Representing Three Dimensional Figures Using Nets
Student Probe
Can this net be folded to form a cube?
Answer: Yes
Lesson Description
Using a prism made of Polydrons, students will
create a net of the prism. The purpose of the
lesson is to help students develop an
understanding of nets and their representation
of three dimensional figures.
Rationale
Students frequently have difficulty visualizing
that two dimensional figures can be folded to
form three dimensional figures such as prisms, or
that prisms may be decomposed into two
dimensional nets. The ability to visualize the
“skin” of a prism is an important step to
understanding surface area and to conceptually
understand how it is computed.
At a Glance
What: Represent three dimensional figures
using nets made up of rectangles and triangles
Common Core Standard: CC.6.G.4. Represent
three-dimensional figures using nets made up
of rectangles and triangles, and use the nets to
find the surface area of these figures. Apply
these techniques in the context of solving realworld and mathematical problems.
Mathematical Practices:
Model with mathematics.
Use appropriate tools strategically.
Who: Students who have difficulty visualizing
three dimensional figures
Grade Level: 6
Prerequisite Vocabulary: rectangle, triangle,
three dimensional
Prerequisite Skills: knowledge of shapes
Delivery Format: small group, whole group
Lesson Length: 15 to 30 minutes
Materials, Resources, Technology: Polydrons,
chart paper, rulers or straightedges
Student Worksheets: none
Preparation
Use Polydrons to create a rectangular prism and
a triangular prism for each student (or pair of
students). Retain a Polydron model for teacher
demonstration. Cut several sheets of chart paper for tracing nets.
Lesson
The teacher says or does…
Expect students to say or do…
1. Look at your Polydron
prism. Every prism has a
pattern or “footprint”
when it is unfolded.
Sketch the pattern, or
“footprint” that you think
your prism will have when
it is unfolded.
Mathematicians call this
pattern a net.
2. Now we are going to
carefully unfold our
prisms.
(Model for students.)
3. Trace the outline of your
net on the chart paper.
Answers will vary.
Trace the outline of their net.
Assist students who have
difficulty.
Use your straightedge to
make dashed lines where
the folds occurred to
make your prism.
4. Does your net look like
your prediction?
5. Compare the net of your
prism with the net of your
neighbor’s prism.
Make dashed lines along the
folds.
Students may need to re-fold
the prisms to determine the
fold lines.
How are they alike?
How are they different?
6. Why do you think this is?
Will they fold back up to
make the same figure?
7. Fold your Polydron net
again to make the prism.
Now carefully unfold your
prism again, but
differently than the first
time.
If students do not, then the
teacher says or does…
Do not correct students at this
time.
Answers will vary.
Prompt students.
They are made up of squares
and rectangles.
The squares and rectangles
are put together in different
ways.
Demonstrate with your prism.
The teacher says or does…
Expect students to say or do…
8. Trace the outline of this
net on your chart paper.
Use your straightedge to
make dashed lines along
the fold lines.
Trace the outline of their net.
9. How is this net like the
first one?
How is it different?
They are made up of squares
and rectangles.
The squares and rectangles
are put together in different
ways.
10. Fold your Polydron net
again to make the prism.
Is the prism the same?
Why do you think that
both nets can be refolded
to make the same prism?
11. Repeat the process with
the triangular prisms.
Make dashed lines along the
folds.
If students do not, then the
teacher says or does…
Assist students who have
difficulty.
Students may need to re-fold
the prisms to determine the
fold lines.
Assist students who have
difficulty.
Yes
Answers will vary.
Teacher Notes:
1. Repeat the same dialogue using the triangular prism.
2. Additional Polydron prisms and pyramids can be made to enhance and reinforce students’
spatial visualization.
Variations
1. Give students a net diagram worksheet, and ask them to predict what three dimensional
figures each net will make.
2. Let students create their own Polydron prisms. Have students exchange their figures and
draw the nets.
Formative Assessment
Can this net be folded to form a cube? How do you know?
Answer: No. It will be missing one side.
References
Russell Gersten, P. (n.d.). RTI and Mathematics IES Practice Guide - Response to Intervention in
Mathematics. Retrieved Feb. 25, 2011, from rti4sucess