Western Canadian Teacher Guide - SD67 (Okanagan Skaha) · Western Canadian Unit 3: Geometry AA ... • How did the children make the sand castle? ... students will design and build

Teacher GuideWestern Canadian

Unit 3: 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

“In the elementary grades,experiences in geometry shouldprovide for the development ofthe concepts of shape, size,symmetry, congruence, andsimilarity in both two-dimensional and three-dimensional space. Experiencesshould begin with familiarobjects and should utilize awide variety of concretematerials to develop appropriatevocabulary and to buildunderstanding.”

Marilyn Burns

Mathematics Background

What Are the Big Ideas?

• Figures and solids can be described, compared, and sorted according totheir attributes.

• Two figures or two solids are congruent if they have the same size and shape.

• Figures can be combined to make other figures.

• Solids have faces that are figures. The shape of the base tells the nameof the solid.

• Different figures can be used to build models of solids.

• A model of a solid can be made from a net.

How Will the Concepts Develop?

Students investigate the attributes of figures using pictures and cutoutsof figures, geoboards, and dot paper. They describe, compare, and sortfigures in a variety of ways.

Students describe angles in relation to the right angle and use ageoboard to make figures with a given number of right angles.

Students investigate congruent figures using geoboards and cutouts offigures. They develop strategies for testing figures for congruency.

Students use Pattern Blocks and tangrams to make figures by combiningother figures. They describe each new figure according to the number ofits sides.

Students use three-dimensional models to explore the attributes ofsolids. They describe, compare, and sort solids according to theirattributes. Students learn to describe and name pyramids and prisms bythe shapes of their bases.

Students use cardboard figures and nets to build models of solids. Theycombine solids to build structures.

Why Are These Concepts Important?

Active exploration of figures and solids contributes to the developmentof spatial sense and spatial reasoning. These spatial abilities have manyapplications in everyday life and are also essential in such areas as thearts, surveying, architecture, carpentry, and design and technology. Inaddition, geometry tasks, such as those provided in this unit, help toprepare students for the more formal, deductive geometry curriculum oflater years.

FOCUS STRANDShape and Space: 3-D Objectsand 2-D Shapes

SUPPORTING STRANDPatterns and Relations: Patterns

ii Unit 3: Geometry

3 Geometry

Unit 3: Geometry iii

Lesson 1:Describing FiguresLesson 2:Describing AnglesLesson 3:Naming FiguresLesson 4:Sorting FiguresLesson 5:Congruent FiguresLesson 6:Making Pictures with FiguresLesson 7:Strategies Toolkit

Curriculum Overview

General Outcome• Students describe, classify,

construct and relate 3-D objectsand 2-D shapes.

Specific Outcomes• Students recognize congruent

(identical) ... 2-D shapes. (SS27)• Students sort, concretely and

pictorially, using two or moreattributes. (PR1)

LaunchAt the Beach

Cluster 1: Exploring Figures

General Outcome• Students describe, classify,

construct and relate 3-D objectsand 2-D shapes.

Specific Outcomes• Students identify and count faces,

vertices and edges of 3-D objects.(SS22)

• Students identify and name faces ofa 3-D object with appropriate 2-Dnames. (SS23)

• Students describe and namepyramids and prisms by the shapeof the base. (SS24)

• Students demonstrate that arectangular solid has more than onenet. (SS25)

• Students compare and contrast two3-D objects. (SS26)

• Students recognize congruent(identical) 3-D objects ... (SS27)

• Students explore, concretely, theconcepts of perpendicular, paralleland intersecting lines on 3-Dobjects. (SS28)

• Students sort, concretely andpictorially, using two or moreattributes. (PR1)

Cluster 2: Exploring SolidsLesson 8:Identifying Prisms and PyramidsLesson 9:Sorting SolidsLesson 10:Making Models from FiguresLesson 11:Making a Structure from Solids

Show What You Know

Unit ProblemAt the Beach

iv Unit 3: Geometry

Curriculum across the Grades

Grade 2

Students explore faces,vertices, and edges of 3-Dobjects. They identify,name, and describespecific 3-D objects ascubes, spheres, cones,cylinders, and pyramids.

Students build a skeletonof a 3-D object, anddescribe how the skeletonrelates to the object. Theymatch and make identical(congruent) 2-D shapes.

Grade 3

Students identify andcount faces, vertices, andedges of 3-D objects. Theyidentify and name faces ofa 3-D object withappropriate 2-D names.

Students describe andname pyramids andprisms by the shape of thebase. They demonstratethat a rectangular solidhas more than one net.

Students compare andcontrast two 3-D objects.They recognize congruent(identical) 3-D objects and2-D shapes.

Students explore,concretely, the concepts ofperpendicular, parallel,and intersecting lines on3-D objects.

Grade 4

Students design andconstruct nets for pyramidsand prisms. They relatenets to 3-D objects.

Students compare andcontrast pyramids, prisms,and pyramids and prisms.They recognize, fromeveryday experience, andidentify point, line,parallel lines, intersectinglines, perpendicular lines,vertical lines, andhorizontal lines.

Students classify angles ina variety of orientationsaccording to whether theyare right angle, less thanright angle, or greaterthan right angle. Theyidentify and sort specificquadrilaterals, includingsquares, rectangles,parallelograms, andtrapezoids.

Materials for This Unit

Gather a large quantity of empty boxes, packages, and containers in avariety of shapes and sizes for Lessons 8 and 11, and the Unit Problem(e.g., cereal, tissue, pudding, and cracker boxes, aluminum foilcontainers, Toblerone boxes). Have students bring as many of these aspossible from home throughout the unit.

Prepare 5-cm by 5-cm cardboard squares and large cutouts of figures inthe Student Book, p. 106 (Master 3.6) for Lesson 1.

Prepare large cutouts of figures in the Student Book, p.113 (Masters 3.7 and 3.8) for Lesson 4, p.116 (Master 3.9) for Lesson 5, andp. 138 (Master 3.13) for Show What You Know, question 4.

Prepare cardboard cutouts of figures in the Student Book, p.132 for Lesson 10. (Patterns for the figures can be found on Master 3.11: MakingModels from Figures.)

Prepare a copy of the arrow in the Student Book, p. 121(Master 3.10) for Lesson 6, question 4, and of the nets on p. 134(Master 3.12) for Lesson 10, questions 1 and 3.

Regular FiguresFor Extra Practice (Appropriate for use after Lesson 3)Materials: straws cut into 10-cm lengths, pipe cleaners, scissors, Regular Figures (Master 3.14)

The work students do: Students work alone. They build as many regular figures as they can usingthe straws for the sides of the figures. They cut pipecleaners into short lengths and insert them into thestraws to hold the sides of the figures in place.

Take It Further: Students use the straws and pipecleaners to build figures that are not regular.

Kinesthetic/MathematicalIndividual Activity

Additional Activities

Making FiguresFor Enrichment (Appropriate for use after Lesson 6)Materials: Making Figures (Master 3.16), Pattern Blocktriangles, triangular grid paper (PM 24)

The work students do: Students work with a partner.Students use 5 Pattern Block triangles. They make asmany different figures as they can using 5 greentriangles. Each triangle must have at least one side fullytouching another triangle. Students sketch each figure ontriangular grid paper and record the number of sides.

Take It Further: Students repeat the activity using6 Pattern Block triangles.

Kinesthetic/Logical/MathematicalPartner Activity

Congruent FiguresFor Extra Practice (Appropriate for use after Lesson 5)Materials: Congruent Figures (Master 3.15),geoboards, geobands, square dot paper (PM 22)

The work students do: Students work with apartner. Students use a geoboard to make the rectangleshown below. They make as many congruent rectanglesas they can, and record each rectangle on square dot paper.

Take It Further: Students make a triangle that hasone right angle on the geoboard. They make as manycongruent triangles as they can, and record eachtriangle on square dot paper.

Kinesthetic/SocialPartner Activity

Unit 3: Geometry v

Comparing BoxesFor Extra Support (Appropriate for use after Lesson 9)Materials: Comparing Boxes (Master 3.17), empty boxes of different shapes and sizes

The work students do: Students work with a partner.Each student selects a box. Students take turns to describetheir box in as many different ways as they can. Then,one student describes how the two boxes are alike, andthe other student describes how they are different.

Take It Further: One student selects 6 boxes, chooses 2 attributes, and sorts the boxes. The other studentguesses the sorting rule.

Linguistic/SocialPartner Activity

vi Unit 3: Geometry

Planning for Unit 3

Planning for Instruction

Lesson Time Materials Program Support

Suggested Unit time: About 3 weeks

Unit 3: Geometry vii

Purpose Tools and Process Recording and Reporting

Planning for Assessment

Lesson Time Materials Program Support

2 Unit 3 • Launch • Student page 102

At the Beach

LESSON ORGANIZER

Curriculum Focus: Activate prior learning about figuresand solids.Vocabulary: figure, solid

10–15 min

L A U N C H

ASSUMED PRIOR KNOWLEDGE

Students can compare some figures and solids accordingto their attributes.Students can name and describe some figures and solids.

✓

✓

ACTIVATE PRIOR LEARNING

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

Ask questions, such as:• How did the children make the sand castle?

(They used different shapes and sizes of containersand filled them with sand to make solids.)

• Which part of the castle looks like a cube?(The part in the middle) A pyramid? (The solids with flags on top of them)

• What other objects do you see that look likesolids? Which solids do they look like? (The beach ball looks like a sphere. The pop canlooks like a cylinder. The picnic cooler looks like arectangular prism.)

Have students examine the impressions in thesand. Ask:• What figures do you see in the sand?

(I see 2 circles, a rectangle, a hexagon, a triangle,and an octagon.)

• Which objects could have been used to makethe circles? (The pail and the pop can) Theoctagon? (The cup the boy is drinking from)

Discuss the questions in the Student Book.Encourage students to consider attributes, suchas number of sides and number of vertices.Remind students the plural of vertex is vertices.

To answer the first question, students may say:the circles have the same shape, but one isbigger than the other; the triangle has 3 sidesand the rectangle has 4 sides.

To answer the second question, students maysay: the two juice boxes have the same size andshape; the two hexagonal prisms have the sameshape but different sizes.

Tell students that, in this unit, they willdescribe, compare, sort, and construct figuresand solids, and solve geometry problems. At theend of the unit, students will design and builda model of a sand castle.

LITERATURE CONNECTIONS FOR THE UNIT

DIAGNOSTIC ASSESSMENT

What to Look For

✔ Students cancompare somefigures and solidsaccording to theirattributes.

✔ Students can nameand describe somefigures and solids.

What to Do

Extra Support:

Students who have difficulty describing the attributes of figures and solids maybenefit from being directed to consider a specific attribute. For example, askquestions, such as: “What do you notice about the sides of this figure?” or “Howmany edges does this solid have?”Work on this skill during Lessons 1 to 4.

Students who have difficulty comparing and contrasting figures or solids maybenefit from focusing on one attribute at a time. For example, you might ask,“How are the faces of these two solids alike? How are they different?”Work on this skill during Lessons 1 to 4.

Students who have difficulty identifying and naming figures and solids may benefitfrom making a reference chart of labelled pictures. Associations to real-worldobjects may also help students to remember the names (for example, a ball lookslike a sphere).Work on this skill during Lessons 3 and 5 to 11.

Unit 3 • Launch • Student page 103 3

Some students may benefit from using thevirtual manipulatives on the e-Tools

CD-ROM. The e-Tools appropriate for this unit includeGeometry Shapes.

REACHING ALL LEARNERS

The Greedy Triangle by Marilyn Burns. New York:Scholastic Press, 1994.ISBN: 0590489917This is the story of a triangle that thought life would bebetter if it had one more side and one more angle. Thetriangle goes to “the shape-shifter” who changes thetriangle into a quadrilateral, then later into a pentagon, ahexagon, and so on. Finally, the figure realizes that beinga triangle is best after all.

Three Pigs, One Wolf, and Seven Magic Shapes by GraceMaccarone. New York: Scholastic Press, 1999.ISBN: 0613089022This book is a variation of the traditional story, The ThreeLittle Pigs. It tells the story of three other little pigs who aregiven a set of seven magical figures. The third little piguses her figures to create a house, a friend, and othersurprising things.

4 Unit 3 • Lesson 1 • Student page 104

Describing Figures

LESSON ORGANIZER

Curriculum Focus: Use attributes to describe figures. Student Materials Optional� Describing Figures � Step-by-Step 1 (Master 3.18)

(Master 3.6) � Extra Practice 1 (Master 3.30)� square dot paper (PM 22)� geoboards and geobandsVocabulary: attribute, parallelAssessment: Master 3.2 Ongoing Observations: Geometry

40–50 min

L E S S O N 1

Key Math Learnings1. An attribute is a way to describe a figure.2. Parallel sides are always the same distance apart and

never meet.3. On a drawing of a figure, hatch marks are used to show

equal lengths, and arrows are used to show parallel lines.4. The lengths of the sides and parallel sides are two attributes

of figures.

