Western Canadian Teacher Guide - SD67 (Okanagan …€¦ · Teacher Guide Western Canadian Unit 9:...

Teacher GuideWestern Canadian

Unit 9: Length, Perimeter,and Area

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

“Meaningful measurement andestimation of measurementdepend on a personalfamiliarity with the unit ofmeasure being used.”

John A. Van de Walle

Mathematics Background

What Are the Big Ideas?

• The centimetre, the decimetre, the metre, and the kilometre can beused to measure the length, width, and height of an object.

• Standard units of measure, such as the centimetre and the metre, areused to measure the perimeter of two-dimensional figures.

• Uniform non-standard units can be used to estimate and measureperimeter and area.

How Will the Concepts Develop?

Students use metre sticks and rulers to explore standard units ofmeasure. They measure the lengths, widths, heights, and perimeters of a variety of real world objects and they establish benchmarks for the standard units, the centimetre, the decimetre, and the metre.Students use these benchmarks to estimate linear dimensions. After much practical experience, students will be better able to select the most appropriate unit to measure length.

Students measure and compare the perimeters of two-dimensionalfigures using standard units. They use non-standard units such asPattern Blocks and paper squares, to cover a figure and measure its area.Students find the areas of figures drawn on grid paper by countingsquares and partial squares. Through exploration, students see thatfigures with the same area can have different perimeters.

Why Are These Concepts Important?

Measuring skills are practical skills students will use. Experience inmeasurement lays a foundation for the use of measuring tools andformulas that students will encounter in later grades. As their measuringskills improve, students should be able to solve increasingly complexmeasurement problems. These skills may be applied in other areas, suchas science, art, and geography.

FOCUS STRANDShape and Space: Measurement

SUPPORTING STRANDSNumber, Shape and Space: 3-D Objects and 2-D Shapes

Length, Perimeter, and Area

ii Unit 9: Length, Perimeter, and Area

9

Unit 9: Length, Perimeter, and Area iii

Lesson 1:Measuring Length in CentimetresLesson 2:Measuring Length in MetresLesson 2A:Measuring Length in DecimetresLesson 3:The Kilometre

Curriculum Overview

General Outcome• Students estimate, measure and

compare, using whole numbers andprimarily standard units of measure.

Specific Outcomes• Students select the most appropriate

unit, including km, to measurelength. (SS1)

• Students describe the relationshipsamong cm, dm, and m. (SS2)

• Students estimate, measure, record,compare and order objects bylength, height, ..., using standardunits. (SS3)

LaunchDesign a Playground

Cluster 1: Measuring Length

Show What You Know

Unit ProblemDesign a Playground

General Outcome• Students estimate, measure and

compare, using whole numbers andprimarily standard units of measure.

Specific Outcomes• Students estimate, measure, record,

compare and order objects by ...,perimeter, using standard units. (SS3)

• Students select an appropriatenonstandard unit to measure area.(SS4)

• Students estimate, measure, record,compare and order shapes by area,using non-standard units. (SS5)

• Students construct a variety ofshapes given a specific area innonstandard units. (SS6)

Cluster 2: Measuring Perimeter and AreaLesson 4:Measuring Perimeter in CentimetresLesson 5:Measuring Perimeter in MetresLesson 6:Covering FiguresLesson 7:Measuring Area in Square UnitsLesson 8:Using Grids to Find AreaLesson 9:Comparing Area and PerimeterLesson 10:Strategies Toolkit

iv Unit 9: Length, Perimeter, and Area

Curriculum across the Grades

Grade 2

Students construct itemsof specific lengths (cm, dm, m).

Students select the mostappropriate standard unit(cm, dm, m) to measure a length.

Students estimate,measure, record,compare, and orderobjects by length, height,and distance around,using standard units.

Students estimate,measure, record, andcompare the area ofshapes, usingnonstandard units.

Students construct a shapegiven a specific area innonstandard units.

Grade 3

Students select the mostappropriate standardunit, including km, tomeasure length.

Students describe therelationships among cm, dm, and m.

Students estimate,measure, record,compare, and orderobjects by length, height,and perimeter, usingstandard units.

Students select anappropriate nonstandardunit to measure area.

Students estimate,measure, record,compare, and ordershapes by area, usingnonstandard units.

Students construct avariety of shapes given a specific area innonstandard units.

Grade 4

Students construct itemsof specific lengths,including mm.

Students select the mostappropriate standard unitto measure length.

Students describe therelationships among mm,cm, dm, m, and km.

Students estimate,measure, record, compare,and order objects bylength, height, perimeter,and circumference, usingstandard units.

Students estimate,measure, record,compare, and ordershapes by area, usingstandard units (cm2, m2).

Students construct anumber of shapes given aspecific area (cm2).

Students select the mostappropriate standard unitto measure area.

Students relate the size ofa unit to the number ofunits used to measurelength and area.

Materials for This Unit

You may want to prepare paper cutouts for use in place of Pattern Blocksand tangram pieces in Lesson 6. If you intend to use the suggestedBEFORE in Lesson 6, cut out many cardboard equilateral triangles, eachwith side length 20 cm. You may want to prepare some cardboardfigures that have areas that can be found using whole and part gridsquares for Lesson 8.

Measuring PenniesFor Extra Practice (Appropriate for use after Lesson 1)Materials: Measuring Pennies (Master 9.9), a tub ofpennies, rulers or measuring tapes

The work students do: Students work in pairs. Eachstudent takes a handful of pennies and puts the penniesside by side in a straight line. Each student estimates thelengths of both lines of pennies, and then measures heror his line to the nearest centimetre. The student whoseestimate is closer to the actual length in each case gets 1 point. The first player to score 5 points wins.

Take It Further: Partners play again, this time stackingthe pennies, and then estimating and measuring theheight.

SocialPartner Activity

Additional Activities

Cover UpFor Extra Support (Appropriate for use after Lesson 6)Materials: Cover Up (Master 9.11), yellow, red, green,and blue Pattern Blocks, lima beans

The work students do: Students work in pairs.Partners estimate how many yellow Pattern Blocks it willtake to cover a figure. They then cover the figure tocheck and record its area. They repeat the activity withred, then blue, and then green Pattern Blocks.

Take It Further: Students draw their own figure. Theyestimate and then find the area of the figure in limabean units.

Kinesthetic/SocialPartner Activity

Blob PerimetersFor Extension (Appropriate for use after Lesson 4)Materials: Blob Perimeters (Master 9.10), a variety of“blob shapes” cut from cardboard, scissors, string,rulers

The work students do: Students work alone. Eachstudent chooses a blob shape and estimates itsperimeter in centimetres. The student then lays stringaround the edge of the blob, cuts the string, andmeasures and records its length to the nearestcentimetre. The student repeats the activity with 3 otherblobs. The student then orders the 4 blobs from least togreatest perimeter.

Take It Further: The student traces her or his hand onpaper, and then estimates and measures the perimeterof the tracing to the nearest centimetre. The student thendraws a rectangle with a perimeter equal to theperimeter of the tracing.

SpatialIndividual Activity

Unit 9: Length, Perimeter, and Area v

Areas of Four Square UnitsFor Extra Practice (Appropriate for use after Lesson 8)Materials: Areas of Four Square Units (Master 9.12),geoboards, geobands, square dot paper (PM 22)

The work students do: Students work alone. Thestudent finds as many ways as possible to make a figureon the geoboard with an area of 4 square units. Thestudent records each figure on dot paper.

Take It Further: Students repeat the activity, this timemaking figures with an area of 6 square units.

Spatial/KinestheticIndividual Activity

vi Unit 9: Length, Perimeter, and Area

Planning for Unit 9

Planning for Instruction

Lesson Time Materials Program Support

Suggested Unit time: About 3 weeks

Unit 9: Length, Perimeter, and Area vii

Purpose Tools and Process Recording and Reporting

Planning for Assessment

Lesson Time Materials Program Support

2 Unit 9 • Launch • Student page 332

Design a Playground

LESSON ORGANIZER

Curriculum Focus: Activate prior learning about length,perimeter, and area.Student Materials: metre sticks or rulersVocabulary: length, distance around

15–20 min

L A U N C H

ASSUMED PRIOR KNOWLEDGE

Students can visually compare areas, lengths, anddistances around.

Students can use comparative language to describemeasures (for example, longest, largest).

✓

✓

ACTIVATE PRIOR LEARNING

Invite students to examine the picture of theplayground in the Student Book.

Ask questions, such as: • What do you see? (A playground)• How many sections does the playground

have? (8) What are they? (Sand box,roundabout, hopscotch, climbing structures, slides,basketball, picnic area, and swings and teeter-totters)

• Suppose you went to the playground. Whichsection would you go to? (I would go to the basketball section.)

• What shape is the section where the swings are? (A rectangle)

• What other shapes do you see? (An octagon, circles, squares, triangles)

Discuss the first question in the Student Book.Record students’ answers on the board. (The slide section seems to cover the most space.)

Students should recognize that several sectionscover about the same amount of space as theslide section.

Discuss the second question in the Student Book. (The swing section and the slide section seem to havethe longest distance around.)

Ask: • If you were at the playground, how could

you find which section has the longestdistance around? (I could count how many strides or heel-to-toefootsteps it takes to go around each section.)

Discuss the third question in the Student Bookand record students’ answers on the board. (Sample answer: It is farther from the swings to theroundabout. I can tell just by looking. The slides arenext to the swings, but the roundabout is across theplayground from the swings.)

LITERATURE CONNECTIONS FOR THE UNIT

Let’s Build a Playground! by Edward Myers. Modern CurriculumPress (Pearson Learning Group), 1999.ISBN 0765211602This non-fiction book shows children how to help build aplayground for their community.

Measuring Penny by Loreen Leedy. New York: Henry Holt andCo., 2000.ISBN 0805065725For her measuring project, Lisa chooses to measure everythingabout her dog, Penny, using both standard and non-standardunits. This book includes the concepts of length, mass, time,money, and temperature.

Bigger, Better, Best! by Stuart J. Murphy. New York:HarperCollins, 2002.ISBN 0064462471When Jill, Jeff, and Jenny move into a new house, they use area todecide whose room and whose window is bigger, better, and best.

DIAGNOSTIC ASSESSMENT

What to Look For

✔ Students can visuallycompare areas,lengths, anddistances around.

✔ Students can usecomparativelanguage to describe measures(for example,longest, largest).

What to Do

Extra Support:

Help students establish benchmarks for the centimetre and the metre. For example,the width of a finger is about one centimetre and an arm span is about one metre. Work on this skill during Lessons 1 and 2.

As students measure, ask them to describe how one object compares with anotherto encourage their use of comparative language. Work on this skill during Lessons 1 and 2.

Unit 9 • Launch • Student page 333 3

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

The e-Tools appropriate for this unit include Counters. Whenused in the grid format, Counters can be used to find perimeterin units and area in square units.

REACHING ALL LEARNERS

Watch to see if students can visually compareareas, lengths, and distances around. Do theyuse comparative language in describingmeasures (for example, longest, largest)?

Tell students that, in this unit, they will learnmore about measuring the length of, thedistance around, and the area of figures. At theend of the unit, students will demonstrate whatthey have learned by designing a playground.

4 Unit 9 • Lesson 1 • Student page 334

Measuring Length inCentimetres

LESSON ORGANIZER

Curriculum Focus: Use centimetres to measure length, width,and height. (SS3)Teacher Materials� clear plastic ruler� objects whose lengths are not exact centimetresStudent Materials Optional� metre sticks or 30-cm rulers � Step-by-Step 1 (Master 9.13)� classroom objects to � Extra Practice 1 (Master 9.25)

measure: paper clips, scissors, a tabletop, a shoe, a bulletin board, a marker, a pen, a crayon, an eraser

Vocabulary: centimetre, length, width, heightAssessment: Master 9.2 Ongoing Observations: Length, Perimeter, and Area

40–50 min

L E S S O N 1

Key Math Learnings1. The centimetre is a standard unit of length.2. Measuring to the nearest centimetre results in an

approximate measure.3. Centimetres can be used to measure linear dimensions such

as length, width, and height.

BEFORE Get S tar ted

Display an object whose length is not an exactnumber of centimetres, such as a 13.2-cmpencil. Invite students to estimate its length.Place the pencil on the overhead projector andhave a volunteer use a clear plastic ruler todemonstrate how to align the edge of the pencilwith the 0 mark on the ruler. Establish that thepencil is between 13 cm and 14 cm long, butcloser to 13 cm. Model reporting the pencil’slength as about 13 cm or 13 cm to the nearestcentimetre. Repeat with other objects.

