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Circumference and Area of a Circle: A Middle School Math Hands-On Lesson

Updated on February 4, 2017
Janine Huldie profile image

Janine is a published author in Only Trollops Shave Above the Knees, appears on The Huffington Post and at Confessions of A Mommyaholic.

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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.

Circle Definitions:

Radius:

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.

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Diameter

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.

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Circumference

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...

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Area

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...

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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.


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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.

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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.

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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.

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3. The Difference of the Circumference and Area of the Apple (9 Inch Pan) and Cherry Pie (8 Inch Pan):

Circumference Difference:

28.3 inches (Apple Pie Circumference) - 25.1 inches(Cherry Pie Circumference) = 3.2 inches.

Area Difference:

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.

© 2012 Janine Huldie

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    • Janine Huldie profile image
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      Janine Huldie 5 years ago from New York, New York

      Thundermama, I wish I could still be a teacher and it would be my honor and privilege if I were to be able to teach your daughters. Thank you so much though for all your kindness here and for saying such lovely things about my lesson and teaching too :)

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      Catherine Taylor 5 years ago from Canada

      Janine, how I wish someone like you was teaching my daughters math. It is a shame you are not currently a teacher, but fantastic that you are willing to share your gifts for teaching here.

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      Janine Huldie 5 years ago from New York, New York

      No problem about missing Joseph, believe me I have been there before too. Just happy you did find my article and are here now :) I too had to memorize a lot in school and remember having some really lame excuses for teachers who phoned it in. So that is why I vowed not to be like that myself as a teacher. Thank you for voting, sharing and tweeting too!!

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      Joseph De Cross 5 years ago

      I did miss this one Janine. Totally awesome. There is no better way. Your care and lay out pops in our face. Sadly it was too late for me, by 6th grade I had to memorize these formulas by using them. But You did perfect. Voting this up and sharing and tweeting.

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      Janine Huldie 5 years ago from New York, New York

      Eddy, your words here mean the world to mean. I tried my best when I was teaching to be the best for my students that I could be. I miss teaching greatly and do hope that someday soon in the future that I can return to the profession that I do have a passion for. Thank you seriously for your kindness here and fro your votes/support!! Hope you are enjoying your day too...Janine :)

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      Eddy Jones 5 years ago from Wales.

      Without a doubt you are anamazing teacher and the way in which you do this is wonderful.

      A brilliant hub awesome/useful/interesting .

      Enjoy your day.

      Eddy.

    • Janine Huldie profile image
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      Janine Huldie 5 years ago from New York, New York

      Dianna, thank you so much for the compliment. I have to tell you I really loved the challenge of coming up with a great hands on math lesson and even now have been going through my old lessons trying to retweek hoping that I will et to use these again in the future. Thank you also for the votes and share too!!

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      Dianna Mendez 5 years ago

      Once again you have posted an amazing hub on math. I enjoy the read and the application. Voted way up and shared too!

    • Janine Huldie profile image
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      Janine Huldie 5 years ago from New York, New York

      Any food usually would pull in young kids, lol!! Seriously, kids do love food so when I tried to think f motivation for certain topics this was truly was a winner. Thank you so much Glimmer Twin Fan for your lovely comments and very much do appreciate your continued support on Hubpages :)

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      Glimmer Twin Fan 5 years ago

      Another great math lesson. Loved using the pies as a teaching device. That must have pulled a lot of students in!

    • Janine Huldie profile image
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      Janine Huldie 5 years ago from New York, New York

      Oh Keith, thank you also for being so kind and saying that. Seems you are not alone in your dread of math. I only wish that I could find another full time job to teach math again. I loved it and miss the chance to make that difference. Seriously, thank you for your lovely words, it mean the world to me :)

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      KDuBarry03 5 years ago

      Now this is a great way to teach math and circles! I always dreaded math not because of the subject matter, but the teacher made it so boring! I can see that you are a fun teacher to have and hope your students feel the same way :)

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      Janine Huldie 5 years ago from New York, New York

      Myz, thank you for saying that. I have to tell you the positive feedback really makes me smile, because I know math is not of favorite of many, but did definitely try with my students to infuse the subject with interesting and innovative techniques. Thank you!!