BEFORE Get S tar ted

Invite a volunteer to read aloud theintroduction to the lesson. Have students workin pairs to find at least three figures with eachtype of side. Ask questions, such as:• What figures did you find with straight sides?

(The blackboard, the filing cabinet, and our desks)• What figures did you find with curved sides?

(The computer disc and the globe)• How else can you describe the blackboard?

(It has 2 long sides and 2 short sides. The long sidesare the same length. The short sides are the same length.)

• How are the blackboard and the bulletinboard the same? (Both of them have 4 straightsides.) How are they different? (The blackboard has 2 long sides and 2 short sides.The bulletin board has all sides the same length.)

Present Explore.

DURING Exp lore

Ongoing Assessment: Observe and Listen

As students work, listen for those who describenon-geometric characteristics of a figure insteadof describing the figure in terms of itsattributes. For example, they may say thatFigure H looks like a piece of pie instead ofsaying that it has 2 straight sides and 1 curvedside. Encourage these students to use attributessuch as side lengths, side directions, andnumber of sides in their descriptions.

Ask questions, such as:• What can you say about the sides of your

figure? (My figure has 1 curved side and 1 straight side.)

• Does your figure have any sides that are thesame length? (My figure has 4 sides the samelength.) Any sides that go in the samedirection? (My figure has 2 sides that go in thesame direction.)

Although the content of this lesson does not tie directly to yourcurriculum, the lesson will give students the background theywill need in later lessons.

Curr i cu lum Focus

Unit 3 • Lesson 1 • Student page 105 5

Alternative ExploreMaterials: a set of 8 cutouts, like the figures in ExploreStudents work in groups of 3 or 4. The cutouts are spread out onthe table. One student secretly chooses a figure. The otherstudents take turns to ask “yes” or “no” questions about thefigure. Students eliminate, then remove, cutouts from the tablewhen the answer to a question is no. Students continue to askquestions until there is only one figure remaining.

Early FinishersHave students make a figure on a geoboard and write todescribe it in as many ways as they can.

Common Misconceptions➤Students consider opposite sides of all quadrilaterals to

be parallel.How to Help: Remind students that parallel lines never meet.Draw 2 figures, one with parallel sides and one without. Havestudents watch as you use a ruler to extend the opposite sides.Students will see that the non-parallel lines meet, while theparallel lines are always the same distance apart and never meet.

ESL StrategiesStudents for whom English is a second language may be unableto describe the figures in Explore. Pair these students with apartner who asks “yes” or “no” questions about the chosen figure.


AFTER Connec t

Invite a volunteer to choose a figure fromExplore and describe it in one way. For example, my figure has 4 sides.

Ask questions, such as:• Which figure could it be?

(It could be Figure B, C, D, or F.)

Have the volunteer describe the figure in adifferent way. For example, my figure has only2 sides going in the same direction. Ask:• Which figure could it be? (Figure B or C)

Continue in this manner until the figure isidentified. Repeat with other figures.

Use Connect to introduce the terms attribute andparallel. Discuss the use of hatch marks andarrows on drawings of figures. Ensure studentsunderstand why some sides have one hatchmark or arrow, while other sides have two.

Prac t i ce

Students will need figures cut from DescribingFigures (Master 3.6) for questions 1 and 2.Question 2 requires square dot paper. Question 3 requires geoboards, geobands, andsquare dot paper.

Assessment Focus: Question 3

Students understand that parallel sides arealways the same distance apart. They use ageoboard to make different figures, each withonly 2 parallel sides. They record their figureson dot paper and describe each figure usingattributes such as side lengths, parallel sides,and number of sides.

Students who need extra support to completeAssessment Focus questions may benefit fromthe Step-by-Step masters (Masters 3.18–3.27).

Numbers Every DayStudents could start with 0 as the first number, and find thesecond number. Students should continue in an organized wayby increasing the first number by 1 each time, until the numbersentences start to repeat. If you count, for example, 0 + 10 = 10,and 10 + 0 = 10 as one way, there are 6 ways to make a sumof 10 with 2 whole numbers.


ASSESSMENT FOR LEARNING

What to Look For

Understanding concepts ✔ Students understand that an attribute

is a way to describe a figure.✔ Students understand the concept of

parallel lines.

Applying procedures✔ Students can identify some of the

attributes of figures, such as equalside lengths, parallel sides, andnumber of sides.

Communicating✔ Students use mathematical language

to describe the geometric attributes of figures.

What to Do

Extra Support: Make a rectangle on a geoboard. Havestudents point out equal sides and parallel sides. Have studentschange the figure so that there are only 2 parallel sides. Then,have them change the new figure so that all sides have the samelength. Continue in this manner.Students can use Step-by-Step 1 (Master 3.18) to completequestion 3.

Extra Practice: Have students work in pairs. One student givesa direction, such as “Make a figure with no parallel sides.” Theother student makes a figure on the geoboard. Students switchroles and continue the activity.Students can complete Extra Practice 1 (Master 3.30).

Extension: Have students use dot paper and draw as manydifferent figures as they can with all sides the same length.

Recording and ReportingMaster 3.2 Ongoing Observations:Geometry

Sample Answers2. I chose Figures D and F.

Both figures have 4 sides. Figure D has 2 pairs of sides the same length whileFigure F has no sides the same length.Figure D has 2 pairs of parallel sides whileFigure F has 1 pair of parallel sides.

3. Figure A has 4 sides. Two sides havethe same length. The other two sidesare parallel. Figure B has 4 sides.Two sides are parallel but they donot have the same length. Two sideshave the same length. Figure C has5 sides. Two pairs of sides have thesame length. Two sides are parallel.

REFLECT: A figure has parallel sides if thesides are always the same distance apartand never meet. I can use a ruler toextend pairs of opposite sides. If they staythe same distance apart, the sides areparallel. A rectangle has two pairs of parallel sides.

A

B

C

D

F

Figure HFigures A, B, D, E, F, and G

Figures D, E, and F

0 + 10 = 10 1 + 9 = 10 2 + 8 = 10

3 + 7 = 10 4 + 6 = 10 5 + 5 = 10


L E S S O N 2

Describing Angles

Key Math Learnings1. Two sides of a figure meet at a vertex to form an angle.2. When two sides of a figure make a square corner at the

vertex, the angle is a right angle.3. An angle can be described as a right angle, greater than a

right angle, or less than a right angle.

LESSON ORGANIZER

Curriculum Focus: Describe angles as greater than or lessthan a right angle.Teacher Materials� square dot paper transparency (PM 22)Student Materials Optional� cardboard squares � Step-by-Step 2 (Master 3.19)

(5 cm by 5 cm) � Extra Practice 1 (Master 3.30)� geoboards and geobands� square dot paper (PM 22)� index cardsVocabulary: vertex, angle, right angleAssessment: Master 3.2 Ongoing Observations: Geometry

optional


Show students a large square. Ask:• How can you describe this square?

(It has 4 equal sides and 2 pairs of parallel sides.)

• What do you notice about the corners ofthe square? (There are 4 corners. All the corners are square.)

• What other objects in the classroom havesquare corners? (The blackboard, the bulletin board, the window)

Present Explore.

DURING Exp lore


Ask questions, such as:• How many corners does your figure have? (4)• Which corner is smaller than the corners in a

square? (The corner in the bottom right)• Which corner is larger than the corners in a

square? (The corner in the top right)• Which of your figures has a corner that

matches the corners in a square? (My pentagon)• How many types of corners does this figure

have? (3)

The word “figure” is used consistently in the Student Bookand this Teacher Guide to describe a two-dimensionalobject. The word “shape” is an attribute and should notbe used in place of “figure.” For example, we say, “Theshape of this figure is triangular.”

Math Note

In this lesson, students learn to name square corners asright angles, and they compare angles in figures to theright angle. Although the content of this lesson is notspecified by your curriculum, students need to visualize aright angle to understand perpendicular edges on a solid.

Curr i cu lum Focus

Making ConnectionsLiteracy: As you read the story, The Greedy Triangle, havestudents describe the angles in each successive figure as a rightangle, less than a right angle, or greater than a right angle.


Alternative ExploreMaterials: cardboard cutouts of various figures, index cardsStudents choose 3 figures: 1 with a corner smaller than, 1 with a corner larger than, and 1 with a corner equal to the corners in a square. Students use the corner of an index card to checkthe corners.

Early FinishersHave students use a geoboard to make as many figures as theycan with each type of corner.

Common Misconceptions➤Students think that the lengths of the sides of a figure

determine the size of the angle.How to Help: Draw 2 figures with right angles on the board.Make the sides of one figure much longer than the sides of theother. Have students use the corner of an index card to verifythat the angles are the same size. Draw another figure where the2 sides that form the right angle have different lengths. Havestudents check that the angle is a right angle.

ESL StrategiesEnsure that students for whom English is a second languageunderstand that the word right has a specific mathematicalmeaning in the context of angles, and that it does not mean theopposite of wrong.


A right angle Less than aright angle

Greater thana right angle

Watch for students who do not recognize asquare corner that is oriented on a slant. Havestudents rotate their geoboards or dot paperuntil the sides of the figures are horizontal andvertical. Alternatively, have students use thecorner of an index card to check the relativesize of the corner of the figure.

AFTER Connec t

Invite volunteers to draw one of their figureson a transparency of square dot paper on theoverhead projector. Have students describe eachcorner of their figure as smaller than, largerthan, or equal to the corners in a square.

Use Connect to introduce the terms vertex,angle, and right angle. Have students work inpairs, using the figures they made in Explore.Students take turns to describe each angle intheir figures as a right angle, greater than aright angle, or less than a right angle. Have

students use the corner of an index card tocheck their descriptions.

Prac t i ce

Have a piece of paper with a square corneravailable for all questions. Students requiregeoboards, geobands, and square dot paper tocomplete question 4.


Students understand that a right angle isformed when two sides of a figure make asquare corner at the vertex. Students makefigures on a geoboard with exactly 1, 2, and3 right angles. Students record each figure onsquare dot paper and write to describe howthey made each figure.

Sample Answers3.

4. a) b) c)

I made each figure by first making 1, 2, or 3 square corners.Then I added more sides, making sure that no more rightangles were formed.

5. I can draw a right angle without using dot paper by tracing asquare corner of a piece of paper or an index card.

REFLECT: I can tell that an angle is a right angle bytesting it with a square corner of a piece ofpaper. If the two sides make a square corner atthe vertex, the angle is a right angle. In somedrawings, a right angle is marked with a small square.

yellow Pattern Block blue Pattern Block

green Pattern Block



What to Look For

Understanding concepts ✔ Students understand the concepts of

angle and right angle.

Applying procedures✔ Students can identify an angle as

being a right angle, less than a rightangle, or greater than a right angle.

✔ Students can construct figures withright angles, angles less than a rightangle, and angles greater than aright angle.

What to Do

Extra Support: Students predict which Pattern Blocks haveright angles. They use a corner of an index card to check theirpredictions. Students repeat the activity for angles less than andangles greater than a right angle.Students can use Step-by-Step 2 (Master 3.19) to completequestion 4.

Extra Practice: Have students work in pairs. Each student makesa figure on a geoboard. Her partner describes each angle as aright angle, less than a right angle, or greater than a right angle.Students can complete Extra Practice 1 (Master 3.30).

Extension: Challenge students to draw on dot paper as manyfigures as they can with all three types of angles.


Numbers Every DayStudents should recall that, in a two-digit number, the first digit isthe tens digit, the second digit is the ones digit, and 1 ten isequal to 10 ones. For 3 tens and 2 ones, the number is 32. Oneten is the same as 1 ten and 0 ones or 10. Ten ones are thesame as 0 tens and 10 ones or 10. Four tens and 12 ones arethe same as 5 tens and 2 ones or 52. 32 is the same as 3 tensand 2 ones so, 2 fewer tens than 32 is 1 ten and 2 ones or 12.

Figure B

Figures C and DFigure A

Figure C

3210

105212


Naming Figures

Key Math Learnings1. A regular figure has all sides equal and all angles equal.2. A trapezoid, a parallelogram, and a rhombus are 4-sided

figures. A pentagon is a 5-sided figure. A hexagon is a6-sided figure.

3. A trapezoid has 2 parallel sides. A parallelogram has2 pairs of parallel sides. A rhombus is a parallelogram withall sides equal.

LESSON ORGANIZER

Curriculum Focus: Name figures and compare their attributes. Teacher Materials� square dot paper transparency (PM 22)Student Materials Optional� geoboards and geobands � Step-by-Step 3 (Master 3.20)� square dot paper (PM 22) � Extra Practice 2 (Master 3.31)Vocabulary: regular figure, trapezoid, parallelogram, rhombusAssessment: Master 3.2 Ongoing Observations: Geometry

40–50 min

L E S S O N 3


Have a volunteer make a triangle on a largegeoboard. Show students the triangle. Ask:• How do you know this is a triangle?