Present Explore. Discuss with students otherpossible ways to record their work, such asmaking a chart or a graph. Remind students toestimate before they measure.

DURING Exp lore

Ongoing Assessment: Observe and Listen

As students work, watch for those who arehaving trouble measuring to the nearestcentimetre. Show them several lengths on aruler and model how to find the nearestcentimetre.

Ask questions, such as:• How long do you estimate your thumb is?

(About 3 cm)• How can you use the length of your hand to

estimate the length of your foot? (I know my hand is 10 cm long and my foot isabout one and a half times as long as my hand. I estimate that my foot is about 15 cm long.)

• Is that an exact measurement? (No, it is an estimate. I did not measure the lengthof my foot.)

Unit 9 • Lesson 1 • Student page 335 5

Alternative ExploreMaterials: a collection of small objectsStudents collect 5 or 6 objects, then estimate and measure thelength of each object to the nearest centimetre.

Early FinishersHave students estimate and measure the width of their hand,foot, arm, and thumb to the nearest centimetre.

Common Misconceptions➤Students align the end of the ruler with the object to be

measured, instead of using the 0-cm mark as the startingpoint. (Note: some rulers do begin at the 0-cm mark, asillustrated in this text.)

How to Help: Have students examine a ruler carefully to seewhen the 0-cm mark is positioned in from the end of the ruler.Discuss the possible reasons for this.

➤Students have difficulty explaining how to measure an objectnot aligned with the end of a ruler (as in question 7).

How to Help: Students may not understand that it is the spaceson rulers and not the numbers that denote the length. Havestudents place a finger between 2 numbers on a ruler and count“1,” move to the next space and count “2,” and so on.Alternatively, this concept can be compared to “jumps” on anumber line. Place a ruler on paper and draw “jumps” fromnumber to number as students count.


• How can you record a measurement that isnot exact? (I can record it as about a certain length or to thenearest centimetre.)

AFTER Connec t

Invite volunteers to share the methods theyused to record their work.

Ask questions, such as:• Were any of your measurements an exact

number of centimetres? Which one(s)? (Yes, my nose was exactly 3 cm long.)

• Which of your body parts is the shortest?(My nose) The longest? (My arm)

• How did you decide whether to use a ruleror a metre stick to make each measurement?(I used a metre stick for longer body parts, such asmy arm and my leg.)

Ask students for their responses to Show andShare. They may suggest that since their thumbis about 4 cm, they could measure the width ofthe book in thumbs, then multiply by 4. Forexample, the book is about 6 thumbs wide;multiply 6 � 4 = 24, so the book is about 24 cm wide.

Discuss the benchmarks presented in Connectwith students. Have students use thesebenchmarks to estimate the length and width oftheir math book and the height of the classroomdoor. Help students think of objects that areabout 50 cm wide, long, or tall. (Open notebook, desktop, bookshelf, garbage can,window ledge)

24

12

Sample Answers1. a) A paper clip: 3 cm long, 1 cm wide

b) Scissors: 20 cm long, 7 cm widec) Tabletop: 90 cm long, 60 cm wide

2. a) 16 cmb) 95 cmc) 12 cm

4. I can measure to check or I can use benchmarks.5. The shoe is the longest. The eraser is the shortest.6. My plastic mirror is 10 cm wide. I have to find an object

that is 10 cm + 10 cm or 20 cm wide. This calendar is 20 cm wide.

Prac t i ce

All questions require a metre stick or a ruler.Question 1 requires a paperclip, scissors, and atabletop. Question 2 requires a student’s shoe,a bulletin board, and a marker pen. Question 5requires a crayon, an eraser, and a shoe.

Assessment Focus: Question 6

Students first find an object, such as acalculator, a textbook, or a notebook, andmeasure its width. They then add 10 cm to thewidth and try to find another object in theclassroom with a width close to thismeasurement.

Students who need extra support to completeAssessment Focus questions may benefit fromthe Step-by-Step masters (Masters 9.13–9.22).


Numbers Every DayStudents should explain the strategies they used to find howmany pieces there were in all. For example, they may havedrawn a picture on a grid: 3 congruent rectangles, each with 8 squares; they may have used multiplication: 3 � 8 = 24; orthey may have used addition: 8 + 8 + 8 = 24. To find how manychildren could have 2 pieces each, students may have useddivision: 24 � 2 = 12; or they may have circled pairs of pieces,then counted how many circles.

Lamp: 32 cm; 36 cm

A calculatorA student desk

Making ConnectionsScience: Invite students to plant a bean seed, then measure andrecord the height of the plant weekly.Math Link: Have students measure the length of a toothpick tothe nearest centimetre. Have them divide to find about howmany toothpicks, placed end to end, it would take to make a line30 cm long. Then, have them multiply to find how far 9 toothpicks would stretch.Literacy: The height of a horse is measured in hands. Havestudents research to find the length of a hand, in centimetres.


ASSESSMENT FOR LEARNING

What to Look For

Understanding concepts ✔ Students have a sense of the length of

one centimetre.

✔ Students understand that centimetrescan be used to measure length, width,and height.

✔ Students understand that measuring tothe nearest centimetre results in anapproximate measure.

Applying procedures✔ Students are able to measure length

to the nearest centimetre.

What to Do

Extra Support: Students who have difficulty measuring lengthto the nearest centimetre may benefit from further practicemeasuring objects. Have students name the two centimetre marksthe length lies between and then determine which mark the lengthis closer to.Students can use Step-by-Step 1 (Master 9.13) to complete question 6.

Extra Practice: Students who need extra practice estimating andmeasuring lengths to the nearest centimetre can use the AdditionalActivity, Measuring Pennies (Master 9.9).Students can complete Extra Practice 1 (Master 9.25).

Extension: Provide students with a collection of small boxes.Challenge them to estimate and measure the length, width, andheight of each box to the nearest centimetre.

Recording and ReportingMaster 9.2 Ongoing Observations:Length, Perimeter, and Area

7. Daniel lines up the 20-cm mark on the ruler with the edge ofhis desk and counts the number of centimetres from 20 to 30: 10 cm. He marks the 30-cm mark with his fingerand then moves the ruler so that the 20-cm mark lines up withhis finger, and keeps counting. Each time he moves the ruler,he counts by 10. He keeps doing this until he gets close to theend of his desk. Then he counts the number of centimetresbetween 20 cm and the end of his desk.

8. 10 small paper clips6 large paper clipsI know this because I can skip count by 3s ten times to reach30, and I can skip count by 5s six times to reach 30.(Alternatively, I divide 30 by 3 to get 10, and divide 30 by 5 to get 6.)

REFLECT: I know my hand is about 10 cm long. I can hold thepencil up to my hand to see if it is longer or shorter than my hand.

16 cm, 8 cm, 5 cm


Measuring Length inMetres

Key Math Learnings1. The metre is a standard unit of length. One metre is a length

of 100 cm.2. Metres can be used to measure linear dimensions, such as

length, width, and height.3. A length of more than one metre can be reported in

centimetres, or in metres and centimetres.

LESSON ORGANIZER

Curriculum Focus: Use metres to measure length, width, and height. (SS3, SS1, SS2)Teacher Materials� lengths of string between 1 m and 3 m longStudent Materials Optional� cardboard tubes � 3-column charts (PM 18)� counters � Step-by-Step 2 (Master 9.14)� cotton balls � Extra Practice 1 (Master 9.25)� metre sticks or

measuring tapesVocabulary: metreAssessment: Master 9.2 Ongoing Observations: Length, Perimeter, and Area

40–50 min

L E S S O N 2

Students do not learn decimals until grade 4, so theycannot use decimals to record a length in metres, insteadof metres and centimetres.

Math Note


Demonstrate how to measure with a metrestick. Model measuring lengths longer than 1 m. Mark the position of the end of the metrestick; pick up the metre stick and align the 0-m end with the mark to continue measuring.

Provide each pair of students with a metre stickand a piece of string between 1 m and 3 m long.Have partners estimate and then measure thelength of their string to the nearest centimetre.Record students’ measures on the board. Elicitfrom students that 100 cm = 1 m. Explain thatlengths longer than 1 m can be reported inmetres and centimetres.

For example, 123 cm can also be reported as 1 m 23 cm. Invite volunteers to record thelengths of their strings on the board in this way.

Arrange students in groups of 3 or 4. Provideeach group with a cardboard tube, a counter,and a cotton ball. Have volunteers read aloudand model the events presented in Explore.Make sure students understand what they are todo. Discuss the expectations for Show and Share.You may wish to suggest that students use achart like the one below to record their lengths.

Students measured length to the nearest centimetre in Lesson 1,and to the nearest metre in this lesson. Your curriculum alsorequires that students use decimetres to measure length. Lesson2A: Measuring Length in Decimetres, has been providedfollowing this lesson to address decimetres.

Curr i cu lum Focus


Alternative ExploreMaterials: measuring tapesHave students find objects in the classroom that have a length,width, or height greater than one metre (for example, the lengthor width of a desk or the height of a bookshelf). Have studentsmeasure each object and record their measurements.

Early FinishersHave students create another event for the Mini-Olympics. Remindstudents that the event should involve measuring distances. Havestudents try the new event 2 times and record their results.

Common Misconceptions➤Students have difficulty measuring lengths greater than 1 m

using only one metre stick.How to Help: Provide students with a long length of string orribbon marked off in metres. Have students repeat the measuringactivities in this lesson and record their measurements to thenearest metre.


Numbers Every DayIn both the first and fifth pair, the same number is being dividedby two different numbers. The expression with the smaller divisoris greater than the expression with the larger divisor. In thesecond pair, 6 is greater than 5, so 6 � 1 is greater than 5 � 1. In the third pair, 5 + 5 + 5 = 3 � 5; 4� 5 is greaterthan 3 � 5. In the fourth pair, 3 + 3 + 3 + 3 = 3 � 4, and 4 + 4 + 4 = 4 � 3; both 4 � 3 and 3 � 4 equal 12, so theexpressions are equal.

a broom handlea baseball bat

a cara rake

DURING Exp lore


Watch how students measure lengths longerthan one metre. Do they use a single metrestick and move it from position to position?Listen to how students report theirmeasurements. Do they recognize that 135 cm is equivalent to 1 m 35 cm?

Ask questions, such as:• How far did the counter go, in centimetres?

(My counter went 150 cm.) Is that less than orgreater than one metre? Why? (That is greater than 1 m because there are 100 cmin 1 m, and 150 is greater than 100.)

• I see your tube rolled 110 cm. What isanother way of saying that? (1 m 10 cm)

• In which event did you get the longestdistance? (The Tube Roll) The shortest distance?(The Cotton Ball Puff)

• Who came in first in the Tube Roll? How doyou know? (Bobbie came in first in the Tube Roll. Her tuberolled 135 cm. Her tube rolled the farthest.)

AFTER Connec t

Invite volunteers to share the winning resultsof each event. Record the measurements on theboard and then have students determine theoverall winner of each event. Ask:• Why is 150 cm the same as 1 m 50 cm?

(A metre is 100 cm, so 150 cm is 1 m with 50 cm left over.)

• What is another way of saying 170 cm? (1 m 70 cm)

Event First Try Second Try

Tube Roll

Counter Flick

Cotton Ball Puff

Sample Answers4. Answers will vary.

a) 1 m 52 cmb) 1 m 95 cmc) 1 m 10 cm

5. a) Centimetres; a cereal box is much less than 1 m high.b) Metres; a hallway is much longer than 1 m.c) Metres; a tree is much taller than 1 m.d) Centimetres; a goldfish is much less than 1 m long.

6.

You can skip count by 100s. The number of centimetres is thenumber of metres with two zeros at the end.

Metres

Centimetres

1100

2200

3300

4400

5500

6600

7700

8800

9900

101000

• What object is about 1 m long? (A tabletop) 1 m wide? (A bulletin board) 1 m tall? (A bookshelf)

• Would you measure the length of theclassroom in metres or centimetres? Why?(I would measure the length of the classroom inmetres. I use metres to measure long lengths.)

Introduce the benchmarks presented in Connect.Students can refer to these in futuremeasurement activities.

Prac t i ce

Questions 1, 2, 4, and 9 require a metre stick ormeasuring tape.


Students could round 18 cm to the nearest ten,which is 20 cm. They can then use a metre stickand skip count by 20s until they reach the endof the metre stick.


6 m300 m

1 m

centimetres

metres

metres

centimetres

Making ConnectionsMath Link: Encourage students to turn back to Unit 5 to seeexamples of horizontal and vertical bar graphs.



