western canadian teacher guide - sd67 (okanagan skaha) · at the amusement park cluster 1: ... the...

Teacher GuideWestern Canadian

Unit 7: Motion Geometry

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

“Young children come to schoolwith intuitions about howshapes can be moved. Studentscan explore motions such asslides, flips, and turns by usingmirrors, paper folding, andtracing. Later, their knowledgeabout transformations shouldbecome more formal andsystematic. In grades 3 – 5students can investigate theeffects of transformations andbegin to describe them inmathematical terms.”

Principles and Standards for School

Mathematics, NCTM 2000

Mathematics Background

What Are the Big Ideas?

• A geometric figure can be described in terms of its location on a grid.

• Figures in a plane can be moved. These movements can be described in terms of translations (slides), reflections (flips), and rotations (turns).

• Some figures have more than one line of symmetry.

How Will the Concepts Develop?

Students describe movements on maps and grids. They use directionallanguage (left, right, up, down, north, south, east, west) to describe howto move from one space or place to another, then from one point ofintersection to another.

Students use pictures, cutouts, Pattern Blocks, and Miras to exploreslides, turns, and reflections. They use mathematical language todescribe these transformations.

Students use paper folding and Miras to investigate lines of symmetry.They sort figures according to the numbers of lines of symmetry.

Why Are These Concepts Important?

The skills and concepts developed in this unit enhance students’ abilityto navigate their spatial world. Active exploration of motion geometry atthis level establishes a solid foundation that is necessary for learningand applying math in higher grades. The work in this unit is closelyconnected to other areas of study, such as art, science, and social studies.

FOCUS STRANDShape and Space: Transformations

Motion Geometry

ii Unit 7: Motion Geometry

7

Unit 7: Motion Geometry iii

Curriculum Overview

General Outcome• Students use numbers and direction

to describe the relative positions ofobjects in one dimension, usingeveryday contexts.

Specific Outcomes• Students communicate and apply

terms of direction, such as north orsouth and east or west, and relateto maps. (SS29)

• Students trace a path, using oral orwritten instructions. (SS21)

LaunchAt the Amusement Park

Cluster 1: Exploring Grids and Maps

Show What You Know

Unit ProblemAt the Amusement Park

General Outcome• Students use numbers and direction

to describe the relative positions ofobjects in one dimension, usingeveryday contexts.

Specific Outcomes• Students graph whole number

points on a, . . ., vertical numberline. (SS30)

• Students communicate and applyterms of direction, such as north orsouth and east or west, . . . (SS29)

Cluster 2: Exploring Transformations and Symmetry

Lesson 2:Looking at SlidesLesson 3:Strategies ToolkitLesson 4:What Is a Turn?Lesson 5:Exploring ReflectionsLesson 6:Lines of Symmetry

Lesson 1:Grids and MapsLesson 14:Using Directions

iv Unit 7: Motion Geometry

Curriculum across the Grades

Grade 2

Students communicateand apply positionallanguage in oral, written,or numerical form. Theycreate symmetrical 2-Dshapes by folding andreflecting.

Grade 3

Students communicateand apply terms ofdirection, such as northor south and east or west,and relate to maps. Theygraph whole numberpoints on a horizontalnumber line or a verticalnumber line.

Students trace a path,using oral or writteninstructions.

Grade 4

Students communicateand apply terms ofdirection, such as north,south, east, west, andrelate to maps and grids.They place an object on agrid, using columns androws.

Students trace a path,using oral or writteninstructions, and writeinstructions for a givenpath. They create andverify symmetrical 2-Dshapes by drawing linesof symmetry.

A large part of this unit goes beyond the requirements ofyour curriculum. This content has been labelled optional,and can be omitted.To ensure curriculum coverage, this Teacher Guidemodule contains:• One new lesson and an alternative Unit Problem and

Show What You Know• Suggestions for how to align other assessment pieces

with the outcomes of your curriculum

Curr i cu lum Focus

Additional Activities

Draw the PathFor Extra Practice (Appropriate for use after Lesson 1A)Materials: Draw the Path (Masters 7.14a and 7.14b),red, blue, and purple pencil crayons

The work students do: Students work alone. Thestudent follows written directions to draw 3 differentpaths on a map, using a different colour for each path.

Take It Further: Students choose 2 places on themap. They draw the path from one place to the other.They describe the path they drew to a classmate, usingdirection words.

Linguistic/LogicalIndividual Activity

Left or RightFor Extra Practice (Appropriate for use after Lesson 1)Materials: Left or Right (Master 7.12), 2 numbercubes labelled 1 to 6, 1 counter

The work students do: Students work alone. Thestudent puts her counter on Start on the game board.She rolls the number cubes and adds. If the sum is even,the student moves the counter one space to the left. If thesum is odd, she moves the counter one space to theright. The student keeps playing until she lands on Winor Lose.

Take It Further: Students play again, this time with apartner. They play until one player lands on Win orLose.

Kinesthetic/SpatialIndividual Activity

Unit 7: Motion Geometry v

Symmetrical MasterpieceFor Enrichment (Appropriate for use after Lesson 6)Materials: Symmetrical Masterpiece (Master 7.15), 1-cm grid paper (PM 20), rulers, crayons or pencil crayons

The work students do: Students work with a partner.One student draws a horizontal or vertical line on a sheetof grid paper. He colours a square on his side of the line.The other student finds the corresponding square on herside of the line, then colours it using the same colour.Students continue to colour squares in this way, until theyhave created a symmetrical masterpiece.

Take It Further: Challenge students to draw a verticaland a horizontal line on the grid, then create a designwith 2 lines of symmetry.

Social/VisualPartner Activity

Stay on the PathFor Enrichment (Appropriate for use after Lesson 1A)Materials: Stay on the Path (Master 7.13), 1-cm gridpaper (PM 20), number cube, 2 crayons of differentcolours, paper bag containing 4 small pieces ofcardboard labelled “north,” “south,” “east,” “west”

The work students do: Students work in pairs.Students choose an intersection point near the centre ofthe grid paper. They draw a dot on this point and labelit “Start.” One student rolls the number cube and takesa card from the bag. He then colours a path from“Start” along the grid lines. The number cube tells howmany squares to move, and the card tells the direction.Students take turns until one player’s path takes her orhim off the grid.

Take It Further: Students describe how to move from“Start” to the point where the winner went off the grid.

Kinesthetic/Social Partner Activity

vi Unit 7: Motion Geometry

Planning for Unit 7

Planning for Instruction

Lesson Time Materials Program Support

Suggested Unit time: About 1–2 weeks

Unit 7: Motion Geometry vii

Purpose Tools and Process Recording and Reporting

Planning for Assessment

2 Unit 7 • Launch • Student page 274

At the Amusement Park

LESSON ORGANIZER

Curriculum Focus: Activate prior learning about motion geometry.

10–15 min

L A U N C H

ASSUMED PRIOR KNOWLEDGE

Students understand that people and objects move indifferent ways.

Students can use appropriate language to describedifferent movements.

✓

✓

ACTIVATE PRIOR LEARNING

Invite students to examine the picture of theamusement park in the Student Book.

Ask questions, such as:• What is happening in the picture?

(Children are having fun on the rides.)• Where have you seen rides like these?

(I have seen rides like these in the mall parking lotand at the fair.)

• Which ride would you like to go on? (I would like to go on the Log ride.) Why? (You get splashed when you get to the bottom.)

• Which ride would you not like to go on? (I would not like to go on the Tea Cups.)Why? (I always get dizzy.)

Invite volunteers to relate experiences theyhave had on similar rides. Discuss the questionsposed in the Student Book. Encourage studentsto describe movements using language such asup and down, left or right, turn, and slide.

(Sample answers: Ferris Wheel: turn around; Slide:slide down; Airplanes: turn in a circle; House ofMirrors: move left, right, forward, and backward;Elevator Drop: slide down; Merry-Go-Round: turn in acircle; Roller Coaster: move up, down, and turn; TeaCups: the cups turn and the ride turns; Log Ride: moveup, down, and right; Mini-Coaster: move up and down;Windmill: turn that goes up and down)

Tell students that in this unit, they will learnabout different ways objects and figures canmove, and that at the end of the unit they willshow what they have learned by designing anew ride for the amusement park.

The content of this Launch goes beyond the requirements ofyour curriculum. You may wish to focus on the relativepositions of the rides. (For example, you might ask questionssuch as, Which ride is to the left of the merry-go-round? Onwhich rides are people high above the ground?)

Curr i cu lum Focus

LITERATURE CONNECTIONS FOR THE UNIT

It’s a Fair Day Amber Brown by Paula Danziger. New York:Puffin, 2003.ISBN 0698119827Amber has a less than perfect day at a county fair. Amber’s experiences with the merry-go-round and the airplane ride complement the Unit Launch.

Chess for kids by Michael Basman. New York: DorlingKindersley, 2001.ISBN 078946540XThis is a simple introduction to the basic movements of thepieces, as well as the rules and techniques of chess.

The Bedspread by Sylvia Fair. New York: Morrow Jr. Books, 1982.ISBN 0688008771Two elderly sisters decide to embroider the house they lived in aschildren on a white bedspread. The results surprise them.

DIAGNOSTIC ASSESSMENT

What to Look For

✔ Students can identifydifferent types ofmovements.

