Western Canadian Teacher Guide - SD67 (Okanagan Skaha)sd67.bc.ca/instruction/mathresources/math3/gr03_units_wes/gr03... · Western Canadian Unit 5: Sorting and Data ... Lesson 1:

Teacher GuideWestern Canadian

Unit 5: Sorting and DataManagement

A D D I S O N W E S L E YA D D I S O N W E S L E Y Western

UNIT

“Whatever your difficulties inmathematics, I can assure youmine are far greater.”

Albert Einstein

Mathematics Background

What Are the Big Ideas?

• Objects can be described, compared, and sorted according to their attributes.

• Data can be collected to learn about a topic.

• Data can be organized and presented in many ways.

• Data not specifically displayed on a graph can be obtained by extrapolation.

How Will the Concepts Develop?

Students use 2, then 3 attributes to sort objects and data. They interpretdata from bar graphs, pictographs, and circle graphs, and ask andanswer questions about data displayed in a graph.

Students use a tally chart to keep a count of data, and draw a pictographor bar graph to show the data, using a key or scale of many-to-one.

Students conduct a survey to collect data. They organize the data, thendisplay their data in a graph. Students use their results to answerquestions and draw conclusions.

Why Are These Concepts Important?

The ability to sort objects or data in different ways helps students tomake sense of the data in the world around them. Students need practicemaking charts and drawing graphs so they come to realise that differentrepresentations of data tell different things. When students collect data,they learn organizational skills that are important in their daily lives.

FOCUS STRANDStatistics and Probability: Data Analysis

SUPPORTING STRANDSNumber, Patterns and Relations

Sorting and Data Management

ii Unit 5: Sorting and Data Management

5

Unit 5: Sorting and Data Management iii

Lesson 1:Sorting by Two AttributesLesson 2:Sorting by Three AttributesLesson 3:Interpreting GraphsLesson 4:Interpreting Circle Graphs

Curriculum Overview

General Outcome• Students ... interpret the data to

make predictions.

Specific Outcomes• Students sort, concretely and

pictorially, using two or moreattributes. (PR1)

• Students make predictions andinferences when solving similarproblems. (SP4)

• Students obtain new information byperforming arithmetic operations onthe data. (SP5)

LaunchUsing Data to Answer Questions

Cluster 1: Sorting and Interpreting Graphs

Show What You Know

Unit ProblemUsing Data to Answer Questions

General Outcome• Students collect first- and second-

hand data, display the results inmore than one way, and interpretthe data to make predictions.

Specific Outcomes• Students collect data, using

measuring devices andprinted/technology resources. (SP1)

• Students display data, using rankordering. (SP2)

• Students display the same data inmore than one way. (SP3)

• Students make predictions andinferences when solving similarproblems. (SP4)

• Students obtain new information byperforming arithmetic operations onthe data. (SP5)

• Students graph whole numberpoints on a horizontal or verticalnumber line. (SS30)

Cluster 2: Collecting and Organizing DataLesson 5:Drawing PictographsLesson 6:Drawing Bar GraphsLesson 7:Strategies ToolkitLesson 8:Collecting DataLesson 9:Conducting a Survey

iv Unit 5: Sorting and Data Management

Curriculum across the Grades

Grade 2

Students sort objects andshapes, using one or twoattributes. They identifyattributes and rules inpre-sorted sets.

Students formulate thequestions and categoriesfor data collection, andactively collect first-handinformation. They choosean appropriate recordingmethod, such as tallymarks, to collect data.

Students organize data,using such graphicorganizers as diagrams,charts, and lists. Theyconstruct and labelconcrete/object graphs,pictographs, and bargraphs.

Students discuss data,and draw andcommunicate appropriateconclusions. Theygenerate new questionsfrom displayed data.

Grade 3

Students sort, concretelyand pictorially, using twoor more attributes.

Students collect data,using measuring devicesand printed/technologyresources. They displaydata, using rankordering. Studentsdisplay the same data inmore than one way.

Students make predictionsand inferences whensolving similar problems.They obtain newinformation byperforming arithmeticoperations on the data.

Grade 4

Students sort numbersinto categories, using oneor more attributes.

Students select a sampleor population, andorganize the collection ofdata. They manipulatedata to create an intervalgraph/table for displaypurposes.

Students construct a bargraph and a pictograph,using many-to-onecorrespondence, andjustify the choice ofintervals andcorrespondence used.They discuss the processby which the data wascollected.

Attribute TrainFor Extra Support (Appropriate for use after Lesson 1)Materials: Attribute Train (Master 5.11), AttributeBlocks, pencil crayons

The work students do: Students work with apartner. Each student takes 15 random Attribute Blocks.One player places an Attribute Block in the centre of thetable. The other player finds a block that is differentfrom the block on the table in only one way. She placesthe block on the table beside the other block. Studentstake turns finding a block that differs from the precedingblock in only one way. Students try to make the train aslong as they can, then record their train on paper bytracing the blocks and colouring them.

Take It Further: Students make an attribute train bychanging exactly 2 attributes each time.

Spatial/Visual/SocialPartner Activity

Additional Activities

Colour CountFor Extra Practice (Appropriate for use after Lesson 5)Materials: Colour Count (Master 5.13), small boxes orbags of coloured counters

The work students do: Students work individually.The student sorts the counters by colour, then uses a tallychart to record the number of each colour. She uses thetally chart to draw a pictograph, using an appropriatekey.

Take It Further: Have the student write threequestions she can ask about her graph. Students cantrade graphs and questions for other students to answer.

Visual/MathematicalIndividual Activity

Guess My LabelsFor Extra Practice (Appropriate for use after Lesson 2)Materials: Guess My Labels (Master 5.12), Venndiagram with 2 loops (PM 28), Attribute Blocks, small cards

The work students do: Students play with apartner. Player A chooses 10 Attribute Blocks, thenpicks 2 attributes. He makes label cards for each loop,and places each card face down beside the appropriateloop. He sorts the blocks according to the turned-overlabels. Player B looks at the sorting and guesses whatthe labels are. Players turn over the cards to check. Aplayer gets 1 point for guessing each correct label. Thefirst player to get 10 points wins. Players switch rolesand play again.

Take It Further: Students repeat the activity using 3 attributes and Venn diagrams with 3 loops.(Master 5.8).

Social/Visual/LogicalPartner Activity

Unit 5: Sorting and Data Management v

Boys or Girls?For Extra Support (Appropriate for use after Lesson 6)Materials: Boys or Girls? (Master 5.14), index cards,blue and green Snap Cubes, 1-cm grid paper (PM 20),rulers

The work students do: Students work with a partner.Students write the words “Boys” and “Girls” on 2 indexcards. Students use a green Snap Cube to represent a girland a blue Snap Cube to represent a boy. Students stackSnap Cubes on the index cards to represent the numbersof boys and girls in the class. Students then draw a bargraph, colouring the same number of grid squares asthere are Snap Cubes for each bar.

Take It Further: Students draw another bar graph, thistime using a scale of many-to-one.

Visual/Kinesthetic/SocialPartner Activity

vi Unit 5: Sorting and Data Management

Planning for Unit 5

Planning for Instruction

Lesson Time Materials Program Support

Suggested Unit time: About 2 weeks

Unit 5: Sorting and Data Management vii

Purpose Tools and Process Recording and Reporting

Planning for Assessment

Lesson Time Materials Program Support

2 Unit 5 • Launch • Student page 190

Using Data to Answer Questions

LESSON ORGANIZER

Curriculum Focus: Activate prior learning about interpretingdata from charts and graphs.Vocabulary: data

10–15 min

L A U N C H

ASSUMED PRIOR KNOWLEDGE

Students can interpret displays of data, such as charts and graphs.

✓

ACTIVATE PRIOR LEARNING

Invite students to examine the charts andgraphs on pages 190 and 191 of the StudentBook. Review the meaning of the term data asfacts or information collected to learn aboutpeople or things.

Ask:• What does the pictograph show?

(The number of books read in April)• Who read the most books? (Angie)

The least books? (Shane)• What can you find out from the tally chart?

(I can find out what Grade 3 students eat for lunch.I find that pizza is eaten by the greatest number of students, and tuna is eaten by the least number of students.)

• What does the other chart show? (It shows the favourite sport of 100 Grade 3children. The favourite sport is hockey.)

• What can you find out from the bar graph?(I can find out how many hours Grade 3 students

sleep at night. Most children sleep 10 hours eachnight. The greatest number of hours children sleep atnight is 11 hours.)

Point out that each chart and graph has a titleand is clearly labelled so we know what hasbeen recorded. Ensure students understand thata pictograph must have a key and a bar graphmust have a scale. Ask questions, such as:

• How do you know that Angie read the most books? (Angie has the most symbols next toher name in the pictograph.)

• Why do you think the tally marks aregrouped in 5s? (To make them easy to count)

Tell students that, in this unit, they will sort andclassify objects and data, interpret data from bargraphs, pictographs, and circle graphs, andinvestigate how to collect, organize, and displaydata. At the end of the unit, in the Unit Problem,students will use data to answer questions.

LITERATURE CONNECTIONS FOR THE UNIT

Anno’s Flea Market by Anno Mitsumasa. Philomel, 1984.ISBN: 0399210318At the flea market, set in an old European town, there is a greatvariety of items for sale that can be sorted and resorted. This isone in a series of Anno books that combines mathematicalconcepts with children’s literature.

DIAGNOSTIC ASSESSMENT

What to Look For

✔ Students can interpretdisplays of data, suchas charts and graphs.

What to Do

Extra Support:

Students who have difficulty reading information from a bar graph may benefitfrom using a ruler as a straightedge to help them read the lengths of the bars.Work on this skill during Lesson 3.

Students who have difficulty interpreting data from a graph may benefit frombeing asked specific questions about the graph. Work on this skill during Lessons 3 and 4.

Unit 5 • Launch • Student page 191 3

Some students may benefit from using the virtualmanipulatives on the e-Tools CD-ROM.

The e-Tools appropriate for this unit include Spreadsheet/Data/Grapher. Students can use these e-Tools to organize data intables and to sort data.

REACHING ALL LEARNERS

4 Unit 5 • Lesson 1 • Student page 192

Sorting by Two Attributes

LESSON ORGANIZER

Curriculum Focus: Use 2 attributes to sort objects anddata. (PR1)Teacher Materials� Attribute Blocks� overhead transparency of Venn diagram (PM 28)Student Materials Optional� Attribute Blocks � Step-by-Step 1 (Master 5.15)� Venn diagrams (PM 28) � Extra Practice 1 (Master 5.25)� Sorting by 2 Attributes Chart (Master 5.6)� Sorting by 2 Attributes Venn Diagram (Master 5.7)Vocabulary: attribute, Venn diagramAssessment: Master 5.2 Ongoing Observations: Sortingand Data Management

40–50 min

L E S S O N 1

Key Math Learnings1. Attributes such as colour, shape, and size are used to

describe an object.2. Objects can be sorted using two attributes.3. A Venn diagram and a chart can be used as sorting tools.

BEFORE Get S tar ted

Show students a selection of Attribute Blocks.Tell students that an attribute is used todescribe an object. In Unit 3, we used shape todescribe and sort objects.

Ask:• What other attributes can we use to describe

the blocks? (Size, colour, thickness, and position)

• Why do you think these blocks are calledAttribute Blocks? (Because they have many different attributes)

Present Explore. Ensure students understandthey are to sort the blocks using 2 differentattributes each time, and that they are to recordeach sorting. Discuss possible ways to recordtheir sorting.

DURING Exp lore

Ongoing Assessment: Observe and Listen

Ask questions, such as:• How are all the blocks in this group alike?

(All of them are yellow.)• What attributes did you use to sort?

(Blocks that are yellow and blocks that are big)• Where did you put blocks that were yellow

and big? (I put them in a group.) What blocks were in this group? (The big yellow triangle and the big yellow circle)

• Where did you put blocks that were notyellow and were not big? (I put them in a group by themselves.) What blocks were in this group? (The small red triangle, the small blue square, andthe small green rectangle)

3

0

5

4

Unit 5 • Lesson 1 • Student page 193 5

Alternative ExploreMaterials: magazines, catalogues, newspapers, scissorsHave pairs of students choose a theme, such as animals.Students cut out 10 pictures of animals. Students pick 2 attributes, then sort the pictures and record their sorting.

Early FinishersHave students use a Venn diagram to show their sorting inPractice questions 1 and 2.

