my math path 4 - nelson

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MY

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iii

Book A

1 Numbers to 10 000

2 Addition up to 10 000

3 Subtraction up to 10 000

4 Using Bar Models: Addition and Subtraction

5 Multiplication Facts for 8, 9, and 10

Book B

6 Multiplication

7 Division

8 Using Bar Models: Multiplication and Division

9 Length, Mass, and Capacity

10 Money

11 Time

Book C

12 Fractions

13 Decimals

14 Area and Perimeter

15 Volume of 3-D Objects

16 Angles, Lines, and Locations

17 Geometry

18 Graphs and Statistics

19 Probability

At a Glance

00(M)MIFG4_NonCC_SB(C)_FM.indd 3 04/04/20 6:13 PM

4C

Consultant and AuthorDr. Fong Ho Kheong

AuthorsChelvi Ramakrishnan, Michelle Choo, Gan Kee Soon, and Dr. Ng Wee Leng

Canadian Curriculum Advisor Dr. Douglas Edge

Canadian Program AdvisorJean Ford

Canadian Indigenous ReviewersRachel CosfordMichelle Evans

Student Book


nelson.com/MMPOntarioReport

Learn about the research and efficacy behind Singapore Math®

and Nelson’s My Math Path

v

12.4 Fractions of a Set 27Learn Identify fractions of a set. • Use fractions to describe parts of sets. • Determine the number of items in a fraction of a set.Hands-On Activity Use counters to identify equivalent fractions.Let’s Explore Whole numbers can be written as fractions.

Put on Your Thinking Cap!� 34Chapter Wrap Up� 35

Chapter Opener 38

Recall Prior Knowledge 39Quick Check

13.1 Understanding Tenths 42Learn Express fraction tenths as decimals. • Determine equivalent ones and tenths. • Write decimals. • Count forward by tenths. • Measure lengths using tenths.• Use place value to understand whole-number and decimal amounts.• Write decimals in expanded form.

13.2 Comparing Decimals 53Learn Use models to determine 0.1 more than or 0.1 less than. • Extend a decimal pattern. • Use place values to compare decimals. • Use place values to order decimals.Game Decimal Game!

13.3 Fractions and Decimals 61Learn Express fractions as decimals. • Express decimals as fractions.Hands-On Activity Fold paper strips to identify equivalent fractions and decimals.Game Match Game

Decimals13Chapter


iv

Chapter Opener 1


12.1 Understanding Fractions 5Learn Read and write fractions. • Numerator and denominator of a fraction. • Use models to show fractions as part of a whole. • Count forward by fractionsbeyond 1 whole.

12.2 Equivalent Fractions 10Learn What are equivalent fractions? • Use number lines to identify equivalent fractions.Hands-On Activity Fold paper strips to determine equivalent fractions. • Draw rectangles on grid paper to understand equivalent fractions.

12.3 Comparing Fractions 15Learn Use models to compare like fractions. • Use models to compare and order 3 like fractions. • Compare unlike fractions with the same numerator. • Compare fractions to 0, 1

2, and 1 using number lines. • Compare more unlike

fractions. • Compare and order unlike fractions.Hands-On Activity Fold paper strips to compare fractions with 1

2 as a

benchmark. • Use fraction circles to compare fractions.Math Journal

Fractions

Contents

12Chapter


vi

13.4 Adding Decimals 68Learn Add decimal tenths without regrouping. • Add decimals with regrouping in tenths. • Add decimals with regrouping in ones and tenths.Game Make Wholes

13.5 Subtracting Decimals 73Learn Subtract decimal tenths without regrouping. • Subtract decimals with regrouping in ones and tenths. • Subtract decimals from whole numbers.Game Break a Whole!

Put on Your Thinking Cap! 78Chapter Wrap Up 79

Chapter Opener 81

Recall Prior Knowledge 82 Quick Check

14.1 Area and Perimeter of Rectangles 86Learn Determine the area and perimeter of rectangles. • Rectangles with the same area but different perimeters. • Rectangles with the same perimeter but different areas.Hands-On Activity Making squares and rectangles using a geoboard • Estimate and measure the area and perimeter of square and rectangular faces of objects.Let’s Explore Use a geoboard to explore the perimeter and area of a rectangle. • Use area models to explore the perimeter and area of a rectangle.

