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Pi & the Circumference of a Circle, Easy Project for Visual Reinforcement.
3.14159..... March 14 is Pi Day. As a math teacher I make a point to celebrate pi day with learning and not with pie. I refuse to acknowledge the relationship between the two in order to have a sweet treat in math class.
Here is what I do instead.
I use March 14 as an exploration of why pi exists and how we can find the circumference of a circle using what we know.
One circle of each student (depending on the age group you may want to give them the circle and the center may need to be marked)
A thirst for knowledge
Objective: To find the circumference of a circle without using pi. Show that pi does help find the circumference of the circle.
For this project I needed a circle so I traced a cd onto a piece of paper and cut it out.
I was able to easily find the center of my circle by folding the circle in half twice. The intersection of the two points creates the center point. I marked this with a pen.
Measure the radius of the circle. Write this number down somewhere important, we will need it later. We are going to divide our circle in to several sections using the center of the circle to that we are dividing the circle into equal sections through the center creating multiple radius sections.
I am going to cut my circle into 16 separate sections. The more sections you divide you circle into the more exact the answer will be for finding the circumference. I am going to cut my circle into each section.
I was able to easily divide my circle but repeatedly folding in half. Once I opened the circle I used a ruler to draw the sections.
I then cut the sections apart.
Now that I have all my sections cut out I am going to create a "rectangle" with all the pieces. By laying the pieces down every other way we are able to create an almost rectangle. Remember I said the more pieces you cut into your circle into the more precise it will be. if I had double the number of pieces in this part it would look even more like a rectangle.
I am going to attempt to measure each side of the rectangle. Think about the shape of the circle. Remember that the width of the rectangle is the radius of the circle while both of the lengths of the rectangle add together to make the entire circumference.
So let's go back to the measured radius at the beginning. The formula for circumference is 2r∏.
let's estimate just to make this easy. Radius = 2.375
2 * 2.375 * 3.14 is approximately equal to 14.91
The side of the rectangle is approximately 7.5. there are two sides so add them together 7.5+7.5 = 15 or 7.5 *2 = 15.
Notice that the sides of the rectangle add to the approximate circumference for the circle.
Have your students talk about how the circumference and the length are related. This is a great exploration activity that work well in a geometry unit or simply to talk about pi on Pi Day.
Another extension activity is to use string and measure around cylindrical objects, find the radius and calculate the circumference and measure the string.