(It has 3 sides.)• How can you describe the sides of the

triangle? (Two of the sides are the same length.The third side is longer.)

• How many angles does it have? (3)• How can you describe the angles? (One angle is

a right angle. Two angles are less than a right angle.)

Present Explore. Encourage students to thinkabout sides and angles as they make anddescribe their figures.

DURING Exp lore


Listen as students describe their partner’sfigures. Are they focusing on the geometricattributes of the figure? Are they using termssuch as parallel, angle, and right angle?

Ask questions, such as:• How are these two figures the same?

(Both of them have 4 sides.) Different? (One figure has 4 right angles. The other figure has2 angles greater than a right angle, and 2 anglesless than a right angle.)

• What is the name of that figure? (It is a square because all sides have the same lengthand it has 4 right angles.)

• What do you notice about the number ofsides and the number of angles in eachfigure? (The number of sides and the number ofangles are the same.)

Making ConnectionsVisual Arts: Show students examples of abstract art that wascreated using geometric figures. Have students identify the figures.

Although the content of this lesson is not specified by yourcurriculum, it provides students with the backgroundneeded in later lessons in which they name the faces of 3-D solids (SS22 and SS24).

Curr i cu lum Focus


AFTER Connec t

Display a square dot paper transparency on theoverhead projector. Invite volunteers to draw,then describe, a triangle they made on theirgeoboard. Ask:• How are these triangles alike? (Both of them

have 3 sides and 3 angles.) How are theydifferent? (One triangle has sides of differentlengths. The other triangle has two sides equal.)

Invite volunteers to draw, then describe, a4-sided figure they made on their geoboard.Use these figures to review the rectangle andthe square, and to introduce the trapezoid, the parallelogram, and the rhombus.Introduce other figures such as the pentagonand the hexagon.

Use Connect to establish the key attributes of atrapezoid, parallelogram, rhombus, pentagon,and hexagon, and to introduce the term regular

figure. Ensure students understand thedifference between irregular and regularpentagons and hexagons. Demonstrate withfigures on the board how to use an arc to showequal angles.

The first hexagon in Connect is concave (has anangle greater than 180º). Students do not needto know this term but should see concavefigures. Draw a concave pentagon.

Prac t i ce

Questions 1, 3, 4, and 5 require a geoboard,geobands, and square dot paper.


Students make 3 different 4-sided figures, thendraw the figures on square dot paper. They useattributes such as side length, angle size, andnumber of parallel sides to describe thesimilarities and differences among the figures.

Early FinishersHave students use triangular dot paper to draw as many figuresas they can with equal sides and equal angles.

Common Misconceptions➤Students believe that, on a geoboard, the diagonal distance

from one peg to another is the same as the horizontal orvertical distance.

How to Help: Have students watch as you use a piece of stringto measure the horizontal, vertical, and diagonal distancesbetween two pegs. Students should see that the diagonaldistance is longer.


Sample Answers1. a) b)

c) d)

3. a) b) c)



What to Look For

Understanding concepts ✔ Students understand the concept of a

regular figure.

✔ Students understand that all figures ofthe same type have certain attributes.

Applying procedures✔ Students can sort, compare, and contrast

figures according to their attributes.

✔ Students can construct different figures.

Communication✔ Students use mathematical terminology

to name and describe figures.

What to Do

Extra Support: Have students name, then describe, theattributes of each type of Pattern Block. They then sort the blocksinto those that are regular figures and those that are not.Students can use Step-by-Step 3 (Master 3.20) to completequestion 4.

Extra Practice: Have students complete the Additional Activity,Regular Figures (Master 3.14).Students can complete Extra Practice 2 (Master 3.31).

Extension: Challenge students to explain why a square is arectangle, a parallelogram, and a rhombus.


4. The figures are the same becauseall of them have 4 sides and 4angles. They are different becausetheir sides are different lengths andtheir angles are different sizes.

Figure A is a square. It has 4 equal sides and 4 right angles.Figure B is a trapezoid. It has 2 parallel sides. Two of its sidesare the same length. It has 2 right angles, 1 angle less than aright angle, and 1 angle greater than a right angle.Figure C is a rhombus. It has 2 pairs of parallel sides and allsides equal.

5. My figure has 7 sides. It has 2 pairs of equalsides and 2 pairs of parallel sides. My figurehas 3 right angles and 4 angles greater thana right angle.

REFLECT: A rectangle is like a parallelogram because both ofthem have 2 pairs of parallel sides and 4 angles. A rectangleis different because it has 4 right angles and a parallelogramhas no right angles.This is a rectangle: This is a parallelogram:

A BC

B, (C, F)DA

C, (F)

25

12550

1000

Numbers Every DayStudents skip count by the value of the coin being used. Theyshould skip count by 5s for nickels, 10s for dimes, 25s forquarters, and 200s for toonies.


L E S S O N 4

Sorting Figures

Key Math Learnings1. Figures can be compared and sorted according to their

geometric attributes.2. A Venn diagram can be used as a sorting tool.

LESSON ORGANIZER

Curriculum Focus: Compare and sort figures. (PR1)Teacher Materials� transparencies of Sorting Figures 1 and 2

(Masters 3.7 and 3.8)Student Materials Optional� cutouts of figures from � Step-by-Step 4 (Master 3.21)

Sorting Figures 1 and 2 � Extra Practice 2 (Master 3.31)(Masters 3.7 and 3.8)

� square dot paper (PM 22)� triangular dot paper (PM 23)� Venn diagrams (PM 28)Vocabulary: Venn diagramAssessment: Master 3.2 Ongoing Observations: Geometry

40–50 min


Display figures cut from transparencies ofSorting Figures 1 and 2 (Masters 3.7 and 3.8)on the overhead projector. Invite volunteers tochoose a figure and describe one of itsattributes (for example, Figure K has 2 pairs ofequal sides).

Have a volunteer choose 2 figures. Shedescribes how the figures are alike, and howthey are different.

Present Explore. Ensure students understandthat all the figures should be included in theirsorting. Discuss possible ways to record theirsorting; for example, writing the letter of each figure.

DURING Exp lore


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

(All of them have parallel sides.)• What attributes did you use to sort?

(Figures with equal sides and figures withparallel sides)

• Where did you put figures with equal andparallel sides? (I put them in one group.)

• Where did you put figures that did not haveequal sides or parallel sides? (I put them in another group.)

As students work, listen for the criteria theyuse to determine their sorting groups. Are theyusing attributes such as equal or parallel sides,number of sides, number or type of angles?


AFTER Connec t

Invite volunteers to describe the attributes theyused to sort the figures. Discuss the methodsstudents used to record their work.

Draw a large Venn diagram on the board. Labelthe left loop “Has 4 sides” and the right loop“Has parallel sides”. Introduce the term Venndiagram and discuss how it is used to sort.

Ensure students understand that:• only 4-sided figures with no parallel sides

go in the left loop• only figures with parallel sides and more

than 4 sides go in the right loop• 4-sided figures with parallel sides go in

the middle• all other figures go outside the loops but

inside the rectangle

Have students sort the figures. (Left loop: K; Middle: R, Q, T, G; Right loop: H, J;Outside: S, E, I, P, C, L, N)

Repeat with 2 different attributes. Use Connect to illustrate other ways to sortfigures in Venn diagrams.

Prac t i ce

Questions 1 and 2 require the figures fromExplore (Masters 3.7 and 3.8). Question 3requires square dot paper. Question 1 requiresa Venn diagram. Provide triangular dot paperand square dot paper for students to recordtheir responses to Reflect.


Students should recognize that the figures theydraw do not have the two named attributes in common.

Early FinishersStudents work in pairs. One student sorts 5 or 6 figures fromExplore according to a secret rule. The other student guesses thesorting rule.

Common Misconceptions➤Students do not recognize parallel sides in a figure if the sides

are not horizontal or vertical.How to Help: Have students turn the figure until one side inquestion is horizontal and the other is vertical.


Numbers Every DayStudents can use a hundred chart.Start at 18. Count back by 2s: 18, 16, 14, 12, 10, 8, 6, 4, 2.Students will have coloured every other number (or every evennumber) on the chart going backward from 18.You will say 4, but you will not say 5.Start at 17. Count back by 2s: 17, 15, 13, 11, 9, 7, 5, 3, 1.Students will have coloured every other number (or every oddnumber) on the chart going backward from 17.You will say 3, but you will not say 2.

Sample Answers1. The sorting rule is:

Figures with parallel sides (right loop), and figures with all angles equal (left loop).

Has all angles equal Has parallel sides

E C J T Q H R G

S I L K N P



What to Look For

Understanding concepts ✔ Students understand that geometric

attributes can be used to compareand sort figures.

Applying procedures✔ Students can sort and re-sort a

collection of figures according to their attributes.

✔ Students can use a Venn diagram tosort figures.


to describe their sorting rules.

What to Do

Extra Support: Create a set of 4 or 5 figures from Explorethat fit a sorting rule. Have students find additional figures thatbelong to the set and/or guess the sorting rule.Students can use Step-by-Step 4 (Master 3.21) to completequestion 4.

Extra Practice: Have students work in pairs. One student sortssome of the figures from Explore and gives the sorting rule. Theother student draws a new figure that will fit the sorting rule, thenexplains why the figure fits the rule.Students can also complete Extra Practice 2 (Master 3.31).

Extension: Challenge students to draw 10 different figures onsquare dot paper or triangular dot paper. Have students cut outtheir figures, then sort them using a Venn diagram.


2. I chose the attribute: 3.

Figures with morethan 4 sides. My setof figures is: FiguresH, J, C, P. My partneradded a figure with 6 sides to my set.

4. I chose the attributes: Has parallel sides and has 3 sides. In the first loop, I drew a square, a rectangle, a parallelogram, and a trapezoid. In the second loop, I drew 4 different triangles. A triangle can never have

parallel sides. Outside the loop, I drew a circle and a regular pentagon. These figures have no parallel sides and they do nothave 3 sides.

REFLECT: I chose the attributes: Has 3 sides and has equal sides.I used a Venn diagram to sort the figures. In the first loop, Idrew 2 triangles with no equal sides. In the second loop, Idrew a rhombus and a regular hexagon. Both figures have allsides equal. In the middle, I drew a triangle with 3 equal sides;it belongs to both groups.

Has 3 sides Has equal sides

Has parallel sides Has 3 sides

Right angle Five angles

Yes, No

No, Yes


Congruent Figures

Key Math Learnings1. Congruent figures have the same size and shape.2. Congruent figures have equal matching sides and equal

matching angles.

LESSON ORGANIZER

Curriculum Focus: Match and describe congruent figures.(SS21)Teacher Materials� transparency of Congruent Figures (Master 3.9)� 3 leaves drawn on transparencies (2 congruent and

1 similar, but larger)Student Materials Optional� Congruent Figures � Step-by-Step 5 (Master 3.22)

(Master 3.9) � Extra Practice 3 (Master 3.32)� geoboards and geobands� square dot paper (PM 22)� scissors� tracing paperVocabulary: congruentAssessment: Master 3.2 Ongoing Observations: Geometry

80–100 min

L E S S O N 5


Display transparencies of 3 leaves on theoverhead projector. Two of the leaves should becongruent and the third leaf should have thesame shape but be much larger. Ask:• How are these leaves the same?

(All the leaves are maple leaves. All the leaves havethe same shape. Two of the leaves have the same size.)

• How are they different? (One leaf is larger than the others.)

• How can you tell if 2 leaves are exactly the same? (I can put one leaf on top of the otherand see if they match.)

Present Explore. Distribute copies of CongruentFigures (Master 3.9). Have students carefullycut out the figures to ensure that figures thatare exactly the same size stay the same size.

To save time, you may want to cut out the figuresfor each pair of students before the lesson.

DURING Exp lore


Listen to how students describe the similaritiesand differences among the figures. Do they useside length and angle size to compare andcontrast the figures? Do they place figures ontop of one another to see if they coincide?

Ask questions, such as:• What can you say about all the squares?

(All the squares have 4 right angles.)• What do you notice about 2 of the squares?

(Two of the squares have the same shape and size.)• How do you know the 2 squares are exactly

the same? (I put one square on top of the other square andthey matched.)

• What do you notice about the third square?(It has the same shape as the other squares but ithas a different size.)


AFTER Connec t

Display transparent cutouts of the 3 trianglesfrom Explore on the overhead projector. Arrangethe triangles so that they have differentorientations. Invite volunteers to describe theirobservations. Introduce the term congruent todescribe figures with the same size and shape.Ask:• How can you show that 2 of the triangles are

congruent? (I can put one triangle on top of theother. If they match, they are congruent.)