Common Misconceptions➤Students think that all blocks must be placed inside the loops

of the Venn diagram.How to Help: Provide students with 10 Attribute Blocks. Havethem use the attributes “red” and “square.” Have students groupthe red blocks, then group the squares. Tell students that allleftover blocks will go outside the loops.


• How did you record your sorting? (We drew 4 circles. We drew the blocks that wereyellow in one circle, and the blocks that were big inanother circle. We then drew the blocks that were bigand yellow in another circle. The blocks that wereneither yellow nor big were drawn in the last circle.We labelled all the circles. Some blocks were in morethan one circle.)

• What other attributes did you use to sort?(Blocks that are small and blocks that are square)

AFTER Connec t

Invite volunteers to describe the attributes theyused to sort their blocks. Discuss the methodsstudents used to record their work.Ask questions, such as:• How did you find your classmates’

sorting rule? (We could see all the red blocks weregrouped together and all the thick blocks weregrouped together. We knew the sorting rule wasblocks that were red and blocks that were thick.)

Use an overhead transparency of a Venndiagram on the overhead projector. Label theleft loop “thick” and the right loop “green.”Review the term Venn diagram and discusshow it is used to sort.

Ensure students understand that:• only thick blocks that are not green go in the

left loop• only green blocks that are not thick go in the

right loop• blocks that are thick and green go in

the middle• all other blocks go outside the loops but

inside the rectangleHave volunteers sort a selection of overheadAttribute Blocks using this Venn diagram.

Repeat with 2 different attributes.

Use the examples in Connect to introduce the useof a chart to sort objects and to review the useof the Venn diagram.

Numbers Every DayEncourage students to recall multiplication facts and relate themto addition.

Sample Answers1. 2.

3. 4.

5. a) I chose the attributes:Travels in the air andhas wheels. Only theairplane has both attributes, but you onlysee the wheels when the plane is on or closeto the ground.

b) I chose the attributes: Has windows and hasblue colouring. Only the car and the airplane have both attributes.

Has blue colouringHas windows

TrainHelicopter

CarAirplane

Hot Air BalloonSailboat

Bicycle Scooter Rollerblade

Travels in the airHas wheels

TrainRollerbladeScooterCarBicycle

AirplaneHelicopterHot Air Balloon

Sailboat

BigSquare

Y

YY

YR R

B

B

RB

YellowThin

YY

Y

Y

R

R

B BR B

Red Yellow

Triangle

Circle

ColourShape Blue

Square

Hexagon

Rectangle

Big Small

Thin

Thick

Size

Thickness

Y

Y

Y

Y

R

R

B BR B

Prac t i ce

Question 1 requires Sorting by 2 AttributesChart (Master 5.6). Question 3 requires Sortingby 2 Attributes Venn Diagram (Master 5.7).Questions 4 and 5 require a Venn diagram (PM 28). Have Attribute Blocks available forquestions 1 to 4.

Assessment Focus: Question 5

Students use a Venn diagram to sort thevehicles in 2 different ways. They label eachloop with an attribute that can be used to sortthe vehicles. They sketch each vehicle in theappropriate loop or outside the loops. Somestudents may choose 2 attributes that do notoverlap and therefore may leave theoverlapping part of the loops empty. A fewstudents may take this further and draw 2 loops without an overlap. For example, if a student uses the attributes: Has only 2 wheels and has only 4 wheels, there will be no overlap.

Students who need extra support to completeAssessment Focus questions may benefit fromthe Step-by-Step masters (Masters 5.15–5.22).


6. a) The numbers in Loop 1 have a 6. The numbers in Loop 2have a 9. The numbers in the overlapping part have both a6 and a 9.

b) In Loop 1, I could write 6, 16, 26, 36, . . . etc. I couldwrite any number that has a 6 but does not have a 9. InLoop 2, I could write 19, 39, 49, 59, . . . etc. I could writeany number that has a 9 but does not have a 6. In theoverlapping part, I could write 96, 619, 916, . . . etc. Icould write any number that has both a 6 and a 9.

c) I would write 4, 25, 37, 112, . . . etc. I would write anynumber that does not have a 6 or a 9.

REFLECT: It is better to use a Venn diagram when I want to showobjects that have attributes in common. It is better to use achart when I want to sort each object by its attributes, andwhen I am not looking for any overlap. For example, when Iwant to sort objects according to their size and shape, I would use a chart. When I want to find which objects arebig and triangular, I would use a Venn diagram.


ASSESSMENT FOR LEARNING

What to Look For

Understanding concepts ✔ Students understand that attributes

such as colour, shape, and size canbe used to describe an object.

Applying procedures✔ Students can use 2 attributes to sort

objects and data.

✔ Students can use a Venn diagram anda chart to sort objects and data.

Communicating✔ Students can describe the attributes

they used to sort objects.

What to Do

Extra Support: Students can complete the Additional Activity,Attribute Train (Master 5.11).Students can use Step-by-Step 1 (Master 5.15) to completequestion 5.

Extra Practice: Have students work in pairs. One student usesa Venn diagram to sort 10 Attribute Blocks. The other studentlooks at the sorting and finds her partner’s sorting rule. Studentsswitch roles and continue the activity.Students can complete Extra Practice 1 (Master 5.25).

Extension: Have students use the letters of the alphabet.Challenge students to find 2 attributes to sort the letters so that there is no overlap. Have students draw the resulting Venn diagram.

Recording and ReportingMaster 5.2 Ongoing Observations:Sorting and Data Management

Making ConnectionsAt Home: Things that are sorted at home may include groceryitems (refrigerated or not refrigerated), clothing, dishes, cutlery,and CDs.


Sorting by Three Attributes

Key Math Learnings1. Objects can be sorted using 3 attributes.2. A Venn diagram with 3 loops can be used to sort objects

using 3 attributes.

LESSON ORGANIZER

Curriculum Focus: Use 3 attributes to sort objects. (PR1)Teacher Materials� Attribute Blocks� transparency of 3-Loop Venn Diagram (Master 5.8)� buttonsStudent Materials Optional� Attribute Blocks � Step-by-Step 2 (Master 5.16)� 3-Loop Venn Diagram � Extra Practice 1 (Master 5.25)

(Master 5.8)� Practice Venn Diagram (Master 5.9)Assessment: Master 5.2 Ongoing Observations: Sortingand Data Management

40–50 min

L E S S O N 2


Show students a collection of buttons.

Ask questions, such as:• What attributes do the buttons have?

(Colour, shape, thickness, and number of holes)• Which 3 attributes can we use to sort

the buttons?(Buttons with 2 holes, buttons that are round, andbuttons that are white)

• Do any of the buttons have 2 of theattributes? (Yes, this button is white with 2 holes and thisbutton is round and white.)

• Do any of the buttons have all 3 attributes?(Yes, these two buttons are white and round, with 2 holes.)

Present Explore. Distribute copies of 3-LoopVenn Diagrams (Master 5.8) to pairs of

students. Ensure students understand they areto sort the blocks using 3 attributes.

Ask:• Why are we using Venn diagrams with

3 loops? (We are using 3 attributes to sort the blocks.)

• Why are there 4 overlapping areas? (The blocks can have 3 different pairs of attributes incommon or they can have all 3 attributes in common.)

DURING Exp lore


Ask questions, such as:• Which attributes did you use to sort?

(Blocks that are blue, blocks that are big, and blocksthat are circles)

• How did you label the loops? (I labelled the loops “Blue,” “Big,” and “Circles.”)

Sample Answers1. LargeHexagon

Thin

R

Y

R

Y

Y

B

B

R

BR


• How did you know where to put each block?(I put each block inside a loop or outside of all theloops. I then looked at pairs of loops to see if anyblocks shared both attributes. If there were blocksthat shared both attributes, I moved them to theoverlapping part of the loops. I then tried to findblocks that had all 3 attributes. I put these blockswhere the 3 loops overlap.)

• Why did you put that block outside of the loops? (It does not have any of the three attributes.)

• Why did you put that block where the 3 loops overlap? (It has all the attributes.)

• Is it easier to use Venn diagrams with 2 loops or with 3 loops? (I think it is easier to use 2 loops because there isonly 1 overlapping part. When there are 3 loops youhave to think about 4 different places where theloops overlap.)

AFTER Connec t

Invite volunteers to describe the attributes theyused to sort their blocks. Discuss how studentsdecided where to put each block.

Use a transparency of a 3-Loop Venn Diagram(Master 5.8) on the overhead projector. Labelthe left loop “Blue,” the right loop “Square,”and the bottom loop “Thick.”Ensure students understand that:• only blue blocks that are not square or thick

go in the left loop• only square blocks that are not blue or thick

go in the right loop• only thick blocks that are not blue or square

go in the bottom loop• blocks that are blue and square go in the top

overlap, where the left and right loops overlap• blocks that are blue and thick go in the

bottom left overlap, where the left andbottom loops overlap

Alternative ExploreMaterials: an assortment of about 10 stickers, 3-Loop VennDiagram (Master 5.8)Students look at their stickers, then pick 3 attributes. They use theVenn diagram to sort the stickers, sticking them in theirappropriate positions.

Early FinishersHave students sort the Attribute Blocks in Connect so that none ofthe loops overlap.

Common Misconceptions➤Students have difficulty knowing where to place a block on the

3-loop Venn diagram.How to Help: Have students work with one block at a time. Ifthe block has 1 of the attributes, it goes in a single loop. If theblock has 2 of the attributes, it goes where the 2 loops overlap.If the block has all 3 of the attributes, it goes where the 3 loopsoverlap. If the block has none of the attributes, it goes outside ofthe loops.


2.

3. a) Some of the loops of the Venn diagram should not overlap.It is impossible to find an Attribute Block that is both largeand small. It is also impossible to find a block that has all 3 attributes: red, large, and small.

b) To correct the Venn diagram I would change one of theattributes. I would change “Large” to “Square.”

4. a) The blocks were sorted according to shape, thickness, andcolour. All the blocks in Loop A are triangles. All the blocksin Loop B are thin. All the blocks in Loop C are yellow.

5. I chose 10 books, then picked the attributes: Hardcover, non-fiction, and more than 100 pages. I put the books that wereboth hardcover and more than 100 pages where these 2 loops overlap. I put the books that were both more than100 pages and non-fiction where these 2 loops overlap. I putthe books that were both hardcover and non-fiction wherethese 2 loops overlap. I put Math Makes Sense 3 where the 3 loops overlap because it is non-fiction, hardcover, and morethan 100 pages. I put all other books in single loops, oroutside the loops if they had none of the attributes.

More than 100pages

Hardcover

Non-fiction

Where's Waldo

Atlas

The Story of Anne Frank

The ThiefLord

Math Makes Sense 3

Harry Potter and the Philosopher's Stone

DictionaryMath Makes Sense 3 Practice and Homework Book

Love You Forever

In Aunt Lucy's Kitchen

BlueThin

Square

R

Y

BY B

B

R

B

BR

• blocks that are square and thick go in thebottom right overlap, where the right andbottom loops overlap

• blocks that are blue, square, and thick go inthe centre, where the left, right, and bottomloops overlap

• all other blocks go outside the loops butinside the rectangle

Have volunteers sort a collection of overheadAttribute Blocks using this Venn diagram.

Repeat with 3 different attributes.

Ask:• How would the Venn diagram change if it

were impossible for an object to have two ofthe attributes at the same time? (The two loops for those attributes would notoverlap. There would only be 2 areas of overlapinstead of 4.)

Review the problem in Connect.

Prac t i ce

Questions 1, 2, 3, and 5 require a 3-Loop VennDiagram (Master 5.8). Question 6 requiresPractice Venn Diagram (Master 5.9). HaveAttribute Blocks available for questions 1 to 4.


Students sort books in the classroom. Theychoose 3 attributes, such as paperback, poetry,and chapter book. Depending on the attributeschosen, it may be impossible for a book to have2 or 3 of the attributes at the same time. If thisis the case, some students may leave some ofthe overlapping areas empty. Students shouldexplain how they sorted the books.


Triangle

Yellow

Thin

6. I would put boys in Loop 1, girls in Loop 2, and children withglasses in Loop 3. Loops 1 and 2 would not overlap becausea child is either a boy or a girl. I would put boys who wearglasses where Loops 1 and 3 overlap. I would put girls whowear glasses where Loops 2 and 3 overlap.

REFLECT: I chose the attributes: Square, big, and blue. Thespace where the loops for square and blue overlap is emptybecause I did not have a block that was blue and square. Thespace where the 3 loops overlap is empty because I did nothave a block that was big, blue, and square.

