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4CSAMPLELESSONSINSIDE
At a GlanceBook A1 Numbers to 10 0002 Addition up to 10 0003 Subtraction up to 10 000ACCESS THE DEMO VERSION OF THE MY MATHPATH GRADE 4 ONLINE TEACHING CENTRE (OTC)FOR FREE!Features include: Additional teaching materials that support the detailed lessonsfound in the print Teacher’s Resource Indigenous Connections through meaningful and authenticactivities Extra practice Blackline Masters to reinforce lesson conceptsand allow independent practice Revisit and Enrichment Blackline Masters to differentiateinstruction Virtual Manipulatives and Games to model concepts andenhance instructionMY MATH PATH 44A4 Using Bar Models: Addition andSubtraction5 Multiplication Facts for 8, 9,and 10Book B6 Multiplication9 Length, Mass, and Capacity7 Division10 Money8 Using Bar Models: Multiplicationand Division11 TimeBook C12 Fractions16 Angles, Lines, and Locations13 Decimals17 Geometry14 Area and Perimeter18 Graphs and Statistics15 Volume of 3-D Objects19 ProbabilityAccess your demo now!Teacher’s ResourcePlease visitnelson.com/mmp4 OTCdemoTeacher’s Resourcemmp4a ontr cover.indd 32020-02-27 10:03 AMFor assistance contact Customer Support atE-mail: inquire@nelson.comPhone: 1-800-268-222iii
Learn about the research andefficacy behind Singapore Math and Nelson’s My Math Path4CStudent BookConsultant and AuthorDr. Fong Ho KheongAuthorsChelvi Ramakrishnan, Michelle Choo, Gan Kee Soon, and Dr. Ng Wee LengCanadian Curriculum AdvisorDr. Douglas EdgeCanadian Program AdvisorJean FordCanadian Indigenous ReviewersRachel CosfordMichelle Evansnelson.com/MMPOntarioReport
Contents12.4 Fractions of a SetLearn 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.Chapter12FractionsPut on Your Thinking Cap! Chapter Wrap Up Chapter Opener1Recall Prior KnowledgeQuick Check212.1 Understanding Fractions5Learn 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 Fractions10Learn What are equivalent fractions? Use number lines to identifyequivalent fractions.Hands-On Activity Fold paper strips to determine equivalent fractions. Draw rectangles on grid paper to understand equivalent fractions.12.3 Comparing FractionsLearn Use models to compare like fractions. Use models to compare andorder 3 like fractions. Compare unlike fractions with the same numerator. Compare fractions to 0, 1 , and 1 using number lines. Compare more unlike2fractions. Compare and order unlike fractions.Hands-On Activity Fold paper strips to compare fractions with 1 as a2benchmark. Use fraction circles to compare fractions.Math Journaliv27153435Chapter13DecimalsChapter Opener38Recall Prior KnowledgeQuick Check3913.1 Understanding Tenths42Learn 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 Decimals53Learn Use models to determine 0.1 more than or 0.1 less than. Extend adecimal pattern. Use place values to compare decimals. Use place valuesto order decimals.Game Decimal Game!13.3 Fractions and Decimals61Learn Express fractions as decimals. Express decimals as fractions.Hands-On Activity Fold paper strips to identify equivalent fractions anddecimals.Game Match Gamev
13.4 Adding Decimals6814.2 Area and Perimeter of PolygonsLearn Add decimal tenths without regrouping. Add decimals with regroupingin tenths. Add decimals with regrouping in ones and tenths.Game Make Wholes13.5 Subtracting DecimalsLearn Estimate and measure the area and perimeter of polygons.Hands-On Activity Estimate the areas of 6- and 7-sided polygons. Writeproblems about polygons.73Learn Subtract decimal tenths without regrouping. Subtract decimals withregrouping in ones and tenths. Subtract decimals from whole numbers.Game Break a Whole!Put on Your Thinking Cap!Chapter Wrap Up7879Area and PerimeterChapter Opener81Recall Prior KnowledgeQuick Check8214.1 Area and Perimeter of Rectangles86Learn Determine the area and perimeter of rectangles. Rectangles with thesame area but different perimeters. Rectangles with the same perimeter butdifferent areas.Hands-On Activity Making squares and rectangles using a geoboard Estimate and measure the area and perimeter of square and rectangular facesof 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.Put on Your Thinking Cap!Chapter Wrap