This series of brief videos will help students question the relationship between the volumes of:

• a pyramid and a rectangular prism
• a pyramid and a triangular prism
• a cylinder and a cone

This is a great resource to use if you are working with the volume formulas and want to help students understand how they are connected. It is easier to show that the area of a triangle is half the area of a rectangle or a square, but it can be harder to illustrate similar connections in 3-D. These videos can help.

Note: Each sequence of videos use a simplified three-act math task structure.

Act One: What’s the question?

• Watch the first video, a few times if need be.
• Have students share what they notice and then generate questions.
• The focus question for each of the three sets of videos is:

How many _______’s will it take to fill up a ________?

• Students estimate some possible answers.

Act Two: Giving up More Information

• Watch a second video
• Revise estimates (or not)
• Explain reasoning.

Act Three: Experience the Answer

• Watch the final video and see how close your estimate was.
• Write “What can we say about the relationship between a ______ and ______?”
• Look at the formulas for calculating the volumes of the two shapes in the video and discuss whether and how student observations can be found in the formula equations.

For more on using three-act math tasks in adult numeracy and HSE math classes, see Inspiring Student Creativity (What’s “real” about real-world math?)