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Common Core State Standards

468 Unit 6 Geometry

Advance PreparationFor Part 1, place a cereal box near the Math Message. Construct a prism by taping 3 or 4 of the same

pattern-block shapes together. For the optional Enrichment activity in Part 3, copy a set of geometry

riddle cards (Math Masters, page 201) on cardstock for each small group.

Teacher’s Reference Manual, Grades 1–3 pp. 144–146

Key Concepts and Skills• Compare faces on prisms. 

[Geometry Goal 2]

• Identify the faces of polyhedrons. 

[Geometry Goal 2]

• Identify and name prisms. 

[Geometry Goal 2]

• Identify the faces, edges, and vertices

of prisms. 

[Geometry Goal 2]

Key ActivitiesChildren identify the bases, faces, and

vertices of various prisms. They classify

prisms according to the shapes of their bases.

Key Vocabularyrectangular prism � triangular prism �

hexagonal prism

MaterialsMath Journal 1, p. 153

Student Reference Book, p. 115

Home Link 6�11

pattern-block prism � cereal box � per group:

4 of each pattern-block shape (square,

triangle, trapezoid, hexagon), transparent

tape � paper

Playing Beat the Calculator (Multiplication)Math Journal 1, p. 156

Student Reference Book, p. 279

per group: calculator

Children practice multiplication facts.

Ongoing Assessment: Recognizing Student Achievement Use an Exit Slip (Math Masters, p. 398). [Operations and Computation Goal 3]

Math Boxes 6�12Math Journal 1, p. 154

Children practice and maintain skills

through Math Box problems.

Home Link 6�12Math Masters, p. 199

Children practice and maintain skills

through Home Link activities.

READINESS

Illustrating PrefixesStudent Reference Book, p. 103

paper

Children illustrate prefixes used to

name polygons.

ENRICHMENTSolving Geometric RiddlesMath Masters, pp. 200 and 201

Student Reference Book, pp. 112–114

scissors � slate

Children solve geometric riddles.

Teaching the Lesson Ongoing Learning & Practice

132

4

Differentiation Options

Polyhedrons, Part 2Objective To provide opportunities to explore the

characteristics of prisms.c

�������

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Lesson 6�12 469

1 Teaching the Lesson

� Math Message Follow-Up WHOLE-CLASSDISCUSSION

Briefly go over the answers regarding the cereal box. rectangular prism; 6 faces; 12 edges; 8 vertices; rectangular

� Identifying the Bases of a WHOLE-CLASSDISCUSSION

Rectangular PrismExplain that this lesson further explores the characteristics of prisms.

Review the characteristics of the bases of prisms:

� They are flat, opposite each other, and parallel.

� They are the same shape and the same size, so they arecongruent.

Have children discuss which faces are the bases of the cereal box. Ask: Does each face have an opposite face that is parallel and congruent to it? Yes How many pairs of parallel faces does the box have? 3 pairs

In a rectangular prism, any pair of opposite faces can be the bases of the prism. Choose a pair of opposite faces to be the bases. Once you have made a choice, the other two pairs of faces are not considered the bases.

Getting Started

Math Message What kind of shape is the cereal box? How many faces does it have? How many edges? How many vertices? What is the shape of its faces? Write your answers on paper and discuss them with a partner.

Home Link 6�11 Follow-Up Have children share some of the 3-D objects and pictures that they brought to school. Encourage them to use geometry vocabulary to name the objects and pictures.

Mental Math and Reflexes Write decimals on the board. Children read them aloud. Encourage them to exaggerate the th sound so that decimal numbers are not confused with whole numbers.

Suggestions:

0.42 forty-two hundredths

1.34 one and thirty-four hundredths

6.09 six and nine-hundredths

0.5 five-tenths

2.4 two and four-tenths

20.50 twenty and fifty-hundredths

5.813 five and eight hundred thirteen-thousandths

45.030 forty-five and thirty thousandths

80.102 eighty and one hundred two-thousandths

Ask questions like Which digit is in the tenths place? What is the value of the digit x? How many hundredths are there?