✔ Students can useappropriatedirectional languageto describemovement.

What to Do

Extra Support:

Students who cannot identify different types of movements may benefit fromparticipating in the development of charts that list objects that turn, objects thatslide, and objects that can be flipped.Work on this skill during Lessons 2 to 5.

Students who do not use appropriate directional language to describe movementmay benefit from playing Simon Says. For example, students could be instructed toshake their left hand, take 2 steps to the left, or turn to the right.Work on this skill throughout the unit.

Unit 7 • Launch • Student page 275 3

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

The e-Tools appropriate for this unit include Geometry Drawing.Students can use these tools to draw figures, then flip and rotate them.

REACHING ALL LEARNERS

4 Unit 7 • Lesson 1 • Student page 276

Grids and Maps

LESSON ORGANIZER

Curriculum Focus: Describe how to move from one place toanother on a grid. (SS29, SS31)Teacher Materials� chessboard and chess pieces� Chessboard transparency (Master 7.7)� Playground Grid transparency (Master 7.8)� countersStudent Materials Optional� 1-cm grid paper (PM 20) � Step-by-Step 1 (Master 7.16)� Playground Grid � Extra Practice 1 (Master 7.24)

(Master 7.8)Vocabulary: grid, up, down, left, rightAssessment: Master 7.2 Ongoing Observations: Motion Geometry

40–50 min

L E S S O N 1

Key Math Learnings1. The chessboard is a grid.2. To move from one place to another on a grid, move left or

right, and up or down.

BEFORE Get S tar ted

Show students a chessboard. Ask:• What games can you play on this board?

(Checkers and chess)

Have students who play these games tell what they know about them. Show studentsthe chess pieces and invite volunteers to name them.

Have students describe the chessboard. (Sample answer: It has 8 rows, with 8 squares in eachrow. Every other square is dark.) Introduce theterm grid to describe the chessboard.Read through the introduction to the lessontogether. Display a transparency of achessboard on the overhead projector. Invitevolunteers to demonstrate the moves a knightcan make. Stress that all moves must behorizontal or vertical, and not diagonal.

Present Explore. Demonstrate how to record themoves by counting the number of squares ineach direction. For example, to move from Tomto Joe, move 3 squares left and 3 squaresdown. Distribute copies of Playground Grid(Master 7.8), so students do not mark theirStudent Books.

DURING Exp lore

Ongoing Assessment: Observe and Listen

Ask questions, such as:• How can Lee move to get to Ada?

(He can move 4 squares right and 3 squares downor he can move 4 squares down, 4 squares right,and 1 square up.)

• How else can Lee move to get to Ada? (He can move 3 squares down and 4 squares rightor he can move 1 square down, 1 square right, 1 square down, 1 square right, 1 square down, and 2 squares right.)

Unit 7 • Lesson 1 • Student page 277 5

Early FinishersHave students use the playground grid in Explore to describe howAmy could move to get to Joe, then to Ann, and then to Tom.

Common Misconceptions➤Students think they must always move left or right and up or

down to go from one square to another on a grid, even if thetwo squares in question are in the same row or column.

How to Help: Explain that if two squares are in the same rowor column, students only need to move right or left, or up ordown to get from one square to the other. Moving both right orleft, and up or down would result in a longer way thannecessary.

ESL StrategiesStudents for whom English is a second language may feel more comfortable using arrows instead of words to record their moves.


• Suppose Jane moves 2 squares down and 1 square right. Which child will she get to?(Joe)

Listen for students who include the start squarein their count. Use a counter on a grid todemonstrate why the start square is notcounted. Watch for students who confuse leftand right. Tape a reference card, labelled asfollows, on their desks:

AFTER Connec t

Display a transparency of the playground gridon the overhead projector. Invite volunteers todemonstrate, then describe, one of the movesthey made. Record the moves in a chart on theboard. For each move, ask students to describean alternative way. There are many ways tomove from one person to another, but only 2 ways to describe the shortest route.

Ask:• How can you find the shortest way to move

from one person to another? (Move left or right until you get to the same columnas the person, then move up or down until you getto the person. Alternatively, move up or down untilyou get to the same row, then left or right until youget to the person.)

Have students examine the two maps inConnect. Ask:• How are the maps alike?

(Both of them are drawn on grids.)• How are they different?

(The first map shows the locations of the cars andthe school with coloured squares. The second maphas dots to show the locations of the buildings. Each dot is where two grid lines meet.)

L R

Numbers Every DayStudents could use hundred charts. To count on by 2s to 68,students may note the pattern in the ones digits: 2, 4, 6, 8, 0, ....To count on by 5s to 92, students may note the pattern in theones digits: 2, 7, 2, 7, 2, 7, .... To count on by 10s to 132,students may note that the ones digit repeats and the tens digitincreases by 1.

42, 44, 46, 48, 50, 52, 54, 56, 58, 60, 62, 64, 66, 6842, 47, 52, 57, 62,

67, 72, 77, 82, 87, 92 42, 52, 62, 72,

82, 92, 102, 112, 122, 132

Sample Answers1. a) 4 squares right and 3 squares down, or 3 squares down

and 4 squares rightb) 2 squares left and 4 squares up, or 4 squares up and

2 squares leftc) 2 squares left and 4 squares down, or 4 squares down and

2 squares leftd) 2 squares right and 3 squares up, or 3 squares up and

2 squares right2. The first two moves take me to the bank. From the bank, the

next two moves take me to the grocery store.3. I know I started at the gas station because I followed the

moves in the opposite direction. From the train station, Imoved 4 squares left and 2 squares up. I ended up at the gas station.

4. a) I am on 16, and to get to 35, I move 1 square left and 2 squares down, or 2 squares down and 1 square left.

b) I am on 15, and to get to 4, I move 1 square left and 1 square up, or 1 square up and 1 square left.

c) I am on 12, and to get to 9, I move 7 squares right and 1 square up, or 1 square up and 7 squares right.

d) I am on 49, and to get to 20, I move 1 square right and 3 squares up, or 3 squares up and 1 square right.

5. Move 3 squares right and 1 square up, or 1 square up and 3 squares right.

Ensure students understand that on the secondmap, each dot represents the location of abuilding, each building is at an intersection,and to move from one building to another, youmust move along the lines of the grid.

Prac t i ce

Question 6 and Reflect require 1-cm grid paper.

Assessment Focus: Question 3

Students locate the train station on the map.Some students may be able to reverse the orderof the given moves to determine the startingpoint on the grid. Other students may useguess and check to find the starting point.Students provide a reasonable explanation ofhow they know their answer is correct.

Students who need extra support to completeAssessment Focus questions may benefit fromthe Step-by-Step masters (Masters 7.16–7.21).


At the grocery store

At the gas station


ASSESSMENT FOR LEARNING

What to Look For

Understanding concepts ✔ Students understand that movements

on a grid are made to the left orright, and up or down, and can bedone in more than one way.

Applying procedures✔ Students can find the shortest way to

move from one place to another on a grid.

Communicating✔ Students use correct terminology to

describe how to move from one placeto another on a grid.

What to Do

Extra Support: Provide students with a counter and anenlarged copy of the playground grid in Explore (Master 7.8).Have them count as they move the counter from square to square(for example, 1, 2, 3 squares right and 1, 2 squares down).Students can use Step-by-Step 1 (Master 7.16) to completequestion 3.

Extra Practice: Have students complete the Additional Activity,Left or Right (Master 7.12).Students can complete Extra Practice 1 (Master 7.24).

Extension: Students can complete the Additional Activity, Stay on the Path (Master 7.13).

Recording and ReportingMaster 7.2 Ongoing Observations:Motion Geometry

6.

The rule for my pattern is: Move 2 squares left and 2 squaresdown, or 2 squares down and 2 squares left.

REFLECT: To get from A to B, move 5 squares left and 4 squares up, or 4 squares up and 5 squares left. To get from B to A, move 5 squaresright and 4 squares down, or 4 squares down and 5 squares right.

A

B

Start

End


Discuss the map in the Student Book. Invite students to suggest ways to describe the given routes.

Present Explore. Remind students that their instructions must be clear enough so that someone elsewill be able to follow them and find the treasure.

DURING Exp lore


Ask questions, such as:• What are the first things you should put in your instructions?

(Where to start and which direction to face)• How can you tell how far to go before you make a turn?

(We can count the steps.)

Watch to see if students develop a set of instructions that is clear and precise enough for someoneelse to follow. Do their instructions describe both direction and distance?

8 Unit 7 • Lesson 1A

Using Directions

Key Math LearningDirection terms, such as north, south, east, and west, can be usedto describe how to get from one location to another on a map.

LESSON ORGANIZER

Curriculum Focus: Use terms of direction. (SS29, SS31)Teacher Materials� globeStudent Materials Optional� Lesson 1A (Master 7.11) � Step-by-Step 1A � Maps of Blueberry (Master 7.17)

(Master 7.6) � Extra Practice 1A (Master 7.25)

Assessment: Master 7.2 Ongoing Observations: Motion Geometry

40–50 min

L E S S O N 1 A

Sample Answers1. Go west on Queen St. to Water St. Turn north.

Go 1 block to Cardinal Rd. Turn east.Go past the Dollar Store and the Drug Store.The library is on the right just before Hill St.