Up15Volume of 3-D ObjectsChapter Opener104Recall Prior KnowledgeQuick Check10515.1 Building 3-D Objects Using Unit Cubes107Learn 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 Objects111Learn Compare the volumes of objects. Measure the volumes of cubesand rectangular prisms in cubic units. Measure the volume of a 3-D objectin cubic units. Compare the volumes of 3-D objects. Use units ofmeasurement 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 Prisms121Learn Draw cubes and rectangular prisms on isometric dot paper. Draw cubes and rectangular prisms without showing the unit cubes.Put on Your Thinking Cap!Chapter Wrap Upvi102103ChapterChapter1496125126vii
ChapterChapter1617Angles, Lines, and LocationsGeometryChapter Opener127Chapter Opener156Recall Prior KnowledgeQuick Check128Recall Prior KnowledgeQuick Check15716.1 Identifying Angles13417.1 Quadrilaterals160Learn Compare angles to benchmark angles.Hands-On Activity Identify benchmark angles.16.2 Drawing Perpendicular Line Segments13917.2 ReflectionLearn Use a set square to draw perpendicular line segments.Hands-On Activity Use a straightedge or a ruler to draw perpendicularline segments.16.3 Drawing Parallel Line Segments142146171Learn 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 Grids17.3 Geometric PatternsLearn Draw a line segment parallel to segment PQ. Draw a parallelline segment that goes through a given point.Hands-On Activity Draw parallel line segments.16.4 Horizontal and Vertical LinesLearn Identify a square and its properties. Identify a rectangle and itsproperties. Identify other quadrilaterals and their properties. Classifyquadrilaterals by their properties.178Learn Create patterns by reflecting 2-D shapes. Extend a repeating shapepattern and predict terms.Hands-On Activity Pattern Block PatternsLearn Identify horizontal and vertical lines.16.5 Locations on a Grid Map148Learn Read points on a grid map. Describe locations on a grid map.Put on Your Thinking Cap!Chapter Wrap Upviii153154ix
17.4 Prisms and Pyramids182Learn Identify and describe prisms and pyramids. Classify prismsand pyramids.Hands-On Activity Construct prisms and pyramids.Let’s Explore Compare prisms and pyramids.17.5 Nets of Prisms and Pyramids188Learn 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.Put on Your Thinking Cap!Chapter Wrap Up197198Chapter18Graphs and StatisticsChapter Opener200Recall Prior KnowledgeQuick Check20118.1 Double Bar Graphs205Learn Display 2 sets of similar data in a double bar graph. Interpret adouble bar graph.Hands-On Activity Collect data and display it in a double bar graph.18.2 Median and Range212Learn 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 Plots220Learn Make a stem-and-leaf plot. Use a stem-and-leaf plot to determinethe median, mode, and range.Hands-On Activity Make a stem-and-leaf plot.18.4 Comparing Data225Learn Compare 2 sets of data using a double bar graph. Compare 2 setsof data using stem-and-leaf plots.Put on Your Thinking Cap!Chapter Wrap Upx231232xi
ChapterChapter19ProbabilityChapter Opener234Recall Prior KnowledgeQuick Check23519.1 Predicting Outcomes of an Experiment23812FractionsLearn Predict the frequency of an outcome of a simple event. Predict thefrequency of an outcome involving 2 simple events.Hands-On Activity One-Coin Toss Two-Coin TossLet’s Explore Number Cube SumsMath JournalPut on Your Thinking Cap!Chapter Wrap Up247248Glossary249Index267Credits278xiiIG I D EALessons12.1 Understanding Fractions12.2 Equivalent Fractions12.3 Comparing Fractions12.4 Fractions of a SetBHow many of the quilt squaresshow a heart or hearts? Whatfraction of the quilt are thesesquares?A fraction can be represented indifferent ways.1
RECALL PRIOR KNOWLEDGEReading a number line0Understanding fractions2345678910The numbers on this number line increase by 1.The arrow points to 6.A fraction names equal parts of a whole.1 whole 3 thirds11 whole 4 fourths or 4 quarters1 whole 2 halvesQuick CheckMatch the unit fractions with their correct models.1Identifying unit fractionsModelsUnit fractions 1 fifth 1 third 1 sixth 1 quarterA unit fraction names one of the equal parts of a whole.1 third is a unit fraction.1 third1 third1 third1 third3 fourths is not a unit fraction.1 quarter 1 quarter 1 quarter 1 quarter3 fourthsFractions of a setThere 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.2Chapter 12FractionsChapter 12Fractions3