Area and Perimeter14Chapter


vii

Chapter Opener 104

Recall Prior Knowledge 105 Quick Check

15.1 Building 3-D Objects Using Unit Cubes 107Learn Build 3-D objects using unit cubes.Hands-On Activity Use unit cubes to build 3-D objects.Let’s Explore Build as many different 3-D objects as possible.

15.2 Volume of 3-D Objects 111Learn Compare the volumes of objects. • Measure the volumes of cubes and rectangular prisms in cubic units. • Measure the volume of a 3-D object in cubic units. • Compare the volumes of 3-D objects. • Use units of measurement to describe volume. • Compare the volumes of 3-D objects.Hands-On Activity Use a given number of cubes to form different 3-D objects.Let’s Explore Explore a formula for the volume of a rectangular prism.

15.3 Drawing Cubes and Rectangular Prisms 121Learn Draw cubes and rectangular prisms on isometric dot paper. • Draw cubes and rectangular prisms without showing the unit cubes.


14.2 Area and Perimeter of Polygons 96Learn Estimate and measure the area and perimeter of polygons.Hands-On Activity Estimate the areas of 6- and 7-sided polygons. • Write problems about polygons.


Volume of 3-D Objects15Chapter


viii

Chapter Opener 127


16.1 Identifying Angles 134Learn Compare angles to benchmark angles.Hands-On Activity Identify benchmark angles.

16.2 Drawing Perpendicular Line Segments 139Learn Use a set square to draw perpendicular line segments.Hands-On Activity Use a straightedge or a ruler to draw perpendicular line segments.

16.3 Drawing Parallel Line Segments 142Learn Draw a line segment parallel to segment PQ. • Draw a parallel line segment that goes through a given point.Hands-On Activity Draw parallel line segments.

16.4 Horizontal and Vertical Lines 146Learn Identify horizontal and vertical lines.

16.5 Locations on a Grid Map 148Learn Read points on a grid map. • Describe locations on a grid map.


Angles, Lines, and Locations16Chapter


ix

Chapter Opener 156


17.1 Quadrilaterals 160Learn Identify a square and its properties. • Identify a rectangle and its properties. • Identify other quadrilaterals and their properties. • Classify quadrilaterals by their properties.

17.2 Reflection 171Learn Identify and draw lines of symmetry. • Identify and perform reflections.Hands-On Activity Mirror Images • Lines of ReflectionLet’s Explore Symmetric Designs with Pattern Block Grids

17.3 Geometric Patterns 178Learn Create patterns by reflecting 2-D shapes. • Extend a repeating shape pattern and predict terms.Hands-On Activity Pattern Block Patterns

Geometry17Chapter


x

17.4 Prisms and Pyramids 182Learn Identify and describe prisms and pyramids. • Classify prisms and pyramids.Hands-On Activity Construct prisms and pyramids.Let’s Explore Compare prisms and pyramids.

17.5 Nets of Prisms and Pyramids 188Learn Identify the net of a cube. • Identify the net of a rectangular prism. • Identify the net of a triangular prism. • Identify the net of a pyramid.Hands-On Activity Nets of Cubes • Identify a prism from a net. • Construct a 3-D object to identify its net. • Nets of PyramidsLet’s Explore Identify the net of a cube.



xi

Chapter Opener 200


18.1 Double Bar Graphs 205Learn Display 2 sets of similar data in a double bar graph. • Interpret a double bar graph.Hands-On Activity Collect data and display it in a double bar graph.

18.2 Median and Range 212Learn Determine the median of a data set. • Determine the range of a data set.Hands-On Activity Determine the median by marking off pairs of ordered data, or on a line plot.Let’s Explore Use number cards to identify a median.

18.3 Stem-and-Leaf Plots 220Learn Make a stem-and-leaf plot. • Use a stem-and-leaf plot to determine the median, mode, and range.Hands-On Activity Make a stem-and-leaf plot.