What to Look For

Understanding concepts ✔ Students understand that a metre is a

unit of linear measure. It can be usedto measure length, width, and height.

✔ Students understand that lengthsgreater than one metre can bereported in centimetres, as well as inmetres and centimetres.

✔ Students understand the relationshipbetween centimetres and metres.

Applying procedures✔ Students can use a metre stick to

measure lengths greater than one metre.

What to Do

Extra Support: Students who have difficulty measuring lengthsgreater than 1 m with one metre stick should tape two metre stickstogether. Have them measure objects in the classroom that have alength, width, or height between 1 m and 2 m. Students shouldrecord their measurements.Students can use Step-by-Step 2 (Master 9.14) to complete question 9.

Extra Practice: Students can complete Extra Practice 1 (Master 9.25).

Extension: Have students estimate to find objects that fit each ofthe following descriptions. Have them measure and record themeasures in both centimetres, and in metres and centimetres:• between 1 m and 2 m wide • between 2 m and 3 m tall• between 3 m and 4 m long


7. Molly: about 1 m 35 cm; Emma: 1 m 40 cm; Rhey: 1 m 20 cm; Nico: 1 m 30 cmFrom shortest to tallest: Rhey, Nico, Molly, Emma

8. I know a baseball bat is about 1 m long, so I would comparethe object to a baseball bat.

9. About 5 pencils would fit along a metre stick. I know thisbecause 1 m = 100 cm and 18 cm is close to 20 cm. 20 cm + 20 cm + 20 cm + 20 cm + 20 cm = 100 cm

REFLECT: I would not use metres to measure objects that areshorter than 1 m. My math book, my pencils, and my eraserare shorter than 1 m, so I would measure them in centimetres,not metres.


Present Explore. Remind students to record which linear dimension (length, width, or height) they are measuring.

DURING Exp lore


Ask questions, such as:• How did you estimate the length of the shelf? (The shelf is about 3 times as long as this straw. The straw

is almost 2 rods long, so I estimated 6 rods for the length of the shelf.)• How did you decide which number to round to? (The shelf was between 5 and 6 rods long, but closer

to 6, so I rounded to 6 rods.)

12 Unit 9 • Lesson 2A

Measuring Length inDecimetres

L E S S O N 2 A

Key Math LearningA decimetre is a unit of length equal to 10 cm.

LESSON ORGANIZER

Curriculum Focus: Use decimetres to measure length,width, and height. (SS2, SS3)Student Materials Optional� Lesson 2A (Master 9.8) � Step-by-Step 2A � orange Cuisenaire Rods (Master 9.15)

or strips of paper � Extra Practice 1A 10 cm long (Master 9.26)

� 3-column charts (PM 18)� 30-cm rulers� metre sticks or measuring tapesVocabulary: decimetreAssessment: Master 9.2 Ongoing Observations: Length, Perimeter, and Area

40–50 min

Sample Answers1. a) fish tank; 38 cm b) a crayon; 8 cm

c) pencil; 16 cm d) table; 95 cm2. 8 cm, 16 cm, 38 cm, 95 cm3. a) 7 dm = 70 cm b) 3 dm = 30 cm

c) 5 dm = 50 cm d) 60 cm = 6 dme) 90 cm = 9 dm f) 20 cm = 2 dm

4. a) 70 dm = 7 m b) 90 dm = 9 mc) 30 dm = 3 m d) 4 m = 40 dme) 8 m = 80 dm f) 5 m = 50 dm

5. a) 25 cm is longer than 2 dm because 25 is greater than 20.b) 94 cm is longer than 9 dm because 94 is greater than 90.c) 8 dm is longer than 51 cm because 80 is greater than 51.d) 75 dm is longer than 6 m because 75 is greater than 60.e) 10 m is longer than 63 dm because 100 is greater than 63.f) 27 dm is longer than 2 m because 27 is greater than 20.

6. My calculator is about 1 dm long.My paste jar is about 1 dm tall.

7. I know that 1 dm = 10 cm. So, I could measure the table incentimetres, then divide by 10 to find how many decimetresit is. I might have to round the number of centimetres to thenearest 10 before I divide. For example, if the table is 82cm long, I would round to 80, then divide by 10.

8. 7 dm is the same as 70 cm. So, Mabel’s train is 70 cmlong. 82 cm is greater than 70 cm, so Charles’ train islonger than Mabel’s train. 82 – 70 = 12 cm; Charles’ trainis 12 cm longer than Mabel’s train.

REFLECT: I think it would be easier to estimate height indecimetres because decimetres are longer than centimetres,so the number of units would be smaller. My hand is about1 dm long and my finger is about 1 cm wide. I could usemy hand to measure the height of the door. That wouldgive a good estimate. It would be too hard to measure thedoor with my finger.

Unit 9 • Lesson 2A 13


What to Look For

Understanding concepts✔ Students understand that the

decimetre is a unit of length, and thata length of 1 dm is 10 cm and alength of 10 dm is 1 m.

Applying procedures✔ Students can measure the length,

width, or height of an object to thenearest decimetre.

What to Do

Extra Support: Students who have difficulty measuring indecimetres may benefit from using a string marked in decimetresrather than a ruler or metre stick.Students can use Step-By-Step 2A (Master 9.15) to completequestion 8.

Extra Practice: Students can complete Extra Practice 1A (Master 9.26).

Extension: Provide students with lengths of string. Studentsestimate each length in decimetres and centimetres (for example, 2 dm 6 cm), then measure to check their estimates.

Early FinishersHave students find classroom objects with a length, width, or height close to: 1 dm, 3 dm, 10 dm.

Common Misconceptions➤Students have difficulty changing a measure from one unit to another, for example, 7 dm to 70 cm.How to Help: Help students develop a table such as this, which they can use as a reference.

1 dm10 cm

2 dm20 cm

3 dm30 cm

4 dm40 cm

5 dm50 cm

6 dm60 cm



AFTER Connec t

Invite students to describe the strategies they used to estimate and to round to the nearest unit.Use Connect to introduce the decimetre and its relationship to the centimetre and metre. Havestudents line orange rods along the length of their rulers to establish that a length of 30 cm is equalto 3 dm, and have students line orange rods along the length of one metre stick to establish that alength of 10 dm is equal to 1 m.

Ask:• What can you think of that is about one decimetre long? (My hand, a marker)

Two decimetres long? (A straw, a new pencil)• When might you use decimetres to measure? (When the object is longer than ten centimetres and I don’t

need an exact answer)

Prac t i ce

All questions require a ruler or a metre stick.


Students’ responses should indicate an understanding that 1 dm is equal to 10 cm. Students use thisrelationship to compare the lengths.


The Kilometre

Key Math Learnings1. The kilometre is a unit of length equal to 1000 m.2. Kilometres are used to measure long distances.

LESSON ORGANIZER

Curriculum Focus: Understand when the kilometre is used tomeasure distance. (SS1, SS2, SS3)Student Materials Optional

� Step-by-Step 3 (Master 9.16)� Extra Practice 2 (Master 9.27)

Vocabulary: kilometreAssessment: Master 9.2 Ongoing Observations: Length, Perimeter, and Area

40–50 min

L E S S O N 3


Briefly review the units of length students haveused to date (centimetre, decimetre, and metre).

Ask:• Would you use any of these units to measure

long distances, such as the distance betweentwo cities? (No) Why not? (It would take too many metres or decimetres orcentimetres to measure a long distance.)

Introduce the term kilometre and its symbol,km. Use landmarks, such as a store or anintersection that are about 1 km from theschool, to give students a sense of how far 1 km is. Tell students that it takes about 15 minutes to walk 1 km.

Present Explore. Encourage students tobrainstorm a list of strategies, decide on thebest strategy, and then write up a plan todescribe the strategy.

Ensure students understand that they shoulddevelop a plan for presenting their strategy tothe class.

DURING Exp lore


Ask questions, such as:• How long does it take to walk 1 km?

(It takes about 15 minutes to walk 1 km.)• How will you use that information in your

plan? (I can walk around the playground once to see howmuch time it takes. Then I can divide that numberinto 15 minutes to find how many times I wouldhave to walk around the playground to travel 1 km.)

• What must you include in your plan to keeptrack of the time? (I need a stopwatch, a timer, or a watch.)

Numbers Every DayStudents should explain their strategies.For 27 + 25, add 25 and 25 to get 50, then add 2 to get 52.For 55 + 49, add 55 + 50 = 105, then subtract 1 to get 104.For 100 – 3, count back by 1s: 100, 99, 98, 97. For 35 – 18, find 35 – 20, then add 2 to get 17. For 18 + 15 + 2, add 18 + 2 first to get 20, then add 20 + 15 to get 35.

52104971735


Early FinishersHave students make a list of places they walk to from home, suchas the store, the park, or a friend’s house. Have them estimatethese distances in kilometres.

ESL StrategiesHave students draw pictures of two things they would measureusing each unit: centimetre, metre, and kilometre. Have themcomplete this sentence about each picture: I would use (unit) tomeasure (picture).


AFTER Connec t

Invite groups to share their strategies with theclass. Encourage students to ask questions.Ask:• How are your strategies alike? How are they

different? (Amy and Ben’s strategy is to set a timer for 15 minutes and count the number of times they canwalk around the playground before the timer goesoff. My strategy is to walk around the playgroundonce and time how long it takes. Then I will dividethat number into 15 minutes to see how many timesI could walk around the playground. We are bothwalking and timing our walk, but I am using mathinstead of walking for 15 minutes.)

• If we tried each strategy, do you think wewould all get about the same answer? Why?(Yes, our strategies are similar and we all walk atabout the same speed.)

• How long do you think it would take you torun 1 km? (8 minutes) Ride your bike 1 km?(6 minutes)

Review Connect to inform students that 1 km = 1000 m.

Prac t i ce


Students should recognize that there are 1000 m in 1 km. Some students might add 500 m + 500 m to find out how many metresthey would walk in total.

Making ConnectionsNumber Sense: Ask students to calculate how many kilometresthey could walk in 30 minutes, 45 minutes, and 1 hour, andhow long it would take them to walk 5 km.Social Studies: Have students locate two points of interest on alarge map of their community and use the scale on the map toestimate the distance between them.

kilometres

kilometres

Sample Answers2. a) I would measure the distance from my house to my

Grandma’s house in kilometres, and the distance fromVancouver to Calgary in kilometres.

b) It would not make sense to use kilometres to find the lengthof the classroom because the classroom is only a fewmetres long and 1 km is 1000 m.

4. Yes, I would walk 1 km because 1 km is 1000 m, and it is 500 m to the store and 500 m from the store to home; 500 m + 500 m = 1000 m.

REFLECT: The road sign near the highway reads, “50 km to Edmonton.”



What to Look For

Understanding concepts ✔ Students understand that the kilometre

is a standard unit of length and it isused to measure long distances.

✔ Students have a sense of how far akilometre is.

✔ Students understand the relationshipbetween metres and kilometres.

Communication✔ Students can explain when to use

each of the 4 units they know, tomeasure distance.

What to Do

Extra Support: Have students who are having difficultydistinguishing linear dimensions make comparisons withoutreference to a unit. For example, this table is longer than it iswide, and taller than it is wide.Students can use Step-by-Step 3 (Master 9.16) to complete question 4.

Extra Practice: Give students a distance and ask them whetherthey would use centimetres, decimetres, metres, or kilometres tomeasure it. For example: What unit would you use to measure thedistance between our school and the town library?Students can complete Extra Practice 2 (Master 9.27).

Extensions: Challenge students to use a map of their province toplan a trip from home to two or three other cities and then backhome. Have them use the scale on the map to estimate how farthey would travel.


10 km

10 m

25 cm


L E S S O N 4

Measuring Perimeterin Centimetres

Key Math Learnings1. Perimeter is the distance around an object and is measured

in units of length.2. Centimetres are used to measure the perimeter of a

small object.3. Perimeter can be found by measuring the length of each side

of an object, and then adding these lengths.

LESSON ORGANIZER

Curriculum Focus: Estimate and measure perimeter incentimetres. (SS3, SS1)Teacher Materials� 10-cm by 20-cm cardboard rectangle� 30-cm ruler or metre stickStudent Materials Optional� 1-cm grid paper (PM 20) � Step-by-Step 4 (Master 9.17)� 30-cm rulers or metre sticks � Extra Practice 2 (Master 9.27)� 3-column charts (PM 18)� books of various sizes� calculatorsVocabulary: perimeterAssessment: Master 9.2 Ongoing Observations: Length, Perimeter, and Area

This text uses the word “figure” and not “shape,” exceptwhere we quote directly from the curriculum. Shape is anattribute, like colour, and, hence, we cannot measure ashape. A figure may have a particular shape; forexample, “The shape of this figure is a rectangle.” Wecannot say, “The shape of this shape is a rectangle.”

