Spheres, Cylinders, and
Rectangular Prisms
Objectives To guide the identification of spheres, cylinders,
and
rectangular prisms; and to facilitate the investigation
a
of their characteristics.
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eToolkit
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Practice
EM Facts
Workshop
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Teaching the Lesson
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]
Family
Letters
Assessment
Management
Common
Core State
Standards
Ongoing Learning & Practice
1 2
4 3
Playing Coin Exchange
My Reference Book, pp. 128 and 129
per partnership: tool-kit coins, 2 dice
Children practice exchanging coins
with equivalent values.
Math Boxes 7 5
Math Journal 2, p. 145
Children practice and maintain skills
through Math Box problems.
Key Activities
Home Link 7 5
Children 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.
Math Masters, p. 211
Children practice and maintain skills
through Home Link activities.
Ongoing Assessment:
Recognizing Student Achievement
Curriculum
Focal Points
Interactive
Teacher’s
Lesson Guide
Differentiation Options
READINESS
Comparing Plane Shapes
and Solid Figures
per partnership: 3-dimensional shapes,
rectangular prism, cylinder
Children compare 2- and 3-dimensional
shapes.
ENRICHMENT
Sorting Shapes by Their Faces
Math Masters, p. 212
3-dimensional shapes
Children sort 3-dimensional objects
by the shapes of their faces.
ELL SUPPORT
Describing Shapes
Children describe shapes in the
Shapes Museum.
Use Mental Math and Reflexes. [Number and Numeration Goal 3]
Key Vocabulary
sphere cylinder rectangular prism surface face
Materials
Home Link 74
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
Advance Preparation
Place 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
644
Unit 7
Geometry and Attributes
Mathematical Practices
SMP1, SMP2, SMP4, SMP5, SMP6
Content Standards
Getting Started
Mental Math and Reflexes
1.G.1, 1.G.2
Math Message
Which of these objects can roll?
Display 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.
Home Link 74 Follow-Up
Suggestions:
Review polygons. Briefly discuss what is
necessary for a shape to be a polygon.
3 longs and 5 cubes 35
4 longs and 11 cubes 51
1 flat, 2 longs, and 16 cubes 136
Ongoing Assessment:
Recognizing Student Achievement
Mental Math
and
Reflexes
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]
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-CLASS
DISCUSSION
of Spheres, Cylinders, and
Rectangular Prisms
Ask 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.
Lesson 7 5
645
Representations of 3-dimensional Figures
sphere
cylinder
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.
rectangular prism
corner
flat face
curved face
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.
Adjusting the Activity
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.
ELL
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 Objects
Review 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 sort objects into categories to create a
Shapes Museum.
646
Unit 7 Geometry and Attributes
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.
Making Cylinders and
Student Page
SMALL-GROUP
ACTIVITY
Rectangular Prisms
Date
LESSON
Math Boxes
75
1. Circle the name of this
2. Circle the 4 polygons.
3-dimensional shape.
(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:
pyramid
prism
52–53
56
2. Fold the rectangle into a tube. The circles should be at the
top and the bottom of the tube.
3.
4. Draw a line to cut the
First-Grade Heights
Inches Tall
1. Cut out the cylinder template from Math Masters, page 212A.
Make sure the circles remain connected to the rectangle.
48
pizza in half.
47
Sample answer:
46
45
44
43
42
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.
0
1
2
3
4
5
Number of Children
Least inches tall:
42
inches
Most inches tall:
48
inches
44
Math Journal 2, p. 145
137-150_EMCS_S_SMJ_G1_U07_576396.indd 145
2/2/11 9:47 AM
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.
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.
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
INDEPENDENT
ACTIVITY
(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
Lesson 7 5
647
Home Link Master
Name
Date
HOME LINK
Practicing with Fact Triangles
75
Family
Note
27
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.
Home Link 7 5
INDEPENDENT
ACTIVITY
(Math Masters, p. 211)
Continue practicing all of the addition and subtraction
facts at home.
Home Connection Children cut out a fifth set of Fact
Triangles to continue their fact practice at home.
5
9
7
9
READINESS
Comparing Plane Shapes
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13 • 4
1
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14
⫹,
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6
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14 • 3
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3 Differentiation Options
PARTNER
ACTIVITY
5–15 Min
and Solid Figures
Math Masters, p. 211
196-220_EMCS_B_MM_G1_U07_576930.indd 211
To 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.
2/2/11 10:10 AM
NOTE The shapes for this activity can come
from the Shapes Museum or from a set of
geometric solids.
ENRICHMENT
Sorting Shapes by Their Faces
INDEPENDENT
ACTIVITY
5–15 Min
(Math Masters, p. 212)
Teaching Master
Name
LESSON
75
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.
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
When children have completed Math Masters, page 212, have them
sort the objects into 3 groups by the shapes of the objects’ faces.
Other
ELL SUPPORT
Describing Shapes
SMALL-GROUP
ACTIVITY
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.
Math Masters, p. 212
196-220_EMCS_B_MM_G1_U07_576930.indd 212
648
Unit 7 Geometry and Attributes
2/2/11 10:10 AM