18.4 Comparing Data 225Learn Compare 2 sets of data using a double bar graph. • Compare 2 sets of data using stem-and-leaf plots.


Graphs and Statistics18Chapter


xii

Chapter Opener 234


19.1 Predicting Outcomes of an Experiment 238Learn Predict the frequency of an outcome of a simple event. • Predict the frequency of an outcome involving 2 simple events.Hands-On Activity One-Coin Toss • Two-Coin TossLet’s Explore Number Cube SumsMath Journal


Glossary 249

Index 267

Credits 278

Probability19Chapter


1

How many of the quilt squares show a heart or hearts? What fraction of the quilt are these squares?

12Chapter

Fractions

Lessons12.1 Understanding Fractions 12.2Equivalent Fractions12.3Comparing Fractions12.4Fractions of a Set

A fraction can be represented in different ways.

BIG IDEA

12(M)MIFG4_NonCC_SE(C)_Ch12.indd 1 04/04/20 6:17 PM

2 Chapter12 Fractions

Understandingfractions

A fraction names equal parts of a whole.

Identifyingunitfractions

A unit fraction names one of the equal parts of a whole.

1 third is a unit fraction.

3 fourths is not a unit fraction.

Fractionsofaset

There are 12 swans in a pond.8 of the swans are black.The rest of the swans are white.

2 thirds of the swans are black.1 third of the swans are white.

1 whole � 2 halves

1 quarter 1 quarter 1 quarter 1 quarter

3 fourths

1 whole � 4 fourths 1 whole � 3 thirds

1 third

1 third

1 third

1 third

RECALL PRIOR KNOWLEDGE

or 4 quarters


Chapter12 Fractions 3

Matchtheunitfractionswiththeircorrectmodels.

1 Models Unit fractions

• •1 fifth

• •1 third

Readinganumberline

The numbers on this number line increase by 1.The arrow points to 6.

0 1 2 3 4 5 6 7 8 9 10

QuickCheck

• • 1 sixth

• • 1 quarter



Whatarethemissingnumbers?

2

3

Fillintheblanks.

4 The stars are sorted according to colour.

There are stars in equal groups.

3 of the stars are yellow.

1 of the stars are blue.

Usethenumberlinetocompletethesentence.

5 The arrow points to .

The rectangle has equal parts.

eighths of the rectangle is red.

eighths of the rectangle is blue.

eighths and eighths make a whole.

The circle has equal parts.

tenths of the rectangle is green.

tenths of the rectangle is orange.

tenths and tenths make a whole.

2221201918171615141312


Lesson12.3 Comparing Fractions 15

LEARN Usemodelstocomparelikefractions.

Which is greater, 14 or

34?

14

34

14

34

14 and

34 have the same denominator

They are likefractions.

34 is greater than

14.

When fractions have the same denominator, the greater fraction is the one with the greater numerator.

Goals• Compare and order like fractions and unlike

fractions.• Compare and order fractions using benchmark

fractions.

12.3Lesson

Comparing Fractions

Vocabularylike fractions

unlike fractions

benchmark fraction

The 2 wholes are the same size, with the same number of equal parts.

There are more parts of the whole shaded in 34 than in 14.



GUIDED LEARNINGComplete.

1 Which is less, 25 or

45?

25

45

GUIDED LEARNINGOrderthefractionsfromleasttogreatest.

2

is the greatest.

is the least.

, ,

least greatest

35

55

25

LEARN Usemodelstocompareandorder3likefractions.Order the fractions from greatest to least.

24

34

14

In order from greatest to least, the fractions are34 ,

24 ,

14

greatest least

34 is the greatest.

14 is the least.



3 Rachel bakes 2 equal-sized chicken pies.She cuts each pie into 10 equal parts.

Clara eats 3

10 of a pie, and Priscilla eats 2

10 of the other pie.

a Who eats more?310

210

Clara

Priscilla

is greater than .

eats more.

Priscilla gives her remaining pie to Tom to eat.

b What fraction of the pie does Tom eat?

c Who eats the most?

is greater than and .

eats the most.

d Who eats the least?

eats the least.

Tom eats of the pie.