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Adjusting the Activity

470 Unit 6 Geometry

Pattern-Block PrismsLESSON

6 � 12

Date Time

Work in a group.

1. Each person chooses a different pattern-block shape.

2. Each person then stacks 3 or 4 of the shapes together to make a prism. Use

small pieces of tape to hold the blocks together.

3. Below, carefully trace around each face of your prism. Then trace around each

face of 2 or 3 more prisms on a separate sheet of paper. Ask someone in your

group for help if you need it. Share prisms with other people in your group.

See children’s work.

Math Journal 1, p. 153

Student Page

PolyhedronsA polyhedron is a solid whose surfaces are all flat andformed by polygons. It does not have any curved surfaces.The faces of a regular polyhedron are all formed bycopies of one regular polygon that have the same size.

Three important groups of polyhedrons are shown below.These are pyramids, prisms, and regular polyhedrons.Many polyhedrons do not belong to any of these groups.

Geometry

Pyramids

triangularpyramids

rectangularpyramids

pentagonalpyramid

hexagonalpyramid

Prisms

triangular prisms rectangular prisms hexagonal prism

Regular Polyhedrons

regulartetrahedron

(pyramid) (4 faces)

cube(prism)

(6 faces)

regularoctahedron

(8 faces)

regulardodecahedron

(12 faces)

regularicosahedron

(20 faces)

Student Reference Book, p. 115

Student Page

� Constructing Pattern-Block SMALL-GROUP ACTIVITY

Prisms and Tracing Their Faces(Math Journal 1, p. 153)

Give each group 16 pattern blocks (four each of triangles, squares, trapezoids, and hexagons). Draw a square on the board. Ask: Why is the drawing not a prism? The drawing is a 2-dimensional figure. It has no thickness. Hold up a square pattern block and ask the class why it is a prism. The pattern block is a 3-dimensional object because it has thickness.

Hold up a pattern-block prism that you taped together. (See Advance Preparation.) Each group will make different pattern-block prisms by taping together 3 or 4 congruent pattern blocks. Each child in a group should make a different prism. Children in each group then share their pattern-block prisms to complete journal page 153.

� Discussing the Shapes of WHOLE-CLASSDISCUSSION

the Faces of Prisms(Student Reference Book, p. 115)

When most children have completed their tracings on the journal page, discuss children’s work as a class. Ask several children to name the shape of the bases of their prisms. Ask: What is the shape of the faces that are not bases? rectangles

Prisms are named after the shapes of their bases. For example, the bases of a rectangular prism are rectangles. A prism whose bases are triangles is a triangular prism. The bases of a hexagonal prism are hexagons.

Discuss the shapes on page 115 in the Student Reference Book. Point out that pyramids, as well as prisms, are named after the shape of their bases. Children should also notice that there are other polyhedrons besides pyramids and prisms. Some children might count the number of edges or vertices on the five polyhedrons at the bottom of the page. Ask: What kind of pyramid is the tetrahedron? Triangular pyramid

Have children name a prism with a 5-sided base, pentagonal prism

7-sided base, heptagonal prism 8-sided base, octagonal prism 9-sided base,

nonagonal prism and 10-sided base. decagonal prism Write the names on the

board. Ask children how the names are related to the names of 2-dimensional

shapes. Pentagonal is related to pentagon, which is the shape of the base of the

pentagonal prism; heptagonal is related to heptagon, which is the shape of the

base of the heptagonal prism, and so on.

A U D I T O R Y � K I N E S T H E T I C � T A C T I L E � V I S U A L

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5. Connect 3 points to make a right

triangle. Label the points.

Which letter names

the right angle? C

Sample answer:

3. Number of days for one revolution

around the sun:

A. Mercury C. Venus

B. Earth D. Mars

Date Time

2. Draw all the lines of symmetry.

There are 5 lines of symmetry.

4. Write the numerals.

five-tenths 5 _ 10 or 0.5

five-hundredths 5

_

100 or 0.05

three-tenths 3 _ 10 or 0.3

three-hundredths 3

_

100 or 0.03

6. Divide.

30 ÷ 6 = 5

12 ÷ 4 = 3

20 ÷ 5 = 4

2 = 14 ÷ 7

3 = 9 ÷ 3

1. Draw a line, � � AB , parallel to line

segment, _

CD . Draw a ray, � EF ,

that intersects the ray, � GH .

Math BoxesLESSON

6 �12

100 101

79

122 123

33 34

106 107 52 53

A B

FEC D

H

G

Mercury 88

Venus 225

Earth 365

Mars 687

Which planet

takes the fewest

days to revolve

around the sun?

B

C

A

Fill in the circle for the best answer.

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Math Journal 1, p. 154

Student Page

Lesson 6 �12 471

Name Date Time

Making a Solid ShapeHOME LINK

6�12

Our class has been exploring the characteristics and parts of various 3-dimensional shapes—especially prisms. The pattern on this page can be used to make one type of prism. Prisms are named for the shapes of their bases.

Please return this Home Link to school tomorrow.

Family Note

117

Cut on the dashed lines. Fold on the dotted lines. Tape or paste each

TAB inside or outside the shape.

Discuss the following questions with someone at home:

1. What is this 3-D shape called?

2. What is the shape of the bases?

3. What is the shape of the other faces?

4. How many edges does the shape have?

5. How many vertices does the shape have? 10 vertices

15 edges

rectangle

pentagon

pentagonal prism

TAB

TAB

TAB

TAB

TAB

TAB

TAB

TAB

TAB

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Math Masters, p. 199

Home Link Master

2 Ongoing Learning & Practice

� Playing Beat the Calculator PARTNER ACTIVITY

(Multiplication)(Math Journal 1, p. 156; Student Reference Book, p. 279)

Children develop automaticity with multiplication facts by playing Beat the Calculator. Have children keep a record of the facts for which they get the product first when playing the role of the Brain by making a check mark on their Fact Power Table, journal page 156. For Fact Power Table directions, see Lesson 4-5. For game directions, see page 279 in the Student Reference Book. Remind children to fill in the product on their Fact Power Table when they have 3 check marks for a fact.

Ongoing Assessment: Exit Slip

�Recognizing Student Achievement

Use an Exit Slip (Math Masters, page 398) to assess children’s progress toward

demonstrating automaticity with multiplication facts through 10 × 10. Children

record the facts from the Fact Power Table for which they recorded at least

one check mark. Children are making adequate progress if they record all of

the facts from the unshaded portion of the table. Some children may record

additional facts from the shaded portion.

[Operations and Computation Goal 3]

� Math Boxes 6�12 INDEPENDENTACTIVITY

(Math Journal 1, p. 154)

Mixed Practice Math Boxes in this lesson are paired with Math Boxes in Lesson 6-10. The skill in Problem 6 previews Unit 7 content.

� Home Link 6�12 INDEPENDENTACTIVITY

(Math Masters, p. 199)

Home Connection Children cut out a pattern and make a pentagonal prism. Then they talk about the shape with someone at home.

NOTE For practice identifying

congruent figures, go to

www.everydaymathonline.com.

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472 Unit 6 Geometry

Polygons are named after the number of their sides. The prefix for a name tells the number of sides.

Geometry

triangle quadrangle orquadrilateral

pentagon

heptagon

hexagon

octagon nonagon

1. Name the polygon.a. 6 sides b. 4 sides c. 10 sidesd. 8 sides e. 12 sides

2. Draw a pentagon whose sides are not all the same length.Check your answers on page 339.

Prefixestri- 3

quad- 4

penta- 5

hexa- 6

hepta- 7

octa- 8

nona- 9

deca- 10

dodeca- 12

flag of Nepal

flag ofSwitzerland

The flag of Nepal is the only flag in the world with 5 sides. All other flags have 4 sides. The flag ofSwitzerland has a whitecross with an edge that is a dodecagon (12 sides).

Student Reference Book, p. 103

Student Page

3 Differentiation Options

READINESS PARTNER ACTIVITY

� Illustrating Prefixes 15–30 Min

(Student Reference Book, p. 103)

To explore polygon names, have children discuss prefixes used to name polygons and relate the prefixes to other words they know. Children refer to the chart of prefixes on page 103 in the Student Reference Book. They fold a blank page into 4 boxes and illustrate 4 or more (use the back of the page) of the prefixes with pictures that will help them remember the prefix meanings.

Examples:

� Tricycles have three wheels like a triangle has three angles and sides.

� A dollar is made of four quarters like a quadrangle is made of four angles and sides.

� The Pentagon building in Washington, D.C. is in the shape of a pentagon.

� The x in hexa- is like the x in six.

� An octopus has eight legs like an octagon has eight sides.

� The Ns in nona- are like the Ns in nine.

� Decades are made of 10 years like decagons are made of 10 angles and sides.

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LESSON

6�12

Name Date Time

Geometry Riddles

1. Work in teams of 2 to 4.

2. Cut out the Geometry Riddles cards from Math Masters, page 201

and place them facedown on the playing surface.

3. The team of readers chooses a card and silently reads all the clues.

They write the answer to the riddle on a slate without showing it to

the other team, the guessers. Then they read only the first clue

aloud to the guessers. The guessers discuss the clue and guess

the shape. If their guess is correct, the turn is over. If it is not

correct, the readers read the second clue. Continue until the

guessers name the shape on the card. Then switch roles.

4. Readers assign one tally mark for every clue needed. Record the

tallies on the chart below.

5. If teams disagree on an answer to a riddle, they may use the Student

Reference Book section on Geometric Solids, pages 112–119.

6. Teams switch roles. The game ends when all the cards have been

used. The team with the fewest tally marks wins.

112–119

Names of Team Members Points

Team 1:

Team 2:

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Math Masters, p. 200

Teaching Master

LESSON

6�12

Name Date Time

Geometry Riddles Cards

1. I am a geometric solid.

2. I have only 1 surface.

3. My 1 surface is curved.

4. I have no base.

What am I?

A sphere

1. I am a polyhedron.

2. I have the fewest number of

faces of all the polyhedrons.

3. All of my faces are triangles.

4. I come to a point at the top.

What am I?

A triangular pyramid

1. I am a polyhedron.

2. I have 6 faces.

3. All of my faces are congruent.

4. All of my faces are squares.

What am I?

A rectangular prism or cube

1. I am a geometric solid.

2. I have 2 surfaces.

3. My base is formed by a circle.

4. I have a point at the top.

What am I?

A cone

1. I am a polyhedron.

2. I have 2 triangular bases.

3. I have 3 other faces.

4. My other faces are rectangles.

What am I?

A triangular prism

1. I am a polyhedron.

2. I have 5 faces.

3. Four of my faces are triangles.

4. My base is a square.

What am I?

A rectangular pyramid

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Math Masters, p. 201

Teaching Master

Lesson 6 �12 473

ENRICHMENT SMALL-GROUP ACTIVITY

� Solving Geometric Riddles 15–30 Min

(Math Masters, pp. 200 and 201; Student Reference

Book, pp. 112–114)

To apply children’s knowledge of geometric solid attributes, have them solve geometry riddles. Directions are found on Math Masters, page 200. Children may refer to the Geometric Solids pages in the Student Reference Book as needed.

Planning Ahead

Make the prism from Home Link 6�12 for the Home Link Lesson 6�13 Follow-Up.

Have children keep Math Journal 1 accessible throughout Unit 7 as they will need to cut out the remaining Fact Triangles on Activity Sheets 3 and 4 for Lesson 7-2. Children also need to copy the Length of Day graph on journal page 125 to the graph on journal page 279. They need the data from the National High/Low Temperatures Project on journal page 43 for Lesson 7-8. Have children copy their body measures from journal page 251. They will revisit their body measures in Lesson 10-7.

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