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:
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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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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