Topic 9: 3-D Figures
for use after Covering and Surrounding Investigation 5
Tom and Keitra are drawing models of local historic landmarks for their
social studies class. Tom asks Keitra how to draw things that are not flat on
a flat piece of paper. Keitra suggests that he think about the parts that make
up the shape.
Two-dimensional shapes are flat.
They have sides that are labeled
as lengths and widths.
Three-dimensional shapes
have length, width, and height.
They can be drawn using
two-dimensional parts.
w
h
l
l
w
The two dimensional parts of a three-dimensional figure have names.
Face
Vertex
Edge
Base
l
h
w
Problem 9.1
A. The base of one statue is a cube. To draw the base, Tom needs to know
the two-dimensional parts that form the base.
1. How many two-dimensional shapes make a cube? Describe them.
2. Draw a three-dimensional model of a cube.
3. Draw a model of a cube that is unfolded and made flat, called a net.
B. The base of a second statue is a cylinder.
1. How many two-dimensional shapes form a cylinder? Explain your
answer.
2. Draw a three-dimensional model of a cylinder.
3. Draw a net of a cylinder.
C. Tom draws a diagram of one of the landmarks.
1. a. What is missing in Tom's diagram?
b. Redraw Tom's diagram. Correct his mistakes.
c. Make a table to record the number of faces, edges,
and vertices in Tom's drawing.
2. Next to this landmark is a small gift shop.
a. Make a table to record the number of faces, edges, and
vertices in this drawing.
b. How do the diagrams compare in terms of faces, edges, and
vertices?
Exercises
Use the drawing to answer Exercises 1 and 2.
1. How many edges does this shape have?
2. Draw a two-dimensional model of the shape.
3. A shape has 4 faces that are triangles and 1
face that is a square.
a. Draw the shape.
b. How many edges are in the shape?
c. How many vertices are in the shape?
4. Draw a three-dimensional picture of the net.
List the two-dimensional shapes used to make the faces of each object.
5. A prism, such as a shoebox.
6. A cylinder, such as can of soup.
7. A pyramid, like the structures built by the Egyptians.
8. A cone, like a traffic cone.
At a Glance
Topic 9: 3-D Figures
PACING 1 day
Mathematical Goals
• Describe and give examples of three-dimensional figures including
spheres, cones, cyclinders, prisms, and pyramids.
• Identify the parts of a three-dimensional figure.
Guided Instruction
Show students examples of three-dimensional geometric objects (cones,
pyramids, prisms, etc.). To represent a three-dimensional shape on a flat
page, such as in a book, you must draw a two-dimensional representation of
that shape. Read the introduction with students and review the dimensions
of three-dimensional figures; length, width, and height. Point out that threedimensional objects consist of such parts as faces, edges, and vertices, and
that by turning the object it can have the appearance of different twodimensional shapes.
For Problem 9.1 A, give each student a cube to study. Ask:
• What do you notice about the sides and faces of a cube? (The sides are
all equal in length and the faces are all squares.)
• How can you show hidden faces when you know draw a picture of a
cube? (Use dotted lines to show the hidden edges.)
• How could you use an actual cube to make a two-dimensional model?
(Trace each of the faces on paper.)
• What is meant by congruent parts? (Congruent means that matching
parts are the same size and the same shape.)
For Problem 9.1 B, show students a cyclinder. Cut the cyclinder apart to
show students the two circles and rectangle that make up a cyclinder.
• What two-dimensional shapes make up a cyclinder? (two circles and a
rectangle)
• Which part of three-dimensional shapes is not found on a cyclinder?
(vertices)
For Problem 9.1 C, ask:
• What two 3-D figures make up Tom's drawings? (a pyramid and a
rectangular prism)
Another way for students to explore two-dimensional and threedimensional shapes is through origami paper folding. Try making a box
from piece of paper.
You will find additional work on 3-D Figures in the grade 7 unit Filling
and Wrapping.
Vocabulary
•
net
Assignment Guide for Topic 9
Core 1-8
Answers to Topic 9
Problem 9.1
A. 1. 6, all of the faces in a cube are squares.
c.
2.
2. a.
3.
faces
9
edges
16
vertices
9
faces
9
edges
17
vertices
10
b. The gift shop and landmark have the
same number of faces. The gift shop
has an additional vertex and edge.
B. 1. 3, two sides are circles and one side is a
rectangle.
Exercises
1. 12 edges
2.
2.
3.
3. a.
b. 8 edges
C. 1. a. The top of Tom's drawing does
not show all of the sides of
three-dimensional shape.
c. 5 vertices
4.
b.
5. rectangles
6. circles and a rectangle
7. triangle and squares
8. circles and a curved triangular shaped figure