## Unrolling Circles in GSP ☆

From my own experiences, students often struggle to understand what circumference means as a measurement. (Such difficulties are also reiterated on student’s performance on standardized test questions.) In order to help their conceptualization, I created a GSP document that allows students to roll and unroll a circle, keeping visual track of its length. The aim is to help students conceptualize how curves can be measured with linear (straight) units, as well as to understand, for example, how circumference is a different measurement than the diameter.

(password: mathematicalmusings)

Building on this idea, another similar GSP document could be used to develop a functional perspective on the measurement of circumference (in relation to its diameter) as well.

(password: mathematicalmusings)

Thanks so much for posting the second GSP file where you unroll the circles vertically so that students can visualize circumference as a function of the radius. I will definitely keep this in mind for next year.

In my more low-tech classroom, I simply give students yarn to “measure” the circumference of a few circular objects they brought in. Then they use a meter stick to measure the length of the yarn and the diameter of the object in order to determine the ratio of the two values and relate it to pi.

A cool extension would be to create a class graph of all those pieces of yarn like the GSP graph you created!

Unfortunately I have an older version of Sketchpad (v 4.06), and I am unable to open, “Lesson 3–rolling circles.” Is there anyway you can post or send a version that is backwards compatible? I understand if you cannot, but just thought I’d ask! Thanks :).

Unfortunately I created it with GSP5, so I don’t have a backwards compatible version of the files. Sorry about that.