LessonWhat are the missing numbers?2The rectangle hasequal parts.12.3Comparing Fractionseighths of the rectangle is red.eighths of the rectangle is blue.Goalseighths and The circle has3eighths make a whole. equal parts.tenths of the rectangle is green.Vocabularylike fractionsunlike fractionsbenchmark fractionCompare and order like fractions and unlikefractions.Compare and order fractions using benchmarkfractions.tenths of the rectangle is orange.tenths andtenths make a whole.LEARN Use models to compare like fractions.1Fill in the blanks.3Which is greater, 4 or 4 ?4 The stars are sorted according to colour.The 2 wholes are thesame size, with the samenumber of equal parts.14341434There arestars inequal groups.3of the stars are yellow.13and44 have the same denominator1of the stars are blue.They are like fractions.There are more parts of3the whole shaded in 41than in 4 .314 is greater than 4 .Use the number line to complete the sentence.When fractions have the same denominator, the greater fractionis the one with the greater numerator.121314155 The arrow points to4Chapter 12Fractions16171819202122.Lesson 12.3 Comparing Fractions15
GUIDED LEARNING3 Rachel bakes 2 equal-sized chicken pies.She cuts each pie into 10 equal parts.Complete.132Clara eats 10 of a pie, and Priscilla eats 10 of the other pie.a Who eats more?24Which is less, 5 or 5 ?2531045Clara210LEARN Use models to compare and order 3 like fractions.PriscillaOrder the fractions from greatest to least.24341434 is the greatest.14 is the least.2,4greatest.eats more.Priscilla gives her remaining pie to Tom to eat.In order from greatest to least, the fractions are3,4is greater thanb14What fraction of the pie does Tom eat?leastTom eatsGUIDED LEARNINGOrder the fractions from least to greatest.2355525,16Chapter 12Who eats the most?is greater thanis the greatest.and.eats the most.is the least.dWho eats the least?eats the least.,leastcof the pie.greatestFractionsLesson 12.3 Comparing Fractions17
HANDS-ON ACTIVITYLEARN Compare unlike fractions with the same numerator.111 Cut out 2 paper strips of the same size.Which is greater, 4 or 5 ?14The fractions have the samenumerator, so compare thedenominators.15Materials: 2 paper strips ofthe same sizeSTEP1 Fold each paper strip in half twice.STEP2 Unfold the paper strips.Use a pencil to draw alongthe fold lines.11and45 have different denominators.STEPThey are unlike fractions.13 Shade 1 strip to show a fraction greater than 2 .114 is greater than 5 .The shaded fraction isWhen fractions have the same numerator, the greater fraction is the one with thesmaller denominator.STEP14 Shade the other paper strip to show a fraction that is less than 2 .The shaded fraction is22Which fraction is less, 10 or 3 ?.21022islessthan103.23LEARN Compare fractions to 0, 1 , and 1 using number lines.When fractions have the same numerator, the smaller fraction is the one with thegreater denominator.1Zoe ate 2 of a vegetarian pie.212GUIDED LEARNING3Complete.1134 Which is greater, 3 or 4 ?is greater than18Chapter 12Fractions.Lena ate 4 of an equal-sizedvegetarian pie.35 Which is less, 10 or 5 ?133101435is less than.You can only comparefractions from the samewhole or equal-sizedwholes.341Abby ate 4 of anotherequal-sized vegetarian pie.14Lesson 12.3 Comparing Fractions19
GUIDED LEARNING3412Zoe14Compare the fractions.64556AbbyLena12Lena had a bigger part than Zoe.314 is greater than 2 .314 211 42Abby had a smaller part than Zoe.114 is less than 2 .is greater than7778101 1123The number lines show 2 , 4 , and 4 .0is less than11212are2 and 4equivalent.01434241 38Fractions2503511111314 is less than 2 . So 4 is greater than 4 .31Compare the fractions to 1. 4 is closer to 1 than 4 is.31So 4 is greater than 4 .13Compare the fractions to 0. 4 is closer to 0 than 4 is.13So 4 is less than 4 .Chapter 12.Fill in the missing fractions on the number lines.Compare the fractions to 2 . 4 is greater than 2 .20.01102104105106107108101Use the number lines in 8 to compare the fractions. Choose or .49103159 510 10Lesson 12.3 Comparing Fractions21