2. a) Go east on Cardinal Rd. to the secondintersection. Turn south on Erb St.Go 2 blocks south to Park St. Turn west.The Fitness Centre is on the left.

b) Go east on Park St. Turn north at the secondintersection.Go north 2 blocks. Turn east on Cardinal Rd.The mall is on the left.

REFLECT: I learned that you can use the directionsnorth, south, east, and west to explain how to getfrom one place to another on a map.

AFTER Connec t

Invite a pair of students to share their instructions with the class. Have them tell whether theclassmates to whom they gave the instructions were successful in finding the treasure, and why.

Use the map in Connect to introduce the direction terms north, south, east, and west. Discuss usingthese terms to describe how to get from one location to another using a map.

You may wish to use a globe to explain how the directions are defined in relation to the North Pole.Distribute copies of the map of Blueberry (Master 7.6).

Prac t i ce


Students use the terms north, south, east, and west to describe a route from one location to theother. Some students may recognize that more than one answer is possible and provide alternativeroutes.

Unit 7 • Lesson 1A 9


What to Look For

Understanding concepts✔ Students understand the cardinal

directions north, south, east, and west.

Applying procedures✔ Students can apply the cardinal

directions and relate them to maps.

Communicating✔ Students can describe how to move

from one location to another usingcardinal directions.

What to Do

Extra Support: Have students choose 2 places on the map inConnect. Have them slide their fingers along the roads to movefrom one location to the other. As they slide, have them say, for example — I’m going right. That’s east.Students can use Step-by-Step 1A (Master 7.17) to completequestion 2.

Extra Practice: Have students complete the Additional Activity,Draw the Path (Master 7.14).Students can complete Extra Practice 1A (Master 7.25).

Extension: Have students complete the Additional Activity, Stay on the Path (Master 7.13).


Alternative ExploreMaterials: large sheets of blank paperStudents draw a map of their classroom. They mark 2 places on the map and describe how to get from one place to the other.Early FinishersInvite students to write instructions describing how to get from their classroom to the principal’s office.



Looking at Slides

Key Math Learnings1. A slide moves an object along a line. The way the object

faces does not change.2. Slides can be in different directions. Slides can be vertical,

horizontal, or diagonal.3. A slide is sometimes called a translation.

LESSON ORGANIZER

Curriculum Focus: Identify slides (translations) using PatternBlocks and pictures.Teacher Materials� cutout of a small, non-symmetrical figureStudent Materials Optional� Pattern Block triangles � Step-by-Step 2 (Master 7.18)

(PM 25) � Extra Practice 1 (Master 7.24)Vocabulary: slide, vertical, horizontal, diagonal, translationAssessment: Master 7.2 Ongoing Observations: Motion Geometry

optional

L E S S O N 2


Display a cutout of a non-symmetrical figure onan overhead transparency. Trace around thefigure with a marker. Slide the figurehorizontally to a new position. Ask:• How did I move the figure?

(You moved the figure by sliding it in a straight line.)• In which direction did the figure move?

(It moved to the right.)• What did you notice about the way the

figure was facing during the slide? (It was always facing the same way. It did not turn.)

Return the figure to its original tracing andrepeat the process. Include examples of verticaland diagonal slides. Emphasize that the figuredoes not turn during the slide.

Have students read the introduction to thelesson. Ask:• How does the picture show a slide?

(The moving walkway moves the people along a lineand the way the people face does not change.)

Invite volunteers to give examples of otherthings that slide people from one position toanother. (Sample answer: sled, playground slide, skis)

Present Explore. Students should find pairs oftriangles that show a slide. They verify theirchoices by placing a green Pattern Block on one triangle in a pair and sliding it to theother triangle.

These blocks show a slide: A to G, B to F, C to E, D to HAll other combinations of pairs of blocks do not show a slide.

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

Curr i cu lum Focus


Early FinishersHave students choose a small object that is easy to trace. Studentsplace the object on paper, trace it, slide the object, then trace itagain. Students turn the object, trace it in a different position onthe paper, slide the object, then trace it again. Students repeatthis process several times. Students trade papers with a classmateand try to find the pairs of tracings that show a slide.

Common Misconceptions➤Students have difficulty finding pairs of figures that show a

slide, as in Explore.How to Help: Encourage students to focus on one side or onone vertex of a given figure. Have them find a second figurewith the corresponding side or vertex facing the same way.

ESL StrategiesReinforce the meanings of the terms vertical, horizontal, anddiagonal by having students slide a counter in the correspondingdirection as they say each word. Repeat until students arecomfortable with the terms.


Numbers Every DayEncourage students to discuss the strategies they used. Studentsshould recognize that to get the second number you double thefirst number and add 1. Therefore, when you say 35, I will say71. That is, I say two times what you say, plus 1. Or, when I saya number, you subtract 1 and divide by 2 to get your number.So when I say 101, you said 50.

DURING Exp lore


• How do you know that triangles A and Gshow a slide? (I can slide the Pattern Blocktriangle along a line from A to G.)

• In what direction does A move to get to G?(It moves on a slant, down and to the right.)

• Name 2 triangles that do not show a slide. (B and C) How do you know? (They are not facing the same way.)

• What changes when you slide a figure? (The position of the figure changes.) What does not change? (The way the figure faces does not change.)

Watch for students who find only 2 or 3 pairsof triangles and then stop. Encourage them tocontinue to look for other pairs.

AFTER Connec t

Invite students to identify the pairs of blocksthat show a slide. Record each pair on theboard. Ask questions, such as:• What did you do to find a pair of blocks that

shows a slide? (I looked for 2 blocks facing the same way.)

• How do you know those blocks show aslide? (I can slide from one block to the other alonga line. The blocks face the same way.)

• How would you describe that slide? (Straight down)

• How do you know that 2 blocks do not showa slide? (The blocks do not face the same way.)

• How do you know you have found allpossible slides? (I have found all pairs of blocksthat face the same way.)

71

50

Double the number, then add 1.

Sample Answers1. I know pictures a, d, and e show a slide because the figures

have been moved along a line and they face the same way.I know pictures b, c, and f do not show a slide because thefigures do not face the same way.

3. a) A chair, a drawer in the teacher’s desk, and the cover onmy calculator slide.

b) A ball, the wheels on a toy car, and the hands on the clockmove but do not slide.

4. Jill could have started on 9, and moved 3 squares down and 2 squares right. She could also have started on 14, andmoved 3 squares right and 2 squares down; on 30, andmoved 3 squares left and 2 squares right; on 35, and moved 3 squares up and 2 squares down. Each of thesestarting squares would take Jill to the red square.

Use the cutout figure from Before on theoverhead projector to introduce the termshorizontal slide, vertical slide, and diagonalslide. Have students describe the slides inExplore using these terms. Use the pictures inConnect as further examples of slides and non-slides, and the possible directions of slides.

Prac t i ce


Most students should realize that to determine apossible starting square, they could reverse theorder of the slides. Students could start on thered square and move 2 squares up and 3 squares left, or 2 squares left and 3 squares up.Some students may realize that they can move 2 squares up and 3 squares down, or 2 squaresleft and 3 squares right. Some students may usea guess and check strategy. These students couldstart at any number, perform the slides in order,and repeat with different start numbers untilthey find a solution.


Pictures a, d, and ePictures b, c, and f

Horizontal slide Diagonal slide Vertical slide



What to Look For

Understanding concepts ✔ Students understand that a slide

moves an object along a line and thatthe object does not turn.

✔ Students understand that slides can bein different directions.

Applying procedures✔ Students can identify pairs of objects

that show a slide.

Communicating✔ Students can describe slides using

correct mathematical terminology.

What to Do

Extra Support: Provide students with a Pattern Block. Have themdemonstrate a horizontal slide to the right, a vertical slide down, adiagonal slide up to the right, and so on.Students can use Step-by-Step 2 (Master 7.18) to complete question 4.

Extra Practice: Have students work in pairs. Students take turns todescribe a slide (for example, a horizontal slide to the left). The otherstudent performs the slide using a small object such as an eraser.Students can complete Extra Practice 1 (Master 7.24).

Extension: Challenge students to use a Pattern Block to create adesign with slides.


REFLECT: A slide moves an object along a line. The object doesnot turn. The way the object faces does not change. Slides canbe in different directions. They can be horizontal, vertical,or diagonal.

At Home: For things that slide, children may suggest: my handdown the banister rail; my chair as I move away from thetable; the water leaving the tap and reaching the sink. For things that do not slide, children may suggest: the tapwhen I turn it on; the light switch when I turn the light on; the front door when I open it.Jill could have started on 9, 14, 30, or 35.


Strategies Toolkit

Key Math LearningA problem involving motion geometry can be solved using thestrategy draw a picture.

LESSON ORGANIZER

Curriculum Focus: Interpret a problem and select anappropriate strategy. (SS30, SS29)Teacher Materials� copy of The Tortoise and the Hare� 1-cm grid transparency (PM 20)Student Materials� 1-cm grid paper (PM 20)Assessment: PM 1 Inquiry Process Check List, PM 3 Self-Assessment: Problem Solving

40–50 min

L E S S O N 3


Present Explore. Have students who know thestory explain how the situation presented issimilar to and different from the fable.