HANDS-ON ACTIVITY

1 Cut out 2 paper strips of the same size.

STEP

1 Fold each paper strip in half twice.

STEP

2 Unfold the paper strips. Use a pencil to draw along

the fold lines.

STEP

3 Shade 1 strip to show a fraction greater than 12 .

The shaded fraction is .

STEP

4 Shade the other paper strip to show a fraction that is less than 12 .

The shaded fraction is .

Materials: • 2 paper strips of

the same size

12

34

14

You can only compare fractions from the same whole or equal-sized wholes.

LEARN Comparefractionsto0, 12

,and1usingnumberlines.

Zoe ate 12 of a vegetarian pie.

Lena ate 34 of an equal-sized

vegetarian pie.

Abby ate 14 of another

equal-sized vegetarian pie.



LEARN Compareunlikefractionswiththesamenumerator.


15 ?

14 and

15 have different denominators.

They are unlikefractions.14 is greater than

15.

When fractions have the same numerator, the greater fraction is the one with the smaller denominator.

Which fraction is less, 210 or

23 ?

210

23

When fractions have the same numerator, the smaller fraction is the one with the greater denominator.


4 Which is greater, 13 or

14 ? 5 Which is less,

310 or

35 ?

is greater than . is less than .

14

15

13

14

35

310

The fractions have the same numerator, so compare the denominators.

210 is less than

23 .



GUIDED LEARNINGComparethefractions.

6

is greater than .

7

is less than .

Fillinthemissingfractionsonthenumberlines.

80

0 1

125

110

210

410

610

710

810

510

35

Usethenumberlinesin 8 tocomparethefractions.Chooseor .

945

910

10 3

10 15

56

12

45

78

12

710



34 1214 12

0 114

24

34

0 112 1

2 and 24 are equivalent.

Lena had a bigger part than Zoe.34 is greater than

12 .

Abby had a smaller part than Zoe.14 is less than

12 .

The number lines show 12 ,

14 , and

34 .

Compare the fractions to 12.

34 is greater than

12 .

14 is less than

12 . So

34 is greater than

14.

Compare the fractions to 1. 34 is closer to 1 than

14 is.

So 34 is greater than

14.

Compare the fractions to 0. 14 is closer to 0 than

34 is.

So 14 is less than

34.

12

34

14

Zoe Lena Abby



GUIDED LEARNINGUsethenumberlinestocomparefractionswith 1

2.


14 ?

12

fractions less than

12

13

23

12

fractions greater than

14

24

34

0 1

0 1

0 1

Is each fraction greater

than or less than 12 ?


710 ?

Determinethepossiblefractions.

13 Write 3 fractions, 2 of which are

greater than 12 .

12

fractions less than

12

15

25

35

45

12


110

210

310

410

610

710

910

510

810

0 1

0 1

0 1

You could also compare both fractions to 0 or 1.



LEARN Comparemoreunlikefractions.


15 ?

Compare the fractions 34 and

15 with the benchmarkfraction

12 .

12

fractions less than

12

14

34

24

12


15

25

35

45

0 1

0 1

0 1

34

12

15

12

So 34

15 .

224 or

210

423 or

35


HANDS-ON ACTIVITY

When you compare fractions with 12 like this, you are

using 12 as a benchmark fraction. Benchmark fractions

can help you compare fractions.

Which fraction is greater?Use fraction circles to help you.

145 or

23

33

10 or24



Method2. Usemodels.

Compare 34 and

110 with

12 .

34 is greater than

12 .

110 is less than

12 .

110 ,

12 ,

34

least greatest

GUIDED LEARNINGOrderthefractionsfromleasttogreatest.

14 45 ,

14 ,

12 , ,

Orderthefractionsfromgreatesttoleast.

15 12 ,

910 ,

25 , ,

110

12

34

12

LET’S PRACTISECompare.

1 Which is less, 3

10 or 35 ? 2 Which is greater,

13 or

25 ?

Orderthefractionsfromleasttogreatest.

3 4

10 , 34 ,

12 , ,

Orderthefractionsfromgreatesttoleast.