Math Note


Show students a 10-cm by 20-cm cardboardrectangle. Ask:• Which unit of measure would you use to

measure the perimeter of this figure? Why?(I would use the centimetre because all the sides ofthe rectangle are less than one metre.)

• How can you find the perimeter? (We can add the lengths of the sides to get the perimeter.)

Present Explore. Ensure students understandthat they should round each length to thenearest centimetre. Have students write anumber sentence to show how they found each perimeter.

DURING Exp lore


As students work, watch to see that they aligntheir rulers correctly. Remind students how toround to the nearest centimetre. Watch forstudents who find shortcuts for finding theperimeter, such as measuring length and widthonce and recording them twice. Make a note tohave these students explain their strategies later.

Ask questions, such as:• How did you decide which object to measure?

(We looked for objects that had lengths and widthsshorter than our 30-cm ruler.)

0–50 min

Numbers EverdayHave students explain their strategies for solving the problem, suchas multiplying the number of hours spent in school each day bythe number of school days in a year. Students should use acalculator to find the answer. For example, 6 hours spent in schooleach day � 5 school days in a week � 36 weeks in a schoolyear = 1080 h: I spend about 1080 hours in school a year.


Alternative ExploreMaterials: figures from construction paperProvide students with various figures cut from construction paper.Have students estimate each perimeter, then measure to find theperimeter of each figure. Students record a number sentence foreach perimeter, and then order the figures from least to greatestperimeter.

Early FinishersHave students draw a figure on 1-cm grid paper with a perimetertwice that of one of the objects they measured in Explore.

ESL StrategiesThis unit provides many opportunities for students to work withpartners and in groups. Try to group students with differentlanguage abilities for cooperative activities and discussions.

Common Misconceptions➤Students have difficulty counting the units along the perimeter

of a figure drawn on 1-cm grid paper.How to Help: Suggest students put a hatch mark through eachunit as it is counted.


• How did you estimate the perimeter of this book? (My hand is 10 cm long. The book isabout 2 hands long and about 1�

12

� hands wide. Thatis about 20 cm long and 15 cm wide. So, theperimeter is about 20 cm + 20 cm + 15 cm + 15 cm,which is 40 cm + 30 cm = 70 cm.)

AFTER Connec t

Invite volunteers to share the methods theyused to record their work.

Ask questions, such as:• Which of your objects had the greatest

perimeter? (The spelling book had the greatestperimeter because the sum of its side lengths was thegreatest number of centimetres.) Which had theleast perimeter? (The eraser)

• What shortcut can you use to find theperimeter of a rectangle? (You can measure thelength and width once, add them, and thenmultiply their sum by 2.)

Use the illustrations in Connect to show studentshow to count the units along the outside of afigure drawn on grid paper. Point out that eachside of a square on the grid is 1 cm. Ensurestudents understand that the measurements in the trapezoid were obtained using acentimetre ruler.

Prac t i ce

Have rulers available for all questions. Questions4 and 6 require 1-cm grid paper. Questions 5 and 8 require books of various sizes.


Students should know that a rectangle hasopposite sides of equal length. The rectangle’sperimeter is 16 cm, so the side lengths mustadd to 16 cm. The sides of the rectangle mightbe 1 cm and 7 cm, or 2 cm and 6 cm, or 3 cmand 5 cm, or 4 cm and 4 cm.

10 cm 12 cm 18 cm



What to Look For

Understanding concepts ✔ Students understand that perimeter is

the measure of the distance aroundan object.

✔ Students understand that thecentimetre is used to measure theperimeter of small figures.

Applying procedures✔ Students can measure and add the side

lengths of a figure to find its perimeter.✔ Students can find the perimeter of a

figure drawn on 1-cm grid paper.✔ Students can draw a figure with a

given perimeter.

What to Do

Extra Support: Have students create models of rectangles withColour Tiles. Each tile has a side length of 1 unit. Students findthe perimeter of each rectangle in units.Students can use Step-by-Step 4 (Master 9.17) to completequestion 6.

Extra Practice: Provide students with a collection of small boxlids. Have them estimate and measure, to the nearest centimetre,the perimeter of each lid.Students can also complete Extra Practice 2 (Master 9.27).

Extension: Have students complete the Additional Activity, Blob Perimeters (Master 9.10).

Recording and ReportingMaster 9.2 Ongoing Observations: Length, Perimeter, and Area

Sample Answers4. Answers may vary.

5. Accept students’ estimates. Measurements should be to thenearest centimetre. Sample answer: 96 cm, 68 cm, 90 cmFrom least to greatest: 68 cm, 90 cm, 98 cm

6.

I started with a width of 1 cm, then 2 cm, 3 cm, 4 cm. When Itried a width of 5 cm, I realized I had it already, because Ihad drawn a rectangle with length 5 cm and width 3 cm.

7. I can outline the perimeter of the tracing with string and thenuse a ruler to measure the string.

8. One book is 26 cm by 21 cm, and has a perimeter of 94 cm.The other book is 30 cm by 22 cm, with a perimeter of 104 cm. The perimeter of the first book is about 10 cm lessthan the perimeter of the second book.

REFLECT: I would measure each side of my pencil case with acentimetre ruler and then add the side lengths to get theperimeter.

10 cm 14 cm 12 cm

14 cm, 12 cm, 10 cm

4

40–50 min


Measuring Perimeterin Metres

Key Math Learnings1. Metres are used to measure the perimeter of large regions,

such as a room.2. Measuring side lengths to the nearest metre and then

adding, results in an approximate perimeter.3. Large regions can be represented on 1-cm grid paper using

the scale 1 cm = 1 m.

LESSON ORGANIZER

Curriculum Focus: Measure perimeter in metres. (SS3)Teacher Materials� metre stickStudent Materials Optional� metre sticks or � Step-by-Step 5 (Master 9.18)

measuring tapes � Extra Practice 3 (Master 9.28)� string� 1-cm grid paper (PM 20)Assessment: Master 9.2 Ongoing Observations: Length, Perimeter, and Area

L E S S O N 5


Ask:• Which unit would you use to measure the

sides of a garden? Explain. (I would use the metre because the garden is a large region.)

• Which word do we use for the distancearound a figure? (Perimeter)

Talk about the garden in the Student Book onpage 348. Explain that the garden is drawnmuch smaller than real life. The length and the width are dimensions of the real garden.Ensure students understand how long 20 m and 25 m are.

Present Explore. You may want to brainstormregions of the school and assign a specific regionto each group. Emphasize that students shouldmeasure to the nearest metre. If necessary, use ametre stick to review how to do this.

DURING Exp lore


Watch to ensure students are moving the metrestick or measuring tape from position toposition accurately. Have students write anumber sentence to show how they found theperimeter.

Ask questions, such as:• How will you find the perimeter of this room?

(I will measure each side length to the nearest metreand then add.)

• Is the perimeter exact or approximate? (It is approximate because I rounded the side lengthsto the nearest metre.)

• How will you decide if the approximatelength is 5 m or 6 m? (If the length is closer to 5 m than to 6 m, theapproximate length is 5 m. If the length is closer to 6 m than to 5 m, the approximate length is 6 m.)

Making ConnectionsArt: Have students colour squares on 1-cm grid paper indifferent colours to make a mosaic design. Have them calculatethe perimeter of their design.


Early FinishersHave students sketch a room in their house, estimate its lengthand width, label the dimensions, and calculate its perimeter.

Common Misconceptions➤ In question 5, students have difficulty determining the possible

dimensions of a rectangle, given its perimeter.How to Help: Provide students with a 20-cm length of string ordental floss. Have them lay the string along the lines of 1-cmgrid paper to form a rectangle, and count the 1-cm lengths todetermine the side lengths. Students then try to make differentrectangles using the same length of string. Have students replaceeach centimetre unit with a metre unit, and mark a scale 1 cm = 1 m.


• How will you record your results? (I will draw a picture of the room and write thelength of each side of the room on the picture. Then,I will add the lengths to get the perimeter.)

AFTER Connec t

Invite groups to share their plans with the class,and to show how they recorded their results.

Ask questions, such as:• What problem did you have in finding the

perimeter of your region? (Some of the wallswere not straight.) How did you overcome thisproblem? (I used a string to measure that part ofthe wall, and then measured the length of the string.)

• What number sentence did you use to find theperimeter? (12 m + 20 m + 12 m + 20 m = 64 m)

• Did anyone find a shortcut for measuring theperimeter? (Yes) Why did it work? (The room was square, so I multiplied the length ofone wall by 4.)

• Which group had the region with the leastperimeter? The greatest perimeter?

Review the pictures of the storeroom floor inConnect. Point out that the lengths are the reallengths, but the picture is much smaller thanthe real floor.

Prac t i ce

Remind students that in questions 3 and 4, thelength of each square on the grid represents 1 m.


A rectangle has opposite sides of equal length.The perimeter of the garden is 20 m, so the sidelengths must add to 20 m. Students could alsowork with half of the perimeter and find allpossible pairs of numbers that add to 10. Thesenumbers are the measures of the length andwidth, in metres.

Numbers Every DayStudents could find the difference between 2 consecutivenumbers in the pattern and then decide whether they arecounting on or counting back. Students can use a number line orhundred chart to help.

50 m

125 m 30 m

30 m, 50 m, 125 m

56 63 70

110 80 70

24 28 40

Count on by 7.

Count back by 10.

Count on by 4.

Sample Answers4. The fence has to go around the garden. I find the perimeter of

each garden by adding the side lengths, then compare theperimeters. Garden b has the greatest perimeter so it willneed the most fencing.

5. A rectangular gardenhas opposite sides ofequal length. Thegarden’s perimeter is20 m, so the sidelengths must add to20 m. The sides of thegarden might be 1 m and 9 m, 2 m and 8 m,3 m and 7 m,4 m and 6 m, or 5 m and 5 m. There are 5 ways to do this.

REFLECT: I use centimetres to find the perimeter of somethingsmall, like a book or a sheet of paper. I use metres to find theperimeter of something large, like a room or a blackboard.

1 m by 9 m

2 m by 8 m

3 m by 7 m

4 m by 6 m

5 m by 5 m



What to Look For

Understanding concepts ✔ Students understand that the metre is

used to measure the perimeter oflarge regions.

Applying procedures✔ Students can measure side lengths of

a region to the nearest metre and addto find the approximate perimeter.

✔ Students can calculate perimeter fromlabelled drawings.

✔ Students can find the perimeter of afigure drawn on 1-cm grid paperwhere 1 cm represents 1 m.

What to Do

Extra Support: Have students place string around the perimeterof a large object, such as a box or a table, and then use a metrestick to measure the length of the string. Have them report thismeasurement to the nearest metre.Students can use Step-by-Step 5 (Master 9.18) to complete question 5.

Extra Practice: Ask students to estimate, then measure to thenearest metre, the dimensions of the blackboard or a bulletinboard. Have them sketch the board, label its side lengths, and thenfind the perimeter. Students can complete Extra Practice 3 (Master 9.28).

Extension: Challenge students to research the dimensions of asports field, such as a soccer field or a football field. Have themdraw and label a model of the field on 1-cm grid paper, and thenfind its perimeter.


16 m20 m

18 m

5 ways

18 m10 m14 m


L E S S O N 6

Covering Figures

Key Math Learnings1. The area of a figure is the number of units needed to cover it.2. The units used to find the area of a figure must be congruent.3. The area of a figure can be found by counting the number of

units needed to cover it.

LESSON ORGANIZER

Curriculum Focus: Count congruent non-standard units tomeasure area. (SS5)Teacher Materials� paper equilateral triangles with side length 20 cmStudent Materials Optional� Pattern Blocks (PM 25) � 3-column charts (PM 18)� triangular grid paper � Step-by-Step 6 (Master 9.19)

(PM 24) � Extra Practice 3 (Master 9.28)� tangrams (PM 26)� Covering Figures (Master 9.6)Vocabulary: areaAssessment: Master 9.2 Ongoing Observations: Length, Perimeter, and Area

40–50 min

In Unit 3, students learned about congruent figures.Reinforce that vocabulary here. The units needed to coveran area must be congruent; that is, the units must havethe same size and shape.

Math Note


Show students some cardboard equilateraltriangles with side length 20 cm. Ask:• About how many of these triangles do you

think it would take to cover this table? (18)

Accept students’ estimates and invite avolunteer to cover the table with triangles asthe other students count.Ask:• What did you do when your triangles did

not cover the table exactly? (We estimated howmany half triangles were missing and then put thehalf triangles together to make whole triangles.)

