Engaging students: Finding the circumference of a circle

In my capstone class for future secondary math teachers, I ask my students to come up with ideas for engaging their students with different topics in the secondary mathematics curriculum. In other words, the point of the assignment was not to devise a full-blown lesson plan on this topic. Instead, I asked my students to think about three different ways of getting their students interested in the topic in the first place.

I plan to share some of the best of these ideas on this blog (after asking my students’ permission, of course).

This student submission comes from my former student Jaeda Ransom. Her topic, from Geometry: finding the circumference of a circle.

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How can technology (YouTube, Khan Academy [khanacademy.org], Vi Hart, Geometers Sketchpad, graphing calculators, etc.) be used to effectively engage students with this topic?

Games are a great way to engage students and use technology at once. This online circumference memory game is an engaging way for students to practice their circumference solving skills. Students can work by themselves or with a partner. They have to find the circumference of different circles, 6 to be exact, and then play a memory matching game. The game is cute and adds a little fun to their extra practice. The link to the game: http://www.algebra4children.com/Games/Circumference/Circumference.html

Another great tool is an online circle tool from illuminations. It is already prepped for use and only has 3 functions, an introduction screen, investigation, and practice problems. Students can work independently or with a partner to solve the problems, it also has finding the area of a circle practice problems and investigations as well. The link to the tool: https://www.nctm.org/Classroom-Resources/Illuminations/Interactives/Circle-Tool/

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How could you as a teacher create an activity or project that involves your topic?

An activity that would be great for this topic would be a scavenger hunt. This activity involves the students to go around the school premises and find circular objects, measure the diameter or radius of the circular object and record the object, measurements, and location on their paper. Students would work in pairs and the materials needed would be a ruler, pen/ pencil, clipboard, and long piece of yarn (for students who find circular objects bigger than a ruler/ meter stick). Once the pairs have found the most circular objects with their given measurements in the 8 minutes received for the hunt, students will come back to class and do the calculations using the formula. After calculations are complete the pair with the most objects and completed calculations is the winner of the scavenger hunt. Students will then work with another pair and discuss similar objects found and compare calculations. Students will also be encouraged to discuss why their calculations might have differed or some plausible errors.

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What interesting things can you say about the people who contributed to the discovery and/or the development of this topic?

Evidence of historic use of perimeter and circumference goes back to the ancient Egyptians and Babylonians at around 1800 B.C.E. But, Archimedes is credited to be the first one to formally discover pi in 240 B.C.E. Archimedes is known to be the greatest mathematician to live. Though people did not know much about his life, he was known for many things including the inventor of superweapons such as ‘death ray’ and ‘giant claw’.  Another interesting fact is that Eratosthenes was the first one to discover the circumference of the earth. The circumference of the earth was said to be found sometime between 276 and 195 B.C.E. For Eratosthenes to find the circumference of the entire earth without the resources and technology we have to date now is very impressive. Unfortunately, Eratosthenes’ method to calculate the Earth’s circumference has been lost; and what has been preserved is a simplified version by Cleomedes which helped popularize the discovery.

References:

https://ideagalaxyteacher.com/area-and-circumference-activities/

https://study.com/academy/lesson/circumference-of-a-circle-activities.html

https://www.historyanswers.co.uk/ancient/the-life-of-an-ancient-egyptian-priest-explained/

https://sciencing.com/origins-perimeter-circumference-7815683.html

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