Circumference and Area of a Circle: A Middle School Math Hands-On Lesson
In Middle School Math, yet again another topic that comes to mind that middle schoolers need to learn and will be tested on is circles, specifically circumference and area. These two concepts can be downright boring if taught by the old chalk and talk method.
But lo and behold, I continually tried to find new and creative ways to teach some of the most mundane and boring math topics. Even before getting to actual activity at hand, I was lucky enough to teach alongside some really fabulous teachers and one can me this idea for how to introduce the two concepts. When thinking of circles, students are first and foremost introduced to a few basic principles.
So what are the words that kids must learn the definitions to before they can even begin to work with circles? Well look no further here they are.
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The radius of a circle is the distance from the center of the circle to the outside edge. In the picture to the right, the radius is labeled and is the the yellow line from the edge of the circle to the midpoint.
The diameter of a circle is longest distance across a circle. (The diameter cuts through the center of the circle. This is what makes it the longest distance.) In the picture to the right, the diameter of the circle is clearly labeled and the yellow line that goes from one end of the circle to the other cutting directly through the middle of the circle.
The definition of the circumference of a circle is quite simply the perimeter or the distance around the outer edge of the circle. Looking at the picture to the right, the circumference is the bright yellow line on the outside of the circle.
So the formula for circumference is C = π d, where d= the diameter of the circle and π = 3.141592...
Area is defined as the amount of space inside the boundary of a flat or 2-dimensional object, such as a triangle or circle. In the circle picture to the right, the area is the inside of the circle that is shaded in purple.
The formula for area of a circle is A = π r2, where r = the radius of the circle and π = 3.141592...
So How Can We Remember the Actual Circle Formulas?
Once I briefly introduce these definitions, then I talk a bit about why in real life we would need to find area and circumference of a circle. I model on the smart board a google search about Real Life uses and show the top 5 according to Yahoo. They are as follows:
1. Car makers can measure car wheels to make sure they fit.
2. Race car engineers can use it to find out what size tire gives them the most performance.
3. Bakers can use it to make pies and other circular stuff.
4. Military engineers can use them to balance helicopter blades.
5. Aircraft engineer can use them for propeller efficiency.
Bakers and a Mnemonic Device to Learn the Circumference and Area Definitions:
The real life example that I stop on is Bakers and how they use this with making pies. I bring in two fresh pies to illustrate my point. The reason for this is that I have a cute little mnemonic device to remember the actual formulas for circumference and area. For circumference, I show the class a cherry pie and teach them that "Cherry Pies Delicious" or C = π D. And for area, I then show them an apple pie and teach them that "Apple Pies Are Too" or A = π r2.
Now, we will measure the radius and the diameter of each pie and then will find out the area and circumference of both pies from finding both of these out and plugging them into both the formulas we just learned.
1. Apple Pie:
The apple pie was baked in a 9 inch pie pan. So we know from this bit of information that the diameter is 9 inches. Well, what is the radius? It will be half of the diameter and be 4.5 inches. So now let us plug into our formula to find both the circumference and area too!
So from earlier we know that for circumference, C = π d: C = π 9, (diameter = 9), so C =28.2743338. So if we round to the nearest tenth, the c = 28.3 inches.
Now for the area, we know that the formula is A = π r2. So A = π (4.5)2 = π (20.25) =63.61725123519331. Again, let's round and we get the area to the nearest tenth of the circle to be 63.6 inches.
2. Cherry Pie:
The cherry pie was baked in a 8 inch pie pan. So we know from this bit of information that the diameter is 8 inches. Well, what is the radius? It will be half of the diameter and be 4 inches. So now let us plug into our formula to find both the circumference and area too!
So from earlier we know that for circumference, C = π d: C = π 8, (diameter = 9), so C = 25.132741228718345. So if we round to the nearest tenth, the c = 25.1 inches.
Now for the area, we know that the formula is A = π r2. So A = π (4)2 = π (16) = 50.26548245743669. Again, let's round and we get the area to the nearest tenth of the circle to be 50.3 inches.
3. The Difference of the Circumference and Area of the Apple (9 Inch Pan) and Cherry Pie (8 Inch Pan):
28.3 inches (Apple Pie Circumference) - 25.1 inches(Cherry Pie Circumference) = 3.2 inches.
63.6 inches (Apple Pie Area) - 50.3 inches (Cherry Pie Area) = 13.3 inches.
What we have learned is the at even changing the diameter an inch can change both the circumference and area of the circle ever so slightly.
And now once we are done with the actual lesson, I usually offer a piece of either of the pies to anyone who wants to try them. So a good lesson was learned and a tasty reward to boot!!
Summing This Lesson Up..
I love this lesson, because it is another hands-on lesson using the two different types of pie something that yet again most middle school students are not only aware of, but interested in. Now, when they hear their parents or someone else speaking of making pies maybe they will remember a bit about the circle definitions and formulas learned even after the topic and test are long over and behind them. And as a teacher that is truly something you hope for that the student takes away something from your lesson and doesn't just forget it once the test is long gone! Anyone who has read any of my other math teaching articles previously will know from them that I am a strong believer in using stuff that interests middle school students to help them learn many of the basic concepts that are a requirement. I truly enjoy engaging my students and showing them how we can use math in everyday life and believe this lesson is another one that does just that.
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© 2012 Janine Huldie