Present Explore. Provide students with bluePattern Blocks and a copy of Covering Figures(Master 9.6). This master duplicates the art inExplore and its use should prevent studentsmarking their books. Discuss possible ways forstudents to record their work. For example,students could make a chart:

Alternatively, students could record their

work directly on the pictures of the figures on

Master 9.6.

Figure Estimate of ActualNumber of Number of

Blue Blocks Blue Blocks

A

B

C

D

Making ConnectionsMath Link: Have students look back through Unit 8 to recallhow they used Pattern Blocks to find equal parts of a whole.


Alternative ExploreMaterials: yellow, blue, green, and red Pattern BlocksProvide students with a yellow Pattern Block and a collection ofblue, green, and red Pattern Blocks. Have them cover the yellowblock with only blue, green, or red blocks and record the areaeach time.

Early FinishersHave students repeat Explore using green Pattern Blocks andreport their findings.

Common Misconceptions➤Students forget to report the area using the correct Pattern

Block unit.How to Help: Encourage students to create answer blanks to befilled in as they work. For example: Area = _____ blue PatternBlock units.


Numbers Every DayEncourage students to discuss the strategies they used. Studentsshould recognize that each time, the second number is one-halfthe first number. Therefore, when you say 50, I will say 25. Thatis, I say one-half of what you say. Or, you say two times what Isay. When I say 10, you said 20.

DURING Exp lore


Ask questions, such as:• How many blue Pattern Blocks do you

estimate it will take to cover Figure A? (4)• How did you make your estimate?

(The figure looks a lot bigger than a yellow PatternBlock, and 3 blue Pattern Blocks cover 1 yellowPattern Block.)

• How many blue Pattern Blocks does it taketo cover Figure A? (4)

• Will you need more blocks or fewer blocksto cover Figure B? Why? (Figure B looks bigger than Figure A, so I will needmore blocks to cover it.)

AFTER Connec t

Invite volunteers to share their estimates andresults. Ask questions, such as:• Which figure took the most blue Pattern

Blocks to cover it? (Figure B) The least? (Both Figures A and D took 4 blue Pattern Blocks.)

• Why is it important to use the same unit tocover each figure? (I need to use the same unit so I can compare the areas.)

• How would the results change if you usedgreen Pattern Blocks instead of blue PatternBlocks? (When I measure each area, I find it would takemore green Pattern Blocks to cover the figuresbecause the green Pattern Blocks are smaller. Butwhen I order the figures, the figures would still bein the same order, because the figure that is coveredby the most blue blocks is also covered by the mostgreen blocks.)

Introduce the term area to describe the numberof units needed to cover a figure. Say: The areaof Figure A is 4 blue Pattern blocks.

Ask:• What is the area of Figure B? (6 blue Pattern

Blocks) Figure C? (5 blue Pattern Blocks) Figure D? (4 blue Pattern Blocks)

• How many blue Pattern Blocks would it taketo make a figure with an area of 4 yellowPattern Blocks? (12; 3 blue Pattern Blocks cover 1 yellow Pattern Block; 3 + 3 + 3 + 3 = 12)

Use the figures in Connect to illustrate how to findthe area of a figure using different area units.

Prac t i ce

Questions 1 to 6 require Pattern Blocks.Questions 2, 3, and 4 require triangular gridpaper. Question 7 requires tangram pieces; notethat the pictures in the Student Book are notdrawn to scale, so students cannot use thesepictures to answer the question.


Students should draw a variety of figures using 6 green Pattern Blocks. Some students may makea regular hexagon or a row of triangles. Otherstudents may make other irregular figures.


Sample Answers2. The area is 7 blue Pattern Blocks or

14 green Pattern Blocks.

3. a) b)

c) d)

12 green Pattern Blocks

24 green Pattern Blocks12 green Pattern Blocks

I say one-half of what you say2520

4. I moved the green PatternBlocks around so that atleast one side wastouching another block.

(These are just some ofthe possible figures.)

6. I know that 2 green Pattern Blocks cover 1 blue Pattern Block.So, I can multiply the number of blue Pattern Blocks needed to cover the fish by 2 to get the area of the fish in greenPattern Blocks. 2 � 6 = 12; the area of the fish is 12 greenPattern Blocks.

7. a) 2 small trianglesb) 2 small trianglesc) 2 small trianglesd) 4 small triangles

REFLECT: I know that 2 green Pattern Blocks cover 1 blue PatternBlock. So, I can double the number of blue Pattern Blocks toget the area in green Pattern Blocks.



What to Look For

Understanding concepts ✔ Students understand that the area of a

figure is the number of congruentunits needed to cover it.

✔ Students understand that the unitsused to find the area of a figure mustbe the same size.

Applying procedures✔ Students can find the area of a figure

by covering it with congruent unitsand counting the units.

✔ Students can order figures accordingto area.


What to Do

Extra Support: Have students complete the Additional Activity,Cover Up (Master 9.11).Students can use Step-by-Step 6 (Master 9.19) to complete question 4.

Extra Practice: Provide each student with an index cardlabelled with an area in Pattern Block units: for example, 10 greenPattern Blocks. Have students make a figure with the given area,and then colour triangular grid paper to show their figure.Students can make and record as many different figures aspossible with that area.Students can complete Extra Practice 3 (Master 9.28).

Extension: Challenge students to use Pattern Blocks to create asmany different figures as they can where the area can be measuredin blue Pattern Blocks and red Pattern Blocks. Students record theirwork by colouring their figures on triangular grid paper.

Area is 6 blue Pattern Blocks.


L E S S O N 7

Measuring Area inSquare Units

Key Math Learnings1. Area is measured and reported in square units.2. There is a relationship between the size of the square unit used

and the number of square units needed to cover a surface.

LESSON ORGANIZER

Curriculum Focus: Count congruent square units to measurearea. (SS4, SS5)Teacher Materials� construction paper squares:

thirty-two 6-cm blue squares, eighteen 8-cm orange squares, eight 12-cm purple squares

� construction paper rectangles of various sizes (at least 18 cm by 24 cm)

Student Materials Optional� construction paper squares: � 2-cm grid paper (PM 21)

3-cm red squares, � Colour Tiles4-cm green squares, � paper rectangles,6-cm yellow squares 18 cm, 24 cm, or greater(enough of each to cover � 4-column charts (PM 19)a variety of surfaces) � Step-by-Step 7 (Master 9.20)

� Extra Practice 4 (Master 9.29)


Draw a 24-cm by 48-cm rectangle on the board.Show students some blue 6-cm by 6-cm squares.

Ask:• How can we use these squares to find the

area of the rectangle? (We can cover the rectanglewith squares and count the squares.)

• About how many of these squares do youestimate it would take to cover the rectangle?(About 30)

Accept students’ estimates and invite avolunteer to cover the rectangle with squares,taping them to the board, as the other studentscount.

Ask:• What unit did we use to find the area of the

rectangle? (Blue square)• What is the area of the rectangle in blue

squares? (32 blue squares)

Remove the blue squares from the board andrepeat this procedure with 8-cm orange squaresand 12-cm purple squares.

Present Explore. Provide pairs of students with asupply of red, green, and yellow squares.Emphasize that all squares must touch, with nooverlapping or spaces between them. Studentscould record their findings in a chart:

DURING Exp lore


Watch to ensure students choose a classroomsurface that is appropriate for the number andsize of the squares they are using.

Surface Area in RedSquares

Area in GreenSquares

Area inYellow

Squares

40–50 min

Making ConnectionsArt Link: Invite students to use paper squares of different colours to create a design. Then have students record the area of their design.


Alternative ExploreMaterials: 2 paper rectangles of different sizes (18 cm by 24 cmor greater); red, green, and yellow paper squaresHave students estimate and measure the area of each rectangleusing each colour of square.

Early FinishersHave two pairs of students combine their squares and worktogether to find the area of a larger surface, such as a tabletopor the teacher’s desk.

Common Misconceptions➤Students lose track of their count when counting square units.How to Help: Suggest that students mark each square withan X as they count.


Ask questions, such as:• How many yellow squares do you estimate it

will take to cover the picture? (About 10)• How did you make that estimate?

(About 2 yellow squares cover my hand, and thepicture is about 5 times the area of my hand. So, Imultiplied 2 � 5 to get 10.)

• What will you do if you do not have enoughsquares to cover the surface? (I will count thesquares I have already used and use them again.)

AFTER Connec t

Invite volunteers to describe a surface theycovered, estimate its area, and find itsactual area.

Ask:• How did you make your estimates?

(I remembered how many red squares it took tocover the book and then compared the size of thebook to the size of the desktop.)

• What did you do when the squares did notfit exactly? (I put two half squares together tomake a whole square.)

• What did you notice about the size of thesquares you were using and the number ofsquares it took to cover the surface? (The larger the squares, the fewer squares I neededto cover the surface.)

Use the bulletin boards in Connect to illustratehow the size of the unit is related to thenumber of units needed to cover a surface.

Prac t i ce


Students may say that both Madhu and Jan canbe correct. Students could draw 2 congruentrectangles, one divided into 8 large squares andone divided into 50 small squares. Studentsshould realize that the larger the square unit,the fewer the number of units needed.

12 square units 24 square units

8 square units

25 square units

Numbers Every DayStudents should recognize that since the numbers beingsubtracted are small, they can use counting back to subtract.



What to Look For

Understanding concepts ✔ Students understand that area can be

found by counting how many squareunits are needed to cover a surface.

✔ Students understand that the larger thesquare unit, the fewer the units used.

Applying procedures✔ Students can find the area of a figure

by counting square units.

Communicating✔ Students can report area in

square units.


What to Do

Extra Support: Students who are having difficulty with theconcept of area may benefit from further practice in coveringsurfaces with square units. Invite students to use Colour Tiles tofind the area of other surfaces in the classroom.Students can use Step-by-Step 7 (Master 9.20) to complete question 4.

Extra Practice: Provide students with an assortment of largepaper rectangles. Have them cover the rectangles with3-cm squares, and then with 6-cm squares. Have them comparethe results of the two activities and report their findings.Students can complete Extra Practice 4 (Master 9.29).

Extension: Challenge students to use Colour Tiles or papersquares to create as many different figures as they can with anarea of 16 square units. Students record their work by colouringtheir figures on 2-cm grid paper.

Sample Answers3. a) Large squares: the classroom floor is a large surface.

b) Small squares: the lid of a shoebox is a small surface.c) Small squares: the cover of a book is a small surface.d) Large squares: the playground is a large surface.

4. Both can be correct. Jan is using large square units andMadhu is using small square units.

REFLECT: I think the square is the easiest figure to use becauseyou can put squares together in rows. Also, most of the areaswe measured were rectangles. Squares fit better in a rectanglethan triangles do.

8 square units, 12 square units, 24 square units, 25 square units

148

149147299298297

40–50 min


Using Grids to FindArea

Key Math Learnings1. The area of a figure drawn on a grid can be found by

counting squares and part squares.2. A figure with a given area in square units can be drawn on

grid paper or made on a geoboard.

Making ConnectionsScience Link: Have students trace a leaf on grid paper andfind its approximate area.

LESSON ORGANIZER

Curriculum Focus: Count squares on a grid to measurearea. (SS5, SS6)Teacher Materials� transparency of 1-cm grid paper (made from PM 20)� 5-cm by 7-cm cardboard rectangleStudent Materials Optional� cardboard figures � square dot paper (PM 22)� 1-cm grid paper (PM 20) � Step-by-Step 8 (Master 9.21)� geoboards � Extra Practice 4 (Master 9.29)� geobandsAssessment: Master 9.2 Ongoing Observations: Length, Perimeter, and Area

L E S S O N 8


Display a 1-cm grid on the overhead projector.Establish that it is made of 1-cm by 1-cmsquares. Show a 5-cm by 7-cm cardboardrectangle.

Ask:• How can we use the grid to find the area of

this rectangle, in square units?

Invite a volunteer to place the rectangle on thegrid, aligning the sides with the grid lines.Trace around the rectangle and elicit fromstudents that its area can be found by countingthe squares inside the tracing. Have a studentcount the squares to find the area. Record thearea on the board as 35 square units.

Present Explore. Distribute cardboard figuresand 1-cm grid paper.

DURING Exp lore


Watch to ensure students align, as much aspossible, the sides of the objects with the lineson the grid. Note how they deal with partsquares. Do students attempt to put partsquares together, or do they ignore them?

