section 5.5



a) Manny’s scuba tank weighs 6 kg. His father’s tank is 1.7 times heavier. What is the mass of his father’s scuba tank? Write your answer in grams and in kilograms.

My Calculation

b) A baby beluga weighs 40 000 g at birth. When it reaches adulthood, its weight is 22.5 times greater. What is the difference between the mass of a baby beluga and that of an adult beluga? Write your answer in grams and in kilograms.

My Calculation

c) A seal eats 0.104 kg of herring, 1754 g of salmon and 102 g of shrimp. How many kilograms of food does it eat?

My Calculation

d) The mass of a baby blue whale increases by 81 kg per day during its first months of life. If a baby blue whale weighs 6752 kg at birth, how much will it weigh after 28 days?

My Calculation

Theme 5 B-63


USE REASONING

1 The maximum load of a submarine is 900 kg. There are 7 adults onboard each with a mass of 72 kg. How many more people with the same average mass can the submarine accommodate?

Solution:

2 The mass of a male walrus varies between 900 kg and 1800 kg.

Female walruses weigh 2

3 of that mass.

1

3 of the weight of a healthy

walrus consists of fat. What is the difference in mass between the

heaviest males and lightest females? What is the minimum and

maximum mass of fat on a male walrus?

Solution:

B-64 Section 5.5


LEARN ABOUT IT

MEASUREMENT Establishing Relationships Between

Units of Measure for Time SECTION 5.6

Establishing Relationships Between Units of Measure for TimeTime is measured in years, months, days (d), hours (h), minutes (min) and seconds (s).

One hour = 60 minutes

One day = 24 hours

One minute = 60 seconds

One year = 12 months = 52 weeks = 365 days (366 in a leap year)

Reminder

Use base 60 to convert units of measure for hours, minutes and seconds.

Example of addition 2 h 35 min 23 s + 4 h 15 min 49 s

• Place the units of time in columns. Add.

1 1

2 h 35 min 23 s+ 4 h 15 min 49 s

6 h 50 min 72 s

• Convert the seconds into minutes. 72 s = 60 s + 12 s = 1 min + 12 s

• Result: 6 h 50 min 72 s = 6 h 51 min 12 s

Example of subtraction 7 h 33 min – 2 h 50 min

• Place the units of time in columns.

7 h 33 min– 2 h 50 min

• Subtract in base 60. Borrow from hours: 1 h = 60 min, so 33 + 60 = 93, and subtract 93 min – 50 min: 93 – 50 = 43

6 9 3

7 h 33 min– 2 h 50 min

4 h 43 min

60 min + 33 min

• Result: 4 h 43 min

Theme 5 B-65


WORK IT OUT

1 Circle the longest unit of time in each set.

a) 950 minutes 1

2 day 18 hours

b) 105 weeks 3 years 34 months

c) 26 000 seconds 400 minutes 7 hours

d) 28 hours 1 day and 5 hours

2680 minutes


a) 1 h 25 min = min

b) days = 4320 min

c) 45 min = hour

d) 15 s = min

e) 4 h = s

My Calculations


a) Terry trains at the pool 4 times per week for 2 h 25 min. How much time does he swim each week?

My Calculation

b) Lisa uses a number line to indicate the time she started and finished writing her report on coral reefs. How many minutes did she spend writing her report?

My Calculation

11:00 a.m. Start 12:00 p.m. End 1:00 p.m.

My Calculations

B-66 Section 5.6


USE REASONING

1 Alex and Jasmine are going whale watching in the Bay of Fundy. Alex leaves in a zodiac at 8:15 a.m. and comes back at 10:52 a.m. Jasmine leaves on a cruise ship at 8:25 a.m. and comes back at 11:43 a.m. What is the difference in duration between the 2 excursions? Write your answer in minutes.

Solution:

2 Dolphins breathe 1 to 4 times per minute, while humans breathe 15 to 20 times per minute. What are the minimum and maximum number of breaths for a dolphin and a human in 7 days?

Solution:

Theme 5 B-67


LEARN ABOUT IT

MEASUREMENT Estimating and Measuring Volume SECTION 5.7

Estimating and Measuring VolumeVolume is the measure of space occupied by a solid. Space has 3 dimensions: length, width and height.

Volume is measured in cubic units. The most common units of measure are cubic centimetres (cm3), cubic decimetres (dm3) and cubic metres (m3).

Conversion Table for Common Units of Measure for Volume

Centimetre3 (cm3) 1 cm × 1 cm × 1 cm = 1 cm3

1 cm3 1 dm3 1 m3

cm3

Volume of a glass of water

Decimetre3 (dm3) 1 dm × 1 dm × 1 dm = 1 dm3 10 cm × 10 cm × 10 cm = 1000 cm3 1 dm3 = 1000 cm3 1 cm3 1 dm3 1 m3

dm3 Volume of a fish tank

Metre3 (m3) 1 m × 1 m × 1 m = 1 m3 10 dm × 10 dm × 10 dm = 1000 dm3 100 cm × 100 cm × 100 cm = 1 000 000 cm3 1 m3 = 1000 dm3 = 1 000 000 cm3

1 cm3 1 dm3 1 m3

m3 Volume of water in a lake

The volume of a prism can be calculated with the following mathematical formula:

Volume = length (l) × width (w) × height (h)

Multiply the measurement of the length by the width and by the height.

Examples:

Volume of a Cube

Volume: 4 cm × 4 cm × 4 cm

Volume: 64 cm3, which reads, “64 cubic centimetres.”

4 cm

4 cm4 cm

Volume of a Rectangular Prism

Volume: 5 cm × 2.5 cm × 3 cm

Volume: 37.5 cm3, which reads, “37.5 cubic centimetres.”

3 cm

5 cm2.5 cm

B-68 Section 5.7


WORK IT OUT

1 What is the most suitable unit of measure to calculate the volume of each object?

a) The volume of water in a sea lion tank.

b) An air tank for scuba diving.

c) A box holding 10 tiny shells.

d) A locker for storing fishing nets.

e) The volume of a backpack.

