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Teaching Circumference and Diameter of a Circle

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I am a former maths teacher and owner of DoingMaths. I love writing about maths, its applications, and fun mathematical facts.

Circumference of a Circle Worksheet

Circumference of a circle worksheet

Circumference of a circle worksheet

Circumference of a circle lesson

Introducing a class to circle circumferences and pi is an opportunity for some great hands-on investigation skills. In this lens, I want to share some ideas that I use when teaching this topic.

For this lesson, you will need the worksheet (which can be found below), string (a piece of about 30-40 cm for each student), rulers and calculators.

Start to the lesson

At the beginning of the lesson, have the worksheets and rulers (you can find a link below) out on the desks as the pupils walk in. Pupils can then immediately start measuring the diameters of the circles and recording their answers in the table on the sheet.

I find this to be a great way to start the lesson; it gets the class in, settled and occupied straight away, and hopefully gets them thinking about where the lesson will proceed when they have finished with the diameters.

Circumference and Diameter Worksheet

Circumference and diameter worksheet

Circumference and diameter worksheet

Continuing the worksheet

The circumference of the circles is going to be measured using string. Demonstrate to the class how to do this by drawing a circle on the board and looping a piece of string around it. This is easier said than done on a vertical whiteboard, but this gives a great opportunity to show the class how to measure by holding the string in place with one finger, wrapping around a part of the circle, then holding it down further round the circle and removing the first finger. Keep going on round the circle until you get back to your starting point again.

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Pinch the string at the point where you returned to the starting point and then hold the string against a ruler to measure the length.

Don't pull the string too tight or it will stretch and you will end up with a measurement longer than it should be.

The class now need to measure the circles for themselves and continue to fill in the table. Once finished, each pupil needs to divide the circumference by the diameter for each circle (using a calculator) and fill in the remaining column with their answers.

After the worksheet

Once the students have finished filling in the table, ask them to think about the results that they have found. If they have measured accurately, they should find that all of the answers in their third column are roughly 3.1. Even with slightly dodgy measuring, they should still be somewhere in the range of 2.8-3.4. Once the class have realised this, introduce them to the idea of pi and how, if you were to measure any circle, of any size, to perfect accuracy and divide circumference by diameter, you will get the number pi = 3.14159...

By a quick bit of formula rearranging, you can then introduce how to find the circumference of any circle, once you have measured the diameter. (Use the formulae circumference = pi x diameter).

If you have time once this part of the lesson is finished, give the class some quick questions where they need to find the circumference of some circles. If not, save these questions for next lesson.

Have you used this lesson? Was it successful? What variations did you make? Have your say here.

© 2014 David

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