BigSquare

Blue

B

Y

B

B

B

R Y Y



What to Look For

Understanding concepts ✔ Students understand that objects can

be sorted using 3 attributes.

Applying procedures✔ Students can use 3 attributes to

sort objects.

✔ Students can use a Venn diagram with 3 loops to sort objects using 3 attributes.

Communicating✔ Students can describe the attributes

they used to sort objects.

What to Do

Extra Support: Have students sort blocks using 3 attributes,where all blocks have only 1 of the attributes. As students gainconfidence, gradually introduce blocks that have 2, then 3 of the attributes.Students can use Step-by-Step 2 (Master 5.16) to completequestion 5.

Extra Practice: Students can complete the Additional Activity,Guess My Labels (Master 5.12).Students can complete Extra Practice 1 (Master 5.25).

Extension: Challenge students to sort the vehicles in Lesson 1Practice question 5 using 3 attributes, so that all loops overlapand at least one vehicle has all 3 attributes.


Making ConnectionsMath Link: The pattern rule for this pattern is: green rectanglestanding up, green rectangle turned on its side, red circle, yellow triangle. The next block in this pattern would be the greenrectangle standing up.

Numbers Every DayFor 19 + 15, students could take from one to give to the other:19 + 1 + 14 = 20 + 14 = 34For 27 + 43, students could add on tens, then add on ones: 27 + 40 + 3 = 67 + 3 = 70For 48 + 26, students could take from one to give to the other:48 + 2 + 24 = 50 + 24 = 74

= 34= 70= 74


Interpreting Graphs

Key Math LearningPictographs and bar graphs contain information that can beused to answer questions.

LESSON ORGANIZER

Curriculum Focus: Interpret data from bar graphs andpictographs. (SP4, SP5)Teacher Materials� transparency of the graphs in Explore (optional)� transparency of 1-cm grid paperStudent Materials Optional

� Step-by-Step 3 (Master 5.17)� Extra Practice 2 (Master 5.26)

Vocabulary: pictograph, bar graphAssessment: Master 5.2 Ongoing Observations: Sortingand Data Management

40–50 min

L E S S O N 3


Ask students in which month they were born.Make a tally chart on the board to record theresults. Use a transparency of 1-cm grid paperon the overhead projector to create a bar graphto show the data.

Ask:• Which month has the most birthdays?

(March)• Which month has the fewest birthdays?

(August)• What else does this graph tell you?

(It tells me how many children in the class wereborn in the summer months.)

• If we wanted to show the data on apictograph, what symbol could we use torepresent each child? (We could use a birthday cake.)

Present Explore. Students should record all thethings they know from looking at each graph,as well as their answers to the questions inExplore.

Remind students to look at the symbol and thekey on the pictograph, and the scale on the bargraph to help answer the questions.

DURING Exp lore


Ask questions, such as:• What do the graphs show?

(The number of videos rented in one store on one day)• How do you know that comedy is the most

popular type of movie? (Comedy has the most symbols above it in thepictograph, and the longest bar in the bar graph.)

• Which type of movie is least popular?(Romance)

225 224 221

176 174 168

400 390 375

900 600 500


• What else do you know from looking at each graph? (I know how many of each type of video were rentedon that day. I can also find the total number ofvideos rented by adding the number of each type ofvideo rented.)

• How do you know how many kids’ videoswere rented from looking at the bar graph?(I find the bar for kids’ videos. I run my finger tothe end of the bar to see where it meets the bottomaxis. Fifty kids’ videos were rented.)

• How do you know how many science fiction videos were rented from looking atthe pictograph?(I add up the number of symbols above ScienceFiction. There are 4 symbols. Each symbol represents10 videos; 10 + 10 + 10 + 10 = 40. 40 science fictionvideos were rented.)

• Which graph is easier to read? Why? (I think the bar graph is easier to read because inthe pictograph, I have to count the number ofsymbols and then add that number of 10s.)

AFTER Connec t

Create and display a transparency of the graphsin Explore on an overhead projector. Invitevolunteers to share all the things they knowfrom looking at the graphs.Ask questions, such as:

• Which feature of the graph tells what thegraph shows? (The title)

• Do both graphs give the same information?(Yes, they just show it in different ways.)

• What would you know from the bar graph ifthe numbers at the bottom were missing? (I would know which type of movie was rented themost often. I would know the order of the movies,from least popular to most popular. I would notknow the exact numbers the bars represent.)

Early FinishersHave students find a bar graph in a newspaper or magazine,then list all the things they know from looking at the graph.

Common Misconceptions➤Students ignore the key on a pictograph and just count

the symbols.How to Help: In question 1, for example, have students modelthe symbols with counters. Students use 2 counters to representeach symbol, then add the counters.

ESL StrategiesStudents for whom English is a second language may havedifficulty writing and answering questions about the graphs. Pairthese students with strong English speakers.


Numbers Every DayStudents need to find the number to count by before finding themissing numbers. In the first pattern, students count back by 1s.In the second pattern, students count back by 2s. For the blanksto the left of the first given number, students will count on by 2.In the third pattern, students count back by 5s. For the blank tothe left of the first given number, students will count on by 5. Inthe last pattern, students count back by 100s.

Sample Answers1. I know more children have dogs than any other pet.

I know 4 children have no pets.I know 30 children have pets.

2. b) Dog, cat, panda, cheetah, elephant; or dog, cat, panda,elephant, cheetah

c) There is a total of 14 symbols in the pictograph. Eachsymbol represents 10 people. If I count by 10s fourteentimes, I get 140.

d) I know 10 people like elephants, 10 people like cheetahs,30 people like pandas, 50 people like dogs, and 40people like cats. I also know that the two favourite animalsmentioned most often are pets, and the others are all wildanimals.

3. d) How many children are in Grade 3? (Answer: 90 children)

Use the graphs in Connect to model how to readnumbers off each type of graph. Tell studentsthat when reading a bar graph, it is a good ideato use a ruler or a straightedge to find wherethe bars line up. Tell students that whenreading a pictograph, they must count on bythe number that each symbol represents.Ask:• How would the pictograph change if each

symbol represented 4 videos? (There would be fewer symbols beside each month.For example, December would have only 4 symbols.)

• What conclusions can you draw about theCheung family that are not directly seen onthe graph? (The Cheung family was very busy in Novemberand did not have time to watch many videos. They probably watched a lot of videos over theDecember holiday season.)

Prac t i ce


Students should note the difference in thesubjects of the graphs, as well as the scalesused. Students understand that the longest barrepresents the type of leaf the class collectedthe most of. They understand that to find thetotal number of leaves collected, they add thenumber of each type of leaf collected. Studentswrite a question that can be answered from thegraph, either directly or indirectly.


140

50

Brown Gray

10

25

4. a) The graph in question 3 is about eye colour and thenumbers on the side go up by 5s.The graph in this question is about leaves and the numberson the side go up by 2s.

b) Maple leaves; the bar for maple leaves is the tallest.c) 14 hickory leaves, 19 maple leaves, 12 chestnut leaves,

18 oak leaves, and 16 poplar leaves were collected; 14 + 19 + 12 + 18 + 16 = 79

e) 19 + 12 + 16 = 47; 47 leaves were not hickory or oak.f) How many more oak leaves were collected than

chestnut leaves? (Answer: 18 – 12 = 6; 6 more oak leaveswere collected.)

5. Each symbol represents 2 pizzas. A half-symbol representsone-half of 2, or 1. If I convert the pictograph to totals, I get 7 with cheese, 5 with 1 topping, and 8 with 2 toppings; Chart B matches the pictograph.

REFLECT: I think the pictograph is easier to read because thesymbols are large and they can easily be counted. I just haveto remember that each symbol does not always represent 1.Some of my friends think the bar graph is easier to readbecause they just have to look for the tallest or shortest bar.



What to Look For

Understanding concepts ✔ Students understand that pictographs

and bar graphs contain informationthat can be used to answer questions.

Applying procedures✔ Students can interpret data from bar

graphs and pictographs.

✔ Students can write, then answer aquestion about a graph.

✔ Students can make inferences basedon data displays.

✔ Students can obtain new informationby performing operations on data.

What to Do

Extra Support: Students having difficulty using the key of apictograph may benefit from modelling with counters. Forexample, if the key is one symbol represents 2, have students put2 counters on each symbol, then add the counters.Students can use Step-by-Step 3 (Master 5.17) to completequestion 4.

Extra Practice: Have students write 3 questions about thepictograph in question 5, then trade questions with a classmateand answer each other’s questions.Students can complete Extra Practice 2 (Master 5.26).

Extension: Challenge students to make a bar graph from theinformation shown on the pictograph in question 1 or 2. Theychoose an appropriate scale.


Chart B

47

19

79


Interpreting CircleGraphs

Key Math Learnings1. Circle graphs contain information that can be used to

answer questions.2. A circle graph shows parts of a whole.

LESSON ORGANIZER

Curriculum Focus: Interpret data from circle graphs.Student Materials Optional� calculators � Step-by-Step 4 (Master 5.18)

� Extra Practice 2 (Master 5.26)Vocabulary: circle graphAssessment: Master 5.2 Ongoing Observations: Sortingand Data Management

optional

L E S S O N 4


Invite students to look at the graphs on page204 of the Student Book. Tell students that inLesson 3, they interpreted data from bar graphsand pictographs. In this Lesson, they willinterpret data from circle graphs.

Ask:• What data do the graphs show?

(Favourite things to do after school)• How would you describe a circle graph?

(It is a circle divided into parts. It is like a pie thathas been cut into pieces.)

• How can you tell what the favourite thing todo is by looking at the bar graph? (It has the longest bar.)

• How can you tell what the favourite thing todo is by looking at the circle graph? (It has the largest part of the circle.)

Present Explore. Students should record all thethings they know from looking at each graph,as well as a question about each graph. Reviewhow to represent fractions with a circle. Draw acircle on the board. Model how to represent �

12

�

with a circle divided into 2 equal parts. Repeatwith other fractions, such as �

13

� and �14

�.

DURING Exp lore


Ask questions, such as:• What do you know from looking at the

bar graph? (We know the number of children thatchose each activity as their favourite. We can orderthe activities from most to least popular, and we canfind how many children were asked.)

• What do you know from looking at the circle graph? (We know how popular each activity is. We can orderthe activities from most popular to least popular.)

2, 4, 8, 16, 32, 64, 128, …

This lesson goes beyond the requirements of your curriculum.If you choose to do this lesson, allow 40–50 minutes.

Curr i cu lum Focus


• What question can you ask about the bar graph? (I can ask, “How many children chose readingbooks as their favourite activity?” The answer is 3.)

• What question can you ask about the circle graph? (I can ask, “What is the least popular after-schoolactivity?” The answer is doing homework.)

• How do you know that doing homework isthe least popular activity? (Doing homework has the shortest bar, and thesmallest part of the circle.)

• Which graph tells you more? (The bar graph)Why? (The bar graph gives actual numbers ofstudents. The circle graph shows the fraction of thestudents that do each activity.)

• Can you find how many children choseplaying with friends as their favouriteactivity by looking at the circle graph? (No, I can only see that it was the most popularactivity, and about �

13

� of the children chose it.)

AFTER Connec t

Invite volunteers to share their lists andquestions with the class.Ask:• Look at the circle graph. What fraction of the

children chose watching TV? (About one-fifth)• How do you know that fewer students chose

reading books than playing video games?(The part of the circle for reading books is smallerthan the part of the circle for playing video games.)

• By reading the circle graph only, can you tellhow many students chose doing homework?(No, the circle graph shows fractions of the totalnumber of children, not actual numbers of children.)

• By reading the bar graph, we know that thesame number of children chose watchingtelevision as chose playing sports. Do weknow this from looking at the circle graph?(It looks like the two parts of the circle are the samesize but it is difficult to know for sure.)

Early FinishersStudents use the circle graphs in Practice questions 1, 2, and 3.For each graph, students order the parts of the circle fromlargest to smallest.

Common Misconceptions➤Students think that parts of a circle graph represent whole

numbers instead of fractions.How to Help: Have students use fraction circles as benchmarksto which they can compare the circle graphs.➤Students have difficulty determining the relative size of parts of

the circle graph.How to Help: Have students trace a part of the circle graph andplace it on top of another part to determine the larger part.