• Suppose you cannot move the figures. Howcould you check to see if they are congruent?(I could trace one of the figures and place the tracingon top of the other figure. If they match, the figuresare congruent.)

Review Connect for other examples of congruentfigures, and non-congruent figures. Explainhow one figure may need to be flipped to showit is congruent to another figure.

Prac t i ce

Questions 1, 2, and 3 require geoboards,geobands, and square dot paper. Reflect requiressquare dot paper. Make tracing paper availablefor question 4.


Students make the given parallelogram on ageoboard. They understand that congruentparallelograms will have the same size andshape as the original parallelogram. Studentsmake as many congruent parallelograms asthey can. Some students may realize theparallelograms can be flipped and turned, andthat they can even overlap. These students willfind many congruent parallelograms. Studentsaccurately record the parallelograms on dot paper.

Alternative ExploreMaterials: several sets of 4 congruent triangles made fromlight cardboardGive one triangle to each student. Have students find 3 otherstudents whose triangles match theirs exactly.

Early FinishersHave students work in pairs. One student makes a figure on ageoboard. The other student makes a figure with the same shapeand size.

Common Misconceptions➤Students do not recognize figures as congruent if they have

different orientations.How to Help: Encourage students to trace one of the figures, cutit out, and flip or turn it to see if it coincides with the other figure.


Numbers Every DayTo make your TI-108 calculator a “subtract 2 maker,” enter thestart number. Enter , then continue to press as manytimes as you want to count back by 2s. To make your TI-108 calculator a “doubles maker,” enter

, then continue to press as manytimes as you want to multiply by 2. Other calculators will dothis differently.

==�2

==2–



What to Look For

Understanding concepts ✔ Students understand that figures with

matching sides and equal angles arecongruent.

✔ Students understand that congruentfigures have the same size and shape.

Applying procedures✔ Students can identify congruent figures.

✔ Students can test for congruency byplacing one figure, or its tracing, ontop of the other figure.

What to Do

Extra Support: Provide students with cutouts of 4 hexagons, 2 of which are congruent. Have students find the 2 congruenthexagons. Repeat with pentagons.Students can use Step-by-Step 5 (Master 3.22) to completequestion 3.

Extra Practice: Students can complete the Additional Activity,Congruent Figures (Master 3.15).Students can complete Extra Practice 3 (Master 3.32).

Extension: Challenge students to draw on dot paper 3 congruent pentagons in 3 different orientations.


Sample Answers1. a) b) c)

2. a) b)

3. 4. I know these figures are congruent becausethey are exactly the same size and shape. I used tracings to check.

REFLECT: I can tell if two figures are congruent by putting onefigure on top of the other. If they match exactly, they arecongruent. If I cannot move the figures, I trace one of thefigures and put the tracing on top of the other figure. If the two figures do not match, they are not congruent.

the start number

Congruent Not congruent

Figures A and E are congruent. Figures Cand F are congruent.


L E S S O N 6

Making Pictures with Figures

Key Math LearningFigures can be combined to make other figures.

LESSON ORGANIZER

Curriculum Focus: Make a picture from figures.Teacher Materials� triangular dot paper transparency (PM 23)� Pattern Blocks for the overhead projector, or Pattern Blocks

transparency (PM 25)Student Materials Optional� Pattern Blocks (PM 25) � tracing paper� triangular dot paper � Step-by-Step 6 (Master 3.23)

(PM 23) � Extra Practice 3 (Master 3.32)� 2-column charts (PM 17)� Arrow (Master 3.10)Assessment: Master 3.2 Ongoing Observations: Geometry

optional


Invite students to examine the picture,Swinging, in the Student Book. Explain that thisis an example of abstract art.

Ask questions, such as:• What do you see in the picture?

(I see lots of different figures.)• What figures do you see?

(I see rectangles, circles, half circles, trapezoids,and triangles.)

Have students respond to the question posed.(Sample answers: 7 thin rectangles have been puttogether to make a larger rectangle; 15 small trapezoidshave been put together to make a larger trapezoid;

3 circles, 3 half circles, a trapezoid, and a rectanglehave been put together to make a figure that looks likea mushroom.)

Present Explore. Ensure students understandthat whole sides of blocks should touch.Students should draw each figure on triangulardot paper and then sketch the figure in the firstcolumn of their table. If necessary, demonstratehow to draw each Pattern Block on atransparency of triangular dot paper.

DURING Exp lore


Ask questions, such as:• What figure have you made? (A hexagon)• How would you describe it?

(It has 6 sides, 6 angles, and 3 pairs of parallel sides.)• Which blocks did you use to make

the hexagon? (I used 2 green triangles on oppositesides of 1 orange square.)

Numbers Every DaySince 28 is 10 more than 18, 28 – 2 is greater than 18 + 2.39 – 3 is greater because you are subtracting the smaller number.Subtracting 0 has no effect on the number. 15 is 1 less than 16,and 25 is 1 more than 24. So, the answers are equal.

The content of this lesson is not specified by your curriculum.However, the lesson gives students further opportunities toidentify 2-D figures and describe their attributes.

Curr i cu lum Focus

Sample Answers1. I made a windmill. I used 2 trapezoids to make the centre of

the windmill. They made a regular hexagon. I used6 rhombuses to make the arms of the windmill. The 2 trapezoids are congruent. The 6 rhombuses are congruent. I know these figures are congruent because when I put them on top of each other, they match exactly.


• Suppose you use 2 blocks. How can youmake a pentagon? (I can use 1 green triangleand 1 orange square.) An octagon? (I can use1 orange square and 1 yellow hexagon.)

AFTER Connec t

Have students use overhead Pattern Blocks onthe overhead projector to display their figures.Ask:• Which Pattern Blocks did you use to make

your figure? (I used 2 blue rhombuses and 1 green triangle.)

• How would you describe your figure? (It is a trapezoid. It has 4 sides, with 2 sides equal,and 2 sides parallel.)

• Can you use the same blocks to make afigure with more sides? How? (If I move thegreen triangle, I can make a figure with 6 sides.)With fewer sides? (I cannot make a figure with fewer sides.)

• How can you make a parallelogram? (I can put 3 blue rhombuses side by side.)

Review Connect for further examples of figuresmade with smaller figures.

Prac t i ce

Questions 1, 2, and 3 require Pattern Blocks.Question 4 requires copies of Arrow (Master 3.10). Have triangular dot paperavailable for questions 1, 2, 3, and Reflect. Havetracing paper available for question 3.


Some students may realize that only 3 differentfigures are possible. Other students mayinclude figures that are congruent to these 3 figures, but oriented differently.

Alternative ExploreMaterials: 2 congruent paper squares, one of them cut in halfalong the diagonalStudents make, then name, as many different figures as they canusing the square and 2 triangles. Each figure must have at leastone side fully touching another figure.

Early FinishersProvide students with 2 triangles formed by cutting a rectanglealong the diagonal. Have students use the triangles to make asmany different figures as they can with equal sides fully touching.

Common Misconceptions➤Students believe they have made 2 different figures when one

figure is the same as the other figure flipped or turned.How to Help: Have students flip or turn one figure onto theother to see that the two figures are congruent and, therefore,cannot be considered different.




What to Look For

Understanding concepts ✔ Students understand that figures can

be combined to create other figures.

Applying procedures✔ Students can combine figures in

different ways to create other figures.

✔ Students can identify figures within a figure.

What to Do

Extra Support: Provide students with 2 congruent isoscelestriangles. Have them combine the triangles, with equal sidesmatching, to create other figures.Students can use Step-by-Step 6 (Master 3.23) to completequestion 3.

Extra Practice: Provide students with 3 Pattern Blocks of eachcolour. Students make as many different figures as they can bycombining 3 blocks of the same colour. Each block must have atleast one side fully touching another block.Students can complete Extra Practice 3 (Master 3.32).

Extension: Have students complete the Additional Activity,Making Figures (Master 3.16).


2. a) b) c) d)

3. I made 3 different figures. At first, I thought I had made morefigures, but noticed some of my figures were congruent.

4. I see squares, rectangles, triangles, parallelograms, andtrapezoids. The 4 small triangles are congruent. The pink andblue triangles are congruent. The trapezoid made from theorange square and the light blue triangle is congruent to thetrapezoid made from the orange square and the greentriangle. I know they are congruent because when I traced oneof the figures and placed it on top of the other figure, theymatched exactly.

REFLECT: I was able to make 6 different figures, then I drew themon dot paper.

4 sides

3 sides 6 sides

3


Strategies Toolkit

Key Math LearningA problem involving a geometric puzzle can be solved usingthe strategy solve a simpler problem.

LESSON ORGANIZER

Curriculum Focus: Interpret a problem and select anappropriate strategy.Teacher Materials� transparent tangramStudent Materials� tangrams� triangular dot paper (PM 23)Assessment: PM 1 Inquiry Process Check List, PM 3 Self-Assessment: Problem Solving

40–50 min

L E S S O N 7


Use the introduction to the lesson to introducethe tangram and the term tans. Have studentssort their tans into the groupings listed. Invitestudents to examine the tangram square. Havethem make a figure congruent to the squareusing other tans.

Present Explore. Students may use 3 tans of theirchoice to make as many figures as they can.

DURING Exp lore

Ongoing Observations: Observe and Listen

Ask questions, such as:

• Which 3 tans did you choose? (I chose the 2 small triangles and the square.)

• Which figures did you make? (I made a trapezoid, a rectangle, anda parallelogram.)

• What did you do to change the parallelograminto a trapezoid? (I flipped one of the small triangles.)

AFTER Connec t

Work through the problem in Connect with theclass. Encourage students to find as manysolutions as they can for each number of tansused. For each solution found, ask:• How do you know that is a trapezoid?

(It has 4 sides and 2 parallel sides.)• Why do you think “solve a simpler problem”

is a good strategy to use with this problem? (It is easier to make a trapezoid with a smallnumber of tans.)

• Why is it important to look back? (To make sure each figure is a trapezoid)

Prac t i ce

Have tangrams available for all questions.

Making ConnectionsLiteracy: As they read, invite students to use tangrams tocreate the animals and objects in the story, Three Pigs, OneWolf, and Seven Magic Shapes.

Trapezoid, rectangle, triangle, parallelogram, square, pentagon, hexagon, 7-sided figure

(heptagon)

I can make a trapezoid with 2, 3, 4, 5, 6, and 7 tans.

This lesson is not directly tied to your curriculum outcomes.However, it provides opportunities for students to developspatial and problem-solving skills.

Curr i cu lum Focus

Sample Answers1. I can make a triangle, a square, a rectangle, a parallelogram,

a trapezoid, a pentagon, a hexagon, and an octagon.

2. I can make a square with 2, 3, 4, 5, and 7 tans, but not with6 tans.

REFLECT: Squares, rectangles, and triangles were easiest for meto make, but only when I was using 2, 3, or 4 tans.The rhombus was the hardest to make because the rhombushas to have 2 pairs of parallel sides and all sides equal. Theoctagon was also hard to make because I had to play with allthe tans for a long time before I was able to make a figurewith 8 sides.



What to Look For

Problem solving✔ Students can follow the steps of the

problem-solving process to solve aproblem.

✔ Students can use the strategy “solve a simpler problem” to finddifferent ways of combining tans to make figures.

What to Do

Extra Support: Have students use 3 specific tans to make theirfigures in Explore (for example, the 2 small triangles and themedium triangle, or the square and 2 small triangles).

Extra Practice: Have students use all 7 tans to create a picture.Students trace their pictures, trade tracings with a partner, thencover their partner’s tracing with tans.

Extension: Challenge students to use tans to make as manypentagons as they can.

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

Common Misconceptions➤Students think the trapezoids they make in Connect must look

like the red Pattern Block.How to Help: Remind students that a trapezoid is any 4-sidedfigure with one pair of parallel sides.


triangle square rectangle parallelogram

trapezoid pentagon hexagon octagon

2 tans 3 tans 4 tans 5 tans 7 tans


Identifying Prisms and Pyramids

Key Math Learnings1. A pyramid or a prism is named for the shape of its base.2. A pyramid has one base and triangular faces.

A prism has two congruent bases and rectangular faces.3. Solids with the same size and shape are congruent.

LESSON ORGANIZER

Curriculum Focus: Describe and name prisms and pyramidsby the shapes of their bases. (SS22, SS23, SS24, SS27)Student Materials Optional� geometric solids � Step-by-Step 8 (Master 3.24)

(pyramids and prisms) � Extra Practice 4 (Master 3.33)� a collection of small

boxes, packages, and containers that are shaped like pyramids or prisms

Vocabulary: pyramid, prism, base, faceAssessment: Master 3.2 Ongoing Observations: Geometry

40–50 min

L E S S O N 8


Use the introduction to the lesson to introducethe terms pyramid and prism. As studentsrespond to the questions posed, encourage themto use geometric attributes, such as number ofedges, number of faces, and number of vertices.(Sample answers: The two pictures are of solids. Bothsolids have faces, edges, and vertices. The pyramid hastriangular faces. The prism has rectangular faces.)

