8.G.7
PYTHAGOREAN THEOREM IN 3D – Part II
Teacher Directions
Determine the number of pairs of students in your class. Using the net for the cube and rectangular
prism, make half of the number you need per pair of students. For example if you have 14 pairs of
students in a class, make 7 cubes and 7 rectangular prisms. Make the cubes and rectangular prisms
before the class begins. In order to keep the cubes and rectangular prisms for more than one year,
you may want to photocopy the nets on card stock paper.
Photocopy the student worksheet for cubes and rectangular prisms. Pass out the worksheet and
give half of the pairs a cube and half the pairs a rectangular prism. Half of the pairs will start with
the cube and answer questions #1 – 4. Half of the pairs will start with the rectangular prism and
answer questions #5 – 8.
Since the cube has whole number lengths of sides and the rectangular prism has decimal side
lengths, you can differentiate in the classroom by giving students who struggle with the cube first.
This may build their confidence before they move on to the pyramid, which has decimal side lengths.
There is a small hole in the cubes and rectangular prisms in case you’d like the students to thread
an object (coffee stirrer, pipe cleaner etc) into the hole so they can measure the pipe cleaner after
threading through the prism.
When they are finished with one side of the worksheet, they will swap their 3D object with another
pair so that they can complete the other side of the worksheet.
Once a pair of students has completed the entire worksheet, have them group with another pair of
students to compare and discuss their answers.
To wrap up the class, ask if there were any discrepancies in answers between pairs.
8.G.7
PYTHAGOREAN THEOREM IN 3D – Part II
Cube Net (to cut-out)
8.G.7
PYTHAGOREAN THEOREM IN 3D – Part II
Rectangular Prism Net (to cut-out)
8.G.7
PYTHAGOREAN THEOREM IN 3D – Part II
CUBE
1. Using a ruler, measure the length, width, and height of the cube to the nearest tenth of a
centimeter.
length ________________
width _________________
height ____________________
2. Brainstorm some ways you can use a ruler to measure the inner diagonal (distance from one
vertex to the opposite vertex) of the cube?
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3. Using a method from question #2, what is the distance of the inner diagonal to the nearest
tenth? What method did you use?
4. Use the Pythagorean Theorem to prove that you have correctly measured the inner diagonal
of the cube. Show your work below.
8.G.7
PYTHAGOREAN THEOREM IN 3D – Part II
Rectangular Prism
5. Using a ruler, measure the length, width, and height of the rectangular prism to the nearest
tenth of a centimeter.
length ________________
width _________________
height ____________________
6. Brainstorm some ways you can use a ruler to measure the inner diagonal (distance from one
vertex to the opposite vertex) of the rectangular prism?
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7. Using a method from question #6, what is the distance of the inner diagonal to the nearest
tenth? What method did you use?
8. Use the Pythagorean Theorem to prove that you have correctly measured the inner diagonal
of the rectangular prism. Show your work below.