DURING Exp lore


Watch for students who do not understand thatafter 5 hours, the tortoise had completed therace and the hare had gone around the trackonly 4 times. Ask:• How long did the hare run? (1 hour)

How long did he rest? (4 hours) How many hours is that altogether? (5 hours)

• How long did it take the tortoise to goaround the track 5 times? (5 hours) How do you know? (It took 1 hour for the tortoiseto go around the track once. So, it would take 5 � 1 hour = 5 hours to go around the track 5 times.)

Invite volunteers to share their solutions withthe class and to explain the strategies they used.

AFTER Connec t

Work through the problem in Connect with thestudents. Invite volunteers to record the snail’smoves on a transparency of 1-cm grid paper.Ensure students understand that the snailreaches the top of the well on the fifth day andclimbs out. The snail is not in the well on thefifth night to slide back 1 m. Ask:• How far is it from the bottom of the well to

the top? (6 m)• How far did the snail actually climb? (10 m)

Explain. (It took the snail 5 days to get out of thewell. So, it climbed 2 m each day for 5 days; 5 � 2 m = 10 m.)

Prac t i ce

Encourage students to refer to the Strategies listto help in selecting an appropriate strategy.

The tortoise

5 days

Sample Answer

REFLECT: Drawing a picture helps me to solve a problembecause the picture makes it easier to see the solution. It iseasier to use the picture to find the answer than it is to figureit out in my head.


Common Misconceptions➤Students assume the hare will win the race and, as a result,

they do not work through the problem.How to Help: Remind students of the outcome of the race in thefable. Encourage students to work through the problem carefullyto see if a similar outcome occurs.

ESL StrategiesStudents for whom English is a second language may havedifficulty reading and interpreting the Explore problem. Read theproblem aloud, stopping at the end of each sentence to rephraseit, to ensure understanding.



What to Look For

Problem solving ✔ Students can read and interpret a

problem involving motion.

✔ Students can draw and label a pictureto solve a problem involving motion.

Communication✔ Students can describe their strategy

clearly and justify their solution.

What to Do

Extra Support: Students may benefit from working with apartner who can help them read and interpret a problem andorganize the given information in a picture.

Extra Practice: Have students create their own probleminvolving slides or direction. Students can trade problems with aclassmate and solve their classmate’s problem.

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

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

Alex Shannon

East30 m


What Is a Turn?

Key Math Learnings1. A turn or rotation moves a figure around a turn centre.2. After 1 turn, a figure is back to where it started. A turn can be

described in terms of the fraction of a turn that the figure moves(for example, quarter turn, half turn, three-quarter turn).

3. A turn can be described by the direction in which the figuremoves (clockwise or counterclockwise).

LESSON ORGANIZER

Curriculum Focus: Identify and perform turns (rotations) usingcutouts and Pattern Blocks.Teacher Materials� demonstration clock� toy pinwheel (optional)Student Materials Optional� 1-cm grid paper (PM 20) � Step-by-Step 4 (Master 7.19)� rulers � Extra Practice 2 (Master 7.26)� scissors� glue� crayons, markers, or pencil crayons� toy clocks� tracing paper� Pattern Blocks (PM 25)Vocabulary: turn, turn centre, quarter turn, half turn, three-quarter turn, clockwise, counterclockwise turn, rotationAssessment: Master 7.2 Ongoing Observations: MotionGeometry

optional

L E S S O N 4


Display a demonstration clock. Invite avolunteer to show 2:00 on the demonstrationclock. Slowly move the hands to show 3:00.Ask:• What time is it now? (It is 3:00.)• What happened to the hour hand?

(The hour hand moved from 2 to 3.)• What happened to the minute hand?

(The minute hand started at 12. It moved aroundthe clock, and ended up back at 12.)

Use the introduction to the lesson to establishthat the minute hand moves 1 complete turn inone hour and that the centre of the clock iscalled the turn centre.

Show students a toy pinwheel with the armspositioned horizontally and vertically. Relate thepositions of the arms to the 12, 3, 6, and 9 on aclock. Slowly rotate the arms to demonstratehow the arms move about the turn centre.

Present Explore. Ensure students understand theyshould use the lines on the grid paper as a guidewhen positioning the arms of the pinwheel.

DURING Exp lore


Ask questions, such as:• How do you know the 4 arms of your

pinwheel are congruent? (I can put them one on top of the other and theymatch exactly.)

This lesson goes beyond the requirements of yourcurriculum. If you choose to complete this lesson, allow40–50 minutes.

Curr i cu lum Focus


Alternative ExploreMaterials: Pattern Block rhombuses (PM 25), 1-cm grid paper (PM 20)Have students draw a dot in the centre of the grid paper.Students make a pinwheel by tracing a Pattern Block rhombus inthe 12, 3, 6, and 9 o’clock positions around the dot.

Early FinishersHave students trace a Pattern Block rhombus onto a piece ofpaper. Students turn the rhombus a quarter turncounterclockwise, trace the rhombus in its new position, returnthe rhombus to its original position, then turn the rhombus athree-quarter turn clockwise. Students describe what they see.

Common Misconceptions➤Students think all turns must start at the “12 o’clock” position.How to Help: Draw a turn centre on a piece of paper. Place aPattern Block in the “6 o’clock” position, with one vertex at theturn centre. Have students turn the block 1 turn, then a half turn,and so on. Repeat with other starting points.


• How will you show that the arms turnaround a centre? (I will draw a dot for the turn centre.)

• How will you place the arms? (I will put the arms along the grid lines in the 12, 3, 6, and 9 o’clock positions.)

• How much of 1 turn is it from one arm to the next? (One fourth)

Watch for students who are unable to describethe turn from one arm to the next. Relate theamount of turn to the movement of the minutehand on the clock from the hour to the quarterhour, then the half hour.

AFTER Connec t

Invite volunteers to show their pinwheels tothe class and describe the turn from one arm tothe next. Note students who use fractions intheir descriptions.

Use Connect to introduce the terms quarterturn, half turn, and three-quarter turn. Have students model each turn on a toy clock.Introduce the terms clockwise andcounterclockwise, then have students modelturns in different directions.

Have students draw a turn centre on a piece ofpaper, then use a Pattern Block rhombus todemonstrate various turns. Include bothclockwise and counterclockwise turns, andturns that begin in positions other than the“twelve o’clock” position.

Numbers Every DayStudents use a calculator to find 1 � 89 = 89, 2 � 89 = 178, 3 � 89 = 267, and 4 � 89 = 356. Students should see that thehundreds digit starts at 0 and increases by 1 each time, the tensdigit starts at 8 and decreases by 1 each time, and the onesdigit starts at 9 and decreases by 1 each time. Students usethese patterns to find 5 � 89 = 445, 6 � 89 = 534, 7 � 89 = 623, and 8 � 89 = 712. The pattern stops at 9 � 89 = 801. 10 � 89 = 890; the hundreds digit does notincrease by 1.

89, 178, 267, 356

445, 534, 623, 712

At 9 � 89 = 801

Slide Turn

Sample Answers1. Picture b shows a turn. One figure has moved a quarter turn

clockwise around the turn centre.Picture a shows a diagonal slide. One figure has moved alonga slanted line and both figures face the same way.

2. Pictures a and b show a turn. If the key and the top weremoved 1 turn, both of them would be back where they started.Pictures c and d do not show a turn. Picture c shows a slide.The red game piece is being moved along a line. Picture ddoes not show a turn. Although the coin may be turning, it isalso moving up and down in the air. After 1 turn, the coin isnot back to where it started.

4. a) To make a quarter turn, the hour hand moves from the 3 to the 6. The minute hand would still be on the 12.

b) After a half turn, the hour hand would be half waybetween the 12 and the 1. The minute hand would still beon the 6. After the hour hand passes the 12, the timechanges from p.m. to a.m.

c) After a three-quarter turn, the hour hand would be betweenthe 6 and the 7, but closer to the 7. The minute hand wouldstill be on the 9. After the hour hand passes the 12, thetime changes from a.m. to p.m.

Ensure students understand that after 1 turn, afigure is back to where it started. Tell studentsthat a turn is sometimes called a rotation.Ensure students understand that the direction ofa turn is important. Encourage students to givethe direction of a turn as well as the fraction ofa turn. Students may realize that a quarter turncounterclockwise moves a figure to the sameplace as a three-quarter turn clockwise. And, ahalf turn clockwise moves a figure to the sameplace as a half turn counterclockwise.

Prac t i ce

Have toy clocks available for questions 4, 6, and 7. Question 5 requires 1-cm grid paper.Have tracing paper available for questions 1, 3, and 8.


Students understand that a turn must bedescribed in terms of direction (clockwise orcounterclockwise) and in terms of the fractionof a turn. Students are able to determine theposition of the minute hand, then tell the timeafter each turn described.

Many students will ignore the hour hand asthey move the minute hand, to find that theclock shows 5:30. Some students may considerthe movement of the hour hand and determinethat the clock shows 4:30. In both cases,students should provide a reasonableexplanation of their conclusions including thestart time, the time after the first turn, and thefinal time.


Pictures a and bPictures c and d

A quarter turn counterclockwise or a three-quarter turn clockwise

6:00 a.m.

12:30 a.m.

6:45 p.m.