2 Calculate the volume of each prism.

a)

2 cm

2 cm

2 cm

b)

3.3 dm

5.2 dm

10 dm

Volume:

Volume:

c)

450 cm

9 m

66 dm

d)

29 cm12 cm

5.6 dm

Volume:

Volume:

Theme 5 B-69



a) A crate for storing scuba gear measures 2.3 m long by 1.5 m wide by 1 m high. What is the volume of the crate? Write your answer in cubic metres and in cubic decimetres.

My Calculation

b) The volume of Melina’s box of seashells is 3125 cm3. The box is 25 cm long by 25 cm wide. What is its height?

My Calculation

c) Wayne is shopping for a new fish tank. Which of these 2 fish tanks is larger?

1st Fish Tank 2nd Fish Tank

Length 66 cm Double the width

Width 30 cm 2.4 dm

Height1

3 of the length 3 dm

My Calculation

B-70 Section 5.7


USE REASONING

1 A group of sailors is storing 2 rescue boats in 2 large boxes. Here are the dimensions of the boxes.

Length Width Height

Box 1 4.6 m 1.2 m 60 dmBox 2 4.1 m 140 cm 50 dm

The sailors store the boxes side by side. What is the volume that both boxes take up in the warehouse?

Solution:

2 A sea lion tank has the following dimensions: 8 m long by 5 m wide by 195 cm high. The water in the tank reaches a height of 15 dm.

In cubic metres, what is the volume of water inside the tank? How many more cubic metres of water will it take to completely fill the tank?

Solution:

Theme 5 B-71




1 Which number corresponds to the letter A?

0 18A

a) –2 b) 12

c) –18 d) –12

2 Which numbers complete the series 5, 7, 3, 5, … ?

a) 3, 7, 5 b) 1, 3, –1

c) 2, 4, 0 d) 1, –3, –7

My Calculation

3 It is −8 °C in the morning, then the temperature rises by 3 °C at noon before dropping by 6 °C in the evening. What is the temperature in the evening?

a) –11 °C b) –17 °C

c) 1 °C d) –1 °C

My Calculation

4 What are the coordinates of point A?

a) (0, 4) b) (4, 0)

c) (0, –4) d) (–4, 0)

5 What are the coordinates of point B?

a) (–3, 5) b) (5, 3)

c) (3, –5) d) (5, –3)

0−1

−1 1 2 3 4 5−2−3−4−5

−2

−3

−4

−5

y

x

5

4

3

2

1A

B

MAKING CHOICES

B-72 Making Choices


6 Which geometric transformation(s) produced this frieze pattern?

a) Reflection

b) Translation

c) Translation and reflection

d) Reflection and frieze pattern

7 What is the sum of this addition?

4.04 kg + 375 g + 1200 g = ?

a) 5.615 kg

b) 5065 g

c) 5.015 kg

d) 5650 g

My Calculation

8 Every day from Monday to Friday, Rosa does her homework for 45 minutes. How much time does she study each week?

a) 3 h 35 min b) 4 h 45 min

c) 3 h 46 min d) 3 h 45 min

My Calculation

9 A box takes up 810 dm3 of space. Its length is 15 dm and its height is 12 dm. What is its width?

a) 45 dm b) 41.33 dm

c) 4.5 dm d) 4.51 dm

My Calculation

Theme 5 B-73


TH

EM

E

REVIEW SECTIONS 5.1 TO 5.7

ARITHMETIC

1 Write the integers that correspond to each letter on the number line.

A B C D

C

12

A

0

B

–6

D

a) What is the difference between A and B?

b) What is the difference between C and D?


a) 15 –5 b) –12 –10 c) 0 –1

d) –21 –24 e) 3 –5 f) –36 –26

3 A rare shark species first appeared in the year −34 and disappeared in the year 55. For how many years did this species live on Earth?

4 Use an integer to represent the result of each statement.

a) Lucas paid his friend $12 of the $25 that he had borrowed from him.

b) You get $20 from your parents and just as much from your grandmother.

c) You have $12 and you want a shirt for $19.

B-74 Review


MEASUREMENT

5 Arrange these temperatures from hottest to coldest.

5 °C 16 °C –24 °C –2 °C 0 °C –11 °C


a) 3.7 kg = g b) 2.05 kg = g

c) 55 g = kg d) 95 g = kg

e) 387 g = kg f) 1.36 kg = g

g) 5809 g = kg h) 0.25 kg = g

i) 0.8 kg = g j) 4560 g = kg

7 A raft can accommodate a maximum load of 250 kg. Can Malik and his 5 friends ride in the raft together?

Weight of Malik and His Friends

Malik: 54 000 g Charlie: 43 600 g

Vinnie: 41 300 g Madeline: 45 kg

Ludovic: 49 250 g Salma: 37.2 kg

My Calculation

8 Compare these masses using the <, > or = symbol.

a) 125 g 1.25 kg b) 2.34 kg 2345 g

c) 788 g 0.789 kg d) 4.4 kg 400 g

e) 12 g 0.012 kg f) 8.7 kg 7878 g

Theme 5 B-75


9 Carrie is an instructor at a scuba diving centre. Use the following information to fill in her daily schedule.

• She works from 10:00 a.m. to 2:00 p.m.

• One private lesson takes up 1

8 of her day.

• She teaches 4 private lessons.

• Lunchtime takes up 1

6 of her day.

• Preparing the equipment takes up half the time of a private lesson.

• Her break takes up one quarter of an hour.

• The rest of her day is spent teaching a group lesson.

Activities Duration

Private lessons

Lunchtime

Preparing equipment

Break

Group lesson

My Calculation

10 Milo dives 4 consecutive times with a mask and snorkel to admire the fish. Calculate the total amount of time he spends diving.

• 1st dive: 8 minutes and 47 seconds.

• 2nd dive: 4 minutes and 55 seconds.

• 3rd dive: 6 minutes and 29 seconds.

• 4th dive: 7 minutes and 38 seconds.

My Calculation

B-76 Review


11 Answer these questions.

a) How many days are there in 3 non-leap years?

b) How many weeks are there in 5 years?

c) In one year, how many months have 31 days?

12 Mackenzie is putting away boxes of diving fins in a closet. The closet is 16 dm long by 8 dm wide by 24 dm high. Each box of fins is 2 dm long by 2 dm wide by 6 dm high. How many boxes of fins can he put away in the closet?