LEARN Compare more unlike fractions.3GUIDED LEARNING11Use the number lines to compare fractions with 2 .Which is greater, 4 or 5 ?311Compare the fractions 4 and 5 with the benchmark fraction 2 .fractions less than 1fractions greater than 120141503425314 2115 23501451132314031When you compare fractions with 2 like this, you are1using 2 as a benchmark fraction. Benchmark fractionscan help you compare fractions.27fractions less than 142or5302222or41023 10 or 434 3 or 5Fractionsfractions greater than 12112150Which fraction is greater?Use fraction circles to help you.Chapter 12112 Which is greater, 5 or 10 ?2HANDS-ON ACTIVITY2234240311So 4 5 .11120Is each fraction greater1than or less than 2 ?1fractions greater than 2fractions less than 2124112120211 Which is greater, 3 or 4 ?11021025310410355106104571081019101You could also compareboth fractions to 0 or 1.Determine the possible fractions.13 Write 3 fractions, 2 of which are1greater than 2 .Lesson 12.3 Comparing Fractions23
LEARN Compare and order unlike fractions.Method 2. Use models.Method 1. Use a number line.1 331Order 2 , 4 , and 10 from least to 102.12,least142434134110 ,01Compare 4 and 10 with 2 .34greatest1GUIDED LEARNINGOrder the fractions from least to greatest.011041114 5 , 4 , 21,,Order the fractions from greatest to least.1Use 2 as the benchmark fraction3119215 2 , 10 , 5,,to compare 4 and 10 .314 21110 231From the number line, 4 is the greatest and 10 is the least.In order from least to greatest, the fractions are110 ,least12,34greatestLET’S PRACTISECompare.34313 10 , 4 , 2Fractions2,,Order the fractions from greatest to least.1Chapter 1212 Which is greater, 3 or 5 ?Order the fractions from least to greatest.314 3, 5, 22431 Which is less, 10 or 5 ?,,Lesson 12.3 Comparing Fractions25
LessonMATH JOURNAL12.4Fractions of a SetSolve.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?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.Matthew’s strip shows 7 .10First, I divide Ethan’s strip in half.LEARN Identify fractions of a set.1 is less than 7 .210There are 4 maple leaves.3 out of the 4 maple leaves are red.Ethan’s fraction could be 1 .2I shade 1 part of Ethan’s strip.1 How would you divide and shade Jackson’s fraction strip?Describe your steps.34red maple leavestotal number of maple leavesWhat fraction of the maple leaves are red?1 472 Compare and order 2 , 5 , and 10 . Record your steps.34 of the maple leaves are red.3 Which halves can be compared?Explain your answer.GUIDED LEARNINGIdentify the fractions of a set.1212A12BThere are 8 pencils.12C1 What fraction of the pencils are red?D2 What fraction of the pencils are blue?3 What fraction of the pencils are black?4 What fraction of the pencils are not red?26Chapter 12FractionsLesson 12.4 Fractions of a Set27
LEARN Use fractions to describe parts of sets.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.LEARN Determine the number of items in a fraction of a set.9 out of 12 leaves arered.39541234 is 3 out of 4 equal groups.What fraction of themaple leaves are red?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.3So 4 of 12 is 9.34 of the maple leavesare red.You can determine the itemsin the fractional part of a setby using a bar model.12GUIDED LEARNING?3The shaded parts in the bar model show 4 of the set.Complete.3Determine 4 of 12.124 units1 unit12 4 5 33 units3 35935 The set of bows is divided intoequal groups.6 out of 10 bows arepink.365106 What fraction of the bows are pink?of the bows are pink.5So 4 of 12 is 9.GUIDED LEARNINGComplete.8 Jamal has 10 toy cars.7 What fraction of the bows are blue?of the bows are blue.35 of the toy cars are yellow.How many toy cars are yellow?toy cars are yellow.28Chapter 12FractionsLesson 12.4 Fractions of a Set29
39 Determine 5 of 10 to determine how many cars are yellow.LET’S PRACTISESolve.10Draw a bar model.Divide it into 5 parts.Shade 3 parts.?There are 8 fruits.5 units1 unit3 units3So 5 of 10 5toy cars are yellow.1 What fraction of the fruits are peaches?2 What fraction of the fruits are strawberries?HANDS-ON ACTIVITYLook at the pictures. Then answer the question.Materials: counters (red and yellow)Work in pairs.STEP33 Which set shows the fraction 4 coloured? Set1 Your teacher will give each pair a bag of counters.1Use the counters to show the fraction 2 . For example:STEPSet A12 Show a fraction equivalent to 2 by using more counters. How many morecounters of each colour did you add? Write the equivalent fraction representedby the counters.STEPSet BSet DSet CSTEP3 Repeat 2 3 more times. How many more counters of each colour did you addeach time? Write the equivalent fractions represented by the counters.30Chapter 12FractionsLesson 12.4 Fractions of a Set31
