In my experience as a middle grade teacher, the lessons where students “discovered pi” were frustrating for them and me. On one hand, I wanted them to have some hands on experience with the ratio. On the other hand, I found they didn’t measure accurately enough to find the pattern.
I combined and modified several lessons to emphasize measuring accurately and checking results with the formula. I found this gave the balance between exploring the measurement of circles and explicitly teaching the formulas. Although this lesson does not appear in the Common Core Standards until seventh grade, working with pi is in my third through fifth grade texts. I found this lesson worked well for this age group.
I have included a lesson for linear measurements of a circle: radius, diameter, and circumference. I have the recording sheet for the measurements and calculations with directions for each.
Next, is the lesson for measuring and computing the area of a circle. I used the terms estimate and calculate because making careful measurements of area is nearly impossible with the graph paper. I have included centimeter graph paper for your convenience. I have also included circles in three sizes in case you don’t have plastic lids available.
I added a page for computing cylinders and the last page is directions for the Math Spies Missions that use the formulas in this unit. Math Spies is a math problem-solving website I developed for my classes.
I hope you find these lessons useful in your classroom.