5. The turn centre is where the figures touch. The figures show ahalf turn clockwise or a half turn counterclockwise.

6. When Janetha finished brushing her dog, the clock showed9:15. Janetha was brushing her dog for 15 minutes.

7. 4:30; the clock face shows 5:00. When Rick turns the minutehand a three-quarter turn counterclockwise, the clock shows4:15. When he then turns the minute hand a quarter turnclockwise, the clock shows 4:30.

REFLECT: I turned my body a quarter turn when I rolled from myback to my right side to turn off the alarm. I turned thedoorknob about a half turn to open the front door. I turned thelid on my thermos 3 or 4 whole turns to open it at lunchtime.

Turn centre

StartEnd



What to Look For

Understanding concepts ✔ Students understand that a turn or

rotation moves a figure around a turn centre.

✔ Students understand that a turn mustbe described using the fraction of aturn and the direction of the turn.

Applying procedures✔ Students can perform turns using

cutouts and Pattern Blocks.

Communicating✔ Students can describe turns using

appropriate mathematical language.

What to Do

Extra Support: Students having difficulty with the concept ofturns may benefit from performing turns with their bodies. Giveinstructions such as, “Make a quarter turn clockwise” or “Make ahalf turn counterclockwise.”Students can use Step-by-Step 4 (Master 7.19) to completequestion 7.

Extra Practice: Students can complete Extra Practice 2 (Master 7.26).Extension: Challenge students to make a design with a redPattern Block that contains slides and turns.


15 minutes

4:30

A three-quarter turn clockwiseor a quarter turn counterclockwise


Exploring Reflections

Key Math Learnings1. A reflection or flip creates an image of a figure on the other

side of a reflection or mirror line.2. Under a reflection, a figure and its image are congruent and

face opposite ways.

LESSON ORGANIZER

Curriculum Focus: Identify reflections (flips) using PatternBlocks and pictures.Teacher Materials� 1-cm grid transparency (PM 20)� transparent Pattern BlocksStudent Materials Optional� mirrors � Step-by-Step 5 (Master 7.20)� Pattern Blocks (PM 25) � Extra Practice 2 (Master 7.26)� 1-cm grid paper (PM 20)� MirasVocabulary: reflection, reflection line, flipAssessment: Master 7.2 Ongoing Observations: MotionGeometry

optional

L E S S O N 5


Have students describe what they see whenthey look in a mirror. If necessary, introducethe term image. Ask:• Where else might you see your image?

(I might see my image in a pool of water, in awindow, or in a shiny table.)

Invite students to print their names on a slip ofpaper and hold them in front of a mirror.

Ask:• How is the image of your name in the mirror

different from how you wrote it? (The letters are reversed and the word is backward.)

• How is the image the same? (It has the same letters. The letters are the same size.)

• What words can you think of whose imageswould not be reversed? (MOM, WOW, TOOT)Explain. (The letters look the same forward andbackward. The words are spelled the same forwardand backward.)

Present Explore. Explain that the mirror line canbe horizontal or vertical. Tell students thatwhen they place the Mira on the mirror lineand look into it from the side of the originaldesign, the image in the Mira should overlapthe design on the other side exactly.

DURING Exp lore


Ask questions, such as:• What will you do with your Pattern Block

so that it is the image of your partner’sPattern Block? (I will flip it over so that it faces the opposite way.)

Numbers Every DayStudents could use the strategies they learned in Unit 2, Lessons 7 and 8.


Curr i cu lum Focus


Alternative ExploreMaterials: 1-cm grid paper (PM 20), MirasStudents work in pairs. One student draws a line through thecentre of the grid paper. This is the mirror line. The student drawsa figure on one side of the mirror line. The other student drawsthe reflection image of the figure. Students use a Mira to checktheir work, then switch roles and continue with another figure.

Early FinishersProvide students with cutouts of various figures. Have studentschoose a figure, trace it on one side of a mirror line, flip thefigure, then trace it again.

Common Misconceptions➤Students have difficulty using a Mira to determine if a figure

and its image show a reflection.How to Help: Have students trace a figure, its image, and themirror line on a piece of paper. Have students fold the paperalong the mirror line. If the figure and its image overlap exactly,they show a reflection.

ESL StrategiesHave students prepare a reference card for the terms “translation,”“rotation,” and “reflection.” Each term should be accompanied bya picture and its simpler synonym (slide, turn, flip).


• How can you use the grid paper to help youplace your Pattern Block? (I can count how many squares my partner’s blockis from the mirror line. I can place my block thesame number of squares from the mirror line on myside. I can use the horizontal lines to line up myblock with my partner’s block.)

• How do you know your block is the imageof your partner’s block? (I used the same block as my partner, and I flippedit so my block faced the opposite way. I put it in thesame spot as my partner’s block, but on my side ofthe mirror line.)

• How did you use the Mira to check the image? (I put the Mira on the mirror line. The image in theMira overlapped my partner’s design exactly.)

Watch for students who do not consider thedistance from the mirror line when placing ablock. Have students place the Mira on themirror line, then adjust the position of the

block until it coincides with the image in the Mira.

AFTER Connec t

Invite students to share their designs with theclass. Have students describe how they usedreflections to make their designs. Ask questions, such as:• How are the designs the same?

(Both designs have the same blocks. Each block andits image are the same distance from the mirror line.)

• How are the designs different? (The blocks in the designs face opposite ways.)

Display a transparency with a horizontal mirrorline on the overhead projector. Place a PatternBlock on one side of the mirror line and tracearound it. Introduce the terms reflection,reflection line, and flip as you model areflection by flipping the block over the lineand tracing it in its new position.

621955

Making ConnectionsMath Link: The sign says AMBULANCE. It is written backwardso that drivers can read the word in their rear-view mirrors.Art: Have students find slides, turns, and reflections in samplesof wallpaper or in the drawings of Dutch artist, M. C. Escher.Some students may want to use slides, turns, and/or reflectionsto create their own wallpaper design.

Ask:• What changes when a figure is flipped?

(The image faces the opposite way.)• What stays the same?

(The figure and its image are the same size and shape.)

• How are a slide and a reflection the same?(In both a slide and a reflection, the figure and itsimage are congruent.)

• How are a slide and a reflection different? (In a slide, the figure and its image face the sameway. In a reflection, the figure and its image faceopposite ways.)

Use the examples in Connect to illustrate areflection in a vertical mirror line, and areflection when one vertex of a figure is on the mirror line.

Prac t i ce

Reflect requires Pattern Blocks and 1-cm gridpaper. Have Miras available for all questions.


Students understand that a figure and its mirrorimage are congruent, but face opposite ways.Students realize that the snowman’s body andsome of its features, such as the eyes andbuttons, will look the same when flipped.Other features, such as the hat, nose, mouth,scarf, and arms, will face the opposite way.Some students may trace the snowman’s body,eyes, and buttons to make the figurescongruent, then add the other features in theirflipped positions. Other students may use aMira to reflect the image, then draw its image.


Sample Answers1. Pictures a, b, and f show a reflection because the figures are

congruent and face opposite ways. The mirror line in picturesa and f is a vertical line halfway between the 2 figures. Themirror line in picture b is a horizontal line between the 2 figures.

2. Picture e shows a slide because the figures are congruent andface the same way. The first D slides horizontally to the rightto get the second D.Picture c shows a turn because the figure has been turned aquarter turn counterclockwise or a three-quarter turnclockwise around a turn centre, and the figures are congruent.The turn centre is the common vertex.Picture d shows a turn because the figure has been turned ahalf turn clockwise or counterclockwise around a turn centrethat is the common vertex, and the figures are congruent.Pictures a, b, and f also show a turn because, in thesepictures, a reflection is the same as a rotation of a half turn.In part a, the turn centre is on the mirror line, halfwaybetween top and bottom vertices that face the mirror line. Inpart b, the turn centre is at the halfway point along thecommon side. In part f, the turn centre is on the mirror line,halfway between the top and bottom of each D.

Pictures a, b, and f

Slide: picture eTurn: pictures a, b, c, d, and f

3. Pictures a and d show a reflection because the figures arecongruent and face opposite ways. The mirror line for both ofthe pictures is a vertical line halfway between the 2 figures.

4.

The figure has the hat tilted to theright; the nose pointing to the left; the arms and the dots of the mouthreversed; and the scarf flipped to theleft of the button. The eyes and buttonslook the same when flipped. The 2 figures are congruent.

REFLECT: I put 2 trapezoids on the grid paper like this:The trapezoids show areflection because theyface opposite ways.When I put a Mirabetween them, theimage in the Miramatches the block onthe other side exactly.

The trapezoids also show a turn. If I turn one trapezoid a half turn around a turn centre between the 2 trapezoids, it overlaps the other trapezoid exactly.The trapezoids do not show a slide because they do not facethe same way.

Turncentre

Mirrorline



What to Do

Extra Support: Place 2 congruent Pattern Blocks on gridpaper to show a flip, a slide, or a turn. Have students identify themovement shown, then explain how they know.Students can use Step-by-Step 5 (Master 7.20) to completequestion 4.

Extra Practice: Students can complete Extra Practice 2 (Master 7.26).Extension: Have students draw a figure on light cardboard,then cut it out. Students place the cutout on a strip of paper, tracethe cutout, flip it, then trace again. Students continue flipping andtracing until they reach the end of the strip.


What to Look For

Understanding concepts ✔ Students understand that, under a

reflection, a figure and its image arecongruent and face opposite ways.