Ask questions, such as:• What is your estimate for the area of that

tracing? (About 200 square units)How did you make that estimate? (I know that the area of the smaller lid is about100 square units. This lid is about twice as big.)

• How are you keeping track of the squares asyou count? (I am marking the squares as I count them.)

• What are you doing with part squares? (I am trying to put the part squares together tomake whole squares.)


Alternative ExploreMaterials: geoboards, geobands, square dot paper (PM 22)Establish that a 1 by 1 square on the geoboard has an area ofone square unit. Have students make different figures on thegeoboard, record the figures on dot paper, and find and recordtheir areas.

Common Misconceptions➤Students have difficulty drawing a figure with a given area.How to Help: Provide students with Colour Tiles whose numberis equal to the given area. Have students place the tiles to formfigures, and then copy the figures on 2-cm grid paper.

Early FinishersHave students cut out their tracings and order them from least togreatest area.


AFTER Connec t

Invite volunteers to describe or demonstrate onthe overhead projector the strategies they usedto find the areas of the objects.

Ask:• For which figures was it easiest to find the

area? (The square and the rectangle were theeasiest because they had only whole squares.) The hardest? (The figures with part squares were the hardest.)

• Do you think you found the exact area ofthat tracing? Explain. (No, it was an approximate area because there weremany part squares.)

Have students show how they identified theobjects with the greatest area and the least area.

Discuss the strategy in Connect for finding thearea of a figure on a grid by counting wholesquares and half squares.

Ask:• How does this strategy compare with your

strategy? (It is better than mine because I did not count allthe part squares.)

Prac t i ce

Question 2 requires geoboards and geobands.Questions 3, 5, and 7 require grid paper.


Students should work with rectangles withsides that are whole numbers. They shouldthink of different ways to arrange 18 squares tomake a rectangle. For example, the rectanglecould be 1 row of 18 squares, 2 rows of9 squares, or 3 rows of 6 squares. Somestudents may take this question further andmake a rectangle that uses half squares, such as12 rows of 1�

12

� squares.

Sample Answers2. 3.

a) b)

c) d)



Yes

Each piece has an area of4 square units.



What to Look For

Understanding concepts ✔ Students understand that the area of

a figure drawn on grid paper can be found by counting whole and part squares.

Applying procedures

✔ Students can find the area of a figure by counting whole squares and part squares.

✔ Students can make a figure with agiven area on grid paper or on ageoboard.

What to Do

Extra Support: Students who have difficulty counting partsquares may benefit from working with figures containing onlywhole and half squares. Students can use Step-by-Step 8 (Master 9.21) to completequestion 7.

Extra Practice: Students who need extra practice can use theAdditional Activity, Areas of Four Square Units (Master 9.12).Students can also complete Extra Practice 4 (Master 9.29).

Extension: Challenge students to trace the outline of their handon grid paper and find its approximate area.


4. J: 7 square units; O: 10 square units; E: 10 square unitsOrder: J, O, and E, or J, E, O

5. E = 10 squares; D = 11 squares;Order: D, E

7. I thought of all thedifferent ways I couldmake a rectangleusing 18 squares. Icould have 1 row of18 squares, 2 rows of9 squares, or 3 rowsof 6 squares. There

are 3 possible rectangles. If I used part squares, I could findmore rectangles.

REFLECT: I know that I can find the area of a figure by coveringit with squares and counting. I know that if I use big squares,there will be fewer squares than if I used small squares. I knowthat I can count whole squares and part squares to find area.

Sandbox, shed, rose bed, hot tub, gazebo, shrubs, patio36 square units 10 square units

12 square units

16 square units

19 square units


Numbers Every DayStudents should recognize that the figure is drawn on grid paperand has an area of 16 square units. Students should find thearea of each piece and compare the results.


L E S S O N 9

Comparing Area andPerimeter

Key Math Learnings1. Different figures may have the same area.2. Different figures may have the same perimeter.

Making ConnectionsMath Link: Have students use Colour Tiles or congruentcardboard squares to make squares with side lengths 1 unit,2 units, ..., 6 units. Have students record the perimeters andareas of the squares in a chart and look for patterns in the chart.

LESSON ORGANIZER

Curriculum Focus: Show that different figures may have thesame area or the same perimeter. (SS5, SS6)Teacher Materials� transparency of a geoboard (made from PM 22)� markersStudent Materials Optional� geoboards � Colour Tiles or congruent� geobands cardboard squares� square dot paper (PM 22) � calculators� 2-cm grid paper (PM 21) � Step-by-Step 9 (Master 9.22)

� Extra Practice 5 (Master 9.30)Assessment: Master 9.2 Ongoing Observations: Length, Perimeter, and Area

40–50 min


Display a transparency of a geoboard (drawnon square dot paper) on the overhead projector.Demonstrate how to form the smallest possiblesquare on the geoboard.

Establish that:• Each side of the square is 1 unit long.• The perimeter of the square is 4 units.• The area of the square is 1 square unit.

Invite a volunteer to draw a figure on the dotpaper using only horizontal and vertical lines(no diagonal lines). You may want to clarifythis condition by showing examples. Havestudents find the perimeter of the figure inunits, and its area in square units.

Present Explore. Encourage students to comparethe areas and perimeters of their figures withthose of their classmates.

DURING Exp lore


Watch to ensure students use only horizontaland vertical lines. Note how they find theperimeter and area of each figure.

Ask questions, such as:• Can you tell me how you found the

perimeter of that figure? (I counted the number of units around the outside ofthe figure.)

• Can you make a different figure with thesame perimeter as that figure? (Yes; I can change the shape of the figure and keepthe number of units around the outside the same.)

Sample Answers1. a) P = 12 units A = 7 square units

b) P = 14 units A = 7 square unitsc) P = 16 units A = 7 square units

2.

P=10 unitsA=4 square units




Alternative ExploreMaterials: Colour Tiles or congruent cardboard squares,2-cm grid paper (PM 21)Have students make 5 different figures with Colour Tiles orcongruent cardboard squares, record the figures on grid paper,then find the area and perimeter of each one. Students writewhat they notice about the areas and perimeters.

Early FinishersHave students make 2 figures with an area of 8 square unitseach but with different perimeters, and 2 figures with aperimeter of 10 units each but with different areas.

Common Misconceptions➤Students have difficulty differentiating the unit squares on a

geoboard, and counting to find the area.How to Help: Provide students with a geoboard that has asticky dot in the centre of each small square. This may helpstudents “see” the small squares.


49 + 1 = 50

8 � 6 – 8 = 40

AFTER Connec t

Invite volunteers to model their figures on theoverhead projector and to demonstrate howthey found the perimeters and areas. For eachfigure, ask volunteers to model:• a different figure with the same perimeter• a different figure with the same area• a different figure with the same perimeter

and area

Ask:• What did you learn about figures with the

same perimeter? (They do not always have thesame area.)The same area? (They do not always have thesame perimeter.)

Prac t i ce

Questions 2 and 5 require geoboards,geobands, and grid paper or dot paper.Question 4 requires grid paper.


Students should determine the area andperimeter of the 2 squares. They should noticethat the perimeter of the larger square is doublethe perimeter of the smaller square, and thearea of the larger square is 4 times the area ofthe smaller square.



What to Look For

Understanding concepts ✔ Students understand that different

figures can have the same area.

✔ Students understand that differentfigures can have the same perimeter.

Applying procedures✔ Students can find the area and

perimeter of a figure.

What to Do

Extra Support: Have students use Colour Tiles to make 5 figures. Have them find the area and perimeter of each figure,then compare their results.Students can use Step-by-Step 9 (Master 9.22) to completequestion 4.

Extra Practice: Invite each partner to make a figure on ageoboard using only vertical and horizontal lines. Have eachstudent exchange geoboards with her partner, draw her partner’sfigure on grid paper, and then find its area and perimeter.Students can complete Extra Practice 5 (Master 9.30).

Extension: Challenge students to make figures on a geoboardthat include diagonal lines. Students draw the figures on dotpaper, then find their approximate areas.


4. The area of the second square is4 times the area of the firstsquare. The perimeter of thesecond square is 2 times theperimeter of the first square.

5. The given figure has a perimeterof 14 units and an area of 12 square units.

REFLECT: Each of these 2 figureshas an area of 10 square units.The first figure has a perimeterof 22 units. The second figurehas a perimeter of 14 units.





P = 14 unitsA = 12 square units





Numbers Every DayEncourage students to experiment with their calculators. Studentsshould recognize that Julia needs to add, subtract, multiply, ordivide to show 50 on the calculator. Students could find severalways to calculate 8 � 5 without using the key. For example,Julia could add 8 five times, or she could multiply 8 � 6 andthen subtract 8.

5


Strategies Toolkit

Key Math LearningUsing a model can help you solve a problem.

LESSON ORGANIZER

Curriculum Focus: Interpret a problem and select anappropriate strategy. (SS6)Teacher Materials� Colour Tiles for the overhead projectorStudent Materials� Colour Tiles or congruent cardboard squares� 2-cm grid paper (PM 21)Assessment: PM 1 Inquiry Process Check List, PM 3 Self-Assessment: Problem Solving

40–50 min

L E S S O N 1 0


Present Explore. Ask questions, such as:• What must you measure to find how much

fencing the pen will need? (Perimeter)• What strategy could you use to solve the

problem? (I could use square pieces of cardboardand arrange them in different ways.)

• How will you record your findings? (I willdraw a picture and label the lengths of the sides.)

Arrange the students in pairs. Make ColourTiles or congruent cardboard squares, and largegrid paper, available.

DURING Exp lore

Ongoing Observations: Observe and Listen

Ask questions, such as:• What do you know about Zoe’s pen?

(The floor is made of 4 square units. Whole sides ofthe squares are touching.)

• Which shape of pen gives the leastperimeter? (Square) What is the perimeter ofthe square? (8 units) The area? (4 square units)

• How do you know your solution is correct? (We made drawings of all the possiblearrangements, found the perimeter of each one, thencompared perimeters.)

AFTER Connec t

Complete the problem in Connect. Have studentscompare the two problems. When the tiles donot make a large square, the least perimeteroccurs with the rectangle that has the leastdifference between length and width.

Prac t i ce

Have Colour Tiles or congruent cardboardsquares and 2-cm grid paper available.Encourage students to refer to the Strategies listto assist in selecting an appropriate strategy.

Sample Answers1. Zoe could make 2 different shapes.

Each shape would take 8 units of fencing.2.

3.

REFLECT: I can use Colour Tiles to solve a problem about areaand perimeter. Each Colour Tile has an area of 1 square unit.One side of a Colour Tile has a length of 1 unit.

I can put the tiles together to make different figures. I can thenfind the perimeter and area of each figure.



What to Look For

Problem solving✔ Students demonstrate an

understanding of the problem.

✔ Students select an appropriatestrategy to solve the problem.

✔ Students can justify their solutions.

Communicating✔ Students can describe their strategy

clearly, using appropriate language.

What to Do

Extra Support: Students who have trouble interpreting the problemsmay benefit from restating the problem using new words. Here is oneway of restating the Explore problem: “Zoe has 4 squares. She wantsto arrange them so that whole sides touch and the figure has thesmallest perimeter possible. What shape is the figure?”

Extra Practice: Have students write a similar problem, tradeproblems with a classmate, and solve each other’s problem.

Extension: Students can repeat Practice question 3, but change theproblem to: Raji’s garden has the shape of an octagon. Its area is 7 square units. Its perimeter is greater than 8 units. Draw Raji’s garden.

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

326 units, 16 units, and

14 units3 by 44 units and

3 units

2 shapes8 units

H1

Sample Answers1. a) My atlas: 31 cm

b) A crayon: 9 cmc) My teacher’s desk: 1 m 52 cm

2. The paper clip and the rod; for each object, if I count thecentimetres on the ruler that are covered by the object, I get 4 cm.

3. Jerry’s arm is about 5 cm shorter than mine. I measuredmy arm. My arm is 36 cm long. I measured Jerry’s arm.His arm is about 31 cm long. 36 cm – 31 cm = 5 cm

4.

6. A rectangle with dimensions: 1 unit by 16 units, 2 units by 8 units, 4 units by 4 units, or any irregularfigure with an area of 16 square units.

7. a) The pasture has the greatest perimeter; 28 units. Thetoolshed has the least perimeter; 6 units.

b) The pasture has the greatest area; 39 square units.The toolshed has the least area; 2 square units.