Numbers Every DayStudents could use a calculator to do repeated addition, orrepeated subtraction, or repeated multiplication. Students shouldstart with an even number, then add, subtract, or multiply byanother even number to ensure that all numbers in the pattern areeven. For example, on the TI-108 calculator, students could enter2 and do repeated multiplication.

The pattern rule is start at 2. Multiply by 2 each time.The pattern is: 2, 4, 8, 16, 32, 64, 128, . . .

=====�2ON/C

Sample Answers1. I know that red is the most popular colour.

I know that yellow is the least popular colour.I know that everyone’s favourite colour was red, green,purple, or yellow.

2. a) This graph shows how Lynne spent her day.b) Lynne spent the most time sleeping. Lynne spent the least

time either on the school bus or inside at home.c) Lynne spent about one-quarter of her time at school.d) Sleeping and staying inside at home took about one-half of

her time.e) I know that playing outside at home and riding on the

school bus took about one-quarter of her time. I also knowthat Lynne did not go shopping with her family on that day.

3. a) This graph shows how children get to school.b) Most children get to school by bus; the bus has the largest

part of the circle.c) I know that more than half of the children either walk or

bike to school. I know that the least number of children goto school by car. I also know that no children fly to school.

d) Do more children walk to school or bike to school?(Answer: More children bike to school. The part of thecircle for biking is larger than the part of the circle forwalking.)

Use the graphs in Connect to emphasize that wecannot get actual numbers from a circle graph.Ensure students understand that the circlegraph represents one whole, and it givesinformation about how a whole is divided intoparts. Point out that each part of the circle islabelled and if a label does not fit inside a part,the label is placed outside the circle, with anarrow pointing to the part.

Ask:• When might you use a circle graph?

(When we do not need to know actual numbers; forexample, if we want to find people’s favourite brandof juice.)

Prac t i ce


Students understand that the largest part of thecircle represents the most popular way to get toschool. They can relate the parts of the circle tofractions and draw conclusions.


4. Sita saw the same number of ants and grasshoppers. Theparts of the circle graph for ants and grasshoppers should beequal in size. Sita saw the same number of bees and beetles.The parts of the circle graph for bees and beetles should beequal in size. Circle graph b fits this description.

5. No, the number of each bug type is divided into the total andis shown as part of a whole. The circle graph shows whatfraction of the bugs were bees, but it does not give an exactnumber.

6. I would draw a circle graph because I do not need to knowhow many classmates watch each show. I just want to find theclass’s favourite TV show.

REFLECT: A circle graph gives information about how a whole isdivided into parts. It is easy to compare and order the parts ofthe circle, to find the most and least popular item. However,you cannot read exact values from a circle graph.



What to Look For

Understanding concepts ✔ Students understand that a circle

graph shows parts of a whole.

✔ Students understand that circle graphscontain information that can be usedto answer questions.

Applying procedures✔ Students can interpret data from

circle graphs.

✔ Students can write, then answer, aquestion about a circle graph.

What to Do

Extra Support: Give students circles that have been dividedinto 2, 3, 4, 5, 6, and 8 equal parts, with each part labelled.Have students use these circles to estimate the sizes of the parts ofa circle graph.Students can use Step-by-Step 4 (Master 5.18) to completequestion 3.

Extra Practice: Have students cut out circle graphs fromnewspapers and magazines. Students write 3 questions abouteach graph, then trade graphs and questions with a classmate.They answer each other’s questions.Students can complete Extra Practice 2 (Master 5.26).

Extension: Challenge students to estimate the number ofchildren that chose each colour in Practice question 1, given that20 children were asked.



Drawing Pictographs

Key Math Learnings1. We use pictures and parts of pictures to represent data

in a pictograph.2. A key on a pictograph tells what each picture represents.3. The key for a pictograph depends on the amount of data

that will be shown in the pictograph.

LESSON ORGANIZER

Curriculum Focus: Draw pictographs using scales of many to one. (SP1, SP4)Student Materials Optional� rulers � Step-by-Step 5 (Master 5.19)

� Extra Practice 3 (Master 5.27)Vocabulary: tally mark, tally chart, keyAssessment: Master 5.2 Ongoing Observations: Sortingand Data Management

40–50 min

L E S S O N 5


Invite students to discuss the types of moviesthey like to watch. Make a list of the differenttypes of movies on the chalkboard. Havestudents come up to the board and draw a tallymark beside the type of movie they like best.Remind students that the tally marks should begrouped in 5s. Ask:• What is the most favourite type of movie?

(Science fiction) How do you know?(It has the most tally marks.)

• What is the least favourite type of movie?(Mystery) How do you know?(It has only 1 tally mark.)

Present Explore. Ensure students understand thatthey are to choose a picture as a key and thateach picture must represent more than 1 movie.Remind students that they should use the tallychart on the board and that they should recordboth their questions and answers.

Ask:• What picture could you use in your

pictograph? (We could use a videotape or a movie reel.)

• Why do we let 1 picture represent more than1 movie? (So that we do not have too many symbols on ourpictograph. It would be too hard to read.)

DURING Exp lore


Ask questions, such as:• What title did you give your pictograph?

(Our Favourite Movies)• What did you write down the side of your

pictograph? (We wrote the different types of movies.)

• What picture did you choose? (We chose a movie reel.)

Numbers Every DayFor 4 � 7, students could think addition; 4 + 4 + 4 + 4 + 4 + 4 + 4 = 28. For 6 � 6, students couldmake an array of 6 rows of 6; 6 � 6 = 36. For 4 � 6, studentscould skip count on a number line. Start at 0. Count on by 6sfour times: 6, 12, 18, 24; 4 � 6 = 24. For 5 � 4, studentscould skip count on a number line. Start at 0. Count on by 4sfive times: 4, 8, 12, 16, 20; 5 � 4 = 20.


• What did you let each picture represent? (We let 1 movie reel represent 2 movies.) How did you decide? (All the types of movies had less than 10 tallymarks and it is easy to divide the reel in half toshow 1 movie.)

• Did you have to use one-half of a picture?(Yes, comedy movies had 3 tally marks, so we used 1 reel and 1 half-reel to show 3.)

• What questions can you ask about your graph? (I can ask, “What type of movie do your classmateslike best?” “What type of movie do your classmateslike least?” “How many of your classmates likecomedy movies?” and “How many students are inyour class?”)

Watch to ensure students understand that thepicture they choose should represent more than1 movie.

AFTER Connec t

Invite volunteers to share their graphs andquestions with the class. Have them discuss thedifferent parts of the pictograph. Tell studentsthat it is important to include a title so thatpeople know what has been recorded.Introduce the term key. Tell students that a keytells us what each picture represents.Ask questions, such as:• How did you decide on the key?

(Most of the types of movies had an even number of tally marks, so we decided to let 1 picturerepresent 2 movies.)

• What does a half-picture represent on yourpictograph? (Since 1 picture represents 2 movies, a half-picture represents 1 movie.)

• Did anyone else use a different key? (Yes, we used 1 picture to represent 5 movies. Wehad to use a picture that could be easily divided into5 parts.)

Alternative ExploreMaterials: coloured countersHave each student pick one counter of his or her favouritecolour. Each student places his or her counter on the teacher’sdesk. Have volunteers pile counters of the same colour, thencount the number of each colour. Record the results on theboard. Students make a pictograph to represent the data.Students can group the counters to help them find what onepicture could represent.

Early FinishersHave students draw pictographs to represent the data in the 2 charts in the Unit Launch.

Common Misconceptions➤Students always use the key 1 picture = 2 items.How to Help: Encourage students to look for patterns in thenumbers. Suggest they count on by 2s, 5s, and 10s to see whichcounting has the most hits. The number you count on by that hasthe most hits would probably make a good key.


Sample Answers1. a) b) Yoshi included “Other” in his

list to include classmates whohad a favourite fruit that wasnot listed.

d) I know Yoshi asked 36 classmates. I know the same numberof children liked apples as did “other” fruits.

2. a) Fasil asked his classmates for their favourite pet. He gavethem 4 choices: cat, fish, bird, dog. This is his tally chart.

b) c) From the graph, I can tell thedog was the most popular petand the bird was the leastpopular. I know Fasil asked 45 classmates for theirfavourite pet.

3. a) b) I know that soccer is the mostpopular recess game andhopscotch is the least popular. I know there are 52 students inthe two Grade 3 classes.

c) I think the results would be similar because we are also aGrade 3 class and our recess activities are the same. Thenumber of children asked will be fewer, but I still thinksoccer will be the favourite.

SkippingTag

HopscotchSoccer

Hide and Seek

Our Favourite Recess Game

represents 2 children

CatFishBirdDog

Our Favourite Pet


Pet Tally Number of Children

CatFishBirdDog

12114

18

IIII IIII IIIIII IIII IIIIIIIII IIII IIII III

AppleOrangeBanana

PearStrawberry

Other

Our Favourite Fruit


Discuss the data and pictograph in Connect.

Ask:• How would the pictograph look if 1 ice

cream cone represented 1 child? (There would be twice as many ice cream conesymbols and the graph would be harder to read.)

• If 1 ice cream cone represented 5 children,would you still be able to use the samecone? Why? (No, the symbol does not divide into 5 equal parts.)

Elicit from students that a many-to-one key isuseful when you have a large set of data. Tell students that they should keep the pictures simple and ensure that they can easily be divided.

Prac t i ce

Encourage students to use rulers when drawingtheir pictographs.


Students examine the chart to see that a key ofone-to-five or one-to-ten is suitable. Studentsunderstand that if they choose a key of one-to-ten, they must choose a picture that can easilybe divided into 2 equal parts, as all numbersare divisible by 5; 10 � 5 = 2. Students shouldinclude a title, labels, and a key on theirpictographs.


Orange Pear

4. a) b) I chose the key 1 picturerepresents 5 children becausewhen I counted on by 5s, I hitall the numbers.

c) I know more people wear glasses in Grade 4 than in anyother grade. I know fewer Grade 2 students wear glassesthan in any other grade. I know 125 students are inGrades 1 to 6. I know that from least to greatest, 5 Grade 2 students, 10 Grade 6 students, 15 Grade 1students, 25 Grade 3 students, 30 Grade 5 students, and 40 Grade 4 students wear glasses.

d) Which 2 grades have the same number of children whowear glasses as Grade 5? (Answer: Grades 2 and 3: 5 + 25 = 30)

5. a) b)

c) When the key was changed so that 1 picture represented10 children, I had fewer pictures on my pictograph.

d) Graph a is easier to read because I did not have to useany half-pictures.

REFLECT: To decide what key to use, I count on by 2s, 5s, and10s to see which counting hits the most numbers in the data.The number I count on by that has the most hits is probably a good key.

Grade 1Grade 2Grade 3Grade 4Grade 5Grade 6

Children Who Watched the Game



Children Who Watched the Game



Children Who Wear Glasses




What to Look For

Understanding concepts ✔ Students understand that pictures and

parts of pictures are used to representdata in a pictograph.

✔ Students understand a key on apictograph tells what each picturerepresents and the key depends on theamount of data that will be shown.

Applying procedures✔ Students can select a key to represent

a set of data in a pictograph.

✔ Students can draw a pictograph thatincludes a title, labels, and a key.

What to Do

Extra Support: Students having difficulty finding a key maybenefit from modelling the data with counters. Students cangroup the counters to help them find a suitable key.Students can use Step-by-Step 5 (Master 5.19) to completequestion 4.

Extra Practice: Students can complete the Additional Activity,Colour Count (Master 5.13).Students can complete Extra Practice 3 (Master 5.27).

Extension: Have students survey their classmates to find theirfavourite flavour of juice. Students should record the results in atally chart, then make a pictograph to display the results.


= 28

= 20= 24= 36


Drawing Bar Graphs

Key Math Learnings1. A bar graph shows data using bars on a grid. A bar graph

has both a horizontal and a vertical axis, which are labelledto tell what data they display.

2. The scale is the number of items each square on a bar graphrepresents.

3. The scale of a bar graph is chosen to best display the data.

LESSON ORGANIZER

Curriculum Focus: Draw bar graphs using scales of many to one. (SP1, SP3)(SS30)Teacher Materials� 1-cm grid transparency (PM 20)Student Materials Optional� 1-cm grid paper (PM 20) � Step-by-Step 6 (Master 5.20)� rulers � Extra Practice 3 (Master 5.27)� Calendars (Master 5.10)Vocabulary: scale, horizontal axis, vertical axisAssessment: Master 5.2 Ongoing Observations: Sortingand Data Management

40–50 min

L E S S O N 6


Display a transparency of 1-cm grid paper onthe overhead projector. Draw twoperpendicular lines on grid lines to representthe axes. Tell students, as you model, thatwhen they draw a bar graph they shouldinclude a title and labels, and they shouldthink about the number of items each squareon the bar graph should represent.