My Calculation

13 Calculate the volume of each prism.

a)

15 cm

25 cm

12.5 cm

b)

2.2 dm

3.7 cm0.4 dm

14 The dimensions of a fish tank are 45 cm long

by 25 cm wide by 35 cm high. If water is added

to 3

4 of the fish tank, how much water is in

the tank?

My Calculation

Theme 5 B-77


GEOMETRY

15 Give the coordinates of the following points.

0−1

−1 1 2 3 4 5 6 7 8−2−3−4−5−6−7−8

−2

−3

−4

−5

−6

−7

−8

8

7

6

5

4

3

2

1

A

B F

G

H

C

E

D

y

x

A:

B:

C:

D:

E:

F:

G:

H:

16 Plot the coordinates in the Cartesian plane. Use your ruler to connect the points in order.

A: (3, 1) B: (6, –2)

C: (3, –5) D: (3, –3)

E: (–4, –3) F: (–4, –1)

G: (3, –1)

What figure do you get? 0

−1−1 1 2 3 4 5 6−2−3−4−5−6

−2

−3

−4

−5

−6

6

5

4

3

2

1

y

x

B-78 Review


17 Complete the frieze pattern.

18 Carry out the following translations.

a) b)

c) d)

19 The figure below was created using different translations. Colour in all the triangles in each translation the same colour.

Theme 5 B-79


What I Know What I’m Looking For

PROBLEM SOLVING

The Public AquariumThe biologist at the city’s public aquarium would like to introduce 2 polar bears, 60 jellyfish, 42 clownfish and 30 eels to new tanks.

• Each eel needs 22 m3 of space.

• A polar bear needs 600 m3 of space to live on its own. It does not live with any other species.

• Each jellyfish needs 5 m3 of space. Jellyfish can cohabit with fish.

• Each clownfish needs 10 m3 of space.

• A polar bear eats 56 000 g of meat per week.

• One kilogram of meat costs $5.45.

Which tank is best suited for each species? Use the diagram on the next page.

How much does it cost to feed the polar bears for one year?

PROBLEM SOLVING



My Solution

Validation

Solution:

Tank A Tank B Tank C Tank D

4 m

4 m

4 m

4 m

9 m

20 m

Tank A

Tank B

Tank CTank D

20 m 15 m 16 m

15 m11 m 9.5 m

Theme 5 B-81


Puzzle Challenge

Solve each puzzle with the puzzle pieces provided. Some pieces may need to be flipped. Do not leave any empty spaces.

a)

b)

c)

B-82 Game Time


Job FairT

he

me

6.1 Enumerating Possible Outcomes of a Random Experiment Using a Table and a Tree Diagram

6.2 Comparing the Outcomes of a Random Experiment with Known Theoretical Probabilities

6.3 Describing and Classifying Prisms and Pyramids Using Faces, Vertices and Edges

6.4 Nets of Solids or Convex Polyhedrons

6.5 Testing Euler’s Theorem on Convex Polyhedrons

WhAT I’LL LeARN

Polyhedrons for Everyone

The study of polyhedrons is important in many fields of work. Architects, engineers and carpenters depend on these solids and their nets to build a variety of structures.

Interest in probability only goes back to the 16th century, when princes and lords wanted to win more at gambling. Today, probability is used in many fields, such as meteorology and economics.

Probability

13329_decimale_6b_th06_an.indd 83 14-02-25 16:14

LEARN ABOUT IT

SecTIoN 6.1 Probability Enumerating Possible Outcomes of a Random

Experiment Using a Table and a Tree Diagram

Enumerating Possible Outcomes of a Random Experiment Using a Table and a Tree DiagramThe outcome of a random experiment is based on chance. It is therefore impossible to know the outcome in advance. For instance, it is impossible to know:

• the colour of a marble picked at random from a bag;

• the section on which a spinner’s arrow will stop;

• a contestant whose name is randomly drawn from a hat.

A tree diagram or table can be used to represent all the possible outcomes of a random experiment.

tree Diagram representation

Here are all the possible outcomes of randomly drawing 2 paintbrushes from a set of 4.

All PossibleOutcomes

2nd Draw1st Draw

If you take into account the order in which the paintbrushes are drawn, there are 12 possible combinations.

There are also 6 possible pairs of colours: green and red, green and blue, green and purple, red and blue, red and purple, and blue and purple.

B-84 Section 6.1


LEARN ABOUT IT

table representation

1st Draw 2nd Draw All Possible Outcomes

Tous les résulatspossibles

2e tirage1er tirage

There are 12 possible outcomes.

The results indicate that the probability of drawing a blue paintbrush is 6

12 or

1

2, so 50%.

WoRk IT ouT

1 Harley and Sabrina are playing a board game. They each spin the wheel 2 times to determine their starting points. Each time, they have a possibility of getting 3, 4 or 5 points.

a) Create a tree diagram showing all the possible outcomes.

1st Spin 2nd Spin all Possible outcomes

b) What is the number of possible combinations?

c) What are the chances of starting the game with a total of 8 points?

3 4

5

3 4

5

Theme 6 B-85


2 Five students volunteer to make a poster about careers. Valerie randomly draws 2 of their names.

a) In the table, indicate all the possible name combinations.

Volunteers: ariana, becky, Charles, Danny, Jack

1st Draw 2nd Draw Possible Combinations

b) What is the number of possible combinations?

3 Dylan wants to paint each glass square a different colour to make a stained glass window. He will use yellow (Y), red (R), blue (B) and green (G) paint. Draw all the possible combinations of 4-colour strips that Dylan can paint.

How many different strips can you draw?

example Y R B G

B-86 Section 6.1


LEARN ABOUT IT

Probability Comparing the Outcomes of a Random

Experiment with Known Theoretical Probabilities SecTIoN 6.2

Comparing the Outcomes of a Random Experiment with Known Theoretical Probabilities

A random experiment is based on chance. It is impossible to know

the outcome in advance.

However, it is possible to determine the probability that an event

will happen. theoretical probability relies on mathematics.

For example, it can be determined that the probability of randomly

drawing a spade from a standard deck of 52 playing cards is

13

52 or

1

4, therefore 25%.

