Discovering Pi - A Fun Pi Day Activity

Discovering Pi an activity to make sense of pi a hand measuring a circular bottle with a black piece of yarn

Looking for an engaging activity to help your middle school math students understand pi?  This fun discovering pi activity will do the trick. The best part of this discovering pi activity is that this helps students makes sense of pi.  They will have a concrete experience that they can draw upon to help them remember the ratio of pi as the circumference to the diameter. 

Objective:  Students will discover pi as the ratio of the circumference to the diameter of a circle. 

Supplies:  String, ruler, recording sheet, and at least 10 different cylindrical objects that you can use to measure the circumference of a circle.  If you look around your classroom or house you will be able to find a lot.   I have used cans, lids, bottles, etc...

Activity:  Students will measure the circumference and diameter of 10 circles.  Students will calculate the ratio between the circumference and diameter.  

When I have done this I have put students into groups.  Usually two students will need to help with measuring.  One to hold the object, and another student to wrap the string around. 
A hand holding a black piece of yarn around the circumference of a glass bottle
Students will measure the length of the string with a ruler.  
A hand holding a black yarn on top of a ruler measuring

Another student can measure the diameter of the object. 
A ruler on top of lid of a glass bottle measuring diameter

Measurements will likely not be exact, but encourage your students to take as accurate measurements as they can.  Have them measure at least 10 different objects.  The best way to do this is to give each group a couple of objects to measure.  Set a time limit, once the time is over, everybody passes their objects to the next group.  Students will record the object (so they can keep track of what they have done), circumference, and diameter.  After everyone has recorded the measurements of at least ten objects, have them write ratios of the circumference to the  diameter.  Then have them write their answer in decimal form, (at least to the nearest thousandth) and average their ten ratios. 

To take it one step further, I had each group write their average on the board and we took the average of all of them.  I also compared the averages of all my different classes.  Students will be amazed how close this number is to pi.  

Now that your students have a conceptual understanding of pi they will also need to be fluent with using this information to determine the circumference and area of circles.  Here is a FUN ACTIVITY you can check out so your students can become fluent with area and circumference. 

a colorful pi colored and an accompanying worksheet to calculate circumference and area of circles


pin image a hand holding a black piece of yarn around a circular lid of a glass bottle

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