Prisms and Pyramids

How many pyramids does it take to fill the prism?

Ontario Alignment By Grade
CCSS Alignment By Grade
CCSS Alignment By Standard

How Many Pyramids Does It Take To Fill a Prism?

Prisms and Pyramids - 3 Act Math Task - Real World Math

In this multi-step 3 act math task, the teacher will show three sets of 3 Act Math Style tasks involving comparisons between rectangular prisms and pyramids, triangular base prisms and pyramids, and cylinders and cones. While the intention has been to leave Act 1 of each set very vague to allow for students to take the problem in other directions, the learning goal becomes obvious shortly after seeing the first set of videos.

Task #1: Rectangular Prisms vs. Rectangular Pyramids

Act 1: What’s the question?

Show the following short video clip:

I gave my students some time to chat with a partner and come up with some possible questions for this video. Some questions that came up were:

  • Which has more sides/edges/vertices and how many more?
  • Which has the greater surface area?
  • What would the net of each look like?
  • What are some similarities and differences about both 3D Shapes?
  • Which holds the most volume and by how much?

We then narrow the question down to:

How many rectangular pyramids would it take to fill the rectangular prism?

Students then have a moment to come up with their best guess and we share out and record the guesses in class.

Act 2: Giving More Information

Students then watch this video:

Act 3: Experience the Answer

Students will then watch Act 3 in order to determine how close they were to the actual number.


Task #2: Triangular Prisms vs. Triangular Pyramids

Act 1: What’s the question?

Show the following short video clip:

Act 2: Giving More Information

Students then watch this video:

Act 3: Experience the Answer

Students will then watch Act 3 in order to determine how close they were to the actual number.


Task #3: Cylinder vs. Cone

Act 1: What’s the question?

Show the following short video clip:

Act 2: Giving More Information

Students then watch this video:

Act 3: Experience the Answer

Students will then watch Act 3 in order to determine how close they were to the actual number.


Making Connections / Consolidation

Once students have experienced the three sets of videos above, we can then start making conclusions about what the volume formulas for pyramids and cones should be:

Volume of Any Pyramid = Volume of Prism Divided By 3

*Note that the area of the base and the height of both the pyramid and prism must be equal*

Download The Task and Resources

Grab all the videos, images and resources by clicking download below:


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About Kyle Pearce

I’m Kyle Pearce and I am a former high school math teacher. I’m now the K-12 Mathematics Consultant with the Greater Essex County District School Board, where I uncover creative ways to spark curiosity and fuel sense making in mathematics. Read more.


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