Reflection Paper About Pi

Throughout the past few days, my class and I have been learning about Measurement. In this class, we have been learning about how to find the circumference of a circle, the area of a circle and the volume of a cylinder. During these classes, I have learned a lot that I had never known before. Before these classes, I had no idea how to measure a circle and find the area. By the end of the first class, I knew exactly how to do it, but there were some steps to eventually get there.

The first thing that we did in class was brainstorm in our groups of how to find the area and circumference of a circle. I started to think but nothing came to mind. Our group knew that it had to do something with pi (3.141592654…), but didn’t know how to apply it

First, we talked about pi and how important the number is to math. Pi is an infinite number and is the ratio between a circle's circumference and diameter. To create pi, you divide 22 by 7. I thought this was very interesting because of how long and important this number is to math. It was incredible. Next, we learned about how to find the circumference of a circle. The formula for this was 2πr which didn’t really make sense. I didn’t understand it until the teacher explained it. 2πr was just another way of saying πd. You take pi and multiply it by the diameter. This made sense to me because pi is the constant between the circumference and diameter of a circle. In theory, if we multiply pi by the diameter or radius*2, we should end up with the circumference. Then, we talked about the area of a circle. Just like the circumference of a circle, the formula to find the area was just a bunch of numbers until it was explained to me. In this picture below, it visualized how πr² equals area. It shows the circle chopped up into different triangles. On the left, it visualizes the height, or in this case radius, of the circle. On the bottom, it shows the lengths of all of the triangles put together with is pi*radius. Now all you would have to do it combine both to make a formula. Pi would stay the same and the 2 r’s (radius) would

I learned how to find the circumference of a circle, find the area of a circle and find the volume of a cylinder. This lesson also helped me to understand why each formula to find each measurement was the way it was. A strategy that helped me understand these formulas was to visualize and break down each step to get the answer. Finding the area of a circle I could picture different parts of the circle broken down to make a rectangular-like object to help communicate why the formula is πr². Visualization also helped me to understand the formula to find the volume of a cylinder. I could see the multiple circles stacked on top of each other to create the 3D shape. Also, I can apply this lesson to real life. Careers like architecture and design jobs depend on these shapes and formulas to create an eye-pleasing design. When building houses you need to know the amount of material you might need for cylindrical pillars to support it which can be found by using the formula, πr²*h, to find the volume of the pillars. In conclusion, I learned a lot of new skills that I can use in math and everyday life. One question that I still have, even after researching a bit about circles and their relationship with pi is, why is pi or 3.141592654 the constant between the radius and the circumference of a circle and what does it have to do with creating a circle. Overall, I think that I used a good strategy to