Present Explore. Students should have real solids,labelled as indicated, rather than pictures ofthem. Ensure students realize that each object is

either a pyramid or a prism. Encourage studentsto describe their chosen solid using its attributesand without identifying it as a pyramid or aprism. You may wish to demonstrate thisactivity. Describe one of the solids to the classand have volunteers guess the solid.

DURING Exp lore


Listen as students describe a solid. Do they useattributes such as number of faces, number ofedges, number of vertices, or shapes of thefaces, or do they describe the solid innon-geometric terms (for example, its colour,or what it is made of)?

Ask questions, such as:• How many faces does your solid have?

(It has 6 faces.)• What shapes are the faces?

(All the faces are rectangles.)

Your curriculum requires that students explore the conceptsof perpendicular, parallel, and intersecting lines on 3-Dobjects (SS28). The Curriculum Focus Activity, ExploringEdges (Master 3.17a) is provided to cover this outcome.Have students complete the activity after this lesson, usingthe same materials.

Curr i cu lum Focus


• Are any of the faces congruent? (Yes. There are 3 pairs of congruent faces)

• Is your solid the Ritz Cracker box? (Yes)

AFTER Connec t

Have students sort their collections of solidsinto 2 groups: pyramids and prisms. Have themexamine the pyramids.

Ask:• How are all the pyramids the same? (All the

pyramids have some triangular faces. The top of apyramid is pointed.)

• How are they different? (The face on the bottomof each pyramid is not always the same shape. Somepyramids have more faces, edges, and vertices thanother pyramids.)

Use Connect to introduce the term base. Tellstudents that the shape of the base determinesthe name of the pyramid.

Ask: • Why does a square pyramid have

4 triangular faces while a hexagonal pyramidhas 6 triangular faces? (A square has 4 sides and a hexagon has 6 sides.)

• What would you call a pyramid with apentagon as its base? (A pentagonal pyramid)

• How many triangular faces would it have? (5)

Draw students’ attention to the prisms in theircollection. Follow a similar line of questioningto introduce students to the attributes andnames of prisms.

Have students work in pairs to name eachpyramid and prism in their collection of solids.

Show students 2 congruent prisms orpyramids. Elicit from students that the prismsor pyramids are congruent because they havethe same size and shape.

Alternative ExploreMaterials: models of a pyramid and a prismStudents write to describe one of the solids in as many ways asthey can. Students explain how the solids are different and howthey are alike.

Early FinishersHave students choose a pyramid or a prism and trace each of itsfaces. Students trade tracings with a classmate and try to identifythe solid.

Common Misconceptions➤Students have difficulty counting the number of faces, edges,

or vertices on a geometric solid.How to Help: Suggest students put a small dot of Plasticine oneach face, edge, or vertex as they count.

ESL StrategiesStudents for whom English is a second language may not beable to describe their chosen solid in Explore. Have theirpartners ask questions about the solid to which the ESL studentcan reply “Yes” or “No.”


Sample Answers1. A has 2 rectangular bases.

It has 6 faces, 12 edges, and 8 vertices. C has 2 square bases. It has 6 faces, 12 edges, and 8 vertices. Each of G and K has pentagonal bases. Each has 7 faces, 15 edges, and 10 vertices. F has 2 triangular bases. It has 5 faces, 9 edges, and 6 vertices.

2. B has 1 triangular base and 3 triangular faces (4 faces in all).It has 6 edges and 4 vertices. Each of D and J has 1 hexagonal base and 6 triangular faces(7 faces in all). Each has 12 edges and 7 vertices. E has 1 square base and 4 triangular faces (5 faces in all). It has 8 edges and 5 vertices. H has 1 pentagonal base and 5 triangular faces (6 faces in all). It has 10 edges and 6 vertices.

3. a) The two solids have the same size and shape.b) The two solids have the same size and shape.

4. a) It has 2 congruent square bases and 4 other square faces.All the faces are congruent.

b) It has a triangular base and 3 other congruenttriangular faces.

c) It has 2 congruent triangular bases and 3 congruent rectangular faces.

Use the pictures at the bottom of Student Bookpage 125 to show that the base of a prism is notnecessarily the face the prism “sits on.” Thetriangular prism is shown “sitting on” a base.The pentagonal prism “sits on” a face that is not a base.

Prac t i ce

Have models of geometric solids available forall questions.


Students are able to accurately count thevertices of pyramids and prisms they know.Students find a pyramid and prism that havethe same number of vertices. Most studentswill only find one answer but keen studentsmay come up with other answers, usingpyramids they are not familiar with. Studentsexplain why they believe there is, or is not,more than one answer.


rectangular prism triangularpyramid

square prismor cube square pyramid

hexagonal pyramid

pentagonal prism

pentagonal pyramid triangular prism pentagonal prism

hexagonal pyramid

D and JG and K

5. a) It could be a square pyramid. A square pyramid has1 square base and 4 triangular faces. It could also be atriangular prism. A triangular prism has 2 triangular basesand 3 rectangular (square) faces.

b) It could be a hexagonal prism. A hexagonal prism has2 hexagonal bases and 6 rectangular faces.

c) It could be a triangular prism. A triangular prism has2 triangular bases and 3 rectangular faces. It could be anypyramid (triangular, square, rectangular, pentagonal,hexagonal, octagonal, and so on). All pyramids havetriangular faces.

6. Both a triangular prism and a pentagonal pyramid have6 vertices. A pyramid with a base that has 7 sides would have8 vertices, just like a rectangular prism. A pyramid with a basethat has 9 sides would have 10 vertices, just like a pentagonalprism. I could keep naming pyramids with an even number ofvertices, and matching them up to different prisms.

REFLECT: Prisms and pyramids are alike because both of themare solids with faces, edges, and vertices. Both are named fortheir bases. They are different because a pyramid has 1 baseand triangular faces, and a prism has 2 congruent bases andrectangular faces.



What to Look For

Understanding concepts✔ Students understand that pyramids

and prisms are named for their bases.

Applying procedures✔ Students can count the faces, vertices,

and edges of pyramids and prisms.

✔ Students can identify congruentpyramids and prisms.

Communicating✔ Students can use mathematical

language to describe the geometricattributes of pyramids and prisms.

What to Do

Extra Support: Place a set of pyramids and prisms on thetable. Place one solid from an identical set in a paper bag. Havea student reach into the bag, feel the solid, then find the identicalsolid on the table. Repeat with other solids. Students can use Step-by-Step 8 (Master 3.24) to completequestion 6.

Extra Practice: Take students on a walk around the school orneighbourhood to look for objects shaped like pyramids andprisms. When students return to the classroom, they record theobjects they found in a chart on the board. Students can also complete Extra Practice 4 (Master 3.33).

Extension: Provide students with straws and Plasticine. Havethem construct skeletal models of prisms and pyramids.


A cube or a square prism

Triangular pyramid

Triangular prism

24

108

Numbers Every DayFor the first equation, think about related facts. Students couldthink addition and solve 8 + = 10. For the second equation,students could think subtraction and solve 9 – 5 = . For thethird equation, students could add 2 + 3 to get 5, then adddoubles. For the fourth equation, students could make 10 byadding 7 + 3, then subtract 2.

42


Sorting Solids

Key Math LearningGeometric solids can be compared and sorted according totheir attributes.

LESSON ORGANIZER

Curriculum Focus: Compare and sort solids. (PR1)(SS22, SS23, SS26)Student Materials Optional� geometric solids � Step-by-Step 9 (Master 3.25)� loops of yarn � Extra Practice 4 (Master 3.33)� Venn diagrams (PM 28)Assessment: Master 3.2 Ongoing Observations: Geometry

40–50 min

L E S S O N 9


Show the models of the solids in Explore tostudents. Invite a volunteer to secretly chooseone solid. Have the volunteer name her solidand describe it in as many ways as she can.Encourage the student to use the terms faces,congruent, edges, and vertices in herdescriptions. Have other students say whichsolid they think has been described.

Review the cone, the sphere, and the cylinder,which students studied in grade 2. PresentExplore. Provide loops of yarn for students whowish to make a Venn diagram to help them sorttheir solids. The desktop can be the rectanglethat frames the Venn diagram.

DURING Exp lore


Watch for students who have difficultydetermining their partner’s sorting rule.

Ask questions, such as: • Which solids are in Group 1?

(A, B, C, D, E, and F)• Which solids are in Group 2?

(E, J, and K)• Which attribute do the solids in

Group 1 share? (All solids in Group 1 have 2 bases.)

• Which attribute do the solids in Group 2 share? (All solids in Group 2 have triangular faces.)

• Which solids do not belong in either group?(G and H) Why? (They do not have 2 bases and they do not havetriangular faces.)

Making ConnectionsMath Link: Have students explore the pattern in the numbersof edges, faces, and vertices of a solid using other solids, suchas the triangular pyramid, the rectangular prism, and thesquare pyramid.


• Where would you put these 2 solids in aVenn diagram? (Outside the loops and inside the rectangle)

• Do the loops overlap? (Yes) Why? (E has 2 bases and they are triangular.)

• How is the cylinder like the hexagonal prism? (Both solids have 2 bases.) How are these solids different? (The bases of the cylinder are circles. The bases ofthe prism are hexagons. The cylinder has a curvedsurface joining the bases. The hexagonal prism hasrectangles joining its bases.)

• How is the cone like the triangular pyramid? (Both solids have 1 base.)

How are these solids different? (The base of the cone is a circle. The base of thepyramid is a triangle. The cone has a curvedsurface. The pyramid has triangular faces.)

• How many faces does a sphere have? (None, it has a curved surface.) How many vertices does a sphere have? (None) How many vertices does a cone have? (1)

Listen as students identify the attributes of thesolids. Do they use appropriate mathematicalterminology? Are they able to accurately countthe faces, vertices, and edges of their solids?

Alternative ExploreMaterials: geometric solids, loops of yarn, index cardsStudents work in groups of 4. They use 2 loops of yarn to makea Venn diagram. One student names an attribute, writes it on anindex card, then places the card above one of the loops.Another student does the same for a second attribute, and placeshis card above the other loop. Students take turns placing thesolids on the Venn diagram until all solids have been sorted.

Early FinishersHave students choose a solid, then write a riddle about it.Students exchange riddles and guess their partner’s solid.

Common Misconceptions➤Students consider the rounded surfaces on cylinders, cones,

and spheres to be faces.How to Help: Explain that a face is a flat surface of a solid.Therefore, a cylinder has 2 faces, a cone has 1 face, and asphere has no faces.


Numbers Every DayFor 4 dimes and 3 nickels, students will skip count by 10s, then 5s. For 3 quarters and 2 dimes, students will skip count by25s, then 10s. For 2 quarters and 4 nickels, students will skipcount by 25s, then 5s. For 4 quarters, 3 dimes, and 2 nickels,students will skip count by 25s, then 10s, and then 5s. Studentsmay use a hundred chart to help them.

Sample Answers1. He used the sorting rule: Solids with 6 faces and solids that do

not have 6 faces. I would label Loop 1: Solids with 6 faces.I would label Loop 2: Solids that do not have 6 faces.

2. Assume D is a pentagonal pyramid. a) I put D in the loop on the left. Figure D has 6 faces. None

of its faces is rectangular. I put B in the loop on the right. Figure B has rectangularfaces, but it does not have 6 faces. I put A and E in the middle. Each has 6 rectangular faces. I put C outside the loops. It does not have 6 faces and itdoes not have rectangular faces.

b) I chose a pentagonal prism. It belongs in the loop on theright because it has rectangular faces, but it does not have 6 faces.

Note: A square is a rectangle, so, in question 2a, both solidsA and E go in the middle loop. If, at this time, you have nottaught this inclusive property, then some students may put E inthe loop on the left.

3. My sorting rule is: Solids withcongruent faces and solidswith circular faces.

4. My sorting rule is: Solids with2 bases and solids withcircular faces.


AFTER Connec t

Invite volunteers to demonstrate one way theysorted their solids, and have other studentsname the sorting rule. Review the sortingexample in Connect.

Ask: • Why is the cube in the middle of the loops?

(A cube has 8 vertices and all faces congruent.) • Why is the square pyramid outside

the loops? (It does not have 8 vertices, nor does it have all faces congruent.)

• How else could we sort these solids? (We could use the sorting rule: Solids that arepyramids and solids that are prisms.)

• Would the loops overlap? Explain. (No, because a solid cannot be both a pyramid and a prism.)