4 13 ,

35 ,

12 , ,



LEARN Compareandorderunlikefractions.

Method1. Useanumberline.

Order 12 ,

34 , and

110 from least to greatest.

From the number line, 34 is the greatest and

110 is the least.

In order from least to greatest, the fractions are

110 ,

12 ,

34

least greatest

Use 12 as the benchmark fraction

to compare 34 and 110 .

34 1

2

110 12

0 112

0

0 1

1

34

1414

24

110


MATH JOURNAL

Solve.

Matthew, Jackson, and Ethan each have an equal-sized fraction strip.Matthew divides his fraction strip into 10 equal parts and shades 7 parts.The fraction he shades is greater than Jackson’s and Ethan’s.Jackson’s fraction is less than Ethan’s.How would you divide and shade Jackson’s and Ethan’s fraction strips?

1 How would you divide and shade Jackson’s fraction strip? Describe your steps.

2 Compare and order 12,

45, and

710 . Record your steps.

3 Which halves can be compared? Explain your answer.

Matthew’s strip shows 710

.

First, I divide Ethan’s strip in half.12

is less than 710

.

Ethan’s fraction could be 12

.

I shade 1 part of Ethan’s strip.

12

12

12

12

A B C D



Lesson12.4 Fractions of a Set 27

LEARN Identifyfractionsofaset.There are 4 maple leaves. 3 out of the 4 maple leaves are red.

What fraction of the maple leaves are red?34 of the maple leaves are red.

GUIDED LEARNINGIdentifythefractionsofaset.

There are 8 pencils.

1 What fraction of the pencils are red?

2 What fraction of the pencils are blue?

3 What fraction of the pencils are black?

4 What fraction of the pencils are not red?

red maple leaves3

4

total number of maple leaves

12.4Lesson

Goals• Read, write, and identify fractions of a set.• Determine the number of items in a fraction of a set.• Express whole numbers as fractions.• Recognize fractions that are equal to whole numbers.

Fractions of a Set



LEARN Determinethenumberofitemsinafractionofaset.

12 plates are divided into 4 equal groups. 9 out of 12 plates are blue. 3 out of 4 groups of plates are blue.34 of the plates are blue.

So 34 of 12 is 9.

The shaded parts in the bar model show 34 of the set.

Determine 34 of 12.

4 units 12 1 unit 12 4 5 33 units 3 3 5 9

So 34 of 12 is 9.

?

12

You can determine the items in the fractional part of a set by using a bar model.


8 Jamal has 10 toy cars.35 of the toy cars are yellow.

How many toy cars are yellow?

toy cars are yellow.



LEARN Usefractionstodescribepartsofsets.Here is a set of 12 maple leaves.The set of maple leaves is divided into 4 equal groups.3 out of 4 groups of maple leaves are red.

34 is 3 out of 4 equal groups.

What fraction of the maple leaves are red?

34 of the maple leaves are red.


5 The set of bows is divided into equal groups.

6 What fraction of the bows are pink?

of the bows are pink.

7 What fraction of the bows are blue?

of the bows are blue.

9 out of 12 leaves are red.912

5 34

6 out of 10 bows are pink.610

5 35


9 Determine 35 of 10 to determine how many cars are yellow.

5 units

1 unit

3 units

So 35 of 10 5

toy cars are yellow.

?

10

Draw a bar model.Divide it into 5 parts.Shade 3 parts.

HANDS-ON ACTIVITY

Work in pairs.

STEP

1 Your teacher will give each pair a bag of counters. Use the counters to show the fraction 12. For example:

STEP

2 Show a fraction equivalent to 12 by using more counters. How many more counters of each colour did you add? Write the equivalent fraction represented by the counters.

STEP

3 Repeat STEP

2 3 more times. How many more counters of each colour did you add each time? Write the equivalent fractions represented by the counters.

Materials: • counters (red and yellow)




Lookatthepictures.Thenanswerthequestion.

3 Which set shows the fraction 34 coloured? Set

Solve.

There are 8 fruits.

1 What fraction of the fruits are peaches?

2 What fraction of the fruits are strawberries?

LET’S PRACTISE

Set C

Set B

Set D

Set A



Solve.

