Name ____________________
Class ____________________
Classroom Cut-ups
Our team focused on the following standard(s) for our learning cycle:
7.G.3 – Describe the two-dimensional figures that result from slicing threedimensional figures, as in plane sections of right rectangular prisms and right
rectangular pyramids.
Mathematics:
The mathematics in our learning cycle is that cross-sections are two-dimensional
shapes that result when three-dimensional geometric figures are cut by planes.
These two-dimensional shapes can be triangles, rectangles, squares or trapezoids
depending on the slice. The slices can me made horizontally, vertically or angled.
Our goal statement is:
Students will differentiate between the various ways to slice a 3D figure (i.e.
vertical slice, horizontal slice, and angled slice) and describe and/or draw the
different 2D cross-sections that will result depending on how you slice the 3D
figure.
Our develop understanding task is:
Our develop understanding task is divided into two parts. We have named it
“Classroom Cutups”. The students will begin with a worksheet that they are able to
draw slices on the two 3D figures that are mentioned in the standard.
The second part of the task requires the students to form 3D figures out of play
dough and make the actual slices to those figures using dental floss or fishing line.
Once the cuts are made, the students will trace the cross-section and identify the 2D
shape that resulted.
In our develop understanding task, we wish to surface ideas such as:
We want our students to understand that while they can make an infinite number of
slices, those slices actually fall into only three different categories. The slices can be
horizontal, vertical or angled.
Name ____________________
Class ____________________
We want our students to understand the difference between face planes and crosssection planes. We also want them to understand that the shapes of the cross-section
planes will be different when a figure is sliced horizontally, vertically or angled.
And highlight:
We want to highlight that the cross-section are located on the inside of the figure and
the faces are located on the outside of the figure. We also want to highlight that
different angles and depths of slices result in different cross-section shapes.
The solidify task we chose is:
“Platonic Solids – Slicing” online manipulative. It is found on this website:
http://nlvm.usu.edu/en/nav/category_g_3_t_3.html
The solidify task goal is:
Students will be able to recognize and draw the shapes of cross-sections from a
variety of different 3D figures sliced at various angles as shown by the computerized
manipulative. This is intended to create a link between the concrete and abstract
concepts presented in the developing task.
The practice task we chose is:
We have prepared a homework assignment that requires the students to draw or
explain the cross-section shapes created by slicing 3D figures.
The practice task goal is:
Students will demonstrate their competence at differentiating between the
various ways to slice a 3D figure (i.e. vertical slice, horizontal slice, and angled
slice) and describe and/or draw the different 2D cross-sections that will result
depending on how you slice the 3D figure.
Name ____________________
Class ____________________
Teacher pages for Classroom Cut-ups
Part 1 – Develop Understanding
Task Goal
Differentiate between the different ways to slice a 3D figure (i.e. vertical
slice, horizontal slice, and angled slice).
Supplies needed


Student worksheets
Writing implements
Anticipation


Students may cut figures in 1/2 horizontally or vertically. You may need to
encourage them to try multiple directions.
Students may not recognize the shapes that are occurring in the cross sections.
They may only see or envision the planes as shapes.
Possible discussion questions and desired answers.
There are actually 3 categories that all cuts fall into. Can you name those categories?
Vertical, horizontal, angled
What do you call the outside or faces of the figures?
Planes
What do you call the inside or the flat part created by the cut?
Cross-section
Name ____________________
Class ____________________
Part 2 – Develop Understanding
Task Goal
Describe the different 2D cross-sections that will result depending on how
you slice the 3D figure.
Supplies needed




Student worksheets
Writing implements
Play dough
Dental floss or fishing line
Anticipation



Students’ figures may not be “perfect”. Remind them that they can use
any flat surface to shape the planes of the figures.
Students may not hold the dental floss or fishing line tightly enough to
get it to slice through straight. Remind them to wrap it around their
fingers once or twice and hold it taught. Students can also wrap the dental
floss or fishing line around the figure and pull the opposite ends together
to cut the play dough.
Students may not distinguish between the face and the cross-section.
Possible discussion questions and desired answers.
What 2D shape(s) resulted when you sliced a right rectangular prism horizontally?
What 2D shape(s) resulted when you sliced a right rectangular prism vertically?
What 2D shape(s) resulted when you sliced a right rectangular prism angled?
What 2D shape(s) resulted when you sliced a right rectangular pyramid horizontally?
What 2D shape(s) resulted when you sliced a right rectangular pyramid vertically?
What 2D shape(s) resulted when you sliced a right rectangular pyramid angled?
What other 3D shapes did you try slicing?
What 2D shape(s) resulted?
Name ____________________
Class ____________________
Part 3 – Solidify Understanding
Task Goal
Students will be able to recognize and draw the shapes of cross-sections
from a variety of different 3D figures sliced at various angles as shown by
the computerized manipulative. This is intended to create a link between
the concrete and abstract concepts presented in the developing task.
Supplies needed



