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 three-dimensional 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 cross-section 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, angledWhat do you call the outside or faces of the figures?

PlanesWhat 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-upsPart 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 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 3-dimensional 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 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 3-dimensional 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 3-dimensional 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 3-dimensional 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.

1. Describe or draw the cross-section shape resulting from cutting the figure below.

2. Describe or draw the cross-section shape resulting from cutting the figure below.

3. 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.

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.

9. Describe the shape resulting from the cross-section of the following figure.

10. 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 cross-section would be impossible to get?

A.

B.

C.

D.