8. a) 6; a rectangle with dimensions 1 cm by 11 cm, 2 cm by 10 cm, 3 cm by 9 cm, 4 cm by 8 cm, 5 cm by 7 cm, 6 cm by 6 cm

b)

The area unit is a square with side length 1 cm.(Note: Students have not yet learned about squarecentimetres.)

c) One half the perimeter is 12 cm. I find 2 numbers thatadd to 12. These numbers are the length and width incentimetres. These numbers are all the pairs of wholenumbers I can find that add to 12.

A=11 square units

A=20 square units

A=27square units

A=32 square units

A=35 square units

A=36 square units

38 Unit 9 • Show What You Know • Student page 366

LESSON ORGANIZER

Student Materials� rulers� metre sticks or measuring tapes� 1-cm grid paper (PM 20)� square dot paper (PM 22)� geoboards� geobandsAssessment: Masters 9.1 Unit Rubric: Length, Perimeter, and Area, 9.4 Unit Summary: Length, Perimeter, and Area

40–50 min

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

40 m

Unit 9 • Show What You Know • Student page 367 39

Show Your WorkEncourage students to show their thinking in their answers toquestions.

The concepts of area and perimeter can be difficult to express inwriting. Suggest students draw figures with side lengths labelled,or draw the figures on grid paper using a scale. A table canalso be used to record and compare the areas and perimeters ofdifferent figures.

Remind students that showing their work includes drawings,numbers, or words.

SHOW YOUR BEST


What to Look For

Reasoning; Applying concepts✔ Question 8: Students understand the difference between perimeter and area.

Accuracy of procedures✔ Question 1: Students can measure length in centimetres and metres.

✔ Question 7: Students can find area in square units and perimeter in units.

Problem solving✔ Question 5: Students can interpret the problem, select the appropriate strategy, and determine how much

fencing is needed to enclose the play area.

✔ Question 8: Students can find different figures with the same perimeter.

Recording and ReportingMaster 9.1 Unit Rubric: Length, Perimeter, and AreaMaster 9.4 Unit Summary: Length, Perimeter, and Area




P = 6 unitsA = 2 square

unitsP = 10 unitsA = 6 square units

A = about 13 square unitsA = 14 square units

Have students turn to the Unit Launch on pages332 and 333 of the Student Book. Remindstudents of the questions they answered aboutthe playground at the beginning of the unit.

Discuss with students the list of learning goals.Invite a volunteer to explain what each goalmeans.

Present the Unit Problem. Invite volunteers toread the guidelines and instructions for theproblem aloud. Clarify any points. Throughquestioning, establish that perimeter should berecorded in units, and area in square units.

Have one student read the Check List aloud toensure all students understand what their workshould show. Discuss possible ways studentsmight record their work. Suggest students usethe Playground Planning Chart (Master 9.7) torecord their table.

Before students begin, ask volunteers to recallthe meanings of area and perimeter and explainhow to find each measurement.

Students will probably measure perimeter inmetres. However, students have not yet learnedabout square metres. So, to describe the area ofeach section, they can use “square units,” anddraw a picture to show 1 square unit as asquare with side length 1 m. Discuss possibleways in which students might make theirdesigns interesting and attractive.

40 Unit 9 • Unit Problem • Student page 368

Design a Playground

LESSON ORGANIZER

Student Grouping: Groups of 3 or 4Student Materials� 1-cm grid paper (PM 20)� rulers� pencil crayons� Playground Planning Chart (Master 9.7)Assessment: Masters 9.3 Performance Assessment Rubric:Design a Playground, 9.4 Unit Summary: Length, Perimeter,and Area

40–50 min

U N I T P R O B L E M

Sample ResponseStudent work should include a plan for the playground, drawnon grid paper, with the dimensions clearly marked. Theplayground should be rectangular, with 4 or 5 sections. Theplan should include a table showing the perimeters and areaof these sections.

For example:

Our plan is for a 15-m by 24-m playground.We are planning to have 4 pieces ofplayground equipment. The sectionfor the swings is 6 m by 8 m, thesandbox section is 6 m by 8 m, theclimbing structure is 5 m by 8 m,and the section for the slides is 4 m by 6 m. All sections are at least 3 m away from other sectionsto make sure children are safe while playing.

Little Owl Daycare Centre Playground

The perimeter of the playground is 24 m + 15 m + 24 m + 15 m = 78 m. So, it will take 78 m offencing to fence the playground. The area of the playground is 360 square units. One square unit is a square with side length 1 m.

Reflect on the UnitThe perimeter is the distance around a figure, in units. The areais the amount of space a figure covers, in square units.

Section Area PerimeterSwings 48 square units 28 metresSlides 24 square units 20 metresClimbing Structure 40 square units 26 metresSandbox 48 square units 28 metres

Swings

Sandbox

ClimbingStructure

Slides

Our Playground Plan

__ = 1 m

Unit 9 • Unit Problem • Student page 369 41


What to Look For

Understanding concepts ✔ Students understand that perimeter is

the distance around a figure and areais the amount of space a figure covers.

Applying procedures✔ Students find the perimeter and area

of each section of their design.

Communicating✔ Students provide a clear explanation

of their plan.

✔ Students use mathematical symbolscorrectly to record their measurementsin a table.

What to Do

Extra Support: Make the problem accessible.

Some students may have difficulty getting started. Brainstorm a listof playground equipment that would be appropriate for youngchildren. Then, help them develop a list of tasks to be completed(for example, outline the perimeter of the playground; identify 4 or 5 pieces of equipment, outline a section of the playgroundfor each piece of equipment, label each piece, and so on). Ifpossible, take students to the school playground and help themestimate how much room is required for the different equipment.

Some students may lose track of their count when finding areaand perimeter. Remind students to put a small mark on each unitas they count.

Recording and ReportingMaster 9.3 Performance Assessment Rubric: Design a PlaygroundMaster 9.4 Unit Summary: Length, Perimeter, and Area

Copyright © 2005 Pearson Education Canada Inc. 42

Evaluating Student Learning: Preparing to Report: Unit 9 Length, Perimeter, and Area This unit provides an opportunity to report on the Shape and Space: Measurement strand. Master 9.4 Unit Summary: Length, Perimeter, and Area 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: Shape and Space: Measurement

Reasoning; Applying concepts

Accuracy of procedures

Problem solving

Communication Overall

Ongoing Observations 2 3 2 2 2 Strategies Toolkit 2 2 Work samples or portfolios; conferences

2 3 2 2 2

Show What You Know 2 3 3 2 3 Unit Test 2 2 2 2 2 Unit Problem Design a Playground

2 3 3 3 2

Achievement Level for reporting 2

Recording How to Report Ongoing Observations

Use Master 9.2 Ongoing Observations: Length, Perimeter, and Area 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 10). 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 9.1 Unit Rubric: Length, Perimeter, and Area 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 9.1 Unit Rubric: Length, Perimeter, and Area may be helpful in determining levels of achievement. #1, 4, and 7 provide evidence of Accuracy of procedures; #2, 3, and 8 provide evidence of Reasoning; Applying concepts; #5 and 6 provide evidence of Problem solving; all provide evidence of Communication.

Unit Test Master 9.1 Unit Rubric: Length, Perimeter, and Area 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 9.3 Performance Assessment Rubric: Design a Playground. 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: Length, Perimeter, and Area Not Yet

Adequate Adequate Proficient Excellent


• recognizes measurement situations in everyday problems (length, perimeter, area)

• selects and applies relevant processes, including units, for estimating and measuring length, perimeter, and area

• describes relationships among standard units, and relates size of unit to number of units needed

needs one-to-one support; may be unable to: – recognize linear

measurement situations in everyday problems

– select and apply relevant processes and strategies

– describe relationships among standard units

– relate size of unit to number of units needed

partially able to: – recognize linear





able to appropriately: – recognize linear





in various contexts, able to appropriately: – recognize linear






• accurately measures, records, compares and orders length, perimeter, and area

• constructs figures and lengths using standard units

limited accuracy; omissions or major errors in: – measuring:

• length (cm, dm, m) • perimeter (cm, m) • area (square units)

– constructing figures and lengths

partially accurate; omissions or frequent minor errors in: – measuring:



generally accurate; few errors in: – measuring:



accurate; no errors in: – measuring:



Problem-solving strategies

• chooses and carries out a range of strategies (e.g., estimation, diagrams, drawing, grid paper, manipulatives, grouping) to solve and create problems involving length, perimeter, and area

may be unable to use appropriate strategies to solve and create problems involving length, perimeter, and area

with limited help, uses some appropriate strategies to solve and create problems involving length, perimeter, and area; partially successful

uses appropriate strategies to solve and create problems involving length, perimeter, and area successfully

uses appropriate, often innovative, strategies to solve and create problems involving length, perimeter, and area successfully

Communication • explains reasoning and

procedures clearly, including appropriate terminology (e.g., perimeter, area, square units)

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, including appropriate symbols

work is often unclear; rarely uses appropriate symbols

presents work with some clarity; uses some appropriate symbols

presents work clearly; uses appropriate symbols

presents work clearly and precisely; uses appropriate symbols

Master 9.1


Name Date

Ongoing Observations: Length, Perimeter, and Area 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: Length, Perimeter, and Area* Student Reasoning; Applying

concepts Accuracy of procedures

Problem solving Communication

Chooses the most appropriate unit to measure length Understands the

relationships of standard units of linear measure, and the concepts of perimeter and area

Measures, records, orders, and compares length, perimeter, and area

Identifies and solves problems involving length, perimeter, and area

Presents work clearly Explains reasoning and

procedures clearly, including appropriate terminology

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

Master 9.2


Name Date

Performance Assessment Rubric: Design a Playground

Not Yet

Adequate Adequate Proficient Excellent


• applies understanding of linear measurement and area to construct a plan for a playground, including: – choosing a

reasonable overall area and features

– selecting appropriate units

– explaining choices

does not apply the required concepts of linear measurement and area; may be incomplete or indicate misconceptions

applies and explains relevant concepts of linear measurement and area to construct and explain the playground; may indicate some misconceptions

applies relevant concepts of linear measurement and area to construct and explain the playground; may have minor flaws in reasoning

applies relevant concepts of linear measurement and area to effectively construct and explain the playground; shows thorough understanding


• accurately calculates and records perimeter and area of each feature

• dimensions are accurately draw on grid paper

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

recording area and perimeter

– drawing dimensions on grid paper

somewhat accurate; some omissions or frequent minor errors in: – calculating and



generally accurate; few minor errors in: – calculating and



accurate and precise; no errors in: – calculating and



Problem-solving strategies

• uses appropriate estimating, measuring, and problem-solving strategies (e.g., grid, table) to devise a plan that could work for a real playground

uses few effective strategies; does not adequately design a playground that meets requirements

uses some appropriate strategies, with partial success, to design a playground that meets some of the requirements

uses appropriate and successful strategies to design a playground that meets most of the requirements (may be somewhat unrealistic)

uses innovative and effective strategies to design a playground that meets all requirements and is realistic

Communication • explains plan clearly,

using mathematical terminology correctly (e.g., perimeter, area, square units)

may be unable to explain the plan; uses few appropriate mathematical terms

explains the plan, but explanation is unclear or incomplete; uses some appropriate mathematical terms

explains the plan clearly, using appropriate mathematical terms

explains the plan clearly, precisely, and confidently, using a range of appropriate mathematical terms

• presents plan clearly, including labels and units

presents plan unclearly and imprecisely

partially explains plan; may be vague and somewhat unclear

presents plan clearly, including labels and units

presents plan clearly and precisely including labels and units

Master 9.3


Name Date

Unit Summary: Length, Perimeter, and Area 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: Shape and Space: Measurement



Problem solving

Communication Overall

Ongoing Observations

Strategies Toolkit (Lesson 10)

Work samples or portfolios; conferences

Show What You Know

Unit Test

Unit Problem Design a Playground

Achievement Level for reporting

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

Comments: (Strengths, Needs, Next Steps)

Master 9.4


Name Date

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

• Estimate and measure in centimetres, decimetres, metres, and kilometres.

• Estimate and measure perimeter in centimetres and metres. • Estimate and measure area using non-standard units. • Recognize that different figures may have the same area. • Recognize that different figures may have the same perimeter.

Measurement is an important tool. The measurement skills students learn and develop in school will be invaluable in their life experiences. Measurement allows students to apply knowledge that they have learned in other areas of mathematics. Here are some suggestions for activities that you can do at home: Have your child estimate how far she travels when she rides her bicycle around the block, or when you take the bus to the mall. Ask your child to estimate and measure the perimeter of things around the house. For example, when your child is setting the table, ask him or her to estimate, and then measure, the perimeter of the table or of a placemat. Here is an activity you can do with your child. Treasure Hunt Look around your home for rectangular or square objects that fit the descriptions listed below. Use a metre stick or ruler to help you. Draw a picture of each item you find, and label the lengths of the sides.