Remind students of the keys they used for thepictographs in Lesson 5. Encourage students tolet one square represent more than 1 item onthe bar graph.

Present Explore. Ensure students understand theyshould use grid paper and a ruler so their workis neat and accurate. Tell students to look at thebar graphs in Lesson 3 to see what is expected.

DURING Exp lore


Ask questions, such as:• What title did you give your bar graph?

(What I Did on Saturday)• What is the greatest length of time shown on

the chart? (170 minutes)• Will 170 fit on the grid paper if you let

1 square represent 2 minutes? (No, our gridpaper is only 20 squares high, so if 1 squarerepresents 2 minutes, 170 minutes will not fit.)

• What did you let 1 square represent? (We let 1 square represent 10 minutes.) How did you decide? (All the minutes in thechart end in a zero. So, we decided to count on by10s and we were able to hit all the numbers.)

Your curriculum requires that students display data using rankordering (SP2). You can address this outcome by havingstudents order the activities in Explore from shortest to longestor vice versa before they draw the graph, so that the datacan be displayed using rank ordering.

Curr i cu lum Focus


• What label did you put along the bottom ofthe graph? (Activity) Along the side? (Time in Minutes)

• What do you know from looking at the graph? (We know that Anna spent the most time watchingTV and the least time playing video games. Bylooking at the lengths of the bars, we were able toorder the activities from the greatest to least amountof time: watching TV, listening to music, reading forfun, watching videos, using the computer, playingvideo games.)

• How is your graph the same as your classmate’s? (Both graphs have the same title and labels, and thenumbers on the sides are the same. The bars foreach activity are the same length.) How is your graph different? (The bars on my graph are not as wide and theyhave been drawn in order from tallest to shortest.)

AFTER Connec t

Invite volunteers to share their graphs. Discussany similarities and differences among thegraphs. Introduce the term scale as the numberof items each square on a bar graph represents.Point to the horizontal axis and the vertical axis and tell students these are thenumber lines along the edges of the graph. We label each axis to tell what data it displays.

Ask:• What scale did you use?

(We used the scale 1 square represents 10 minutes.)• Did anybody try to use a different scale?

(Yes, we tried letting 1 square represent 5 minutes,but some of the bars would not fit on the paper.)

• How would the graph change if you used thescale 1 square represents 20 minutes? (The bars would be shorter.)

Early FinishersHave students look through the sports section of the newspaperfor data, such as the number of wins by baseball teams. Studentsdisplay the data in a bar graph.

Common Misconceptions➤Students choose a scale that is too small and some bars do not

fit on the grid paper.How to Help: Have students look at a sheet of 1-cm grid paper.Point out that there are only 20 grid squares that run the length of the paper. So, no bar on the grid can be taller than 20 squares. Students should choose a scale so the heights of all bars are 20 grid squares or less.

ESL StrategiesStudents for whom English is a second language may have difficulty with the words “horizontal” and “vertical.” Have students write these words on 2 index cards, then draw an arrow from left to right beside the word horizontal, and an arrow from top to bottom beside the word vertical.Students can use these cards for reference.


Numbers Every DayStudents can count on or use multiplication and division.

Sample Answers1. a) b) Most of Stefan’s candies were

red. Stefan had the fewestnumber of brown candies.Stefan had no black candies.

2. a) b) Yes, the graphs matchbecause we both usedthe same scale. But, I drew a verticalgraph, and myclassmate drew ahorizontal graph.

d) He or she probably lives closest to the school because ittakes this child the least amount of time to get there. But, itis also possible that he or she runs to school and does notlive closest to the school.

3. a) b) 40 letters; I usedthe names: BillLee, Mary Elb, EveLam, Larry Ball,Lea Ma, Jim Ray

e) How many of the letters are vowels? (Answer: There are 7 As, 6 Es, and 2 Is: 7 + 6 + 2 = 15. There are 15 vowels.)

Letters in My Classmates' Names

Nu

mb

er o

f T

imes

Let

ter

Ap

pea

rs 12

10

8

6

4

2

0

LetterA B E I J L M R V Y

How Long It Takes to Get to School

Nu

mb

er o

f C

hild

ren

8

7

6

5

4

3

2

1

0

Time in Minutes5 10 15 20 25 30 35 40 45

Stefan's Candy

Nu

mb

er o

f C

and

ies

Brown

16

14

12

10

8

6

4

2

0

Red

Yellow

Blue

Orange

Green

Colour

Tell students that once they have chosen a scale,there are 2 ways to find the number of squaresin each bar on the graph. Use the example inConnect to show students both methods.

Point out that a bar graph may be drawnvertically or horizontally. The bar graph in theUnit Launch is a horizontal bar graph. Thegraphs in this lesson are vertical bar graphs.

Prac t i ce

Question 4 requires Calendars (Master 5.10).Have 1-cm grid paper (PM 20) and rulersavailable for all questions.


Students choose an appropriate scale to representthe data. They draw a bar graph to show the datain their tally chart, then answer questions aboutthe data. Students write a question that can beanswered using the bar graph.


2 children

8

15

7

18

6

To give students practice in displaying data using rankordering, suggest that students order the data inquestions 1 and 3 before drawing their graphs.

Curr i cu lum Focus

4. a)

d) I know the same number of students have a birthday inJanuary as in September.

5. b) c) I know the cheetah is thefastest animal. The human isthe slowest of the animals. Allthe other animals are fasterthan humans. The quarterhorse and the lion have aboutthe same speed.

REFLECT: Bar graphs and pictographs are similar in that theyboth represent data. A pictograph uses a key and smallpictures to represent the data. A bar graph is drawn on grid paper and uses bars to represent the data.

Top Speeds of Some Animals

Sp

eed

s in

Kilo

met

res

per

Ho

ur

120

110

100

90

80

70

60

50

40

30

20

10

0

Human

Greyh

ound

Quarte

r hor

seLio

n

Canad

a go

ose

Cheet

ah

Animal

Our Birthdays

Nu

mb

er o

f S

tud

ents

10

8

6

4

2

0

Month

Janu

ary

Febru

ary

Mar

chApr

ilM

ayJu

ne July

Augus

t

Septe

mbe

r

Octobe

r

Novem

ber

Decem

ber



What to Look For

Understanding concepts ✔ Students understand that a bar graph

shows data using bars on a grid.✔ Students understand that the scale is

the number of items each square on abar graph represents.

Applying procedures✔ Students can choose an appropriate

scale to represent data in a bar graph.✔ Students can draw a bar graph to

display a set of data, usingappropriate labels.

✔ Students can display data in more thanone way, using rank ordering.

What to Do

Extra Support: Students can complete the Additional Activity,Boys or Girls? (Master 5.14).Students can use Step-by-Step 6 (Master 5.20) to completequestion 3.

Extra Practice: Have students draw bar graphs using thecharts from questions in Lesson 5, pages 210 and 211.Students can complete Extra Practice 3 (Master 5.27).

Extension: For each question in Practice, have students use adifferent scale to draw a second graph.


6050

1101008080

March November

5

A, E, I; B, J, L, M, R, V, YL; J, V


Strategies Toolkit

Key Math LearningThe strategy “solve a simpler problem” can be used to solvemany problems.

LESSON ORGANIZER

Curriculum Focus: Interpret a problem and select anappropriate strategy. (PR1)Student Materials� counters� play money (coins) (PM 27)Assessment: PM 1 Inquiry Process Check List, PM 3 Self-Assessment: Problem Solving

40–50 min

L E S S O N 7


Present Explore. Have play money available forstudents to model the problem. Encouragestudents to think about what strategy they willuse before they begin.

DURING Exp lore

Ongoing Observations: Observe and Listen

Ask questions, such as:• How could Shane have paid for the

comic book?(He could have paid with 1 quarter.)

• How did you solve the problem? (We used the strategy “use a model.” We put playnickels, dimes, and quarters on the desk. Wegrouped the coins into different piles. Each pileadded up to 25¢.)

• How many different ways did you find? (4 ways: 5 nickels; 3 nickels and 1 dime; 1 nickeland 2 dimes; 1 quarter.)

AFTER Connec t

Invite volunteers to share their strategies forsolving the problem.

Use the problem in Connect to introduce thestrategy “solve a simpler problem.” Ask:• How many different ways could Amy pay for

the pencil? (9 ways: 2 dimes; 1 dime and 2 nickels; 1 dime, 1 nickel, and 5 pennies; 1 dime and 10 pennies; 4 nickels; 3 nickels and 5 pennies; 2 nickels and 10 pennies; 1 nickel and 15 pennies; 20 pennies.)

• How could you have solved this problemanother way? (I could have made a table and found all the combinations of coins that had 2 dimes, then 1 dime, and then 0 dimes.)

Prac t i ce

Have play money (coins) (PM 27) available forquestion 1. Have coloured counters available forquestion 2.

9 ways

4 ways

Sample Answers1. 2 quarters and 1 nickel; 5 dimes and 1 nickel; 1 quarter,

2 dimes and 2 nickels; 1 quarter and 3 dimes2. I can make 7 different pizzas: pepperoni; mushroom; green

pepper; pepperoni and mushroom; pepperoni and greenpepper; mushroom and green pepper; pepperoni, mushroom,and green pepper

3. I found 7 numbers: 23, 34, 45, 56, 67, 78, 89

REFLECT: I remember when I went to the store to buy a smallbag of potato chips. I had a lot of coins in my pocket and I wanted to use as many of them as I could. I paid for thechips, which cost 87¢, with 1 quarter, 3 dimes, 5 nickels, and 7 pennies.



What to Look For

Understanding concepts ✔ Students understand that solving a

simpler problem is a strategy to solvemany problems.

Problem Solving✔ Students can select an appropriate

strategy to solve a problem.

Communicating✔ Students can describe their strategy

clearly, using appropriate language.

What to Do

Extra Support: In Practice question 3, suggest students writedown all the numbers between 20 and 90, then cross outnumbers that do not fit the description.

Extra Practice: Have students write problems similar to thequestions in Practice for others to solve.

Extension: Challenge students to solve each of the Practicequestions using a different strategy. They check to see that theiranswers are the same each time.

Recording and ReportingPM 1 Inquiry Process Check ListPM 3 Self-Assessment: Problem Solving

Early FinishersHave students repeat Explore. This time Shane bought a usedcomic book for 30¢.(There are 5 possible ways.)

Common Misconceptions➤Students miss combinations of coins that total a given amount.How to Help: Use the Explore problem as an example.Encourage students to use an organized approach. Suggeststudents start with 5 nickels, then decrease the number of nickelsby 1 each time to ensure they do not miss any combinations.


7

7


Collecting Data

Key Math Learnings1. Data are facts or information collected to learn about people

or things.2. Data can be recorded in tally charts and tables, and shown

in graphs.3. Data can be collected through questions.

LESSON ORGANIZER

Curriculum Focus: Collect and organize data. (SP1, SP3)Student Materials Optional� 2-column charts (PM 17) � 1-cm grid paper (PM 20)� metre sticks � Step-by-Step 8 (Master 5.21)� measuring tapes � Extra Practice 4 (Master 5.28)� rulers� calculatorsAssessment: Master 5.2 Ongoing Observations: Sortingand Data Management

40–50 min

L E S S O N 8


Initiate a discussion about collecting data.

Ask:• Why would someone want to collect data?

(To learn about people)• How could you collect data?

(By asking questions or taking measurements)• How could you record the data that

you collect? (I could use a table or a tally chart.)

Present Explore. Distribute a metre stick to eachgroup of 3 students. Invite a volunteer to sit in achair at the front of the classroom. Use a metrestick to model how to measure the distancefrom the student’s knee to the ground. Remindstudents that they should round each length tothe nearest centimetre. For example, if a lengthis between 36 cm and 37 cm, but closer to 37 cm, the length would be rounded to 37 cm.

DURING Exp lore


Ask questions, such as:• How did you record your data?

(We used a table. We recorded student names incolumn 1. We then recorded the correspondinglength in column 2, beside each name.)

• What did you do if a length was, forexample, 34�

12

� cm? (We rounded it up to 35 cm.)

• How do you know whose knee is farthestfrom the ground? (We looked at the lengths in the table. The studentwhose knee is farthest from the ground has thelongest length.)

