Can You Cut It? Slicing Three-Dimensional Figures
Name: ______Period: ______
Can You Cut It? Slicing Three-Dimensional Figures
Lesson Activity
1.The Cube
- Using modeling clay or play-doh, each student creates a model of a cube.
- With your group, predict the type of shapes you could see by cutting the cube at different places and different angles. Do not actually make any cuts, but envision what they would look like and write your predictions below:
Description of “slice” made: / Prediction of shape formed (cross-section):
- Using a plastic knife or dental floss, slice through the middle of the model cube in a direction perpendicular to the base.
To the right, sketch, describe, and name the figure formed by the cross-section.
If the slice was made in a different area (but still perpendicular to the base), would the shape of the cross-section be the same or different? Explain your thinking in the box to the right.
- Put your model back together again before continuing.
- Slice through the middle of the model cube in a direction parallel to the base.
To the right, sketch, describe, and name the figure formed by the cross-section.
If the slice was made in a different area (but still parallel to the base), would the shape of the cross-section be the same or different? Explain your thinking in the box to the right.
- What do you notice about all the cross-sections formed by the intersection of a plane that is either parallel or perpendicular to the base of a cube?
- Put the cube back together and create a cross-section that would make a triangle shape. Describe what you did and how you did it.
- Compare and contrast your group’s triangles to other group’s triangles. Are the cross sections the same? Explain.
- Create other cross-sections with as many two-dimensional shapes as you can. List and explain your steps.
- Are there any two-dimensional shapes that you cannot create from the model? Explain why.
- Can you make a hexagon from a cube with just one slice? Explain .
2.Rectangular Prisms
- Using modeling clay or play-doh, create a right rectangular prism that is not a cube. The bases of the prism are squares and the lateral faces are rectangles.
- With your group, predict the type of shapes you could see by cutting the prism at different places and different angles. Do not actually make any cuts, but envision what they would look like and write your predictions below:
Description of “slice” made: / Prediction of shape formed (cross-section):
- Using a plastic knife or dental floss, slice through the middle of the model prism in a direction that is perpendicular to the base (and parallel to the faces).
To the right, sketch, describe, and name the figure formed by the cross-section.
If the slice was made in a different area (but still perpendicular to the base), would the shape of the cross-section be the same or different? Explain your thinking in the box to the right.
- Put your model back together again before continuing.
- Slice through the middle of the model prism in a direction parallel to the base.
To the right, sketch, describe, and name the figure formed by the cross-section.
If the slice was made in a different area (but still parallel to the base), would the shape of the cross-section be the same or different? Explain your thinking in the box to the right.
- What do you notice about all the cross-sections formed by the intersection of a plane that is either parallel or perpendicular to the bases of a prism?
- Put the prism back together and create a cross-section that would make a triangle shape. Describe what you did and how you did it.
- Compare and contrast your group’s triangles to other group’s triangles. Are the cross sections the same? Are different types of triangles created? Would you classify these triangles by their angles or sides?
- Create other cross-sections in the shapes of pentagons, hexagons, and parallelograms. List and explain your steps.
- Can you create more or less shapes with a rectangular prism than a cube? Explain your answer.
3.Right Rectangular Pyramids
- Using modeling clay or play-doh, create a right rectangular pyramid.
- With your group, predict the type of shapes you could see by cutting the pyramid at different places and different angles. Do not actually make any cuts, but envision what they would look like and write your predictions below:
Description of “slice” made: / Prediction of shape formed (cross-section):
- Using a plastic knife or dental floss, slice through the middle of the model pyramid in a direction that is perpendicular to the base (and slices through the vertex).
To the right, sketch, describe, and name the figure formed by the cross-section.
If the slice was made in a different area (but still perpendicular to the base), would the shape of the cross-section be the same or different? Explain your thinking in the box to the right.
- Put your model pyramid back together again before continuing.
- Slice through the middle of the model pyramid in a direction parallel to the base.
To the right, sketch, describe, and name the figure formed by the cross-section.
If the slice was made in a different area (but still parallel to the base), would the shape of the cross-section be the same or different? Explain your thinking in the box to the right.
- Put your pyramid back together and slice through the pyramid in a direction that is neither parallel nor perpendicular to the base. Sketch and describe the figure(s) formed.