# Follow Up on Friday Bubbles

Upon their return on Monday, I asked for ten groups to volunteer just one set of their circumference and diameter numbers. Then I asked, “What is the relationship between these numbers?” Some quiet mumbling, then just quiet. I asked again, “I have these 10 sets of numbers. What should I do with each set of numbers to see if there’s a relationship between them? I want you to use your calculator to do something with these two numbers and find out for me.”

They were busy punching in numbers. After a few minutes…

Me: What are you punching into your calculator?

Matt: I’m dividing the numbers.

Me: Why divide? Why not add or subtract? Or multiply the numbers?

Matt: Adding and subtracting don’t tell you anything. Just doesn’t make sense.

Sophia: The circumference is always bigger than the diameter. So I think I want to know how many times it’s bigger.

Me: Class, do you agree that we should divide circumference by diameter? (Lots of nods around the room.)

While they continued with their own bubble numbers, I filled in the “relationship” column for the 10 volunteered sets from earlier.

They were skeptical — didn’t know what to make of the “relationship” column. I said, “I think measuring a bubble imprint with a string is not easy. It was fun to blow bubbles, for sure. But what about it that may have affected how your numbers came out?”

The bubbles were sometimes oval shaped.

Hard to keep the string perfect.

It can get messy!

Maybe some people didn’t measure the widest part.

Maybe they measured in centimeters for one part and inches for another.

It was so much fun! (I can always count on a random answer.)

I said, “Because our bubble numbers could use some help. Let’s do a clean run through this again, this time using paper and pencil.”

I asked them to draw two to three different sized circles on notebook paper — measure the diameter and circumference of each one. I showed them how to “walk” the string around the circle for better accuracy — press and let go, press and let go… They knew that if they started from one end of a diameter, walked the string around the circle, to the other end of the diameter, then they just needed to multiply this by two to get the circumference.

I asked them to find the “relationship” number again for each circle.

The paper in top row, left, reads: All of them are around 3, which is close to pi. Other papers didn’t include observations or conjectures, and a few wrote they weren’t so sure.

But when we shared ALL the “relationship” numbers that the class had — over 60 of them as each student did at least 2 circles — and they were pretty well convinced that the diameter was “about 3 times longer” than the diameter!!

I showed them this very short video to reflect the simple work that we did.

Next up, we are going to find the AREA of a circle!!!!!!!