Student worksheets
Writing implements
Access to computers that can connect to the internet
Anticipation






Students may struggle at first with the type of slice that is being made.
Students may not realize that the figures can be rotated.
Students may not realize that the size of the cut can be adjusted.
Students may need encouragement to try different 3D shapes.
Students may not understand that the “view of intersection” shown on the right
side of the manipulative is the cross-section.
Students may not understand that by deselecting “Show Entire Solid” on the
manipulative they can show only the part that is cut off.
Possible discussion questions and desired answers.
What are some new things that you discovered?
What connections can you make to the activities we did earlier and this activity?
Name ____________________
Class ____________________
Part 4 – Practice
Task Goal
Students will demonstrate their competence at differentiating
between the various ways to slice a 3D figure (i.e. vertical slice,
horizontal slice, and angled slice) and describe and/or draw the
different 2D cross-sections that will result depending on how you
slice the 3D figure.
Supplies needed


Student worksheets
Writing implements
Anticipation


There may still be some confusion on the 2D cross-section shapes that result
from angled slices.
A discussion may be needed if there is still confusion.
Name ____________________
Class ____________________
Classroom Cut-ups
Part 1
Take a look at the three-dimensional figures below. Use your pencil to draw the different
ways you could slice through each figure.
Take a look at the diagrams of other members in your group. How are your drawings the
same? How are they different?
What does your new surface look like?
Name ____________________
Class ____________________
Part 2
Take a piece of play dough. Form it into a right rectangular prism. Use the dental floss to
slice through your prism. Record the type of cut you made, the result of the twodimensional shape of the planes because of this cut, and the two-dimensional shape of the
cross-section of the cut. You may lay the play dough on your paper and trace around it if
desired.
What are you noticing or discovering about the 2-dimensional shapes created by slicing 3dimensional figures? Explain your findings.
Take a piece of play dough. Form it into a right rectangular pyramid. Use the dental floss
to slice through your pyramid. Record the type of cut you made, the result of the twodimensional shape of the planes because of this cut, and the two-dimensional shape of the
cross-section of the cut. You may lay the play dough on your paper and trace around it if
desired.
What are you noticing or discovering about the 2-dimensional shapes created by slicing 3dimensional figures? Explain your findings.
Repeat this procedure with a different 3-dimensional shape of your choosing. Record the
type of cut you made, the result of the two-dimensional shape of the planes because of this
cut, and the two-dimensional shape of the cross-section of the cut. You may lay the play
dough on your paper and trace around it if desired.
What are you noticing or discovering about the 2-dimensional shapes created by slicing 3dimensional figures? Explain your findings.
Name ____________________
Class ____________________
Part 3
Start your computer. Launch a web browser and navigate to the National Library of Virtual
Manipulatives at this address: http://nlvm.usu.edu/en/nav/vlibrary.html
Select the Geometry/6-8 manipulatives. It should take you to this address:
http://nlvm.usu.edu/en/nav/category_g_3_t_3.html
Scroll down to the manipulative named “Platonic Solids – Slicing” and launch it.
Explore this manipulative. Try different shapes, different size slices, and different
rotations. The lines you see in red are a representation of the cross section of the 3dimensional figure as it is sliced. Write down the two-dimension shapes that result from
the slices. Explain why you think the result occurred.
Name ____________________
Class ____________________
Part 4
Explain or draw the two-dimensional
shapes of the cross-sections of each of the
three-dimensional shapes after they have
been sliced.
3. Describe or draw the cross-section
shape resulting from cutting the
figure below.
1. Describe or draw the cross-section
shape resulting from cutting the
figure below.
4. Describe or draw the cross-section
shape resulting from cutting the
cone of an ice-cream cone on an
angle.
2. Describe or draw the cross-section
shape resulting from cutting the
figure below.
5. Describe or draw the cross-section
shape resulting from cutting the
cone of an ice-cream cone
vertically.
6. Describe or draw the cross-section
shape resulting from cutting the
cone of an ice-cream cone
horizontally.
7. Describe the shape resulting from
the cross-section of the following
figure.
Name ____________________
Class ____________________
8. Describe the shape resulting from
the cross-section of the following
figure.
11. If you have a gift box like the one
shown below, which shape crosssection would be impossible to
get?
A.
9. Describe the shape resulting from
the cross-section of the following
figure.
B.
C.
10. Describe the shape resulting from
the cross-section of the following
figure.
D.