LET’S EXPLORESolve.4 Jerry had 12 granola bars.Let’s Explore!2His friends ate 3 of them.How many granola bars did his friends eat?2Determine 3 of 12 to determine how many granolabars his friends ate.12 granola barsThe fraction barrepresents division.11 means the same as1 1.Whole numbers can be written as fractions.1The number 1 5 1 .11 151335 1,452 55Whole numbers can be written as other fractions.?23 unitsgranola bars1 unitgranola bars2 unitsgranola bars2So 3 of 125His friends ateThe number 1 can also be written as 2 because 2 2 5 1.3 Write another fraction for 1.486What do you notice about the fractions 2 , 4 , and 3 ?granola barsgranola bars.4 Write another fraction for 2.Write 2 fractions to show each of these numbers.5 5 556 6 55What numbers are shown by these fractions?32Chapter 12Fractions77181029201010324Lesson 12.4 Fractions of a Set33
BAPUT ON YOUR THINKING CAP!IG I D EA fraction can be represented indifferent ways.CHAPTER WRAP UPYou have learned .PROB LEM S O LVING31 The model shows 4 .How much of the shading must be erased so that the remaining3shaded part is 8 of the strip?Try drawing the model in another way.2 Gary, Joey, and Kylie shared a vegetarian pizza.The pizza was divided into 9 equal slices.2Gary ate 9 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 pizzathat Joey and Kylie each ate?What is the greatest possible fraction that describes the part of thepizza that Kylie ate?Try drawing amodel first.34Chapter 12Fractionsto understand fractions, numerator, and denominator:Unit fractions1is one half.21is one third.31is one fourth or41 is one fifth.516 is one sixth.17 is one seventh.18 is one eighth.111 is one eleventh.19 is one ninth.112 is one twelfth.110 is one tenth.one quarter.Identifying fractions to make a whole235 and 5 make 1 whole.Numerator and denominatorNumerator: The number of equal parts shaded.Denominator: The number of equal parts the whole is divided into.24Proper and improper fractions1 3,5 5Proper fractions: The fraction is less than 1 whole. The numerator is lessthan the denominator.5 6,5 5Improper fractions: The fraction is greater than or equal to 1 whole.The numerator is greater than or equal to the denominator.Chapter 12Fractions35
Equivalent fractions:1Using a modelto use number lines and benchmarks of 0, 2 , and 1:Using a number linefractions less than 11 whole1shaded22shaded4120014243410100to compare and order fractions:Like fractions are fractions with the same denominators.Unlike fractions are fractions with different denominators.510110510 is the greatest.110 is the least.5310 ,10 ,greatest15110210Examples: 0 5 4When the denominatorsare the same, compare 81019101So, in order from greatestto least, the fractions are45,12,greatest310least321 5 3462 5 1 5 2 5 312 of the set of circles is red.12 of 8 is 4.least84Chapter 123546 of the buttons are blue.26 of the buttons are not blue.66 of the buttons are reatest3102541 5231 102to determine fractions of a set using models.Comparing unlike fractions with the same numerator1511203102to write whole numbers as fractions.Comparing like fractions36fractions greater than 1212 of the bar model is shaded.12 of 8 is 4.Chapter 12Fractions37
4CMy Math Path 1–8 brings together the proven Singapore Mathapproach with Canadian curriculum–aligned content. The series blendsprocedural and conceptual understanding to support student successand mathematical mastery. My Math Path 1–8 encourages students tothink critically and persevere when solving problems using strategiesthat promote visualization. The purposeful lesson structure aims toboost student confidence and mathematical understanding, fosteringpositive attitudes toward math.@NELSONPK20nelson.com
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 T