Applying procedures✔ Students are able to identify reflections

using Pattern Blocks and pictures.

✔ Students can create a mirror imageusing a mirror line.

✔ Students can differentiate amongtranslations, rotations, and reflections.

reflection

reflection


Lines of Symmetry

Key Math Learnings1. A line of symmetry divides a figure into 2 congruent parts,

so that the 2 parts coincide when the figure is folded alongthe line of symmetry.

2. Some figures have no lines of symmetry. Other figures haveone or more lines of symmetry.

LESSON ORGANIZER

Curriculum Focus: Identify and find lines of symmetry byfolding paper and using a transparent mirror.Teacher Materials� transparency of Lines of Symmetry (Master 7.9)Student Materials Optional� Lines of Symmetry � Step-by-Step 6 (Master 7.21)

(Master 7.9) � Extra Practice 3 (Master 7.27)� rulers� tracing paper� scissors� magazines� Miras� square dot paper (PM 22)Assessment: Master 7.2 Ongoing Observations: MotionGeometry

optional

L E S S O N 6


Invite students to examine the pictures on page 294 of the Student Book. Ask:• What can you say about the 2 halves of the

leaf? (They are exactly the same shape and size.They face opposite ways.)

• How can you tell if the 2 halves arecongruent? (I can trace the picture, then fold thepaper along the dotted line. If the 2 halves matchexactly, they are congruent.)

Review the term line of symmetry and remindstudents that a line of symmetry divides afigure into 2 congruent parts. Ask:• How can you test the figure to see if it has a

line of symmetry? (I can place a Mira on the line. If the image in theMira matches the other part of the figure exactly,then the 2 parts are congruent and the figure has aline of symmetry.)

Present Explore. Distribute copies of Lines ofSymmetry (Master 7.9). Ensure studentsunderstand that a line of symmetry can bediagonal, horizontal, or vertical, and that afigure can have 0, 1, or more than 1 line ofsymmetry. Remind students to use a Mira tolocate the lines of symmetry and to use a ruleror the edge of the Mira to draw the lines ofsymmetry on the figures. Once students havefound the lines of symmetry, they should cutout the figures, then sort them according to thenumber of lines of symmetry.

DURING Exp lore


Ask questions, such as:• How do you know that is a line of symmetry?

(If I fold the figure along the line, the parts on bothsides of the fold line match exactly.)

Figure Lines ofsymmetry

A 4B 2C 1D 6E 5F 8G 3H 1I 0J 0K 0L 0


Curr i cu lum Focus

Numbers Every DayFor the addition question, students should add the ones: 2 + a number = 7. The number is 5. Add the tens: 3 + 8 = 11.Trade 10 tens for 1 hundred. Add the hundreds: 4 + 1 + a number = 9. The number is 4.For the subtraction question, students should see they need moreones. Trade 1 ten for 10 ones. Subtract the ones: 13 – 8 = 5.You cannot subtract the tens. You need more tens. Trade 1 hundred for 10 tens. Subtract the tens: 16 – a number = 7. The number is 9. Subtract the hundreds: 5 – 2 = 3.


Alternative ExploreMaterials: Pattern BlocksStudents trace Pattern Blocks. Students cut out the tracings, then use folding to determine their lines of symmetry.

Early FinishersHave students cut out a simple picture with one line of symmetryfrom a magazine. Students cut the picture along the line ofsymmetry, then glue one-half of the picture to a piece of paper.Students draw the missing half using a Mira.

Common Misconceptions➤Students have difficulty identifying a diagonal line of symmetry.How to Help: Have students rotate the figure until the line ofsymmetry is vertical or horizontal.


• How do you know this figure has no lines of symmetry? (I put the Mira on the figure and moved the Mira tofind a line of symmetry. I could not find a line wherethe image and the other part of the figure matched.)

Watch for students who have difficulty using aMira. Have them cut out the figures and usefolding to determine the lines of symmetry.

AFTER Connec t

Display an overhead transparency of Lines ofSymmetry (Master 7.9). Invite volunteers todraw the lines of symmetry on the figures.Record their findings in a chart on the board:

Number of Lines Figureof Symmetry

0 I, J, K, L

1 C, H

More than 1 A, B, D, E, F, G

Ask:• What does it mean when we say a figure has

no lines of symmetry? (The figure cannot befolded into 2 congruent parts that match exactly.)More than one line of symmetry? (The figurecan be folded into 2 congruent parts that matchexactly in more than one way.)

Use the T-shirt pictures in Connect to show howa mirror line and a line of symmetry are related.

Prac t i ce

Have Miras and tracing paper available for allquestions. Question 4 requires square dotpaper. Have old magazines available for Reflect.


Students understand that a picture with 2 linesof symmetry can be folded into congruent partsin 2 ways.

4 5 93 5

F, G, J, K, L, N, P, Q, R, S, and Z

Sample Answers1. a) 1 line of symmetry: A, B, C, D, E, M, T, U, V, W, and Y

2 lines of symmetry: H, I, O, and XNo letters have more than 2 lines of symmetry.

b) I cannot fold the letters into 2 matching parts.2. Answers will vary.

My name is ARLENE. Three of the letters have 1 line ofsymmetry: A, E, EThere are 6 letters in my name. There are 2 groups of 3 in 6.So, one-half of my letters have 1 line of symmetry.

3. If I draw a vertical line through the centre of flags a and c, Ican fold each flag along the line and the 2 parts match.If I draw a horizontal line through the centre of flags c and d,I can fold each flag along the line and the 2 parts match.Flag c has a horizontal and a vertical line of symmetry.I cannot find a line in flags b, e, and f so that when I foldeach flag along the line, the 2 parts match.

4. I know my picture has 2 lines of symmetry because I can foldit along a horizontal line and a vertical line and the two partsmatch exactly.

REFLECT: I know my picture has 1 line of symmetry because Ican fold it to make 2 congruent parts in only one way.



What to Look For

Understanding concepts ✔ Students understand that a line of

symmetry divides a figure into twocongruent parts, so that the partscoincide when the figure is foldedalong the line of symmetry.

✔ Students understand that some figureshave 1 or more lines of symmetry,while other figures have none.

Applying procedures✔ Students can identify and find

lines of symmetry.

What to Do

Extra Support: Provide students with magazine pictures withlines of symmetry. Have students use a Mira to locate the lines ofsymmetry, then draw the lines with a marker.Students can use Step-by-Step 6 (Master 7.21) to completequestion 4.

Extra Practice: Students draw a line of symmetry on 1-cm gridpaper. They draw a design on one side of the line by colouringsquares, then trade papers with a partner and complete theirpartner’s design. Students can complete Extra Practice 3 (Master 7.27).

Extension: Challenge students to complete the AdditionalActivity, Symmetrical Masterpiece (Master 7.15).


Flags a and c

Flags c and dFlag c

Flags b, e, and f

Unit 7 • Show What You Know • Student page 297 27

SHOW WHAT YOU KNOW

LESSON ORGANIZER

Student Materials� Show What You Know Figures (Master 7.10)� rulers, Miras, tracing paperAssessment: Masters 7.1 Unit Rubric: Motion Geometry, 7.4 Unit Summary: Motion Geometry

40–50 min

Sample Answers1. a) A to B: 3 squares right and 1 square up or 1 square up

and 3 squares rightb) B to D: 3 squares left and 2 squares down or 2 squares

down and 3 squares leftc) B to G: 2 squares right and 2 squares down or 2 squares

down and 2 squares right2. a) A and B, A and D, A and G, B and D, B and G, C and F,

D and G — The blocks have been moved along a line andthey face the same way.

b) A and F, B and E, B and F, C and A, C and B, C and D, Cand G, D and F, F and G — In each pair, if I trace one ofthe trapezoids and rotate it around a turn centre, it willmatch the other trapezoid exactly.

c) A and C, C and D, D and G — The figures are congruentand face opposite ways. For the first 2 pairs, the mirror lineis a horizontal line halfway between the two blocks. For thethird pair, the mirror line is a vertical line halfway betweenthe two blocks.


What to Look For

Reasoning; Applying concepts✔ Question 1: Student understands that figures move left or right and up or down on a grid.✔ Question 2: Student understands the concepts of a slide, a turn, and a reflection.✔ Question 3: Student understands that a line of symmetry divides a figure into 2 congruent parts,

so that the parts coincide when the figure is folded along the line of symmetry.

Accuracy of procedures✔ Question 1: Student can describe movements on a grid.✔ Question 2: Student can identify figures that show a slide, a turn, and a reflection.✔ Question 3: Student can find lines of symmetry in regular figures.

Problem solving✔ Question 3: Student can identify the relationship between the number of lines of symmetry and the number

of sides in a regular figure.

Recording and ReportingMaster 7.1 Unit Rubric: Motion GeometryMaster 7.4 Unit Summary: Motion Geometry

square

regular hexagon regular octagon

regular triangle

4, 6, 8, 3

4, 6, 8, 3

Each figure has the samenumber of lines of symmetry as it has sides. Curriculum Focus

If you did not complete the optional lessons in this Unit, assignonly question 1. An additional assessment question can befound on Extra Practice 1A (Master 7.25).

