This Formative is by: Rebecca Mann
This is an activity introducing volume in a high school geometry class. Using a 3-Act Math Task and an Illuminations Task, students conceptualize the idea of volume and develop the volume of cylinders.
Based on the video, what question(s) could we explore?
Which container will hold more popcorn?
What information do you need to explore the question?
Do you think the two cylinders will hold the same amount? Do you think one will hold more than the other one? Which one? Why?
Describe what happened. Is Cylinder A full, not full, or overflowing?
Was your prediction correct? How do you know?
If your prediction was incorrect, describe what actually happened.
Can a rectangular piece of paper give you the same amount of popcorn no matter how you make the cylinder?
The applet above illustrates how the cylinder is being filled to specific heights. We can think of volume of a cylinder as stacking ____________________ to a specific height.
Calculate the volume of Cylinder A. Label your dimensions on the diagram.
Calculate the volume of Cylinder B. Label your dimensions on the diagram.
Explain why the cylinders do or do not hold the same amount of popcorn. Use the formula for the volume of a cylinder to guide your explanation.
Which measurement impacts the volume of more: the radius or the height?
Why do you believe your response to #19 is true?
By how much would you have to decrease the height of the Cylinder A to make the volumes of the two cylinders equal?
Why do the two solids contain the same amount of volume?
What do you notice?
This applet visually describes the Cavalieri's Principle. Based on what you have observed, what is Cavalieri's Principle in your own words?
