Multiplicative relationships in circles

I can recognise that there is a constant multiplicative relationship (π) between the diameter and circumference of a circle.

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Year 8

Multiplicative relationships in circles

I can recognise that there is a constant multiplicative relationship (π) between the diameter and circumference of a circle.

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Share activities with pupils

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Lesson details

Key learning points

There is a multiplicative relationship between the radius and diameter of a circle.
The ratio between the diameter and circumference of a circle is always the same.
That ratio is called π and it is an irrational number.
The formula for the circumference of a circle is C = πd.
Using the definition of the diameter you can also write this as C = 2πr.

Keywords

Diameter - The diameter of a circle is any line segment that starts and ends on the edge of the circle and passes through the centre.
Radius - The radius of a circle is any line segment that joins the centre of a circle to its edge.
Circumference - The circumference of a circle is the perimeter of the circle.

Common misconception

Pupils may think that the π symbol represents a variable, similar to letters such as r and d.

Reiterate the difference between variables and constants. Explain that while the radius may differ between circles, π is always the same.

Pupils can re-enact the practical demonstration wrapping string around a cylindrical object, cutting it to the length of the circumference and then checking if the string is just over three times the diameter for their object too.