• Whose knee is closest to the ground? Howdo you know? (Ruby’s; the distance from her knee to the groundwas the shortest length.)

Making ConnectionsAt Home: I wanted to know my family’s favourite day of theweek. I asked, “What is your favourite day of the week?” I foundmost of my family prefers Saturdays.


Using only the rounded measurements, ask:• Whose knees are farther from the ground

than yours? (My knees are 35 cm from theground. Any student with a length greater than 35 cm would have knees farther from the groundthan mine.) Closer to the ground? (Those students with a distance less than 35 cm.)

AFTER Connec t

Invite volunteers to share their results with theclass. Tell students that to learn about people andthings, we collect data. Use Connect to introducethe questions that we use to focus our study.

Ask:• Why do we record data in tally charts

or tables? (To keep track of the answers we get to our questions)

• What question could we ask to find out theclass’ favourite pizza topping?(What is your favourite pizza topping?)

Tell students that to include the answers of allpeople asked, it is often necessary to include“Other” as a possible answer choice. Ensurestudents understand that when recording datain tally charts and tables, they should alwaysinclude a title and column headings. The totalnumber of tally marks should be the same asthe number of people asked.

Prac t i ce

Have 2-column charts (PM 17) available forquestions 1 to 4. Have 1-cm grid paper (PM 20)available for question 5. All questions require a ruler.


Students record the data collected in a tallychart, then use the tally chart to create a table.Both the tally chart and the table shouldinclude a title and column headings. Studentsdraw conclusions from the data.

Alternative ExploreMaterials: metre sticks or measuring tapesHave students work in groups of three. Students use a metre stickor measuring tape to find each other’s height. They record thedata in a table, then combine their results with those of anothergroup. Students use the data collected to find the tallest andshortest student.

Early FinishersHave students display the data collected in Explore in a graph.

Common Misconceptions➤Students have difficulty choosing a question to ask, and ask a

question that has a yes or no answer.How to Help: Have students think about what they want to findout. For example, if the student wants to find out what pets theclass has, possible choices are: cat, dog, bird, fish, other. Havestudents think of a question that would be answered with one ofthese choices.


3, 9, 27, 81, 243, …

15 minutesBryan

Ruby

Right-handed

425

Right-handed; 25 > 4

Numbers Every DayStudents could do repeated multiplication, starting with an oddnumber. For example, on the TI-108 calculator, students couldenter:

The pattern rule is: Start at 3. Multiply by 3 each time.The pattern is: 3, 9, 27, 81, 243, . . .

=====�3ON/C

Sample Answers1. b) 45 is the greatest number of minutes on the board.3. a), b), c)

4. b) c)

d) I found out most of the children in my class like summer thebest. The fewest number of students like fall. More childrenlike summer than all the other seasons combined; 17 > 14

5. a) What is your b)

favourite colour?

REFLECT: The dairy might want to know the class’ favourite icecream flavours so when we go on a school trip to the dairy, thedairy will have enough of everybody’s favourite ice creams.

Our Favourite Colours

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Red

10

8

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2

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Blue

Green

Yellow

Other

Colour

Season Number of Children

SpringSummerFallWinter

4 17 3 7

Our Favourite SeasonSeason Number of Children

SpringSummerFallWinter

IIIIIIII IIII IIII IIIIIIIII II

What Is Being Measured Length

LegArmAround WaistAround HeadElbow to WristElbow to Shoulder

58 cm51 cm60 cm43 cm16 cm20 cm



What to Look For

Understanding concepts ✔ Students understand that data are

facts or information collected to learnabout people or things.

✔ Students understand that data can berecorded in tally charts and tables,and shown in graphs.

Applying procedures✔ Students can collect, then record, data

in tally charts and tables. They canshow the data collected in a graph.

Communicating✔ Students can describe their findings

clearly and precisely using appropriatelanguage.

What to Do

Extra Support: Have students fill in prepared tally charts.Students ask the given question and put tally marks beside theresponses they get.Students can use Step-by-Step 8 (Master 5.21) to completequestion 4.

Extra Practice: Students collect data outside the class, such asduring recess, at a dance class, or at a hockey practice. Studentsrecord the data and present their findings to the class.Students can also complete Extra Practice 4 (Master 5.28).

Extension: Students draw graphs to show the data collected inPractice questions 1, 2, and 4.


What pets do you have at home?What is your favourite flavour of ice cream?

What is your favourite TV show?

= 14

Summer


L E S S O N 9

Conducting a Survey

Key Math Learnings1. A survey is conducted to find out about something.2. A survey requires a question and possible answers.3. The results of a survey can be organized in a table or

on a graph.

LESSON ORGANIZER

Curriculum Focus: Conduct a survey to collect data. (SP1, SP3, SP4, SP5)Student Materials Optional� 3-column charts (PM 18) � Step-by-Step 9 (Master 5.22)� 1-cm grid paper (PM 20) � Extra Practice 4 (Master 5.28)� rulersVocabulary: surveyAssessment: Master 5.2 Ongoing Observations: Sortingand Data Management

40–50 min


Invite students to think about their answers tothe questions on page 221 of the Student Book.Point out that there are many possible answersfor 3 of the questions but only 2 possible answersfor the second question. Tell students that oftenthe answers to a question will differ, dependingon the group of people that are surveyed. Ask:• Do you prefer to watch sports or take part

in sports? (I prefer to take part in sports.)

• Do you think your grandparents wouldprefer to watch sports or take part in sports?(I think they would prefer to watch sports.) Why? (Because they are much older than me and they arenot as active)

Present Explore. Distribute 3-column charts (PM 18) to all groups. Have 1-cm grid paperavailable for those students who wish to makea bar graph.

DURING Exp lore


Ask questions, such as:• What topic did you choose?

(We chose colours each classmate is wearing.)• What question did you ask? (We asked, “What

colour are you wearing the most of today?”)• Who did you ask? (Our classmates)• What answers did you think you might get?

(Black, white, blue, red, green, and brown)• How did you record the answers?

(We recorded the answers in a tally chart.)• Which type of graph did you use to display

your data? (We used a bar graph.)• What did you find out?

(Most of our classmates were wearing blue.)• How can you check that each of your

classmates was asked the question? (The total number of tally marks should equal thenumber of students in the class.)

Numbers Every DayStudents could take from one to give to the other; add to match theones digits, then subtract; take away tens, then take away ones.

42

Sample Answers1. b) I know most children spend between 11 and 20 minutes

doing homework. I know the least number of childrenspend more than 30 minutes doing homework.

2. a) Our Favourite After-School Activities

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Play with

brother/

sister/f

riend

14

12

10

8

6

4

2

0

Read

Play with

pets

Do homework

Use th

e computer

Activity

Other

Activity Tally

Play with brother/sister/friendReadPlay with petsDo homeworkUse the computerOther

10

63283

Number ofStudents

IIII IIII

IIII IIIIIIIIII IIIIII


Early FinishersHave students redraw the graphs in questions 2 and 3, this timechanging the type of graph.

Common Misconceptions➤Students have difficulty choosing possible answers for

their question.How to Help: Have students ask their question to 3 or 4 class-mates. Students think about the answers they are given, then usethese answers as a guide when writing the possible answers tothe question.➤Students have difficulty keeping track of tally marks.How to Help: Remind students to group their tally marks in 5s,as this will make it easier to total them. Total tally marks shouldequal the total number of persons surveyed.


AFTER Connec t

Invite volunteers to share their charts andgraphs. Discuss the results of their surveys.

Ask:• Were your results what you expected them to

be? (Yes, most people wear jeans to school and theyare usually blue.)

• Would the results be the same if we askedthe question at your mom’s work? (Probably not, because most people do not wearjeans to work.)

Review the example in Connect. Tell studentsthat when we ask a question to find out aboutsomething, we are conducting a survey. Tellstudents it is often a good idea to give a list ofchoices with a question to limit the number ofpossible answers. The last choice is usually“Other” to include those answers that are notcommon.

Point out that the tally chart has beenextended. A third column has been added toshow the numbers that the tally marksrepresent. This saves having to make both atally chart and a table.

Prac t i ce

Have 3-column charts (PM 18) and rulersavailable for all questions. Have 1-cm gridpaper available for questions 2 and 3.


Students conduct a survey, then record theirdata in a chart and on a graph. Students drawconclusions from the survey, then write 2questions that can be answered using theirdata. Students’ questions and answers willindicate their understanding of the data.

c) We both have the same after-school activities and bothgraphs use the same scale. Our graphs look differentbecause I drew a vertical bar graph and Angie drew ahorizontal bar graph. Angie’s graph shows playing withpets is least popular. My graph shows doing homework isleast popular. My graph also shows 6 possible activitieswhile Angie’s graph shows 5 activities.

3. a)

b) I found most of my classmates wear digital watches. I alsofound a few students do not wear a watch at all.

c) How many more students wear digital watches thanwatches with hands? (Answer: 5 students; 14 – 9 = 5)How many students are in the class? (Answer: 26 students;14 + 9 + 3 = 26)

REFLECT: I conducted a survey to find when most of myclassmates go to sleep at night. I asked the question, “At whattime do you usually go to bed?” I found most of my classmatesgo to bed at 8:00 p.m. Next time, I would ask, “At what timedo you go to sleep?” I found many students go to bed andread or watch TV before they go to sleep. The results of mysurvey were not accurate.

Our Watches

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Digital

16

14

12

10

8

6

4

2

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With

hands

No watch

Type of Watch

Watch Tally

DigitalWith HandsNo Watch

14 9 3

Number ofStudents

IIII IIII IIIIIIII IIIIIII



What to Look For

Understanding concepts ✔ Students understand that a survey is

conducted to find out about something.

Applying procedures✔ Students can create a survey question

with possible answers.

✔ Students can show the data collectedin a chart and on a graph.

Communicating✔ Students can describe the results of a

survey and write what they learnedfrom the results.

What to Do

Extra Support: Have students use a question with only 2 possible answers to gain confidence, for example, yes or no, or boy or girl.Students can use Step-by-Step 9 (Master 5.22) to completequestion 3.

Extra Practice: Have students conduct surveys for the topicsthey did not choose in Explore.Students can complete Extra Practice 4 (Master 5.28).

Extension: Have students conduct the survey in question 1 in agrade 6 class, then compare their findings.

Recording and ReportingMaster 5.2: Ongoing Observations:Sorting and Data Management

= 142= 26

= 29

= 440

29

1231

IIIIII IIIIIIII IIII IIIIII

36 Unit 5 • Show What You Know• Student page 224

LESSON ORGANIZER

Student Materials� Venn diagrams (PM 28)� 3-Loop Venn Diagram (Master 5.8)� metre sticks or measuring tapes� 2-column charts (PM 17)� 1-cm grid paper (PM 20)Assessment: Masters 5.1 Unit Rubric: Sorting and Data Management, 5.4 Unit Summary: Sorting and Data Management

40–50 min

S H O W W H AT Y O U K N O W

2. c) The sparkle donut was bought twice as often as thesugar donut OR the sugar donut was bought twice asoften as the plain donut or the cream donut.

d) I know 55 donuts were sold at the bake sale.3. a) The second circle graph; from the bar graph, I know

100 stickers were collected, and 50 of the stickerswere collected by Samia. Since 50 is one-half of 100,Samia should take half of the circle. I also know Nazcollected 25 stickers. Since 25 is one-quarter of 100,Naz should take one-quarter of the circle. Based onthis information, the second circle graph shows thesame data as the bar graph.

b) The scale on the bar graph is one square represents 5 stickers.

d) No, the number of stickers each child collected isdivided into the total to get their part of a whole. Thecircle graph shows what fraction of the stickers werecollected by Samia, but it does not give an exactnumber.

e) Which two children collected the same number ofstickers? (Answer: Megan and Bobby)

4. a) b)

Distances from Elbow to Fingertip

c) I chose to draw a bar graph because it is easier tocompare the measurements. The tallest bar wouldrepresent the longest measurement, while the shortestbar would represent the shortest measurement.

Child LengthLinda 22 cmArun 21 cm

Shakel 24 cmAash 20 cm

Raymond 22 cmBetty 25 cm

Plain and cream

15

Sparkle

Sample Answers1. a) I chose the attributes:

Buckles and black toe.

b) I used a Venn diagram. I think it is easier to sort with aVenn diagram because I just have to put the shoes into thecorrect loops.

c) I chose the attributes: Closed toe, no buckles, and high heel.