In theory, if you were to repeat this experiment 20 times, you should

draw a spade 5 times since 1

4 is equal to

5

20. In reality, this is not

always the case.

Look at the results obtained by 10 students who conducted the

playing cards experiment 20 times. Here are the number of spades

drawn by each student.

Student 1 Student 2 Student 3 Student 4 Student 53

20

6

20

7

20

2

20

6

20

Student 6 Student 7 Student 8 Student 9 Student 105

20

4

20

8

20

3

20

4

20

The total number of spades drawn by 10 students is 48

200.

Therefore, the result is slightly less than the theoretical probability of 50

200.

As an experiment is repeated more often, the results get closer to the

theoretical probability.

For example, if the results of 25 students who conducted the

playing cards experiment 20 times were tallied, the outcome

would be out of 500. The chances of getting an outcome closer to

the theoretical probability (125 spades out of 500 or 1

4) would be

greater with the results of 25 students than with the results of 10.

Theme 6 B-87


WoRk IT ouT

1 Victor flips 2 coins at the same time.

a) Determine the theoretical probabilities of this experiment by compiling all the possible outcomes.

Probability of getting heads or tails:

b) What are the chances of getting 2 heads or 2 tails?

c) If Victor repeats the experiment 30 times, what are the chances of getting 2 heads or 2 tails?

d) Flip 2 coins 30 times. Tally your results in the table by placing a checkmark in the correct column each time.

Two Heads Two Tails One Head and One Tail

Result:

e) Is your result less than, equal to or greater than the theoretical probability?

2 When you throw a dice, which results correspond to a theoretical

probability of 1

2?

B-88 Section 6.2


3 What is the probability of getting a sum greater than 9 after throwing 2 dice?

4 Form a group of 4 people. Each person throws 2 dice 9 times while aiming to get a sum greater than 9.

a) Indicate the sum obtained after each throw.

Throw 1st Person 2nd Person 3rd Person 4th Person

1

2

3

4

5

6

7

8

9

Outcome (sum > 9)

b) What outcome did your group get after 36 throws?

c) Is this outcome less than, equal to or greater than the theoretical probability?

d) What sum did your group get most frequently?

e) What sum did your group get least frequently?

f) According to theoretical probabilities, which sum is obtained:

• the most frequently?

• the least frequently?

My Calculation

Theme 6 B-89


LEARN ABOUT IT

Geometry Describing and Classifying Prisms and Pyramids SecTIoN 6.3

Describing and Classifying Prisms and Pyramids Using Faces, Vertices and EdgesHere is one way of classifying solids.

Solids

Polyhedrons

These solids are formed by polygons (plane surfaces).

PrismsThese have 2 congruent and parallel polygons as bases.

Triangular Prism

Pentagonal Prism

Square Prism

Hexagonal Prism

PyramidsThese have a single polygon as a base.

Rectangular Pyramid

Hexagonal Pyramid

Pentagonal Pyramid

Octagonal Pyramid

Polyhedrons are characterized by the number of faces, vertices and edges.

An edge is the segment where 2 faces meet.

A vertex is the intersecting point of at least 2 edges.

Vertex

Edge

Base

Face

Curved bodies

These solids have at least one curved surface.

Cone Cylinder Sphere

B-90 Section 6.3


WoRk IT ouT

1 Logan is building polyhedrons. Fill in the table to help him determine the number of each type of polygon he needs.

a)

b)

c)

d)

e)

Theme 6 B-91


2 Look at the polyhedrons and fill in the table.

Name of Polyhedron Number of Faces

Number of Edges

Number of Vertices

a)

b)

c)

3 A decorator suggests different types of vases for Virginia to use in her boutique. Connect each vase to the correct description.

Vase Description

a)

• • I am not a polyhedron.

b)

• • I am made up of two 10-sided polygons and 10 rectangles.

c)

• • I have 4 rectangles and 2 square bases.

d)

• • My 2 bases are trapezoids and I have 4 rectangles.

e)

• • I am made up of 2 hexagons and 6 rectangles.

B-92 Section 6.3


LEARN ABOUT IT

Geometry Nets of Solids or Convex Polyhedrons SecTIoN 6.4

Nets of Solids or Convex Polyhedrons A convex polyhedron contains all the line segments connecting any two vertices (points) within it. Every face of a convex polyhedron can be laid on a flat surface.

A nonconvex, or concave, polyhedron has at least one line segment connecting two vertices outside it.

The net of a polyhedron is the 2-dimensional plane figure obtained when its surfaces are laid flat as if it were unfolded.

Polyhedron Net

WoRk IT ouT

1 Circle the nets that form a cube.

Theme 6 B-93


B-94 Section 6.4


2 Connect each net to the correct polyhedron.

a)

• •

b)

• •

c)

• •

d)

• •

e)

• •

3 Draw one possible net for each polyhedron. Use a ruler.

a)

b)

c)

d)

e)

Theme 6 B-95


4 Emma is an engineer. She wants to build a castle tower based on the prism below. For the roof of the tower, she wants to put a polyhedron on top of the prism. Help her draw the net of the polyhedron. Use a ruler.

Net of roof

5 Gabriel is a carpenter. Draw the net of the convex polyhedron that he can use to build a box to hold the table he made.

6 Complete the net of this square pyramid. Use a ruler.

B-96 Section 6.4


LEARN ABOUT IT

Geometry Testing Euler’s Theorem on Convex Polyhedrons SecTIoN 6.5

Testing Euler’s Theorem on Convex Polyhedrons In the 18th century, the great mathematician Leonhard Euler discovered a formula for easily calculating the relationship between the number of faces (F), vertices (V) and edges (e) of a convex polyhedron. This formula, called “Euler’s theorem,” is: F + V – 2 = e

Example:

Polyhedron Euler’s Theorem: F + V – 2 Number of Edges

Pentagonal prism

7 faces + 10 vertices = 17

17 – 2 = 15 15

Square pyramid


10 – 2 = 88

Cube6 faces + 8 vertices = 14

14 – 2 = 1212

Triangular pyramid


8 – 2 = 66

WoRk IT ouT

1 Indicate if the description of each polyhedron is possible or impossible. Use Euler’s theorem to check your answers.

example A pyramid with 7 faces,

7 vertices and 14 edges.Impossible since 7 + 7 = 14 and 14 – 2 = 12

or 12 edges.

a) A prism with 9 faces, 14 vertices and 21 edges.

b) A pyramid with 5 faces, 5 vertices and 10 edges.