• A rectangle with a perimeter of about 24 cm • A rectangle with a perimeter of about 4 m • A rectangle that has 2 sides about 1 m in length • A rectangle that has 2 sides between 1 m and 2 m in length

Master 9.5


Name Date

Covering Figures

Master 9.6


Name Date

Playground Planning Chart

Little Owl Daycare Centre Playground

Section Area Perimeter

Master 9.7


Name Date

Lesson 2A: Measuring Length in Decimetres EXPLORE You will need orange Cuisenaire Rods or paper strips.

Use the orange rod as your unit of length. Choose a classroom object you can measure. Estimate its length. Measure the object to the nearest unit. Record your results in a table.

Repeat with other objects.

Show and Share Which was the longest object you measured? The shortest? How did you use one measurement to help you estimate the next? CONNECT An orange Cuisenaire Rod is 10 cm long. A length of 10 cm is one decimetre (1 dm). A length of 10 dm is 1 m.

Master 9.8a

Lesson Focus: Use decimetres to measure length, width, and height.

Object Estimate Approximate Measurement

Length of table 10 rods 12 rods

1 dm = 10 cm 10 dm = 1 m


Name Date

Lesson 2A continued PRACTICE Use a ruler or metre stick to help you. 1. Find an object of each length. Then measure each object in centimetres.

a) about 4 dm long b) less than 1 dm long c) between 1 and 2 dm long d) longer than 5 dm

2. Order the measurements in Question 1 from shortest to longest. 3. Copy and complete.

a) 7 dm = ____ cm b) 3 dm = ____ cm c) 5 dm = ____ cm d) 60 cm = ____ dm e) 90 cm = ____ dm f) 20 cm = ____ dm

4. Copy and complete.

a) 70 dm = ____ m b) 90 dm = ____ m c) 30 dm = ____ m d) 4 m = ____ dm e) 8 m = ____ dm f) 5 m = ____ dm

5. Which is longer? How do you know?

a) 2 dm or 25 cm b) 94 cm or 9 dm c) 51 cm or 8 dm d) 75 dm or 6 m e) 63 dm or 10 m f) 27 dm or 2 m

6. Name 2 objects that are about 1 dm long, wide, or tall. 7. How could you measure the length of a table in decimetres using a

metre stick marked in centimetres? Use pictures, words, or numbers to explain. 8. Mabel made a cube train 7 dm long. Charles made a train 82 cm long.

Whose train is longer? By how much? How do you know? Reflect Suppose you want to estimate the height of the classroom door. Which unit would be easier to use — centimetres or decimetres? Explain.

Master 9.8b


Name Date

Additional Activity 1: Measuring Pennies

Work with a partner.

You will need a tub of pennies, and a ruler or measuring tape.

How to play:

Each player takes a handful of pennies.

Put your pennies side by side in a straight line.

Estimate the length of each line of pennies.

Measure your line to the nearest centimetre.

The player whose estimate is closer to the actual length

of each line gets a point.

The first player to get 5 points wins.

Take It Further: Play again. Stack the pennies and estimate, then measure, the heights of the piles.

Master 9.9


Name Date

Additional Activity 2: Blob Perimeters

Work on your own.

You will need cardboard “blobs,” scissors, string, and a ruler or metre stick.

Choose a blob.

Estimate its perimeter in centimetres.

Put the string around the edge of the blob.

Cut the string where the two ends meet.

Measure and record the length of the string.

Repeat with 3 more blobs.

Order the blobs from least to greatest perimeter.

Take It Further: Trace your hand on paper. Estimate and measure the perimeter of the tracing. Draw a rectangle that has the same perimeter.

Master 9.10


Name Date

Additional Activity 3: Cover Up

Work with a partner.

You will need yellow, red, green, and blue Pattern Blocks, and lima beans.

Estimate how many yellow Pattern Blocks will cover this figure.

Cover the figure to check.

Record the area.

Repeat with red Pattern Blocks.

Repeat with green Pattern Blocks.

Repeat with blue Pattern Blocks.

Take It Further: Draw a figure. Estimate, then find, the area of the figure in lima bean units.

Master 9.11


Name Date

Additional Activity 4: Areas of Four Square Units

Work on your own.

You will need a geoboard, geobands, and square dot paper.

This figure has an area of 1 square unit.

This figure has an area of 3 square units.

Make as many figures as you can with an area of 4 square units.

Record each figure on dot paper.

Take It Further: Find as many figures as you can with an area of 6 square units. Record each figure on dot paper.

Master 9.12


Name Date

Step-by-Step 1 Lesson 1, Question 6 Use a ruler. Step 1 Find something that is about 20 cm wide.

Draw a picture.

Step 2 Find something that is about 10 cm wide.

Draw a picture.

Step 3 The item in Step 1 is 10 cm wider than the item in Step 2.

How do you know this?

________________________________________________________

________________________________________________________

Master 9.13


Name Date

Step-by-Step 2 Lesson 2, Question 9 Use a metre stick and a new pencil. Step 1 Start at one end of the metre stick.

Place the pencil against the stick.

Estimate how many pencils fit along the stick. ___________________

Step 2 Move the pencil along the stick.

How many pencils fit? ___________________

Step 3 Draw a picture to show how many pencils fit along a metre stick.

Step 4 Suppose you do not have a pencil or a metre stick.

You know that a pencil is about 20 cm long.

The metre stick is 100 cm long.

About how many pencils fit? ___________________

How do you know? Explain.

________________________________________________________

________________________________________________________

Master 9.14


Name Date

Step-by-Step 2A Lesson 2A, Question 8 Step 1 Continue this counting pattern:

10, 20, 30, _____, _____, _____, _____

Step 2 Use the pattern in Step 1.

Write the correct number on each line.

1 dm = 10 cm

2 dm = _____ cm

3 dm = _____ cm

4 dm = _____ cm

5 dm = _____ cm

6 dm = _____ cm

7 dm = _____ cm

Step 3 How long is Mabel’s train in centimetres? ________

Step 4 Charles’ train is 82 cm long.

Whose train is longer? ________

Step 5 Write a subtraction sentence to show how much longer.

_____________________________________

Master 9.15


Name Date

Step-by-Step 3 Lesson 3, Question 4 Step 1 How far is it from your home to the corner store? _________________

Step 2 How far is it from the corner store to your home? _________________

Step 3 How far do you walk from home to the store, then back home?

________________________________________________________

Step 4 How many metres in 1 km? _________________________________

Step 5 Compare your answers to Steps 3 and 4.

Did you walk 1 km? Explain.

________________________________________________________

________________________________________________________

________________________________________________________

Master 9.16


Name Date

Step-by-Step 4 Lesson 4, Question 6 A rectangle has equal opposite sides. The perimeter of the rectangle is 16 cm. So, the length + width + length + width = 16 cm Step 1 Suppose the width is 1 cm.

What is the length? ___________________

Draw the rectangle on grid paper.

Step 2 Suppose the width is 2 cm.









Step 5 Can you draw any more rectangles with perimeter 16 cm? Explain.

________________________________________________________

________________________________________________________

Master 9.17


Name Date

Step-by-Step 5 Lesson 5, Question 5 Use 1-cm grid paper. Let 1 cm represent 1 m. The perimeter of a rectangle is 20 m. Step 1 Suppose the width of the rectangle is 1 m.



Step 2 Suppose the width of the rectangle is 2 m.












Step 6 Can you draw any more rectangles with perimeter 20 m?

Explain.

________________________________________________________

________________________________________________________

Master 9.18


Name Date

Step-by-Step 6 Lesson 6, Question 4 Use triangular grid paper. Step 1 Use 6 green Pattern Blocks to make a figure.

Draw it on grid paper.

How did you make the figure?

________________________________________________________

________________________________________________________

Step 2 Make a different figure using 6 green Pattern Blocks.

Draw it on grid paper.

How do you know it is different?

________________________________________________________

________________________________________________________

Step 3 Continue to make different figures with 6 green Pattern Blocks.

Draw each figure on grid paper.

Step 4 How many different figures did you make using

6 green Pattern Blocks? ___________________

Master 9.19


Name Date

Step-by-Step 7 Lesson 7, Question 4 The area of the tabletop is the number of squares needed to cover it. Step 1 Jan said the area is 8 square units.

Sketch a picture to show Jan’s tabletop.

Step 2 Madhu said the area is 50 square units.

Sketch a picture to show Madhu’s tabletop.

Step 3 Can both Jan and Madhu be correct? Explain.

________________________________________________________

________________________________________________________

________________________________________________________

Master 9.20


Name Date

Step-by-Step 8 Lesson 8, Question 7 Use grid paper. A rectangle has an area of 18 square units. Step 1 Suppose the width is 1 unit.

Draw a rectangle with 1 row of 18 squares.

Step 2 Suppose the width is 2 units.

Draw a rectangle with 2 rows of squares.

The total number of squares is 18.

Step 3 Suppose the width is 3 units.

Draw a rectangle with 3 rows of squares.

The total number of squares is 18.

Step 4 Can you draw a rectangle with 4 rows of squares,

and the total number of squares is 18? _________________________

Step 5 How do you know you have drawn all possible rectangles?

________________________________________________________

________________________________________________________

Master 9.21


Name Date

Step-by-Step 9 Lesson 9, Question 4 Use 1-cm grid paper. Step 1 Draw a square that has sides 2 units long.

Write its area. How did you find the area?

________________________________________________________

________________________________________________________

Write its perimeter. How did you find the perimeter?

________________________________________________________

________________________________________________________

Step 2 Draw a square that has sides 4 units long.

Write its area. Write its perimeter.

________________________________________________________

Step 3 Look at the two areas.

How do they compare?

________________________________________________________

________________________________________________________

Step 4 Look at the two perimeters.

How do they compare?

________________________________________________________

________________________________________________________

Master 9.22


Name Date

Unit Test: Unit 9 Length, Perimeter, and Area Part A 1. Estimate the length of each line.

Then measure each line to the nearest centimetre.

Record each estimate and measurement in the table.

2. Find the perimeter of each figure.

Record your results in the table.

Line Estimate Measurement

A B

Master 9.23a

Figure Perimeter A B C


Name Date

Unit Test continued 3. Find the area of each figure.

Record your results in the table.

Part B 4. Would you measure each distance in centimetres, decimetres, metres, or

kilometres?

a) the distance from your bedroom to the kitchen ____________________

b) the distance from Canada to China _____________________________

c) the distance travelled by a snail in 1 minute ______________________

d) the distance from your knee to your ankle ________________________

5. Marla made two paper chains.

One chain was 63 cm long.

The other chain was 31 cm long.

Marla joined the two chains together.

Is the new chain longer or shorter than 1 m?

Explain.

________________________________________________________

________________________________________________________

Master 9.23b

Figure Area

A

B


Name Date

Unit Test continued 6. Use the dot paper below.

a) Draw a different figure that has the same perimeter as Figure A.

b) Draw a different figure that has the same area as Figure B. Part C 7. Alice has a rectangular vegetable garden.

She wants to enclose the garden with fencing to keep the rabbits out.

Alice needs 28 units of fencing to enclose the garden.

Use grid paper. Draw a picture to show how long and how wide Alice’s

garden could be. Find as many answers as you can.

Master 9.23c


Name Date

Sample Answers Unit Test – Master 9.23 Part A 1. a) Estimates will vary.

Measurements: Line A: 7 cm; Line B: 15 cm

2. 3. Part B 4. a) metres b) kilometres c) centimetres d) centimetres or decimetres 5. The chain is 63 cm + 31 cm = 94 cm long.

1 m = 100 cm; so, the chain is shorter than 1 m.

6. a) The figure should have a perimeter of

18 cm. b) The figure should have an area of

10 square units.

Part C 7. Possible rectangles: 1 unit by 13 units,

2 units by 12 units, 3 units by 11 units, 4 units by 10 units, 5 units by 9 units, 6 units by 8 units, 7 units by 7 units

Master 9.24

Figure Perimeter A 12 cm B 11 cm C 90 m

Figure Area A 9 square units B 9 square units


Extra Practice Masters 9.25–9.31 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.

All Rights Reserved. This publication is protected by copyright,and permission should be obtained from the publisher prior toany prohibited reproduction, storage in a retrieval system, ortransmission in any form or by any means, electronic, mechanical,photocopying, recording, or likewise. For information regardingpermission, write to the Permissions Department.

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