No BucklesClosed Toe

High Heel

Black ToeBuckles

d) I know Betty has the greatest distance between her elbow andher fingertip. I know Aash has the shortest distance betweenhis elbow and his fingertip. I also know Linda and Raymondhave the same distance between their elbows and theirfingertips.

Distances From Elbow to Fingertip

Len

gth

in C

enti

met

res

26

24

22

20

18

16

14

12

10

8

6

4

2

0

Linda

Arun

Shake

l

Aash

Raym

ond

Betty

Child

Unit 5 • Show What You Know • Student page 225 37


What to Look For

Reasoning; Applying concepts✔ Question 2: Student understands graphs contain information that can be used to answer questions.

Student can obtain new information by performing operations on data.

Accuracy of procedures✔ Question 1: Student can use 2 and 3 attributes to sort objects.✔ Question 3: Student can compare information shown on two different graphs.

Problem Solving✔ Question 4: Student can collect, then show, data in a chart and on a graph.

Student can make inferences based on data displayed in a graph.

Recording and ReportingMaster 5.1 Unit Rubric: Sorting and Data ManagementMaster 5.4 Unit Summary: Sorting and Data Management

50 stickers

Samia

Have students turn to the Unit Launch on pages190 and 191 of the Student Book.

Use the lists of Learning Goals and Key Wordsto review the key learnings of the unit. Tellstudents they will use the skills they havelearned in this unit to complete the UnitProblem.

Present the Unit Problem. Have volunteers readthe instructions aloud. Answer any questionsstudents might have.

Invite a student to read aloud the Check List.Explain that these are the criteria against whichtheir work will be assessed. Have studentswork in groups of 4.

Ensure students understand they are to providepossible answers to their survey question.Remind students to include a scale on a bargraph, and a key on a pictograph.

Encourage students to share the work equally.For example, one student could record thequestion and possible answers, a secondstudent could record the results in a chart ortable, a third student could graph the data, anda fourth student could write an explanation ofwhat they found out.

Suggest that early finishers display their dataon both a bar graph and a pictograph.

38 Unit 5 • Unit Problem • Student page 226

Using Data to Answer Questions

LESSON ORGANIZER

Student Grouping: 4Student Materials� 1-cm grid paper (PM 20)� 2-column charts (PM 17)� 3-column charts (PM 18)� rulersAssessment: Masters 5.3 Performance Assessment Rubric:Using Data to Answer Questions, 5.4 Unit Summary: Sortingand Data Management

40–50 min

U N I T P R O B L E M

Sample ResponseWe asked the question, “What is your favourite lunch?” We gave 6 possible answers: Pizza, hot dog, macaroni and cheese, tacos, spaghetti, other.We recorded the results in this tally chart:

Favourite Lunch Tally Number

Pizza //// /// 8

Hot dog //// 5

Macaroni and cheese /// 3

Tacos //// 4

Spaghetti //// // 7

Other /// 3

We graphed the data in a bar graph: We chose the scale 1square represents 2students because when wecounted by 2s, we hit morenumbers in the chart thanwhen we counted by 5s.We found most Grade 3 students like pizza for lunch. Thelunches, from most to least favourite, are: pizza, spaghetti, hotdog, tacos, macaroni and cheese, other. Twice as many studentslike pizza as like tacos. The same number of students chosemacaroni and cheese as chose other. We added “other” as apossible answer to include any student whose favourite lunchwas not included in the possible answers. For example, Siew’sfavourite lunch was noodles, so she chose the answer “other.”

Reflect on the UnitData can be sorted using 2 or 3 attributes. I could use a chart ora Venn diagram to sort by 2 attributes, but I would use a 3-loopVenn diagram to sort by 3 attributes. I can show data in a tally chart or in a table, as well as on agraph. I could choose a key and draw a pictograph or I couldchoose a scale and draw a bar graph. Circle graphs can alsobe used to display data.

Our Favourite Lunch

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Pizza

Hot D

og

Mac

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i

and

Chees

eTa

cos

Spagh

etti

Other

Lunch

Unit 5 • Unit Problem • Student page 227 39


What to Look For

Understanding concepts ✔ Students understand that a survey can

be used to collect data.

Applying procedures✔ Students can write a survey question

with possible answers.

✔ Students can collect data, display thedata in a chart and on a graph, thendraw conclusions from the data.

Communicating✔ Students can explain their findings

clearly.

What to Do

Extra Support: Make the problem accessible.

Some students may have difficulty deciding on possible answersto their question. Suggest each member of the group answer thequestion first. This should give the group some ideas for possibleanswers.

Some students may have difficulty drawing a graph to representtheir data. Provide students with a blank grid that indicates wherethey should put the title and the axis labels. Remind students thatto determine a scale or key, they could count on by 2s, 5s, and10s to see which count gives the most hits.

Recording and ReportingMaster 5.3 Performance Assessment Rubric: Using Data to Answer QuestionsMaster 5.4 Unit Summary: Sorting and Data Management

Copyright © 2005 Pearson Education Canada Inc. 40

Evaluating Student Learning: Preparing to Report: Unit 5 Sorting and Data Management This unit provides an opportunity to report on the Statistics and Probability strand. Master 5.4: Unit Summary: Sorting and Data Management provides a comprehensive format for recording and summarizing evidence collected.

Here is an example of a completed summary chart for this Unit: Key: 1 = Not Yet Adequate 2 = Adequate 3 = Proficient 4 = Excellent

Strand: Statistics and Probability

Reasoning; Applying concepts

Accuracy of procedures

Problem solving

Communication Overall

Ongoing Observations 2 2 2 2 2 Strategies Toolkit (Lesson 7)

1 1

Work samples or portfolios; conferences

2 2 1 2 2

Show What You Know 2 2 2 2 2 Unit Test 3 2 2 not assessed 2 Unit Problem Using Data to Answer Questions

3 2 2 2 2

Achievement Level for reporting 2

Recording How to Report Ongoing Observations

Use Master 5.2 Ongoing Observations: Sorting and Data Management to determine the most consistent level achieved in each category. Enter it in the chart. Choose to summarize by achievement category, or simply to enter an overall level. Observations from late in the unit should be most heavily weighted.

Strategies Toolkit (problem solving)

Use PM 1: Inquiry Process Check List with the Strategies Toolkit (Lesson 7). Transfer results to the summary form. Teachers may choose to enter a level in the Problem solving column and/or Communication.

Portfolios or collections of work samples; conferences or interviews

Use Master 5.1 Unit Rubric: Sorting and Data Management to guide evaluation of collections of work and information gathered in conferences. Teachers may choose to focus particular attention on the Assessment Focus questions. Work from late in the unit should be most heavily weighted.

Show What You Know Master 5.1 Unit Rubric: Sorting and Data Management may be helpful in determining levels of achievement. #2 provides evidence of Reasoning; Applying concepts; #1 and 3 provide evidence of Accuracy of procedures; #4 provides evidence of Problem solving; all provide evidence of Communication.

Unit Test Master 5.1 Unit Rubric: Sorting and Data Management may be helpful in determining levels of achievement. Part A provides evidence of Accuracy of procedures; Part B provides evidence of Reasoning; Applying concepts; Part C provides evidence of Problem solving; all parts provide evidence of Communication.

Unit performance task Use Master 5.3 Performance Assessment Rubric: Using Data to Answer Questions. The Unit Problem offers a snapshot of students’ achievement. In particular, it shows their ability to synthesize and apply what they have learned.

Student Self-Assessment Note students’ perceptions of their own progress. This may take the form of an oral or written comment, or a self-rating.

Comments Analyse the pattern of achievement to identify strengths and needs. In some cases, specific actions may need to be planned to support the learner.

Learning Skills

PM 4: Learning Skills Check List Use to record and report throughout a reporting period, rather than for each unit and/or strand.

Ongoing Records

PM 10: Summary Class Records: Strands PM 11: Summary Class Records: Achievement Categories PM 12: Summary Record: Individual Use to record and report evaluations of student achievement over several clusters, a reporting period, or a school year. These can also be used in place of the Unit Summary.


Name Date

Unit Rubric: Sorting and Data Management Not Yet

Adequate Adequate Proficient Excellent


• selects, applies, and explains concepts associated with: – sorting objects and

data – collecting and

organizing data – displaying the same

data in more than one way

– interpreting data to make predictions and inferences

may be unable to apply or explain concepts associated with: – sorting objects and





partially able to apply and explain concepts associated with: – sorting objects and





able to apply and explain concepts associated with: – sorting objects and





in various contexts, appropriately applies and explains concepts associated with: – sorting objects and






• accurately collects and records data using measuring devises and printed/technology resources

• displays data using rank ordering

• transfers data to graphs accurately

• constructs graphs correctly, including labels, titles

limited accuracy; omissions or major errors in: – collecting and

recording data – rank ordering – transferring data to

graphs – constructing graphs

partially accurate; omissions or frequent minor errors in: – collecting and



generally accurate; few errors in: – collecting and



accurate and precise; no errors in: – collecting and



Problem-solving strategies

• chooses and carries out a range of data analysis strategies (e.g., tally charts, graphic organizers, grids, arithmetic operations, surveying, measuring) to solve simple problems and conduct simple inquiries

may be unable to use data analysis appropriately to solve simple problems and conduct simple inquiries

with limited help, uses some appropriate data analysis strategies to solve simple problems and conduct simple inquiries; partially successful

uses appropriate data analysis strategies to solve simple problems and conduct simple inquiries successfully

uses appropriate, often innovative, data analysis strategies to solve simple problems and conduct simple inquiries successfully

Communication

• explains reasoning and procedures clearly, including appropriate terminology (e.g., graph, tally, data, survey, most, least)

unable to explain reasoning and procedures clearly

partially explains reasoning and procedures

explains reasoning and procedures clearly

explains reasoning and procedures clearly, precisely, and confidently

• presents work clearly work is often unclear presents work with some clarity

presents work clearly presents work clearly and precisely

Master 5.1


Name Date

Ongoing Observations: Sorting and Data Management The behaviours described under each heading are examples; they are not intended to be an exhaustive list of all that might be observed. More detailed descriptions are provided in each lesson under Assessment for Learning.

STUDENT ACHIEVEMENT: Sorting and Data Management* Student Reasoning;

Applying concepts Accuracy of procedures

Problem solving Communication

Demonstrates and explains: – sorting and

classification of objects and data

– data collection procedures

– interpretations of graphs

Accurately: – sorts and cross-

classifies objects – collects and records

data – constructs graphs – interprets graphs

Uses appropriate strategies to conduct surveys

Presents work clearly Explains reasoning

and procedures clearly, including appropriate terminology

*Use locally or provincially approved levels, symbols, or numeric ratings.

Master 5.2


Name Date

Performance Assessment Rubric: Using Data to Answer Questions

Not Yet

Adequate Adequate Proficient Excellent


• offers an appropriate explanation of the graph and what they learned, may incorporate arithmetic operations to make comparisons (i.e., combine two or more categories)

unable to explain results; may be incomplete or offer misconceptions

partially explains the results; may be vauge or include some flawed reasoning

adequately explains the results

thoroughly and effectively explains the results; may show insights, offer predictions or generalizations


• accurately records data

• transfers data to graph accurately

• constructs graph correctly, including labels, titles

limited accuracy; omissions or major errors in: – recording data – transferring data to

graph – constructing graph

somewhat accurate; some omissions or minor errors in: – recording data – transferring data to


generally accurate; few minor errors in: – recording data – transferring data to


accurate and precise; no errors in: – recording data – transferring data to


Problem-solving strategies

• develops and presents a survey that includes an appropriate question, and strategies for collecting, recording, and graphing results

inappropriate strategies; does not include: – an appropriate

question – a practical method

for collecting and recording data

– an appropriate choice of graph or display

partially appropriate strategies; has flaws in planning for one or more of the following: – an appropriate

question – a practical method

for collecting and recording data


practical, appropriate strategies that include: – an appropriate

question – a practical method for

collecting and recording data


effective strategies, with some innovation or complexity, that include: – an appropriate

question – a practical method for

collecting and recording data


Communication • uses appropriate

mathematical terminology (e.g., graph, tally, data, survey, most, least)

uses few appropriate mathematical terms

uses some appropriate mathematical terms

uses appropriate mathematical terms

uses a range of appropriate mathematical terms with precision

• explains the interpretation of the graph clearly

does not explain the graph clearly

partially explains the graph; may be vague and somewhat unclear

explains the graph clearly

explains the graph clearly, precisely, and confidently

Master 5.3


Name Date

Unit Summary: Sorting and Data Management Review assessment records to determine the most consistent achievement levels for the assessments conducted. Some cells may be blank. Overall achievement levels may be recorded in each row, rather than identifying levels for each achievement category. Most Consistent Level of Achievement*

Strand: Statistics and Probability



Problem solving

Communication Overall

Ongoing Observations

Strategies Toolkit (Lesson 7)

Work samples or portfolios; conferences

Show What You Know

Unit Test

Unit Problem Using Data to Answer Questions

Achievement Level for reporting

*Use locally or provincially approved levels, symbols, or numeric ratings. Self-Assessment:

Comments: (Strengths, Needs, Next Steps)

Master 5.4


Name Date

To Parents and Adults at Home … Your child’s class is starting a mathematics unit on sorting and data management. In this unit, your child will:

• Use 2 and 3 attributes to sort objects and data. • Read and find information from pictographs, bar graphs,

and circle graphs. • Draw pictographs and bar graphs. • Collect and organize data. • Conduct a survey to collect data. • Display the results of a survey.

