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# Prisms and Pyramids

## How Many Pyramids Does It Take To Fill a Prism?

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.

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:

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:

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*

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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