Note: for full lesson w/handouts, open the attached document
String (approx. 5 feet)- for each group of 4
Rulers (1 per student)
Circular objects around the room to measure (trash can, plates, cups, etc)
Begin by having students show you with their hands-arms what circumference, diameter, and radius are.
Explain the task to the group and have them brainstorm some circular objects they can measure. Have someone from each group come get string, rulers and calculators and set the time for 15 minutes for each group to measure the circumference and diameter of 4-6 circular objects. When time is up, have each group calculate the average ratio.
Gather the average ratios from each group and record the number on the board (note that there will be variations depending upon measurement accuracy).
Use think-pair-share to have students answer question #1.
For question #2, you can either let each group test something new or you can do a class demo with a large circle (like an outdoor trashcan!).
Give students 10 minutes of silence to work on problems 3-7, followed by 5 minutes to discuss answers with their group. Then use numbered heads or random selection to have students share answers.
Make sure each student leaves with the formula written down and the ability to explain where it came from!