Theme 6 B-97


2 Sammy is gathering the materials he needs to build polyhedrons. Did he correctly predict the number of rods needed for the edges? Use Euler’s theorem check your answers.

Polyhedron Predicted Number of Rods Exact Number of Rods

a)

10 rods

b)

14 rods

c)

16 rods

d)

8 rods

3 Calculate the number of faces and edges of each prism based on the number of vertices.Use Euler’s theorem.

Vertices Number of Faces Number of Edges

a)

14 vertices

b)

18 vertices

c)

24 vertices

B-98 Section 6.5


uSe ReASoNINg

1 Vanessa made a one-of-a-kind dice that has 20 vertices and 30 edges for a new board game. How many faces does it have?

Solution:

2 Sebastian uses a crane to raise the beams needed to form the edges of a roof in the shape of a square pyramid. If it takes 22 minutes to raise one beam, how much time does it take to raise all the roof beams?

Solution:

Theme 6 B-99




mAkINg choIceS

1 A nurse hands out 3 types of masks and 3 different coloured surgical caps.

How many possible combinations of masks and caps are there?

a) 6 combinations

b) 7 combinations

c) 12 combinations

d) 9 combinations

My Calculation

2 How many outcomes can you get after throwing a 6-sided dice 2 times?

a) 12 b) 24

c) 36 d) 6

My Calculation

3 What is the theoretical probability of getting 1 head and 1 tail after flipping 2 coins?

a) 1

2 b)

1

4

c) 1 d) 1

3

My Calculation

4 Oliver randomly draws a marble out of a bag 20 times. He gets a red marble 9 times. What is his outcome compared to the theoretical probability?

a) Equal to the theoretical probability.

b) Less than the theoretical probability.

c) Greater than the theoretical probability.

d) None of the above.

B-100 Making Choices


5 How many faces, vertices and edges does a pentagonal pyramid have?

a) 5 faces, 6 vertices, 9 edges

b) 6 faces, 5 vertices, 9 edges

c) 5 faces, 5 vertices, 8 edges

d) 6 faces, 6 vertices, 10 edges

6 Which polygons form a hexagonal prism?

a) 2 rectangles and 4 hexagons

b) 2 hexagons and 6 rectangles

c) 6 hexagons

d) 6 rectangles and 6 hexagons

7 Which polyhedron does this net represent?

a) Pentagonal pyramid

b) Hexagonal prism

c) Pentagonal prism

d) Octagonal prism

8 If a prism has 8 vertices, how many faces does it have?

a) 6 faces b) 8 faces

c) 4 faces d) 10 faces

9 How many vertices does an octagonal pyramid have?

a) 8 vertices b) 10 vertices

c) 16 vertices d) 9 vertices

10 How many edges does a hexagonal prism have?

a) 20 edges b) 18 edges

c) 12 edges d) 16 edges

Theme 6 B-101


Th

em

e

RevIeW SeCtioNS 6.1 to 6.5

PRobAbILITy

1 Nolan plays this game of chance with the people who visit his booth at the fair.

A bag has 2 blue tokens and 2 green tokens. Those who choose 2 tokens of the same colour at the same time get a prize.

a) Use a tree diagram to represent all the possible outcomes.

1st token Chosen 2nd token Chosen all Possible outcomes

b) What are the chances of getting 2 tokens of the same colour?

c) What are the chances of getting 2 different coloured tokens?

B-102 Review


2 Eva is an interior decorator. She recommends 3 types of tables (round, square and rectangular) and 4 chair colours (black, white, grey and red) to her clients.

a) Use the table to indicate all the possible combinations of tables and chairs.

Table Chairs Possible Combinations

b) How many possible combinations does Eva recommend?

3 Look at the bag of buttons. Calculate the theoretical probability of randomly picking a red button, blue button, green button or yellow button. Write the result as a fraction, a decimal and a percentage.

Colour Fraction Decimal Percentage

Red

Blue

Green

Yellow

4 Jason randomly picks a button from the bag in the previous exercise and returns it to the bag 20 times. According to the theoretical probability, how many times does he pick a green or yellow button?

Theme 6 B-103


5 Now it’s your turn to do the button experiment. You can replace the buttons with 20 identical objects (tokens, unit cubes, slips of paper).

a) Place 7 red objects, 5 blue objects, 6 green objects and 2 yellow objects in a cup.Pick an object and return it to the cup 20 times, taking note of the colour of each object as you go.

my results

1 2 3 4 5

6 7 8 9 10

11 12 13 14 15

16 17 18 19 20

b) How many times did you pick a yellow or green object?

c) What is your outcome compared to the theoretical probability?

d) Add 4 other students’ outcomes to yours. How many times in all did you pick a yellow or green object? /100

e) What are the combined outcomes compared to the theoretical probability? Are they different from your answer in c)?

B-104 Review


geomeTRy

6 Write the number corresponding to each polyhedron in the correct category.

1 2 3 4

5 6 7 8

Prisms Pyramids Other Polyhedrons

7 Refer to the polyhedrons in Exercise 6 to help you fill in the table.

Polyhedron Name Faces Vertices Edges

1

2

3

4

5

6

7

8

Theme 6 B-105


8 Name 3 different polyhedrons that can be built with these polygons. Each figure may be used only once.

•

•

•

9 Draw the net of each polyhedron.

a)

b)

c)

d)

3 × 7 × 6 ×

B-106 Review


10 Finish drawing the net of each solid below.

a)

b)

c)

11 Use Euler’s theorem to calculate the number of edges for the polyhedrons in Exercise 10.

Number of Faces

Number of Vertices Number of Edges

a)

b)

c)

12 Use Euler’s theorem to calculate the number of edges for these polyhedrons.

Formula Edges

a) A pyramid with 6 faces.

b) A prism with 18 vertices.

c) A prism with 12 vertices.

Theme 6 B-107


What I Know What I’m Looking For

PRobLem SoLvINg

A Solid FoundationPamela is a civil engineer. Her team is installing cement cubes that will form the foundation of a new hospital.