4 Jerry had 12 granola bars.

His friends ate 23 of them.

How many granola bars did his friends eat?

Determine 23 of 12 to determine how many granola

bars his friends ate.

3 units granola bars

1 unit granola bars

2 units granola bars

So 23 of 12 5 granola bars

His friends ate granola bars.

?

12 granola bars


Let’sExplore!

LET’S EXPLORE

Whole numbers can be written as fractions.

The number 1 5 11 . 1 1 5 1

1 3 5 31 , 4 5

2 5 5

Whole numbers can be written as other fractions.

The number 1 can also be written as 22 because2 2 5 1.

3 Write another fraction for 1.

What do you notice about the fractions 42 ,

84 , and

63 ?

4 Write another fraction for 2.

Write 2 fractions to show each of these numbers.

5 5 5 5 6 6 5 5

What numbers are shown by these fractions?

7 71 8

102

9 2010 10

324


The fraction bar represents division. 11 means the same as 1 1.



PUT ON YOUR THINKING CAP!

P RO B L E M S O LV I N G

1 The model shows 34 .

How much of the shading must be erased so that the remaining

shaded part is 38 of the strip?

2 Gary, Joey, and Kylie shared a vegetarian pizza.The pizza was divided into 9 equal slices.

Gary ate 29 of the pizza.

Joey ate more pizza than Kylie.Together they finished the whole pizza.

What are some possible fractions that show the part of the pizza that Joey and Kylie each ate?

What is the greatest possible fraction that describes the part of the

pizza that Kylie ate?


Try drawing the model in another way.

Try drawing a model first.



Youhavelearned...

to understand fractions, numerator, and denominator:

Unit fractions

12 is one half. 1

3 is one third. 14 is one fourth or one quarter.

15 is one fifth. 1

6 is one sixth. 17 is one seventh.

18 is one eighth.

19 is one ninth.

110 is one tenth.

111 is one eleventh.

112 is one twelfth.

Identifying fractions to make a whole

25 and

35 make 1 whole.

Numerator and denominator

Numerator: The number of equal parts shaded.24 Denominator: The number of equal parts the whole is divided into.

Proper and improper fractions15, 35 Proper fractions: The fraction is less than 1 whole. The numerator is less

than the denominator.

55, 65 Improper fractions: The fraction is greater than or equal to 1 whole.

The numerator is greater than or equal to the denominator.

CHAPTER WRAP UPA fraction can be represented in different ways.

BIG IDEA



Equivalent fractions:

Using a model Using a number line

to compare and order fractions:

Like fractions are fractions with the same denominators. Unlike fractions are fractions with different denominators.

Comparing like fractions5

10 is the greatest.

110 is the least.

510 ,

310,

110

greatest least

Comparing unlike fractions with the same numerator

110 is less than

15 .

14 is greater than

15 .

14 ,

15,

110

greatest least

310

510

110

15

110

14

When the denominators are the same, compare the numerators.

1 whole

12 shaded

24 shaded

0 12

0 24

14

34

1

1



to use number lines and benchmarks of 0, 12 , and 1:

45

12

310

12

So, in order from greatest to least, the fractions are45 ,

12 ,

310

greatest least

to write whole numbers as fractions.

Examples: 0 5 04 1 5

33 2 5

21 5

42 5

63

to determine fractions of a set using models.

46 of the buttons are blue.

26 of the buttons are not blue.

66 of the buttons are round.

12 of the set of circles is red.

12 of 8 is 4.

12 of the bar model is shaded.

12 of 8 is 4.

8

4

12

fractions less than

12

15

25

35

45

12


110

210

310

410

610

710

910

510

810

0 1

0 1

0 1


4C

My Math Path 1–8 brings together the proven Singapore Math approach with Canadian curriculum–aligned content. The series blends procedural and conceptual understanding to support student success and mathematical mastery. My Math Path 1–8 encourages students to think critically and persevere when solving problems using strategies that promote visualization. The purposeful lesson structure aims to boost student confidence and mathematical understanding, fostering positive attitudes toward math.

MY

MA

TH PA

TH 4

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