Have students turn to the Launch on pages 274and 275 of the Student Book. Remind studentsof the questions they answered about theAmusement Park at the start of the unit. Usethe lists of Learning Goals and Key Words toreview some of the activities and learnings ofthe unit.

Present the Unit Problem. Encourage students todesign an original ride, and to give their ride aname. Ensure students understand they candesign their ride on paper or build a modelusing the available materials.

Invite a volunteer to read aloud the Check List.Ensure students understand that these are the criteria against which their work will be assessed.

Have materials available in a central locationfor students to access as needed.

Provide time for each group to present its ride and to demonstrate or explain how theride moves.

28 Unit 7 • Unit Problem • Student page 298

At the Amusement Park

LESSON ORGANIZER

Student Grouping: Groups of 3 or 4Student Materials� 1-cm grid paper (PM 20)� construction paper� scissors� glue� rulers� building materials, such as cardboard boxes, craft sticks,

straws, string, wire, thread spools, cardboard tubes� construction setsAssessment: Masters 7.3 Performance Assessment Rubric: At the Amusement Park, 7.4 Unit Summary: Motion Geometry

40–50 min

U N I T P R O B L E M

Teaching notes for the Cross Strand Investigation, Are You aSquare or a Rectangle? are in the Grade 3 Planning andProgram Masters module.

If you omitted the optional lessons in this unit, you maywish to modify the Unit Problem as follows. Have studentsdesign an amusement park. They draw a map of the parkon 2-cm grid paper, label the location of 6 rides, addmore points and labels for other features, then write todescribe their park.Students choose 2 points on their map, then write to describehow to get from one point to the other. They should usedirections and the number of squares in their descriptions.

Curr i cu lum Focus

Sample ResponseWe designed a ride called “Spin and Drop.” We chose to drawa picture. We decided that our ride would use a slide up anddown, and clockwise turns. The people get into a UFO-like car,which slowly slides up a long pole. When the cargets to the top, it stops. After about 5 seconds, itstarts to spin clockwise, gradually spinning fasterand faster. After about 30 seconds, the car stops,and slides suddenly down to the ground. Wewould not go on this ride because we would getvery dizzy.

Reflect on the UnitI learned that figures can slide, turn, or flip.A slide moves a figure in a straight line. Thefigure does not turn. A slide can be horizontal,vertical, or diagonal. A slide is also called atranslation. Here is a picture of a slide.

A turn moves a figure around a turn centre. It can be a quarter turn, a half turn, a three-quarter turn, or a whole turn. A turn can be clockwise or counterclockwise. A turn is also called a rotation. Here is a picture of a quarter turn clockwise.

A flip reflects a figure in a mirror line. The figure and its image face opposite ways. The mirror line can be horizontal or vertical. A flip is also called a reflection. Here is a picture of a flip.

Unit 7 • Unit Problem • Student page 299 29


What to Look For

Understanding concepts ✔ Students understand that rides can

move people in different ways.

Applying procedures✔ Students design a ride that moves

people in at least 2 different ways.

Communicating✔ Students use geometric language to

describe how their ride moves.

What to Do

Extra Support: Make the problem accessible.

Students may design a ride that moves in only one way. Ask questions, such as: How does your ride move? (It turnsclockwise.) What can you do to it so that it also slides up anddown or left and right?

Students may have difficulty coming up with an original ride. Ask questions, such as: What is a ride that you like at theamusement park? Could you add a movement to the ride to makeit better? Can you design the ride using your suggestion?

Recording and ReportingMaster 7.3 Performance Assessment Rubric: At the Amusement ParkMaster 7.4 Unit Summary: Motion Geometry

slide

Turncentre

quarterturn

clockwise

Mirror lineFlip

Copyright © 2005 Pearson Education Canada Inc. 30

Evaluating Student Learning: Preparing to Report: Unit 7 Motion Geometry This unit provides an opportunity to report on the Shape and Space: Transformations strand. Master 7.4: Unit Summary: Motion Geometry 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: Transformations

Reasoning; Applying concepts

Accuracy of procedures

Problem solving

Communication Overall

Ongoing Observations 2 2 2 2 2

Strategies Toolkit 1 1

Work samples or portfolios; conferences

2 2 1 2 2

Show What You Know 2 2 2 2 2

Unit Test 2 3 2 not assessed 2

Unit Problem At the Amusement Park

2 3 2 2 2

Achievement Level for reporting 2

Recording How to Report Ongoing Observations

Use Master 7.2 Ongoing Observations: Motion Geometry 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 3). 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 7.1 Unit Rubric: Motion Geometry 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 7.1 Unit Rubric: Motion Geometry may be helpful in determining levels of achievement. #1 and 2a provide evidence of Accuracy of procedures; #1 and 2 provide evidence of Reasoning; Applying concepts; #2b provides evidence of Problem solving; both provide evidence of Communication.

Unit Test Master 7.1 Unit Rubric: Motion Geometry 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 7.3 Performance Assessment Rubric: At the Amusement Park. 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: Motion Geometry

Not Yet Adequate

Adequate Proficient Excellent

Reasoning: Applying concepts

• shows understanding by explaining relative position and applying terms of direction

shows limited understanding; may be unable to explain position or apply terms of direction

shows some understanding; partially able to explain position and apply terms of direction

shows understanding by explaining position and applying terms of direction

shows thorough understanding in various contexts by explaining position and applying terms of direction


• accurately: – locates objects on a

map or grid – describes relative

position – traces a path

limited accuracy; omissions or major errors in: – locating objects on a

map or grid – describing relative

position – tracing a path

partially accurate; omissions or frequent minor errors in: – locating objects on a



generally accurate; few errors in: – locating objects on a



accurate; no errors in: – locating objects on a



Problem-solving strategies

• uses appropriate strategies to investigate and describe position in everyday contexts (maps, grids, objects, drawings, number lines)

may be unable to investigate and describe position in everyday contexts

with limited help, investigates and describes position in everyday contexts; partially successful

successfully investigates and describes position in everyday contexts

successfully investigates and describes position in an increasing range of everyday contexts; often innovative

Communication • explains reasoning

and procedures clearly, including appropriate terms of direction

unable to explain reasoning and procedures clearly

partially explains reasoning and procedures

explains reasoning and procedures clearly

explains reasoning and procedures clearly, precisely, and confidently

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

presents work clearly presents work clearly and precisely

Master 7.1


Name Date

Ongoing Observations: Motion Geometry 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: Motion Geometry* Student Reasoning; Applying

concepts Accuracy of procedures

Problem solving Communication

Shows understanding by explaining relative position and applying terms of direction

Accurately locates objects on a map, describes relative position, graphs points on a number line, and traces a path

Uses appropriate strategies to solve and create problems involving position in everyday contexts

Presents work clearly Explains reasoning and

procedures clearly, including appropriate terms of direction

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

Master 7.2


Name Date

Performance Assessment Rubric: At the Amusement Park

Not Yet

Adequate Adequate Proficient Excellent


• presentation of ride and explanation of how it moves, shows spatial sense and understanding of direction and relative position

does not present or explain ride appropriately; may be incomplete or offer misconceptions

presentation and explanation of how the ride moves may be incomplete or include some flawed reasoning related to position and direction

presentation and explanation of how the ride moves adequately incorporates relevant concepts of position and direction

presentation and explanation of how the ride moves thoroughly and effectively incorporates concepts of position and direction; may offer generalizations or make connection to other situations/rides


• correctly identifies and describes movements, relative position, and direction of the ride

omissions or major errors in describing movement, position, and direction

omissions or some minor errors in describing movement, position, and direction

few minor errors in describing movement, position, and direction

accurate and precise; no errors in describing movement, position, and direction

Problem-solving strategies

• uses appropriate strategies to successfully design a ride that moves people in at least two different ways

uses few effective strategies; does not adequately design a ride that meets criteria (may move in one way or repeat the same movement twice)

uses some appropriate strategies, with partial success, to design a ride; may be relatively simple or very similar to an existing ride

uses appropriate and successful strategies to design a ride that moves in two different ways

uses innovative and effective strategies to design a ride that moves in two or more different ways

Communication • explains ride clearly,

using appropriate mathematical terminology (e.g., turn, horizontal, clockwise)

does not explain the ride clearly; uses few or no mathematical terms

partially explains the ride; may be vague and somewhat unclear; uses some appropriate mathematical terms

explains the ride clearly using appropriate mathematical terms

explains the ride clearly, precisely, and confidently, using a range of appropriate mathematical terms with precision

Master 7.3


Name Date

Unit Summary: Motion Geometry 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: Transformations



Problem solving

Communication Overall

Ongoing Observations

Strategies Toolkit (Lesson 3)

Work samples or portfolios; conferences

Show What You Know

Unit Test

Unit Problem At the Amusement Park

Achievement Level for reporting

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

Comments: (Strengths, Needs, Next Steps)

Master 7.4


Name Date

To Parents and Adults at Home … Your child’s class is starting a mathematics unit on motion geometry. Through daily activities, your child will use numbers and direction words to describe the relative positions of objects and places on a map. In this unit, your child will:

• Describe movement on a grid. • Use terms of direction, such as north, south, east, and west. • Relate terms of direction to maps.