• The base must measure 1 km long by 500 m wide.

• The steel wire for making the shape of the cube costs $2.05 per metre.

• The edges of the cubes each measure 4 m.

• Pamela’s team can install 30 cubes per day.

• The team has 22 days to do the work. Pamela will be charged a penalty fee of $3575.49 for each day of delay.

Indicate the number of days that Pamela’s team will need to install the cubes and the cost of steel wire needed to make them.

Will the team finish on time? If not, what penalty fee will Pamela owe?



My Solution

Validation

Solution :

Theme 6 B-109


Who Lives Where?

Here, in scrambled order, are the homes of 5 students from Grade 2 to Grade 6 who live on the same street. Use the clues to help you number each house in the correct order and write the name of the student who lives there below it.

Clues

• All 5 houses are side-by-side.

• The first and last houses are not pyramids.

• Meghan’s house has 9 edges.

• Alex is in Grade 6. His house has 7 vertices.

• Nathan’s house is pyramid-shaped.

• Jackie is in Grade 4. She lives in the 5th house.

• Zoe’s house has squares.

• The 4th house has 6 vertices.

• The Grade 5 student lives in the 2nd house, which has 8 edges.

• The Grade 2 student’s house has 12 edges.

Who is in Grade 3?

B-110 Game Time


Final Review

Theme

Theme

Theme

Theme

Theme

Theme

13329_decimale_6b_grande-revision_an.indd 111 14-02-25 16:03

final review

arithmetic

1 Look at these Egyptian symbols. Indicate the numbers that they represent.

= 1 = 10 = 100

= 1000 = 10 000 = 100 000

a) 3 × + 2 × + 5 × + 1 × =

b) + 7 × + 15 × + 4 × + 16 × =

2 Find the value of each digit in red.

a) 935 122 b) 708 385

c) 639 990 d) 467 217

3 How many hundreds do these numbers have?

a) 785 900 b) 428 121

c) 48 676 d) 852 019

4 Decompose the number 483 087 in 2 different ways.

B-112 Final Review


5 Circle the expressions that represent 739 930.

a) 93 T + 39 Th + 7 HTh b) 73 Th + 30 U + 39 T + 9 H

c) 73 TTh + 95 H + 43 T d) 69 TTh + 3 T + 499 H


484 484 844 484 444 884 448 448 488 848

7 Round each number to the positions indicated.

To the Nearest Ten Thousand

To the Nearest Thousand

To the Nearest Hundred

a) 902 489

b) 291 786

c) 371 965

d) 870 289

e) 976 589


a) b) c)

4 7 0 9 × 9 3

9 5 7 6 × 7 4

3 7 8 4 × 6 8

Final Review B-113


9 Fill in the table.

Multiplication Number of Times That the Base is Multiplied Exponential Notation Standard Form

example 3 × 3 = ? 2 32 9

a) 5 × 5 × 5 =

b) 10 × 10 × 10 =

c) 4 × 4 × 4 =

10 Place the numbers in the table below. Numbers may be used more than once.

122 157 749 700 239 400 786 780 625 448

Divisible by:

2 4 6 8 9

11 Decompose each number into prime factors. Use exponential notation to express your answer.

a)

300

b)

504

300 = 504 =

B-114 Final Review



a) b) c)


a) If 9 objects make up 1

4 of a collection,

how many objects are there in the

entire collection?

My Calculation

b) If 12 tokens make up 3

4 of a collection,

how many tokens are there in all?

My Calculation

14 What fraction of each figure is coloured in?

a) b)

14 28 127 8 4 0 8 0 9 2 4 8 8 4

Final Review B-115


15 Circle the fractions that are equivalent to the starting fraction.

a) 2

3 6

4 10

15 6

9 14

12

b) 3

5 24

40 6

10 9

18 18

25

c) 3

4 18

20 21

28 12

24 75

100

16 Write the fraction that each colour represents. Reduce the fractions to their simplest form, then arrange them in decreasing order.

a) Blue:

b) Yellow:

c) Red:

d) Green:

Decreasing order:

17 Arrange the fractions in increasing order.

1

4

1

7

1

6

1

2

1

5

1

12

18 Calculate the result of each operation. Reduce the fractions when possible.

a) 5

8 –

1

4 =

b) 2

3 +

2

6 =

c) 3

5 +

3

15 =

d) 2 – 2

3 =

My Calculations

B-116 Final Review


19 Calculate the product of each multiplication. Reduce the fractions when possible.

a) 5 × 1

4 =

b) 3 × 1

6 =

c) 4 × 3

4 =

d) 8 × 6

10 =

20 If Rob fills 5 glasses each with 2

3 cup of juice, how many cups of juice

does he use?

21 Put each decimal in its standard form. Compare each set of decimals using the <, > or = symbol.

Standard Form <, > or = Standard Form

a) (4 × 1

10) + 0.25 + 32 tenths (7 × 1

100) + 24 tenths + 0.59

b) 45 tenths + 6.8 + (5 × 1

1000) (55 × 1

1000) + 211 tenths

c) (17 × 1

100) + 7.2 + 15 thousandths 0.25 + (71 × 1

10) + 35 thousandths


5.05 5.5 5.505 5.55 5.005 5.055

Final Review B-117


23 Round each decimal to the positions indicated.

To the Nearest Hundredth To the Nearest Tenth To the Nearest Unit

a) 45.748

b) 4.097

c) 56.905

d) 31.639


a) b) c)

d) e) f)

45.7× 1 2

77.24× 26

247.9× 3 5

68.24× 46

98.7× 8 4

63.42× 34

B-118 Final Review


25 Calculate the products and the quotients. Use mental calculation strategies.

754.98 × 100 ÷ 1000 × 100

÷ 100 × 1000 ÷ 10

÷ 100 × 1000

26 Circle the 2 expressions that are equivalent to the starting fraction.

a) 3

4 = 0.7 75% 0.75 7% 0.075 b)

7

20 = 0.35 20% 7% 35% 0.2

c) 3

5 = 35% 0.6 0.06 60% 0.3 d)

8

10 = 80% 0.08 0.8 10% 0.88

27 Sixty Grade 6 students are going

to a summer camp of their choice. 2

5 of the students are going to horseback

riding camp, 1

4 prefer swim camp,

9 choose music camp, while the rest pick

theatre camp. What is the percentage

of students going to theatre camp?