Prac t i ce

Have geometric solids available for allquestions. Have Venn diagrams (PM 28)available for questions 2, 3, 4, and Reflect.


Students are able to name solids from adescription of some of their attributes. Studentsshould realize that different solids could havesome attributes in common. For part b,students should name as many different solidsas they can. Students should provideexplanations for their answers.

Has congruent faces Has circular faces

C D EF G H

J K A B

Has 2 bases Has circular faces

C DG H

JK

AB

E F

D A E

C

B

5. I chose solids C and G. Both C and G are prisms. Each has2 congruent bases. Each has rectangular faces. C and G aredifferent because C has rectangular bases and G hashexagonal bases. C has 6 faces and G has 8 faces. C has12 edges and 8 vertices. G has 18 edges and 12 vertices.

6. a) A square pyramid has 5 vertices and 5 faces.b) A rectangular prism has 6 rectangular faces. A cube has

6 congruent faces. A pentagonal pyramid has 6 faces:1 pentagon and 5 triangles.

c) A triangular prism has 5 faces:2 triangles and 3 rectangles.

d) A cube has 6 congruent faces and 12 edges.REFLECT: I chose a triangular pyramid, a cone, a rectangular

prism, a pentagonal prism, and a triangular prism. I chose the attributes: Solids with triangular faces and solidswith rectangular faces. The triangular prism is in the middlebecause it has both triangular and rectangular faces. The cone is outside the loops because it has neither attribute.

Has triangular faces Has rectangular faces

triangularpyramid

triangularprism

rectangularprism

pentagonalprism

cone



What to Look For

Applying procedures✔ Students compare and sort solids

according to their attributes.


to describe the attributes of solids,and to explain their sortings.

What to Do

Extra Support: Have students complete the Additional Activity,Comparing Boxes (Master 3.17). Students can use Step-by-Step 9 (Master 3.25) to completequestion 6.

Extra Practice: Have students find, then cut out, pictures frommagazines of objects that resemble geometric solids. Students sort the pictures according to the attributes of the solidsthey resemble. Students can complete Extra Practice 4 (Master 3.33).

Extension: Have students sort the solids in Explore using3 attributes. Have students find a way to show that some solids fitinto 2 or 3 groups.


Square pyramidRectangular prism, cube, pentagonal pyramid

Triangular prism

Cube

55¢95¢70¢

140¢


Making Models from Figures

Key Math Learnings1. Figures shaped like the faces of a solid can be taped

together to create a model of a solid.2. A net is a cutout that shows all the faces of a solid joined in

one piece.3. A net can be folded to make a model of a solid.

LESSON ORGANIZER

Curriculum Focus: Use figures to make models. (SS22, SS23, SS24)Teacher Materials� 2 identical cereal boxes (empty)� Making Models from Figures (Master 3.11)Student Materials Optional� cardboard cutouts made � Step-by-Step 10 (Master 3.26)

from Making Models from � Extra Practice 5 (Master 3.34)Figures (Master 3.11)

� Nets (Master 3.12)� tape� scissors� 2-cm grid paper (PM 21)� cereal boxesVocabulary: netAssessment: Master 3.2 Ongoing Observations: Geometry

40–50 min

L E S S O N 1 0


Invite students to examine the picture of thegingerbread house on page 132 of the StudentBook. Have a volunteer read the introduction tothe lesson aloud. Have students respond to thequestion posed. (Sample answers: rectangles,triangles, squares, hexagon)Ask: • Which 2 figures have been put together to

make a new figure? (The triangle and the squarehave been put together to make a pentagon.)

• Which solid will the finished gingerbreadhouse make? (A pentagonal prism)

• Which figures in the gingerbread houseare congruent? (The 2 rectangles for the roof, the2 rectangles for the sides, the 2 squares for the frontand back, the 2 triangles for the front and back)

Present Explore. Ensure students understandthey should decide which solid to build, thenchoose the appropriate cutouts.

DURING Exp lore


Ask questions, such as: • Which model will you make?

(A square pyramid)• Which figures will you need?

(I will need a square and 4 congruent triangles.)• Is it possible to make a cube? (Yes) How?

(I will need 6 congruent squares.)• Which solids could you make using the

hexagon as a base? (A hexagonal prism or a hexagonal pyramid)

• Which model will you make? (A house)What will you use? (A rectangular prism, with a rectangular pyramidon top)

Watch to ensure students match sides of equallengths when making their models.


AFTER Connec t

Invite students to display the models theymade. Ask: • Which model did you make?

(I made a hexagonal pyramid.)• How many faces does your solid have? (7)

What are the shapes of the faces? (One face isa hexagon and 6 faces are congruent triangles.)

• How is your model the same as yourclassmate’s model? (We both used the hexagon as part of our model.)

• How is your model different from yourclassmate’s model? (I used 1 hexagon and 6 triangles to make ahexagonal pyramid. My classmate used 2 hexagonsand 6 rectangles to make a hexagonal prism.)

• How many edges does your solid have? (12 edges) How many vertices? (7 vertices)

• What problems did you have putting yourmodel together? (It was hard to get all the tapededges to stay together.)

Use Connect to introduce the net as a cutout thatcan be folded to make a model. Use a cerealbox to demonstrate how a net can be made bycutting along some of the edges of the box.

Prac t i ce

Students will need copies of Nets (Master 3.12)for questions 1 and 3, and a cereal box forquestion 2. Have 2-cm grid paper available forquestion 4.


Students understand that a cube has6 congruent square faces. They realize that a netis a cutout which, when folded, will bringedges together to form a solid. Some studentsmay be able to visualize the results of foldingeach picture. Other students may need to draw,cut out, then fold each picture to determinewhich picture shows a net for a cube.

Alternative ExploreMaterials: light cardboard, geometric solids (pyramids, prisms)Have students choose one solid. Students trace each face of thesolid onto light cardboard, cut out the faces, then tape themtogether to make a model of their solid.

Early FinishersHave students write to describe the model they built in as manyways as they can.

Common Misconceptions➤Students have difficulty selecting the cardboard figures needed

to make a particular model.How to Help: Provide students with the geometric solid theywant to model. Have them identify the shape of each face, thencount how many of each figure they need.


Numbers Every DayFor 156 + 233, students could round to the nearest 100: 200 + 200 = 400. For 407 + 108, students could use front-endestimation: 400 + 100 = 500. For 38 + 150, students couldround 38 to 50: 50 + 150 = 200. For 198 + 49, students couldround 198 to 200 and 49 to 50: 200 + 50 = 250.

Your curriculum requires that students demonstrate that arectangular solid has more than one net (SS25). The CurriculumFocus Activity, Making Nets (Master 3.17b) is provided to coverthis outcome. Have students do the activity after this lesson.

Curr i cu lum Focus

Sample Answers1. The congruent faces on my model are opposite each other.2. I see 6 rectangles in the net. Pairs of rectangles are congruent.

Each rectangle has 2 pairs of equal parallel sides and 4 right angles.

3. This is the net for a rectangular prism. The sides that join haveequal length.

4. I made a copy of each picture on grid paper. I cut out thepictures, then folded them. The first picture made a boxwithout a top and 2 of its faces overlapped. The secondpicture made a cube, so it is a net for a cube.

REFLECT: I can tell if the picture is a net if it has 3 pairs ofcongruent rectangles, with none of them side by side.

This is a net:

This is not a net:



What to Look For

Understanding concepts✔ Students understand that a net is a

cutout showing all the faces of asolid, which can be folded to make amodel of the solid.

Applying procedures✔ Students can select the appropriate

figures, and join the figures to make a model.

✔ Students can fold a net to make amodel of a solid.

✔ Students can cut along some of theedges of a box to form a net.

What to Do

Extra Support: Give students a net of a pyramid and a prism.Have them predict which solids the nets will form. Have studentscut out, then fold, the nets to check their predictions. Students can use Step-by-Step 10 (Master 3.26) to completequestion 4.

Extra Practice: Provide students with cardboard cutouts of the faces of a pyramid or prism. Have them determine whichsolid the figures will make, then tape the figures together to make the solid. Students can also complete Extra Practice 5 (Master 3.34).

Extension: Challenge students to draw on grid paper as manynets for a cube as they can. Students cut out, then fold, each oneto check.


Green

Blue Red

Green

Blue Red

Cube

About 400About 500About 200About 250


L E S S O N 1 1

Making a Structurefrom Solids

Key Math LearningSolids can be combined to make a structure.

LESSON ORGANIZER

Curriculum Focus: Use solids to make a structure. Student Materials Optional� geometric solids � Step-by-Step 11 (Master 3.27)� a collection of boxes, � Extra Practice 5 (Master 3.34)

containers, and packages� glue or tape� index cards� Pattern Blocks� rulersAssessment: Master 3.2 Ongoing Observations: Geometry

optional


Have a volunteer read the introduction to thelesson. Explain that the Inuit people have beenbuilding inuksuit (plural of inuksuk) forthousands of years and that an inuksuk servesmany purposes, such as to show the way homeor to mark where food is stored.

Have students look at a structure they can seethrough the classroom window and respond tothe question posed. (Sample answer: I can see a house. It looks like asquare prism with a square pyramid on top.)

Present Explore. Invite students to suggestpossible structures they could make (for

example, a tower, a building, an inuksuk, aspace station). Have students write about theirstructures on index cards.

DURING Exp lore


Ask questions, such as: • What structure are you making?

(We are making an apartment building.)• Which solids are you using?

(We are using 1 large rectangular prism, 6 smallerrectangular prisms, and 2 square pyramids.)

Listen as students build their structures. Dothey use appropriate mathematical terminologyto name the solids they are using?

Watch as students sketch pictures of theirstructures. Since students have not learned todraw perspective, they will probably draw aview (front, top, or side) of their structures.

Numbers Every DayFor 233 – 156, students could use front-end estimation: 200 – 100 = 100. For 407 – 108, students could round to thenearest 100: 400 – 100 = 300. For 150 – 38, students coulduse front-end estimation: 100 – 0 = 100, or round 38 to thenearest 50: 150 – 50 = 100. For 198 – 49, students could usefront-end estimation: 100 – 0 = 100, or round to the nearest 10:200 – 50 = 150.

The content of this lesson is not required by yourcurriculum. It does, however, provide further opportunitiesfor students to name and describe solids.

Curr i cu lum Focus


AFTER Connec t

Have students hand in the index cards onwhich they wrote descriptions of theirstructures. Mix up the cards and distribute onecard to each pair of students. Have studentsmove about the room and examine eachstructure until they think they have found theone that matches the description on their card.

Once students return to their places, havevolunteers explain how they found the structure,and how they know it is the right one.

Ask questions, such as: • How is the structure you built like the one

described on the card? (Both structures are made from solids.) How is it different? (I used rectangular prisms and square pyramids.The structure on the card is made from hexagonalprisms, rectangular prisms, a cube, and a square pyramid.)

• In which structures did you see congruentsolids? (I used 6 congruent rectangular prisms inmy structure.) How were they used? (I put 3 oneach side of my building to make the balconies.)

Prac t i ce

Students will need the solids used in Explorefor questions 1 and 3, and Pattern Blocks and aruler for question 4 (the wooden blocks, whichare thicker than the plastic blocks, workbetter). You may wish to have students work insmall groups to complete questions 1 and 3.


Students should discover that the tower thatuses the fewest blocks is made by stacking, onedge, blocks with the greatest height. Somestudents may find it easier to build the towerhorizontally on the desk, then try to get itto balance.

Common Misconceptions➤Students have difficulty sketching the structure they built.How to Help: Tell students it is only necessary to sketch the frontview of their structures.ESL StrategiesStudents for whom English is a second language may havedifficulty writing to describe how they built their structure. Pair them with students who can play the role of a scribe and a prompter.


Sample Answers1. a)

b) I built a tower. I used a rectangular prism for the base.I added more rectangular prisms on top of the base.Each one was smaller than the one before. I put a squarepyramid on the very top.

2. b) rectangular prism, square pyramid, cube, cylinder,hexagonal prism, half sphere, half cylinder

c) 4 of the solids are pyramids. 18 of the solids are prisms.

3. I used 6 congruent cylinders to hold up mybridge. I used the cylinders because they

are strong and they have round, flat faces. I used a longrectangular prism for the bridge. It fits right on top of thecylinders. I put a triangular prism on each end of the bridge.

About 100About 300About 100

About 100 orabout 150

Cars can use the triangular prisms to get on and off the bridge.4. My tower is exactly 15 cm high. I used 3 yellow hexagons

and 1 red trapezoid to build my tower. I put the hexagons ontheir edges, one on top of the other. I put the trapezoid on topof the hexagons. Each hexagon has 6 equal sides and 6 equal angles. Each angle is greater than a right angle.The trapezoid has 1 pair of parallel sides and1 pair of equal sides. It has 2 pairs of equal angles.Two of them are greater than a right angle and2 are less than a right angle. Here is a pictureof my tower.