Here are some suggestions for activities you can do with your child. Play games with your child that involve giving directions, such as Simon Says. For example, one direction could be, “Move 3 steps forward and 2 steps right.” Look at maps with your child. Have your child locate places that are north, south, east, or west of a given place. Talk about the direction you are going as you drive your child to school, or to the park. For example, you might say, “We are travelling north. At the corner, I will turn west.”

Master 7.5


Name Date

Map of Blueberry

Master 7.6


Name Date

Chessboard

Master 7.7


Name Date

Playground Grid

Master 7.8


Name Date

Lines of Symmetry

Master 7.9


Name Date

Show What You Know Figures

Master 7.10


Name Date

Lesson 1A: Using Directions This is a map of King Edward School. Tell how you would get from: • Room 3 to the library • Room 6 to the office EXPLORE With your partner, choose an object to use as a treasure. Place the treasure somewhere in the classroom.

Move to another place in the room. Work out a set of instructions to get from this place to the treasure. Test your instructions to make sure they work.

Show and Share Trade instructions with another pair of classmates. Follow each other’s instructions. Talk about the words that helped you find the treasure.

Master 7.11a

Lesson Focus: Use terms of direction.


Name Date

Lesson 1A continued CONNECT Here is a map of part of Blueberry. The symbol in the bottom left corner of the map shows the directions north, south, east, and west. We use these directions to tell how to get from one place to another on a map. Here is one way to get from the Pet Shop to the Library: Go east on Queen St. to Hill St. Turn north. Go 1 block to Cardinal Dr. Turn west. The Library is on the left across the road from the Pizza Shop. PRACTICE Use the map of Blueberry. 1. Tell another way to get from the Pet Shop to the Library. 2. Tell how to get from:

a) the Dollar Store to the Fitness Centre b) the Post Office to the Mall

Reflect Write one important thing you learned about telling someone how to get from one place to another.

Master 7.11b



Name Date

Additional Activity 1: Left or Right

Work on your own. You will need 2 number cubes and 1 counter. Put your counter on Start.

Roll the number cubes. Add the numbers.

If the sum is even, move the counter 1 space to the left. If the sum is odd, move the counter 1 space to the right. Keep playing until you land on Win or Lose.

Lose Start Win

Take It Further: Play the game with a partner. Take turns until one player lands on Win or Lose.

Master 7.12


Name Date

Additional Activity 2: Stay on the Path

Work with a partner.

You will need 1-cm grid paper, a number cube, 2 crayons of different colours, and a paper bag with 4 cards labelled: North South East West

The object of the game is to be the first player to go off the grid.

How to play:

Find a spot near the centre of the grid paper where 2 lines meet. Draw a dot. Label the dot “Start.”

Take turns to roll the number cube and take a card from the bag. The number cube tells how many squares to move. The card tells the direction to move.

Colour your path along the lines.

The player who goes off the grid first wins. Take It Further: Tell how to move from “Start” to where the winner went off the grid.

Master 7.13


Name Date

Additional Activity 3: Draw the Path

Work alone. You will need: a copy of Robbie’s Neighbourhood, 3 pencil crayons (red, blue, and purple) Follow the directions to draw each path on the map.

Use a red pencil crayon. Start at Robbie’s house. Go north for 1 block. Turn west. After 2 blocks, turn north. Go into the first house on the east side of the street.

Use a blue pencil crayon. Start at the school. Go east for 3 blocks, then turn south. Go into the second building on the west side of the street.

Use a purple pencil crayon. Draw the shortest path from the drug store to the pet shop.

Take It Further: Choose 2 places on the map. Use a green pencil crayon to draw the path from one place to the other. Show your path to a classmate. Describe the path to her or him.

Master 7.14a


Name Date

Robbie’s Neighbourhood

Master 7.14b


Name Date

Additional Activity 4: Symmetrical Masterpiece

Work with a partner.

You will need 1-cm grid paper, a ruler, and crayons or pencil crayons.

Draw a horizontal or vertical line in the centre of the grid. This is the line of symmetry.

Colour a square on your side of the line.

Your partner finds the matching square on her side of the line. She colours the square the same colour.

Switch roles. Continue until you have created a symmetry masterpiece.

Take It Further: Draw a vertical and a horizontal line on the grid. Take turns to colour 2 squares, one for the horizontal line and one for the vertical line. You will make a design with 2 lines of symmetry.

Master 7.15


Name Date

Step-by-Step 1 Lesson 1, Question 3 Step 1 To find where you started, work backward.

Your second move was 4 squares right.

The opposite of this is 4 squares left.

From the train station,

move 4 squares left on the grid.

Mark the spot with an “X.”

Step 2 Your first move was 2 squares down.

What is the opposite move?

________________________________________________________ Step 3 Use your answer to Step 2 to move on the grid.

Where did you start?

________________________________________________________

Step 4 Explain how you know. ________________________________________________________ ________________________________________________________

Master 7.16


Name Date

Step-by-Step 1A Lesson 1A, Question 2 Step 1 Circle the Dollar Store and the Fitness Centre. Step 2 Draw a path from the Dollar Store to the Fitness Centre. Step 3 Start at the Dollar Store. In which direction does your path first go? ____________ Where does your path turn? _____________

In which direction does your path go now? ____________

For how many blocks? __________

Where does your path turn? ______________ In which direction? ______________ For how far? _______________ On which side of the street is the Fitness Centre? ______

Step 4 Circle the Mall and the Post Office. Step 5 Draw a path from the Post Office to the Mall. Step 6 Start at the Post Office. Answer the questions in Step 3 for this new path.

On which side of the street is the Mall? _________

Master 7.17


Name Date

Step-by-Step 2 Lesson 2, Question 4 Work backward. Step 1 From square 29, move 2 squares left.

Where do you land? _________

Now move 3 squares up.


Step 2 From square 29, move 2 squares left.


Now move 3 squares right.


Step 3 From square 29, move 2 squares up.


Now move 3 squares left. Where do you land? _________

Step 4 From square 29, move 2 squares up.


Now move 3 squares down. Where do you land? _________

Step 5 On which squares could Jill have started?

________________________________________________________

Master 7.18


Name Date

Step-by-Step 4 Lesson 4, Question 7 Step 1 What time does the clock show? _____________________________

Turn the minute hand a three-quarter turn counterclockwise.

What number does it point to? _______________________________

What happened to the hour hand? ____________________________

________________________________________________________

What time does the clock show? _____________________________

How do you know? ________________________________________

________________________________________________________

Step 2 Now, turn the minute hand a quarter turn clockwise.

What number does it point to? _______________________________

What happened to the hour hand? ____________________________

________________________________________________________

What time does the clock show? _____________________________

How do you know? ________________________________________

________________________________________________________

Master 7.19


Name Date

Step-by-Step 5 Lesson 5, Question 4 Use tracing paper and a Mira. Step 1 Which parts of the snowman will look the same in a mirror?

________________________________________________________

Step 2 Which parts of the snowman will look different in a mirror?

________________________________________________________

Which way will each part face?

________________________________________________________

________________________________________________________

________________________________________________________

________________________________________________________

________________________________________________________

Step 3 On the figure:

Which side of the snowman will have the arm with 3 fingers? _______

Which side of the snowman will have the arm with 2 fingers? _______

Step 4 Draw the snowman before it was reflected.

Master 7.20


Name Date

Step-by-Step 6 Lesson 6, Question 4 Use a Mira if it helps. Step 1 Draw a horizontal line through

the centre of the dot paper.

Draw a vertical line through the centre.

Step 2 Draw a figure in

the bottom left part of the dot paper.

Step 3 Reflect your figure in

the horizontal line.

Draw the image.

Step 4 Reflect your figure and its image in the vertical line.

Draw the new images.

Step 5 Explain how you know your picture has 2 lines of symmetry.

________________________________________________________

________________________________________________________

Master 7.21


Name Date

Unit Test: Unit 7 Motion Geometry Part A 1. Use the grid at the right.

How do you move to go from:

a) A to F? ________________________

______________________________

b) E to B? ________________________

______________________________

c) C to D? ________________________

______________________________

Part B 2. a) Use a red pencil crayon. Follow these directions to draw a path on the map.

Start at the Bank. Go 1 block north. Turn west. Go 2 blocks west, then 1 block north. Turn west. Go into the second building on the south side of the street.

b) Use a green pencil crayon.

Draw the shortest path from the Flower Shop to the Toy Store.

Master 7.22a


Name Date

Unit Test continued Part C 3. Use the map below.

a) You are at Mary’s house.

To get there, you went 3 blocks north and 3 blocks west.

Where did you start? ___________________________

b) You are at the bakery.

To get there, you went 4 blocks in one direction and 1 block in

another direction.

Where could you have started? ___________________________

Master 7.22b


Name Date

Sample Answers Unit Test – Master 7.22 Part A 1. a) 8 squares down and 2 squares right or

2 squares right and 8 squares down b) 5 squares up and 1 square left or

1 square left and 5 squares up c) 1 square left and 1 square down or

1 square down and 1 square left Part B 2. a) See broken line in map above.

b) See solid line in map above.

Part C 3. a) I started at the Corner Store. b) I could have started at the Corner Store or

at Mary’s house.

Master 7.23


Extra Practice Masters 7.24–7.28 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.

Printed and bound in Canada

1 2 3 4 5 – TC – 09 08 07 06 05

western canadian teacher guide - sd67 (okanagan skaha) · at the amusement park cluster 1: ... the...

Documents