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      IAmForbidden 5 years ago from Neverland - where children never grow up.

      whew!! very creative Janine!! even me, who hates math really love this hub

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      Janine Huldie 5 years ago from New York, New York

      Richard, you are not alone with math not being your favorite subject. I think I have heard this from others time and time again, including my husband. As always, loved your bit of humor with a square pie being a cobbler, lol :) Seriously thank you for your comment and for all your support!!

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      Janine Huldie 5 years ago from New York, New York

      Rema, thank you so much for saying math would have been your favorite subject if I had been your teacher. Thant truly is very much appreciated. Seriously thank you for all your kindness on here, it is so very much appreciated. God bless you too :)

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      Rich 5 years ago from Kentucky

      Math has never been a favorite of mine. You seem to make it much easier than when I struggled, but I have yet to see a square pie. In my day, they were called cobblers. Still, an enjoyable lesson, even though I think I gained five pounds in class today! Great Job!

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      Rema T V 5 years ago from Chennai, India

      Oh My! Janine, I am sure Math would have been my most favorite subject at school if I had a teacher like you or better still if You had been my teacher. Your hubs are great especially the Math lessons (I'm sure to repeat this sentence on your recipe hubs too lol- you seem to be master of everything) and I just loved the Cherry Pies Delicious and Apple Pies R2. Simply wonderful. Very sweet of you to offer a real pie to your students. They are truly blessed. God Bless You. Cheers, Rema.

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      Janine Huldie 5 years ago from New York, New York

      Michelle, I totally love trying new and creative ways to teach math concepts and this one is so fun and tasty too. Seriously thank you for your kind comment, support and for sharing too!!

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      Michelle Liew 5 years ago from Singapore

      Janine, Area of Circle is one of my fave maths concepts. And you've a delicious, creative way of teaching it!! From a fellow teacher, I'm sharing!

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      Janine Huldie 5 years ago from New York, New York

      Nell, very cute math joke indeed. Seriously, you sound like my husband. He too hated math, but would have loved to have become an architect (he had the art skills for it), but it was the math that kept him from pursuing that career. He always jokes that he hopes our girls get my love and knack for math. Seriously, thank you for stopping by and for your comment too. By the way, the pie would have gotten me too if I didn't love math already lol :)

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      Nell Rose 5 years ago from England

      Why couldn't you be my teacher? lol! I hated maths with a vengeance! I think it was because I missed a lot of school when I was young through illness and the teachers didn't give a jot. All the tt = rrr etc totally threw me! I always wanted to be a physicist! believe it or not, but just couldn't get the hang of maths, but pies? yep that will do me, better than Pi! haha! I made a math joke! lol!

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      Janine Huldie 5 years ago from New York, New York

      Same here with math being on of my best subjects in school, Jackie. I very much about trying to make learning easier using short cuts and things to make kids remember math topics easier. I am a firm believer in using all this and more to bring these topics home. Thank you so much again for kind words here, so very appreciated!

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      Jackie Lynnley 5 years ago from The Beautiful South

      Math was one of my best subjects and although I never had any problems I know many students did and I tutored in my sophomore year and taught the short cuts I did in my head before tackling a problem. I think anything that makes learning easier or more fun is great. Looks like you have a winner here.

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      Janine Huldie 5 years ago from New York, New York

      Yes if you were in my class, you could definitely eat the pie Terrye lol :)

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      Terrye Toombs 5 years ago from Somewhere between Heaven and Hell without a road map.

      So, after the lesson, we get to eat the pies? :)

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      Janine Huldie 5 years ago from New York, New York

      Coming for you, this compliment means the world to me. I would have so enjoyed teaching alongside you too and that would have been totally an awesome experience for me. Thank you seriously for your wonderful comment here as always so very appreciated!!

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      Bill Holland 5 years ago from Olympia, WA

      So let me get this straight....you tried to find new and creative ways to teach mundane subjects.....my goodness, Janine, you mean you cared enough about the students to do extra??? LOL You are priceless and I would have been proud to have taught alongside of you. Great lesson!