REFLECT: I look at the faces, top, and base of each solid. If thefaces are triangles and the top has a vertex, it is a pyramid. I look at the base to see what kind of pyramid it is. For example,if the base has 6 sides, it is a hexagonal pyramid. If the facesare rectangles and the top is a face, it is a prism. The top is abase. The shape of the base tells what kind of prism it is. If thebase is a triangle, the solid is a triangular prism.



What to Look For

Understanding concepts✔ Students understand that solids can be

combined to create a structure.

Applying procedures✔ Students use solids to create

a structure.


to describe the solids that make a structure.

What to Do

Extra Support: Make a structure of 3 or 4 solids. Havestudents sketch the structure, name the solids, then describe howthe structure was made.Students can use Step-by-Step 11 (Master 3.27) to completequestion 4.

Extra Practice: Have students work in pairs. One studentbuilds a structure and the other student describes how it wasmade. Students switch roles and repeat the activity. Students can complete Extra Practice 5 (Master 3.34).

Extension: Challenge students to use boxes and containers tomake the tallest freestanding structure they can.


Making ConnectionsLiteracy: Read and discuss The Inuksuk Book by MaryWallace. Toronto: Firefly Books, 1999. ISBN: 1895688914.Note: Inuksuk is often spelled inukshuk. However, the FirstNations people do not include an h in the word.Art: Have students gather stones with some flat surfaces. Havethem make an inuksuk, then write to describe the solids thedifferent parts of the structure resemble.

About 25

418

Note: Students may have difficulty tracing thefigures they make with blue Pattern Blocks inquestion 6. Have students record their figureson triangular dot paper.

Sample Answers1. Figures A, B, and C are alike because all of them have

parallel sides, equal sides, and equal angles. Eachfigure has some angles greater than a right angle.They are different because they have different numbersof sides and different numbers of angles.

2. Figure A has 2 pairs of equal angles. Two angles areless than a right angle, and 2 angles are greater than aright angle.Figure C has 5 angles. Two angles are right angles, and3 angles are greater than a right angle. Two of the 3 angles greater than a right angle are equal.

3. a) The square has 4 equal sides, 2 pairs of parallelsides, 4 equal angles, and each angle is a rightangle. It is a regular figure.

b) The trapezoid has 4 sides, 2 parallel sides, 2 anglesless than a right angle, and 2 angles greater than aright angle.

c) The rhombus has 2 pairs of parallel sides, all sidesequal, 2 angles that are equal and greater than aright angle, and 2 angles that are equal and less thana right angle.

d) The parallelogram has 2 pairs of equal and parallelsides, 2 angles that are equal and greater than aright angle, and 2 angles that are equal and less thana right angle.

e) The triangle has 3 sides, 2 sides equal, 3 angles, andall angles less than a right angle.

f) The rectangle has 2 pairs of equal and parallel sidesand 4 right angles.

4. I chose the attributes: Figures with all sidesequal and figureswith 4 sides.

5. They have the same shape and size.6.

Has all sides equal Has 4 sides

D B F A H E C G

38 Unit 3 • Show What You Know • Student page 138

LESSON ORGANIZER

Student Materials� cutouts of figures from Show What You Know Figures

(Master 3.13)� blue Pattern Blocks (PM 25)� geometric solids� triangular dot paper (PM 23)Assessment: Masters 3.1 Unit Rubric: Geometry, 3.4 Unit Summary: Geometry

40–50 min

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

Figures D and F, andFigures C and E

Square Trapezoid Rhombus

ParallelogramTriangle Rectangle

7. I assume the prism has square bases. They are alike becauseboth of them have faces, vertices, and edges. Both of themhave a square base. They are different because the rectangular prism has 2 square bases and 4 congruent rectangular faces. The pyramid has 1 square base and 4 congruent triangular faces. The prism has 12 edges and 8 vertices. The pyramid has 8 edges and 5 vertices.

8.

9. I assume F is a pentagonal prism. I used the sorting rule: Solids with triangular faces and solids with 6 faces.

10. My structure is an inuksuk. The head is a triangular prism.The arms are two rectangularprisms. The body is a cube. The legs are rectangularprisms. The arms and legs are made of congruent solids.The arms are the same sizeand shape. The legs are thesame size and shape.

Has triangular faces Has 6 faces

A B C F D E

Unit 3 • Show What You Know • Student page 139 39


What to Look For

Reasoning; Applying concepts✔ Questions 7 and 9: Student understands and identifies the attributes of solids.✔ Questions 5 and 10: Student understands the concept of congruency.

Accuracy of procedures✔ Question 4: Student can sort figures according to 2 attributes, using a Venn diagram.✔ Question 10: Student can build and sketch a structure made of solids.

Communication✔ Questions 2, 3, and 7: Student can use mathematical language to describe figures and solids.

Problem solving✔ Question 6: Student can solve a geometric puzzle by combining figures to create new figures.

Recording and ReportingMaster 3.1 Unit Rubric: Geometry Master 3.4 Unit Summary: Geometry

Rectangular prism

Triangular pyramid

Square pyramid

Pentagonal pyramidTriangular prismSquare pyramid Cube

Rectangular prism

Have students turn to the Unit Launch on pages102 and 103 of the Student Book.

Use the lists of Learning Goals and Key Wordsto review the main learnings of the unit.

Present the Unit Problem. Invite volunteers toidentify the solids the children in theillustration are using to build the castle.

Have a volunteer read the instructions for theproblem aloud. Ensure students understandthey will build a smaller model of a sand castlethan the one depicted in the illustration.

Invite a student to read aloud the Check List.Explain that these are the criteria against whichtheir work will be assessed. Ensure studentsunderstand that all group members mustcollaborate to complete all parts of the activity.

40 Unit 3 • Unit Problem • Student page 140

At the Beach

LESSON ORGANIZER

Student Grouping: 4Student Materials� geometric solids� a collection of empty boxes, packages, and containers� glue or tapeAssessment: Masters 3.3 Performance Assessment Rubric: Atthe Beach, 3.4 Unit Summary: Geometry

40–50 min

U N I T P R O B L E M

Unit 3 • Unit Problem • Student page 141 41


What to Look For

Understanding concepts✔ Students can identify the attributes

of solids.✔ Students relate solids to

real-world objects.

Applying procedures✔ Students build a structure using solids.✔ Students sketch a picture of

their structure.


to name the solids in their structureand to explain the process they usedto make the structure.

What to Do

Extra Support: Make the problem accessible.

Some students may have difficulty describing the process theyused to build their structure. Ask questions, such as:

• Which part of the castle did you build first? Which solids didyou use? Why did you choose those solids?

• What part did you build next?

Some students may have difficulty naming the pyramids andprisms in their structure. Remind them that these solids are namedfor their bases. Have students examine the bases and identifytheir shapes.


Sample ResponseWe built a model of a sand castle. We used boxes and solids.We made the back and sides of the castle with congruent boxesplaced on their sides to look like walls. We used 2 congruent smaller boxes for the front of the castle. We left aspace between them for the door. All the boxes are rectangularprisms. We put a cylinder on each of the four corners of thewalls to look like towers. We put a square pyramid on top ofeach cylinder for decoration. We put a rectangular prism in frontof the door. It looks like a drawbridge. We put a triangularprism above the door for support.

Reflect on the UnitFigures and solids are alike because solids have figures as facesand bases. Both solids and figures have vertices.Figures and solids are different because a figure has sides but asolid has edges. Figures have 1 face but solids have many faces.Solids can be combined to make structures while figures can becombined to make pictures or solids.

Teaching notes for the Cross Strand Investigation, How ManyCereal Bits in a Box?, are in the Grade 3 Planning andProgram Masters module.

Copyright © 2005 Pearson Education Canada Inc. 42

Evaluating Student Learning: Preparing to Report: Unit 3 Geometry This unit provides an opportunity to report on the Shape and Space: 3-D Objects and 2-D Shapes strand. Master 3.4: Unit Summary: 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: 3-D Objects and 2-D Shapes

Reasoning: Applying concepts

Accuracy of procedures

Problem solving

Communication Overall

Ongoing Observations 1 2 2 2 2 Strategies Toolkit 1 1 Work samples or portfolios; conferences

1 2 2 2 2

Show What You Know 2 2 2 2 2 Unit Test 2 3 2 2 Unit Problem At the Beach

2 3 2 2 2

Achievement Level for reporting 2

Recording How to Report Ongoing Observations

Use Master 3.2 Ongoing Observations: 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 7). Transfer results to the summary form. Teachers may choose to enter a level in the Problem solving column and/or Communication.

Portfolios or collections of work samples; conferences, or interviews

Use Master 3.1 Unit Rubric: 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 3.1 Unit Rubric: Geometry may be helpful in determining levels of achievement. #1–5, 7, 9, and 10 provide evidence of Reasoning; Applying concepts; #2, 4, and 8–10 provide evidence of Accuracy of procedures; #6 provides evidence of Problem solving; all provide evidence of Communication.

Unit Test Master 3.1 Unit Rubric: 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 3.3 Performance Assessment Rubric: At the Beach. The Unit Problem offers a snapshot of students’ achievement. In particular, it shows their ability to synthesize and applywhat 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: Geometry

Not Yet Adequate Adequate Proficient Excellent

Reasoning; Applying concepts

• shows understanding of solids and their characteristics by: – demonstrating and

explaining relationships between 3-D solids and 2-D shapes (faces)

– comparing and contrasting two 3-D objects

– constructing 2-D shapes, 3-D objects, and nets

may be unable to demonstrate and explain: – relationships

between 3-D objects and 2-D shapes (faces)

– similarities and differences between two solids

– construction of 2-D shapes, 3-D objects, and nets

partially able to demonstrate and explain: – relationships

between 3-D objects and 2-D shapes (faces)



able to demonstrate, apply, and explain: – relationships between

3-D objects and 2-D shapes (faces)



in various contexts, appropriately demonstrates and explains: – relationships between

3-D objects and 2-D shapes (faces)




• accurately: – identifies attributes

(sides, angles, faces, vertices, edges)

– names and classifies 3-D objects and 2-D shapes (names prisms, pyramids by bases)

– identifies congruent 3-D objects and 2-D shapes

limited accuracy; omissions or major errors in: – identifying attributes


– naming and classifying 3-D objects and 2-D shapes (names prisms, pyramids by bases)

– identifying congruent 3-D objects and 2-D shapes

partially accurate; omissions or frequent minor errors in: – identifying attributes




generally accurate; few errors in: – identifying attributes




accurate; no errors in: – identifying attributes




Problem-solving strategies

• chooses and carries out appropriate strategies (e.g., drawing, creating models, constructions, nets) to solve geometric problems

may be unable to use appropriate strategies to solve geometric problems

with limited help, uses some appropriate strategies to solve geometric problems; partially successful

uses appropriate strategies to solve geometric problems successfully

uses appropriate, often innovative, strategies to solve geometric problems successfully

Communication • explains reasoning

and procedures clearly, including appropriate terminology (e.g., prism, pyramid, face, edge, vertex, parallel)

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 3.1


Name Date

Ongoing Observations: 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: Geometry* Student Reasoning; Applying

concepts Accuracy of procedures

Problem solving Communication

Describes geometric attributes and relationships among figures and solids

Accurately describes, names, compares, and sorts figures and solids Accurately

describes angles and matches congruent figures and solids

Uses appropriate strategies to solve and create problems involving geometric figures and solids

Uses appropriate language to describe figures and solids Explains reasoning

and procedures clearly

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

Master 3.2


Name Date

Performance Assessment Rubric: At the Beach

Not Yet

Adequate Adequate Proficient Excellent


• provides a description of their construction and the decisions they made, that shows understanding of attributes of 3-D solids

does not describe the construction or explain their decisions appropriately; may be incomplete or offer misconceptions

partially describes the construction and explains their decisions; may be vague or include some flawed reasoning

adequately describes their construction and explains their decisions

thoroughly and effectively describes their construction and explains their decisions; may offer predictions or generalizations that make connections to other situations


• represents the model accurately by sketching

• identifies solids and describes their attributes correctly when writing about the model

limited accuracy; omissions or major errors in: – representing the

model (sketching) – identifying the

solids used and their attributes (writing)

somewhat accurate; some omissions or minor errors in: – representing the

model (sketching) – identifying the

solids used and their attributes (writing)

generally accurate; few minor errors in: – representing the

model (sketching) – identifying the solids

used and their attributes (writing)

accurate and precise; no errors in: – representing the

model (sketching) – identifying the solids

used and their attributes (writing)

Problem-solving strategies

• uses appropriate strategies to design a sand castle and create a model

uses few effective strategies; does not adequately design a sand castle and create a model OR creates an extremely simple design using few solids

uses some appropriate strategies, with partial success, to design a sand castle and create a model; may be relatively simple

uses appropriate and successful strategies to design a sand castle and create a model

uses innovative and effective strategies to design a sand castle and create a model with some complexity

Communication • uses mathematical

terminology correctly (e.g., names and characteristics of solids and their faces)

uses few appropriate mathematical terms

uses some appropriate mathematical terms

uses appropriate mathematical terms

uses a range of appropriate mathematical terms with precision

• explains the model clearly

does not explain the model clearly

partially explains the model; may be vague and somewhat unclear

explains the model clearly

explains the model clearly, precisely, and confidently

Master 3.3


Name Date

Unit Summary: 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: 3-D Objects and 2-D Shapes



Problem solving

Communication Overall

Ongoing Observations

Strategies Toolkit (Lesson 7)

Work samples or portfolios; conferences

Show What You Know

Unit Test

Unit Problem At the Beach

Achievement Level for reporting

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

Comments: (Strengths, Needs, Next Steps)

Master 3.4


Name Date

To Parents and Adults at Home … Your child’s class is starting a mathematics unit on geometry. Through daily activities, your child will explore figures and solids and the relationships among them. In this unit, your child will:

• Describe angles. • Name, describe, and sort figures and solids. • Identify congruent figures and solids. • Make pictures and models with figures. • Make structures from solids.