My Calculation


a) 5 + 4 × 3 – 22 + 10 = b) 5 × 9 – (3 + 4) × 2 + 32 =

c) 62 + (13 – 4) – 10 × 2 ÷ 4 = d) (15 – 2 + 7) × 3 – 42 + 3 × 7 =

Final Review B-119


29 Match the equivalent chains of operations. Then, check your answers by comparing your results.

a) 3 + 6 + (5 + 7) = • • 10 × (3 + 5) =

b) (10 × 5) + (10 × 3) = • • 4 × 5 × (3 × 10) =

c) 6 + 5 + 3 + 8 = • • 2 × 4 × 3 × 5 =

d) (4 × 5) × 3 × 10 = • • (5 + 6) + 7 + 3 =

e) 4 × 3 × 5 × 2 = • • 3 + 5 + 8 + 6 =


a) b) c)


a) b)

22.8× 13.5

45.8 × 9.7

725.2× 6.3

3 7 828 20 2 2 1 5

B-120 Final Review



a) Kieran buys his parents a gift worth $63.00. He and his 3 sisters evenly split the cost. How much will each child pay?

My Calculation

b) The outdoor adventure centre pays $1962.30 for 5 identical canoes. How much does each canoe cost?

My Calculation

c) Leah is organizing an excursion. She divides 213.15 m of rope into 7 equal lengths for 7 groups. How many metres of rope does each group get?

My Calculation

d) Clara buys a handmade shirt for $136.68. This shirt is 6 times more expensive than Sophie’s shirt. How much does Sophie’s shirt cost?

My Calculation

Final Review B-121


33 Arrange these integers correctly on the number line.

−8 24 4 −28 12

0−12 16


a) –7 –14 b) 0 –1 c) –88 88

d) –5 –15 e) –6 7 f) –12 –2

35 Complete these number series.

a) 2 4 1 3 0

b) 10 6 2 –2

Geometry

36 List the characteristics of each triangle. Then, indicate its type.

a) b)

Type: Type:

37 Name the parts of the circle.

B-122 Final Review


38 Look at the Cartesian plane.

a) Indicate the coordinates of the following points.

0−1

−1 1 2 3 4 5 6−2−3−4−5−6

−2

−3

−4

−5

−6

6

5

4

3

2

1

D

E

B

C

A

y

x

A:

B:

C:

D:

E:

b) Plot these points on the Cartesian plane, then connect them in order.

F: (0, –1) G: (5, –1) H: (4, 2) I: (1, 2)

c) What figure do you get?

39 Carry out the translation of this figure, then create a tessellation by adding 6 more figures.

Final Review B-123


40 Match each polyhedron with the correct net.

a)

• •

b)

• •

c)

• •

d)

• •

41 Use Euler’s theorem to calculate the number of edges for the polyhedrons in Exercise 40.

Polyhedron Euler’s Theorem Number of Edges

a

b

c

d

B-124 Final Review


measurement

42 Measure the specified angle in each polygon. Then, indicate its type.

a) b)

Measurement:

Type:

Measurement:

Type:

c) d)

Measurement:

Type:

Measurement:

Type:

43 Convert these units of measure.

a) 75 m = km b) 4525 mm = dm

c) 47 m = cm d) 6.4 km = dm

44 Arrange these lengths in decreasing order.

170 m 7.5 km 1777 dm 755 mm 7755 cm

45 Christine wants to paint a wall, but not the door. How many square metres will she paint?

7.2 m

3.5 m

0.7 m

1.5 m

My Calculation

Final Review B-125


46 Convert these units of measure.

a) 3469 g = kg b) 862 g = kg

c) 4 kg = g d) 9060 g = kg

e) 8.25 kg = g f) 45 kg = g


a) William plays soccer 45 minutes a day from Monday to Friday. In hours and minutes, how much time does he spend playing soccer all week?

My Calculation

b) Juliette runs for 7 minutes and 22 seconds. How many seconds does this represent?

My Calculation

c) Samson plays tennis 1 h 10 min per day from Monday to Thursday, while Laurie plays for 47 min per day from Monday to Saturday. Who plays longer?

My Calculation

B-126 Final Review


48 Calculate the volume of each prism in cubic metres.

a)

4 m

70 dm

2.5 m

b)

15 dm87 cm

4 m

Volume: Volume:

statistics

49 Look at the circle graph, then answer the questions.

a) If 40 students are organizing a party, how many students are responsible for each task?

Percentage of Students

Decorations25%20%

40% 15%

MusicGames

SnacksDecorations:

Music:

Games:

Snacks:

b) If an average of 15 students per task are expected to help next year, how many students in all will organize the party?


a) 16 8 40 0 7

Arithmetic mean:

b) 145 302 604 109

Arithmetic mean:

c) 4 12.6 7 10.2 6.2 14

Arithmetic mean:

My Calculations

Final Review B-127


ProBaBility

51 Indicate the probability of randomly picking the following cubes as a fraction and a percentage.

Fraction Percentage

a) A blue cube.

b) A green cube.

c) A yellow cube.

d) A red or blue cube.

52 Use the answers from Exercise 51 to complete these statements with more likely, less likely or just as likely.

a) It is to pick a blue cube than a yellow cube.

b) It is to pick a red cube than a yellow cube.

c) It is to pick a yellow or red cube as a green cube.

53 Cedric attempts to pick a blue cube by repeating the cube experiment 20 times. After each cube is picked, he puts it back in the jar. Here is the outcome.

Does Cedric’s outcome match the theoretical probability? Explain your answer.

B-128 Final Review


GLOSSARY

A

Area (p. 26)Measurement of a figure’s surface.

Arithmetic mean (p. 20)Sum of a set of numbers divided by the total number of parts in the set.

Associative property (p. 5)Property applied to addition and multiplication that groups the numbers in an equation in different ways without changing the result.

C

CapacityVolume of matter, often liquid, contained in an object.

Cartesian plane (p. 52)Plane formed of 2 perpendicular lines: the horizontal axis (x) and the vertical axis (y).

