Visually Understanding Area of a Circle and Volume of a Cylinder

Over the past year, I have been on a mission to try and make some of the formulas we use in the intermediate math courses in Ontario (Middle School for our friends in the U.S.). I think it can be difficult for math teachers to explain where formulas come from because we often think of deriving formulas algebraically. Unfortunately, for our younger students, this might be more harmful than helpful. Specifically, this semester I am teaching MFM1P Grade 9 Applied Math where many of these students come into high school with a sour taste of mathematics in their mouths.

Yesterday, we looked at Volume of a Cylinder and began with Dan Meyer’s Hot Coffee 3 Act Math Task as a starting point to understand where students were comfortable and where there was room for growth.

After we had some great discussions about volume and conversions, I felt as though I was really scaffolding students along to discover the formula for volume of a cylinder. I decided that making a visual to help them understand where the formula comes from might be useful. Feel free to check it out below for use in your own classroom:

Stage By Stage PDF File

Here is a stage-by-stage PDF file for you to grab, if you’d like:

If you’re interested in creating animations for your own math class, download Keynote here:

If you want to jump to Dan Meyer’s Hot Coffee 3 Act Math Task, check it out below:
Please let me know if you/your students found this resource helpful to better understand where the Volume of a Cylinder comes from!