Geometry is an important part of a student’s mathematical experience. People with a deep understanding of geometry and good spatial sense will be able to describe the world around them and appreciate the geometry found in art, nature, and architecture. Here are some suggestions for activities you can do with your child. When you are at the grocery store, look for items on the shelves that have the same size and shape, then have your child name the solids. For example, a Toblerone bar is a triangular prism, and a cereal box is a rectangular prism. When you are in the car or on a bus, look for structures that are made of different solids. Have your child name the solids. For example, apartment buildings are often made of rectangular prisms and cubes. Look through magazines with your child to find as many different figures in a picture as you can.

Master 3.5


Name Date

Describing Figures

Master 3.6


Name Date

Sorting Figures 1

Master 3.7


Name Date

Sorting Figures 2

Master 3.8


Name Date

Congruent Figures

Master 3.9


Name Date

Arrow

Master 3.10


Name Date

Making Models from Figures

Master 3.11


Name Date Nets

Master 3.12


Name Date

Show What You Know Figures

Master 3.13


Name Date

Additional Activity 1: Regular Figures

Work on your own.

You will need straws cut into 10-cm lengths, pipe cleaners, and scissors.

Use the straws.

Build a regular triangle.

Cut pieces of pipe cleaner.

Use them to connect the sides of the triangle.

Use the straws.

Build as many different figures as you can.

Write about each figure.

Tell how you know your figures are regular.

Take It Further: Use the straws and pipe cleaners. Build 4 different figures that are not regular figures.

Master 3.14


Name Date

Additional Activity 2: Congruent Figures

Work with a partner.

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

Make this rectangle on your geoboard.

Make as many congruent rectangles as you can.

Record each rectangle you find on dot paper.

Use a different colour for each rectangle.

Take It Further: Use a geoboard. Make a triangle with a right angle. Make as many congruent triangles as you can.

Master 3.15


Name Date

Additional Activity 3: Making Figures


You will need 5 Pattern Block triangles and triangular grid paper.

Put the blocks next to each other to make a figure.

Be sure the sides of the blocks touch.

Draw the figure on triangular grid paper.

Count the number of sides in the figure.

Record the number in the figure.

Use the same 5 blocks.

Make as many different figures as you can.

Draw each figure on grid paper.

Record the number of sides each time.

Take It Further: Repeat the activity using 6 Pattern Block triangles.

Master 3.16


Name Date

Additional Activity 4: Comparing Boxes


You will need empty boxes of different shapes and sizes.

Choose 1 box each. Take turns.

Describe your box to your partner in as many ways as you can.

You tell how the 2 boxes are alike.

Your partner tells how the 2 boxes are different.

Repeat with 2 different boxes.

Take It Further: Choose 6 boxes. Use 2 attributes to sort the boxes. Your partner guesses your sorting rule. Switch roles and repeat the activity.

Master 3.17


Activity Focus: Explore perpendicular, parallel, and intersecting lines on 3-D solids.

Name Date

Curriculum Focus Activity: Exploring Edges

The thicker edges are parallel. The thicker edges intersect. These edges do not intersect. The edges make a right angle. So, the edges are perpendicular. The thicker edges intersect. The edges do not make a right angle. So, the edges are not perpendicular. Work with a partner. You will need the solids you used in Lesson 8.

Take turns to find a solid with edges that are parallel. Run your finger along these edges. Tell how you know the edges are parallel.

Repeat for solids with edges that are: – perpendicular – intersecting but not perpendicular

Take It Further: Find a solid that has some edges that are parallel, some that are perpendicular, and some that are intersecting but not perpendicular.

Master 3.17a


Activity Focus: Explore perpendicular, parallel, and intersecting lines on 3-D solids.

Name Date

Curriculum Focus Activity: Making Nets

You will need: 2-cm grid paper, scissors, tape 1. a) Copy each net onto 2-cm grid paper. b) Cut out your nets. Fold each net to make a solid. c) Draw a different net for the same solid. 2. a) Copy this net onto 2-cm grid paper.

Cut it out, then fold it. b) Cut off one face of the net. c) Tape the face in a different place to

make a different net.

Master 3.17b


Name Date

Step-by-Step 1 Lesson 1, Question 3

Step 1 This figure has only 2 parallel sides.

Make this figure.

Write about the figure.

________________________________

________________________________

________________________________

Step 2 This figure has only 2 parallel sides.

Make this figure.


________________________________

________________________________

________________________________

Step 3 Make a different figure with

only 2 parallel sides.

Write about your figure.

________________________________

________________________________

________________________________

________________________________

Step 4 Repeat Step 3 as many times as you can.

Master 3.18


Name Date


Step 1 This figure has only 1 right angle.

Make another figure like this.

Tell how you made it.

________________________________

________________________________ ______________________________________

______________________________________

Step 2 This figure has only 2 right angles.

Make another figure like this.


________________________________

________________________________ ______________________________________

______________________________________

Step 3 Make a figure that has only

3 right angles.


________________________________

________________________________ ______________________________________

______________________________________

Master 3.19


Name Date


Step 1 Make a figure with 4 sides.


________________________________ ______________________________________

Step 2 Make a different figure with 4 sides.


________________________________ ______________________________________

Step 3 Make another different figure with 4 sides.


________________________________ ______________________________________

Step 4 How are the 3 figures the same?

________________________________

________________________________

________________________________

How are they different?

________________________________

________________________________

________________________________

Master 3.20


Name Date


Step 1 Copy this picture on dot paper.

Use the whole piece of paper.

Step 2 Draw a figure in Loop 1. Call it Figure A.

What attributes does it have?

________________________________________________________

Step 3 Draw a figure in Loop 2. Call it Figure B.

Make sure Figure B has no attributes the same as Figure A.

What attributes does Figure B have?

________________________________________________________

Step 4 Continue to draw figures in each loop.

All the figures in Loop 1 have one attribute the same as Figure A.

Label Loop 1 with this attribute.

All the figures in Loop 2 have one attribute the same as Figure B.

Label Loop 2 with this attribute.

Make sure figures in Loop 1 have no attributes the same

as figures in Loop 2.

Write about your work.

________________________________________________________

________________________________________________________

________________________________________________________

________________________________________________________

________________________________________________________

Master 3.21


Name Date


Use tracing paper if it helps.

Step 1 One side of a parallelogram is drawn.

Draw the other sides to make a

congruent parallelogram.

Step 2 One side of a parallelogram is drawn.

Draw the other sides to make a

congruent parallelogram.

Step 3 Draw 2 congruent parallelograms.

Make sure they are in a different place

from those you drew in Steps 1 and 2.

Master 3.22


Name Date


You need 4 green Pattern Blocks. Step 1 Put the blocks together.

Make a figure.

Draw the figure you made.

How many sides does it have? _______

Step 2 Put the blocks together.

Make a different figure.



Step 3 Put the blocks together.

Make a different figure.



Master 3.23


Name Date


Step 1 How many vertices does:

a triangular prism have? __________

a pentagonal pyramid have? __________


a square prism have? _________

a pyramid with a base with 7 sides have? _________


a pentagonal prism have? _________

a pyramid with a base with 9 sides have? _________

Step 4 Try to find more pairs of a prism and a pyramid with the same number

of vertices.

__________________________________________________________________________

__________________________________________________________________________

__________________________________________________________________________

Master 3.24


Name Date


Step 1 Which solid has 5 vertices and 5 faces? ________________________

Step 2 Which solids have 6 faces?

________________________________________________________

Step 3 Which solid has 5 faces, and 3 of these faces are rectangles?

________________________________________________________

Step 4 Which solid has 12 edges and all faces congruent? _______________

Step 5 Tell how you identified each solid.

________________________________________________________

________________________________________________________

________________________________________________________

________________________________________________________

________________________________________________________

________________________________________________________

Master 3.25


Name Date


You will need 2-cm grid paper and scissors.

Step 1 Draw this picture on grid paper.

Cut out the picture.

Fold it to try to make a cube.

Tell what happened.

________________________________________________________

________________________________________________________

________________________________________________________

________________________________________________________

Step 2 Draw this picture on grid paper.

Cut out the picture.

Fold it to try to make a cube.

Tell what happened.

________________________________________________________

________________________________________________________

________________________________________________________

________________________________________________________

Master 3.26


Name Date


You will need Pattern Blocks and a ruler.

Step 1 Which Pattern Block is biggest? ______________________________

Step 2 Use the Pattern Blocks from Step 1.

Line up these blocks along a ruler until you get close to 15 cm.

How many blocks did you use? _______________________________

Step 3 Find a smaller block to line up with the other blocks,

so the total length is 15 cm.

Which Pattern Block did you use? _____________________________

Step 4 Try to stand each block on end,

one on top of another, to make a tower.

Sketch the tower.

Step 5 Tell about the blocks you used.

What attributes do they have?

________________________________________________________

________________________________________________________

Master 3.27


Name Date

Unit Test: Unit 3 Geometry Part A 1. Look at the figures below. Which figures have: a) all sides the same length? __________________________ b) no sides the same length? _________________________ c) only one pair of parallel sides? ______________________ d) no parallel sides? ________________________________ e) 4 right angles? __________________________________ f ) all angles less than a right angle? ____________________

2. Look at the solids below. a) Circle all prisms. f) On solid B, colour green 2 b) Put a box around all pyramids. edges that are parallel lines. c) Colour the triangular pyramid blue. g) On solid D, colour purple 2 d) Colour the pentagonal prism red. edges that are perpendicular. e) Put an X on 2 congruent solids.

Master 3.28a


Name Date

Unit Test continued Part B 3. Use the solids from Question 2. Sort the solids in the Venn diagram.

Label the loops.

4. a) Write everything you know about the solid below.

______________________________________________

______________________________________________

______________________________________________

______________________________________________

b) Sketch the faces of the solid.

Master 3.28b


Name Date

Unit Test continued 5. a) Use a geoboard. Make 2 different figures.

Draw your figures on the dot paper below.

b) How are your 2 figures the same?

_________________________________________________________ _________________________________________________________

c) How are your 2 figures different? _________________________________________________________ _________________________________________________________

Part C 6. Use 4 Pattern Block hexagons.

Make as many different figures as you can. Make sure that the sides of the blocks touch each other. Copy each figure you make onto triangular dot paper.

Master 3.28c


Name Date

Sample Answers Unit Test – Master 3.28 Part A 1. a) B, C, E, G

b) A c) A, D d) B, C, F, G e) H f) C, G

2. a) B and D should be circled. b) C, E, F, G, and H should have boxes around them. c) E should be coloured blue. d) B should be coloured red. e) C and G should be marked with an X. f) 2 vertical edges on B should be coloured green. g) 2 edges forming a right angle should be coloured purple.

Part B 3. Sample Answer:

4. a) This is a hexagonal prism. It has 2 bases.

The bases are congruent hexagons. There are 6 other faces. They are rectangles. The prism has 18 edges and 12 vertices. It has some parallel edges, and some perpendicular edges, and some edges that are intersecting but not perpendicular.

b)

5. a) Sample Answer:

b) My figures are the same because both of

them have 1 right angle, 2 angles less than a right angle, and 2 equal sides.

c) My figures are different because one figure has 3 sides and 3 angles and the other figure has 5 sides and 5 angles. The triangle has no parallel sides. The pentagon has 2 parallel sides.

Part C 6.

Master 3.29


Extra Practice Masters 3.30–3.35 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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Western Canadian Teacher Guide - SD67 (Okanagan Skaha) · Western Canadian Unit 3: Geometry AA ... • How did the children make the sand castle? ... students will design and build