Data management is the collection and organization of data. Graphs and data are all around us, whether it be in advertising, in opinion polls, in newspapers to show trends or sports data, etc. Children learn to deal with this information by working with data from a young age. Your child will learn to interpret information from displays of data, and will begin to collect data for herself or himself. Here are some suggestions for activities you can do with your child. When you bring groceries home, have your child sort the groceries according to 2 or 3 attributes, for example, fruits, vegetables, and canned goods, OR refrigerated and non-refrigerated. Have your child help with the laundry by sorting the laundry in different ways, for example, light or dark, OR cotton, wool, or silk. Have your child conduct a survey at home to help make an important decision. For example, he or she could use a survey to decide what flavour of birthday cake to order for the next family birthday. Your child should write a question to ask family members, then conduct the survey and record the results.

Master 5.5


Name Date

Sorting by 2 Attributes Chart

Master 5.6


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Sorting by 2 Attributes Venn Diagram

Master 5.7


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3-Loop Venn Diagram

Master 5.8


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Practice Venn Diagram

Master 5.9


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Calendars

Master 5.10


Name Date

Additional Activity 1: Attribute Train

Work with a partner.

You will need Attribute Blocks and pencil crayons.

Take 15 Attribute Blocks each.

Put an Attribute Block in the centre of the table. Find a block that is different from the block on the table in only 1 way. Put the block next to the other block on the table to start a train.

Take turns. Find a block that is different from the last block in only one way. Add the block to the train.

Make the train as long as you can. To record it on paper, trace the blocks and colour them.

Take It Further: Repeat the activity. This time, change exactly 2 attributes each time.

Master 5.11


Name Date

Additional Activity 2 Guess My Labels Play with a partner.

You will need a Venn diagram with 2 loops, Attribute Blocks, and small cards. How to play: Player A

Choose 10 Attribute Blocks, then pick 2 attributes. Make label cards for each loop of the Venn diagram. Place each card face down beside its loop.

Sort the blocks using the Venn diagram.

Player B

Look at the sorting, then guess what the labels are. Turn over the cards to check.

A player gets 1 point for each label guessed correctly. The first player to get 10 points wins. Switch roles and repeat. Take It Further: Repeat the activity. This time, use 3 attributes and Venn diagrams with 3 loops.

Master 5.12


Name Date

Additional Activity 3 Colour Count Work alone.

You will need a small box or bag of coloured counters.

Sort the counters by colour. Count the number of each colour.

Record your results in a tally chart. Draw a pictograph to display your results.

Colour Number

Take It Further: Write 3 questions you can ask about your pictograph. Trade questions and pictographs with a classmate. Answer your classmate’s questions.

Master 5.13


Name Date

Additional Activity 4 Boys or Girls? Work with a partner.

You will need index cards, blue and green Snap Cubes, 1-cm grid paper, and a ruler. A green Snap Cube represents a girl. A blue Snap Cube represents a boy.

Write the words “Boys” and “Girls” on 2 index cards. Put the index cards face-up on the table.

Place 1 green cube on the “Girls” card for each girl in the class. Stack the cubes to make a tower.

Place 1 blue cube on the “Boys” card for each boy in the class. Stack the cubes to make a tower.

Make a bar graph. For each bar, colour the same number of squares as there are cubes.

Label the bars with the words on the index cards.

Take It Further: Draw another bar graph. This time use a scale of many-to-one.

Master 5.14


Name Date

Step-by-Step 1 Lesson 1, Question 5 Look at the vehicles shown on page 195 of the Student Book. Step 1 Use the attributes: Moves on the ground and moves through the air.

Label the loops of the Venn diagram. Which vehicle has both attributes? __________________________

Where will you put this vehicle? ____________________________

Sort the vehicles in the Venn diagram.

______________________ ______________________

Step 2 Choose 2 different attributes. _____________________________________________________

Label the loops of the Venn diagram. Sort the vehicles in the Venn diagram.

________________ ________________

Master 5.15


Name Date

Step-by-Step 2 Lesson 2, Question 5 Step 1 Choose 10 books from the classroom. Step 2 Make a list of attributes that the books might have. Think about the cover, the number of pages, and what the book is about.

_____________________________________________________ ______________________________________________________________

Step 3 Choose 3 attributes. Sort the books. Label each loop in the Venn diagram. Record your sorting.

Step 4 Explain how you sorted them.

_____________________________________________________ ______________________________________________________________ ______________________________________________________________

Master 5.16


Name Date

Step-by-Step 3 Lesson 3, Question 4 Step 1 What scale does this graph use? __________________________

What scale does the graph in question 3 use? ________________

Step 2 Which type of leaves did the class

collect the most of (has the highest bar)? ____________________ Step 3 How many hickory leaves were collected? _______

Maple? _______ Chestnut? _______

Oak? _______ Poplar? _______

How many leaves were collected in all?

_______ + _______ + _______ + _______ + _______ = _______ Step 4 How many leaves were hickory and oak? Show your work.

_______ + _______ = _______

Step 5 How many leaves were not hickory or oak? Show your work.

_______ – _______ = _______

Step 6 Write a question about this graph. _________________________ _____________________________________________________ Answer your question.

_____________________________________________________

Master 5.17


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Step-by-Step 4 Lesson 4, Question 3 A circle graph shows parts of a whole. Look at the circle graph on page 206. Step 1 Look at the title. What does this graph show?

_____________________________________________________

Step 2 Which part of the circle is the largest? _______________________

How do most children get to school? ________________________

Step 3 Which part of the circle is the smallest? ______________________

What else do you know? _________________________________ _____________________________________________________ _____________________________________________________

Step 4 Write a question about this graph.

_____________________________________________________ _____________________________________________________ _____________________________________________________

Step 5 Answer your question.

_____________________________________________________ _____________________________________________________

Master 5.18


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Step-by-Step 5 Lesson 5, Question 4 This table shows how many people in Grades 1 to 6 wear glasses.

Grade Children Who Wear Glasses

1 15 2 5 3 25 4 40 5 30 6 10

Step 1 Choose a key. (Will you count by 5 or 10?) ___________________

Choose a symbol. How many children will it represent?_____________

Step 2 Draw a pictograph.

Step 3 What grade has the most pictures? ____ The least pictures? ____

Write all that you know from the graph. ______________________

_____________________________________________________

_____________________________________________________

_____________________________________________________

Step 4 Write a question about this graph.

_____________________________________________________

_____________________________________________________

_____________________________________________________

Answer your question.

_____________________________________________________

_____________________________________________________

Master 5.19


Name Date

Step-by-Step 6 Lesson 6, Question 3 Step 1 Write your full name and those of 5 classmates.

Step 2 A B C D E F G H I J K L M N O P Q R S T U V W X Y Z

Record all the letters in the names above by placing tally marks under the right letters.

Step 3 For each letter marked in Step 2, count the tally marks by 2s. Draw a bar graph. Use grid paper.

Use a scale of 1 square = 2 times. Put the letters on the horizontal axis. Put the number of times on the vertical axis.

Step 3 How many letters are there in the names? ____________________

Which letter appears most often? ___________________________

Which letter appears only once? ___________________________

Which letters are not used? _______________________________

Step 4 Which letters are vowels? ________________________________

Consonants? __________________________________________ Step 5 Write a question about the letters in the names.

_____________________________________________________

_____________________________________________________

Answer your question.

_____________________________________________________

Master 5.20


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Step-by-Step 8 Lesson 8, Question 4 Which season do you and your classmates like best? Record your choice on the board. Step 1 Use the tally chart below to record the data from the board.

Our Favourite Season


Spring

Summer

Fall

Winter

Step 2 Make a table using the data from the tally chart.

Our Favourite Season


Spring

Summer

Fall

Winter

Step 3 Write to explain what you found out.

_____________________________________________________

_____________________________________________________

_____________________________________________________

Master 5.21


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Step-by-Step 9 Lesson 9, Question 3 Look at the question on page 223. Step 1 What question will you ask? _______________________________

_____________________________________________________

Step 2 Record your data in the tally chart below.

Our Watches

Type of Watch Number of Children

Digital

With Hands

No Watch

Step 3 Use 1-cm grid paper. Draw a bar graph. Choose a scale. Will each square represent 2, 5, or 10 children?

Step 4 What did you find out? ___________________________________

_____________________________________________________

Step 5 Write 2 questions you can answer using your data.

_____________________________________________________

_____________________________________________________

_____________________________________________________

_____________________________________________________

Answer your questions. _____________________________________________________

_____________________________________________________

Master 5.22


Name Date

Unit Test: Unit 5 Sorting and Data Management Part A 1. Look at these numbers.

27, 156, 92, 13, 6, 69, 194, 35, 105, 8 a) Choose 2 attributes. Sort the numbers.

Record the sorting.

b) Choose 3 different attributes. Sort the numbers. Record the sorting.

Master 5.23a


Name Date

Unit Test continued 2. This pictograph shows the favourite flavour

of potato chip of Grade 3 children.

a) How many children like regular

potato chips? ____________________

b) Which flavour of potato chip is

the least popular? _________________

c) Which flavour is twice as popular as salt and vinegar? _____________

d) What else do you know from this graph?

______________________________________________________

______________________________________________________

Part B

3. This table shows the favourite birthday party activity of Grade 3 children. Our Favourite Birthday Party Activity

Activity Number of Children Bowling 10 Swimming 5 Mini Golf 15 Movie 20 Video Games 25

a) Use 1-cm grid paper. Draw a bar graph to display these data.

Order the bars from shortest to longest.

b) What scale did you use? _____________________________

c) Write 3 things you know from the graph.

______________________________________________________

______________________________________________________

______________________________________________________

Master 5.23b


Name Date

Unit Test continued Part C 4. Use numbers or Attribute Blocks.

What could go in each loop? Each overlap? Explain your choices.

____________________________________________________________

____________________________________________________________

____________________________________________________________

____________________________________________________________

____________________________________________________________

____________________________________________________________

____________________________________________________________

____________________________________________________________

____________________________________________________________

____________________________________________________________

Master 5.23c


Name Date

Sample Answers Unit Test – Master 5.23 Part A 1. a) Sample answer:

b) Sample answer:

2. a) 12 children b) Salt and vinegar c) Sour cream and onion

d) I know that barbecue is the most popular flavour. I know that 52 children were surveyed.

Part B 3. a)

b) I used 1 square represents 5 children. c) I know that playing video games is the most

popular activity. Swimming is the least popular activity. Twice as many children like going to a movie as like bowling.

Part C 4. Sample answers:

I put numbers with 1 attribute in a single loop. I put numbers with 2 attributes where 2 loops overlap. I put numbers with no attributes outside the loops. No numbers can have all 3 attributes.

Master 5.24

35 13 27


Extra Practice Masters 5.25–5.29 Go to the CD-ROM to access editable versions of these Extra Practice Masters

Program Authors

Peggy Morrow

Ralph Connelly

Steve Thomas

Jeananne Thomas

Maggie Martin Connell

Don Jones

Michael Davis

Angie Harding

Ken Harper

Linden Gray

Sharon Jeroski

Trevor Brown

Linda Edwards

Susan Gordon

Manuel Salvati

Copyright © 2005 Pearson Education Canada Inc.

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Western Canadian Teacher Guide - SD67 (Okanagan Skaha)sd67.bc.ca/instruction/mathresources/math3/gr03_units_wes/gr03... · Western Canadian Unit 5: Sorting and Data ... Lesson 1: