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Common Core State Standards

644 Unit 7 Geometry and Attributes

Advance PreparationPlace a ball (sphere), a can (cylinder), and a box (rectangular prism) near the Math Message. For Part 1, write the words sphere, cylinder,

rectangular prism, and other on index cards. Display models of a sphere, a cylinder, and a rectangular prism and label each with its name.

Be prepared to add some of your objects to the Shapes Museum. For the optional Enrichment activity in Part 3, gather a variety of

3-dimensional shapes. You may wish to make a poster by enlarging and laminating Math Masters, page 210.

Teacher’s Reference Manual, Grades 1–3 pp. 14, 141–146, 152

Spheres, Cylinders, andRectangular Prisms

Objectives To guide the identification of spheres, cylinders,

and rectangular prisms; and to facilitate the investigation

of their characteristics.

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Key Concepts and Skills• Count the flat faces and corners

on solid figures. 

[Number and Numeration Goal 2]

• Identify and describe solid figures; identify

the flat faces and corners on solid figures. 

[Geometry Goal 1]

• Compose solid shapes.

[Geometry Goal 1]

Key ActivitiesChildren learn the names of three

3-dimensional shapes—sphere, cylinder,

and rectangular prism—and discuss their

characteristics. Children classify items brought

from home to start a Shapes Museum and

construct cylinders and rectangular prisms.

Ongoing Assessment: Recognizing Student Achievement Use Mental Math and Reflexes. [Number and Numeration Goal 3]

Key Vocabularysphere � cylinder � rectangular prism �

surface � face

MaterialsHome Link 7�4

Math Masters, p. 210 (optional); p. 212A

base-10 blocks (longs and cubes) � slate �

ball, can, and box � 3" by 5" index cards �

items for the Shapes Museum � scissors �

tape � per small group: 20 twist-ties and

4 each of 8" straws, 6" straws, and 4" straws

Playing Coin ExchangeMy Reference Book, pp. 128 and 129

per partnership: tool-kit coins, 2 dice

Children practice exchanging coins

with equivalent values.

Math Boxes 7�5Math Journal 2, p. 145

Children practice and maintain skills

through Math Box problems.

Home Link 7�5Math Masters, p. 211

Children practice and maintain skills

through Home Link activities.

READINESS

Comparing Plane Shapes and Solid Figuresper partnership: 3-dimensional shapes,

rectangular prism, cylinder

Children compare 2- and 3-dimensional

shapes.

ENRICHMENTSorting Shapes by Their FacesMath Masters, p. 212

3-dimensional shapes

Children sort 3-dimensional objects

by the shapes of their faces.

ELL SUPPORT

Describing ShapesChildren describe shapes in the

Shapes Museum.

Teaching the Lesson Ongoing Learning & Practice

132

4

Differentiation Options

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Lesson 7�5 645

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Ongoing Assessment: Recognizing Student Achievement

Use Mental Math and Reflexes to assess children’s ability to name numbers

represented by base-10 blocks. Children are making adequate progress if

they are able to answer the first and second questions correctly. Some

children may be able to correctly answer the third question, as well.

[Number and Numeration Goal 3]

Mental Math

and

Reflexes �

Getting Started

Math MessageWhich of these objects can roll?

Home Link 7�4 Follow-Up Review polygons. Briefly discuss what is necessary for a shape to be a polygon.

Mental Math and ReflexesDisplay sets of base-10 blocks on the overhead or draw them on the board. Have children write the value of each set on their slates.

Suggestions:

3 longs and 5 cubes 35

4 longs and 11 cubes 51

1 flat, 2 longs, and 16 cubes 136

1 Teaching the Lesson

� Math Message Follow-Up WHOLE-CLASS ACTIVITY

Ask a child to try to roll the ball, the can, and the box. Have children share their observations.

Tell children that today they will learn about the shapes of objects in their world.

� Discussing the Characteristics WHOLE-CLASSDISCUSSION

of Spheres, Cylinders, and Rectangular PrismsAsk children how they would describe the ball, the can, and the box. Expect answers such as the following:

● The ball is round and smooth.

● The ball has no flat sides.

● The can has a curved side and two flat sides.

● The flat sides of the can are circles.

● The can will sit on either of its flat sides.

● All of the sides of the box are flat.

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646 Unit 7 Geometry and Attributes

corner flat face

curved face

Adjusting the Activity

sphere cylinder

rectangular prism

Representations of 3-dimensional Figures

Children sort objects into categories to create a

Shapes Museum.

NOTE Two-dimensional shapes, such as

squares and circles, have length and width.

They exist entirely in a plane, such as a flat

sheet of paper. Three-dimensional shapes

are often represented in 2-dimensional

drawings, but actual 3-dimensional objects

always extend out of the plane because they

have length, width, and height. Furthermore,

2-dimensional shapes are the faces of

3-dimensional shapes.

Begin to use formal names for these shapes. Tell children that the ball is an example of a sphere, the can is an example of a cylinder, and the box is an example of a rectangular prism. Explain that the outside or “skin” of any of these 3-dimensional shapes is called its surface.

Ask someone to point to the flat sides of the rectangular prism and the cylinder. Say that these sides are sometimes called faces.

NOTE For most children, it will take repeated exposures before these geometric

terms become part of their working vocabulary.

How many flat faces does each shape have? The sphere has 0 flat faces; the rectangular prism has 6; the cylinder has 2. Point to each face as the class counts them together. What are the shapes of the flat faces? All of the flat faces of the rectangular prism are rectangles. (Squares are special rectangles.) The flat faces of the cylinder are circles.

Point to a corner of the rectangular prism. Explain that a corner is a point at which at least three flat faces meet. A cylinder does not have any corners because its flat faces do not meet. How many corners does the rectangular prism have? 8 corners Point to each corner as the class counts.

Have children model the words curve and flat as attributes of surfaces.

They model the word curve by holding their arms in front of them as though they

were holding a large ball. They model the word flat by placing their hands on a

table or desk.

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

Art Link Show children pictures of uniquely shaped skyscrapers. Have them use solid figures to make models of those skyscrapers. Then ask children to identify and label the different solid figures that they used.

� Starting a Shapes WHOLE-CLASS ACTIVITY

Museum with a Display of 3-Dimensional ObjectsReview museums as places to collect, organize, and label objects.

Tell children that they are going to start a Shapes Museum. Help children place objects they brought from home in the museum next to the correct labels. For now, have children put all shapes that are not spheres, cylinders, or rectangular prisms into the “other” category. Add some of your own items to the museum.

Children will have fun looking for other shapes that approximate spheres, cylinders, and rectangular prisms. Actual shapes are often “close, but not quite” the ideal 3-dimensional shapes; for example, books are “almost” rectangular prisms. Encourage children to notice the shapes of objects they see at school and at home. Tell them that they will continue to add to the Shapes Museum tomorrow.

ELL

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Lesson 7�5 647

1. Circle the name of this 3-dimensional shape.

pyramid prism

2. Circle the 4 polygons.

3.

Least inches tall: inches

Most inches tall: inches

4. Draw a line to cut the pizza in half.

Date

Number of Children

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44

Math Boxes LESSON

7�5

Sample answer:

4248

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Math Journal 2, p. 145

Student Page

NOTE You may wish to cut out some

cylinder templates before the lesson (1 per

small group) in case children have trouble

cutting the templates.

� Making Cylinders and SMALL-GROUP ACTIVITY

Rectangular Prisms(Math Masters, p. 212A)

Tell children that they will be making cylinders and rectangular prisms. For the cylinders, give each group scissors, tape, and one copy of Math Masters, page 212A on construction paper. For the rectangular prisms, provide straws and twist-ties. Begin by modeling how to make a cylinder:

1. Cut out the cylinder template from Math Masters, page 212A. Make sure the circles remain connected to the rectangle.

2. Fold the rectangle into a tube. The circles should be at the top and the bottom of the tube.

3. Tape the tube together by taping the tab on one edge of the rectangle to the inside of the other edge of the rectangle.

4. Fold the tabs on each circle and tape them to the top and bottom of the tube to make a cylinder.

Next demonstrate how to make a rectangular prism, reminding children how they constructed polygons in Lesson 7-4.

1. Make two rectangles using the 4" and 6" straws and twist-ties.

2. Have two children hold the rectangles while you anchor a new twist-tie around each corner of each rectangle.

3. Connect a corner of one rectangle to a corner of the other by inserting the anchor twist-ties into both ends of an 8" straw. Continue until four 8" straws connect all four corners of the two rectangles, making a rectangular prism.

Assist children as they construct these solids. When children are finished, have them add their shapes to the Shapes Museum.

2 Ongoing Learning & Practice

� Playing Coin Exchange PARTNER ACTIVITY

(My Reference Book, pp. 128 and 129)

Children make coin exchanges. For instructions, see Lesson 6-10.

� Math Boxes 7�5 INDEPENDENTACTIVITY

(Math Journal 2, p. 145)

Mixed Practice Math Boxes in this lesson are paired with Math Boxes in Lesson 7-7. The skills in Problem 4 preview Unit 8 content.

Writing/Reasoning Have children write, draw, or verbalize an answer to this question: What is a polygon? A reasonable answer should include features of a polygon:

straight sides, corners, and a closed shape.

One child’s work in response to the

Writing/Reasoning prompt

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648 Unit 7 Geometry and Attributes

Your child should cut apart the Fact Triangles below. Add these to the Fact Triangles from earlier lessons. As you help your child practice facts, separate the triangles into piles to show the facts that your child knows and the facts that still need work. Continue to practice all of the facts.

Family Note

HOME LINK

7� 5

Name Date

Practicing with Fact Triangles

Continue practicing all of the addition and subtraction facts at home.

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Math Masters, p. 211

Home Link Master

NOTE The shapes for this activity can come

from the Shapes Museum or from a set of

geometric solids.

LESSON

7� 5

Name Date

Sorting Shapes by Their Faces

1. Find a 3-dimensional shape. 2. Write the name or draw the shape. 3. Match the shape to its face. Put an X in the box.

3-Dimensional Shape Face Face Face Other

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Math Masters, p. 212

Teaching Master

� Home Link 7�5 INDEPENDENTACTIVITY

(Math Masters, p. 211)

Home Connection Children cut out a fifth set of Fact Triangles to continue their fact practice at home.

3 Differentiation Options

READINESS PARTNER ACTIVITY

� Comparing Plane Shapes 5–15 Min

and Solid FiguresTo explore the relationships between plane shapes and solid figures, children trace faces of selected geometric solids. Have children label one side of a sheet of paper “Rectangular Prism” and the other side “Cylinder.” They work with a partner to trace the flat surfaces, or faces, of both shapes on the appropriate side of the paper. They do not have to trace identical faces more than once. Have them discuss the results of their tracing. For example: I traced rectangles when I drew the sides of the box.

ENRICHMENT INDEPENDENTACTIVITY

� Sorting Shapes by Their Faces 5–15 Min

(Math Masters, p. 212)

To explore the characteristics of solid figures, have children record the faces of shapes from the Shapes Museum. They name or draw the shape they have chosen and write an X in the table corresponding to the shape of the faces.

When children have completed Math Masters, page 212, have them sort the objects into 3 groups by the shapes of the objects’ faces.

ELL SUPPORT SMALL-GROUP ACTIVITY

� Describing Shapes 5–15 Min

To provide language support for geometry, have children look at the Shapes Museum and describe some of the shapes. Encourage children to use vocabulary related to plane shapes and solid figures such as side, corner, surface, flat, face, circle, triangle, square, sphere, cylinder, and rectangular prism.

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