Commutative property (p. 5)Property applied to addition and multiplication that moves around the numbers in an equation in different ways without changing the result.

Convex polyhedron (p. 93)Polyhedron containing all the line segments connecting any two vertices (points) within it.

Coordinates (x, y) (p. 52)Pair of numbers that indicate the position of a point in a Cartesian plane. The 1st number corresponds to its position on the horizontal axis (x) and the 2nd number corresponds to its position on the vertical axis (y).

Cubic centimetre (cm3) (p. 68)Unit of measure equal to the volume of a cube with 1 cm sides.

Cubic decimetre (dm3) (p. 68)Unit of measure equal to the volume of a cube with 1 dm sides.

Cubic metre (m3) (p. 68)Unit of measure equal to the volume of a cube with 1 m sides.

Curved body (p. 90)Solid with at least one curved surface.

D

Decimal (p. 8, 12, 14, 24)Number comprised of 2 parts separated by a decimal point: a whole part and a decimal part.

Decimal notation (p. 8, 12, 14, 24)Representation of a base 10 number made up of 2 parts (a whole part and a decimal part) separated by a decimal point.

Distributive property (p. 5)Property applied to multiplication that distributes multiplication over addition or subtraction.

Dividend (p. 12, 24)In a division, the number that is divided.

Division (p. 12, 24)Operation that shares a quantity into a number of equal parts.

Divisor (p. 12, 24)In a division, the number that divides.

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E

Edge (p. 90)Segment of a solid where 2 faces meet.

Euler’s theorem (p. 97)Formula designed to easily calculate the relationship between the number of faces (F), vertices (V) and edges (E) of a convex polyhedron. The formula is: F + V – 2 = E.

F

Factor (p. 8)Multiplication term.

Frieze pattern (p. 57)Rectangular strip with a regularly repeating pattern.

G

Gram (g) (p. 61)Unit of measure for mass 1000 times smaller than a kilogram (0.001 kg).

H

Hexagon Six-sided polygon.

Hour (h) (p. 65)Unit of measure for time lasting 60 minutes or 3600 seconds. There are 24 hours in a day.

Hundredth (p. 12, 14)In the decimal notation of a number, it is the 2nd digit to the right of the decimal point.

One hundredth = 1

100 or 0.01.

I

Integer (p. 44)Number belonging to a group {… –3 , –2, –1, 0, 1, 2, 3, …}. This group includes positive integers (greater than 0) and negative integers (less than 0).

K

Kilogram (kg) (p. 61)Unit of measure for mass 1000 times greater than a gram (1000 g).

L

Litre (L) Unit of measure for capacity 1000 times greater than a millilitre (1000 ml).

M

Mass (p. 61)Quantity of matter in an object or living thing.

Millilitre (ml)Unit of measure for capacity 1000 times smaller than a litre (0.001 L).

Minute (min) (p. 65)Unit of measure for time lasting 60 seconds. There are 60 minutes in an hour.

Multiplication (p. 8)Operation that finds the product of 2 or more factors.

N

Natural number Integer greater than or equal to 0.

B-130 Glossary


Nonconvex polyhedron (p. 93)Concave polyhedron with at least one line segment connecting two vertices (points) outside it.

O

Octagon Eight-sided polygon.

Origin (p. 52)Point at which 2 axes meet in a Cartesian plane with the coordinates (0, 0).

P

PentagonFive-sided polygon.

Polygon Plane figure formed by closed straight lines. A polygon can be convex or nonconvex.

Polyhedron (p. 90)Solids formed only by polygons (plane surfaces).

Prism (p. 90)Polyhedron with 2 congruent and parallel polygons as bases, and rectangles as its remaining faces.

Probability (p. 87)Possibility that a result will occur. Probability can be given a value between 0 and 1. Zero indicates the impossibility that a result will occur, while 1 indicates the certainty that it will happen. An event can be more or less likely than another, or just as likely as another.

Product (p. 8)Result of a multiplication.

Pyramid (p. 90)Polyhedron with a single polygon as a base, and triangles as its remaining faces.

Q

Quadrant (p. 52)Region of a Cartesian plane bordered by its axes.

QuadrilateralFour-sided polygon.

Quotient (p. 12, 24)Result of a division.

R

Random experiment (p. 84)Experiment with an outcome that is based entirely on chance.

S

Second (s) (p. 65)Base unit of measure for time for the international system of units. There are 60 seconds in a minute and 3600 seconds in an hour.

Solid (p. 90)Three-dimensional geometric figure formed by at least one closed surface.

Square centimetre (cm2) (p. 28)Unit of measure equal to the area of a square with 1 cm sides.

Square kilometre (km2) (p. 28)Unit of measure equal to the area of a square with 1 km sides.

Glossary B-131


Square metre (m2) (p. 28)Unit of measure equal to the area of a square with 1 m sides.

Surface (p. 28, 90)Part of a plane figure or a collection of faces of a solid.

Survey (p. 17)Research meant to gather information on a precise subject to obtain statistics.

TTenth (p. 12, 14, 24)In the decimal notation of a number, it is the 1st digit to the right of the decimal point.

One tenth = 1

10 or 0.1.

Tessellation (p. 59)Collection of geometric figures that cover up an entire surface, with no empty space or overlap.

Thousandth (p. 14)In the decimal notation of a number, it is the 3rd digit to the right of the decimal point.

One thousandth = 1

1000 or 0.001.

Translation (p. 57)Geometric transformation that moves all of a figure’s points in the same direction and the same distance. The figure keeps its shape, its orientation and its dimensions.

Translation arrow (p. 57)Arrow showing the direction and length that a translation must move.

Tree diagram (p. 84)Diagram representing all of the possible results of a random experiment.

V

Vertex (p. 90)Intersecting point of at least 2 edges of a solid.

Volume (p. 68)Measure of space occupied by a solid. Space has 3 dimensions: length (l), width (w) and height (h).

B-132 Glossary


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Nathalie Fortier Annie Leblanc - Amazon Web Services · 2020-03-20 · Electronic Publishing Interscript Illustrator Michel Rouleau (p. 47, 96) ENGLISH VERSION Pedagogical Reviewer