## 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.

## 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:

Download

## New to Using 3 Act Math Tasks?

Download the 2-page printable 3 Act Math Tip Sheet to ensure that you have the best start to your journey using 3 Act math Tasks to spark curiosity and fuel sense making in your math classroom!

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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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Grade 4 [4-MD.3, 4.MD.1, 4.MD.2, 4.NBT.6, 4.NF.3, 4.OA.1]

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Practice [MP.1, MP.2, MP.3, MP.4, MP.6, MP.7]

Statistics & Probability [S-ID.6, S-MD.4]

We linked to this post from our own post on the volume of a pyramid. Take a look http://engaging-math.blogspot.ca/2015/01/volume-of-pyramid.html