Knowing all about circles including circumferences and areas used to be a Key Stage 3 topic, sometimes sneaking into Key Stage 2 but after the revamp of the National Curriculum, it’s now firmly set in KS2.

That’s all well and good but children in Key Stage 2 need to experience the learning rather than just be taught it as Key Stage 3 children might be. This is easily achieved using the fun activities detailed below.

Pi is the key to a large proportion of work on circles and by using one of the methods that was used over two thousand years ago to find it; they can enjoy the same sense of discovery.

Choose cylindrical objects of various sizes, be they food tins, paint tubs or tyres and give the children a piece of string. Ask them to use it to measure the distance around the curved part of the object and tell them this is called the circumference. Now they need to find the longest distance across the curved part of the object. This is easily done by holding one end tightly on one edge and keeping the finger loose as the other end is moved along the opposite part of the circle. When the widest part is reached, their finger will stop moving along the string. The distance their fingers are apart will be the diameter. Now, using a calculator, they should divide the circumference by the diameter and they’ll find in every case, the answer, if they’ve measured carefully, will be close to pi – 3.14.

By reversing the process, the children can find the circumference of any circle.

**Finding Pi from the Area of a Circle**

This time draw round a circular object onto 1cm squared paper and ask the children to count the whole squares inside the circle. Now match up part squares to make rough whole squares, keeping a tally of the total. Measure the distance across the centre of the circle (diameter), halve it and then multiply your answer by itself. If you divide the number of squares you counted by the answer you should also get pi.

By reversing this process, the children can calculate the area of any circle.

**Arcs**

Arcs are simply parts of a circle and the best illustration of one is a rainbow. Practise drawing arcs with a compass, reducing the distance between the point and the pencil by the same amount each time. The children will find that if they start and finish their arcs in the same places each time, the arcs will be smaller. By colouring in each space between eight arcs they can make rainbows.

**Extension Activity**

This is an old favourite where they imagine the pattern they are going to draw is the path they would follow to find water after being stranded in the desert. They’ve got to be no more than 1cm away from where they’ve already travelled, a centimetre representing their distance of vision. On the first go they are going to move in increasing quadrilateral movements; one square forward, one left, two down, two right, three up etc. Next go they draw concentric circles a centimetre apart with a single line joining all of them. The third go is harder and involves them drawing a spiral with the arm a centimetre apart all the way round. They need to find out which is the shortest way to ensure they cover all the area of the square their pattern is contained in. The quadrilateral pattern is easy to count, the circles rely on following the formulae discovered above whilst string will help find the length of the spiral. They’ll find that the spiral is almost the same length as the concentric circles pattern. If you want to extend it further, you could get the children to devise their own paths so all the square is covered.

Dave Lewis

Primary Teacher

Great ideas. Just wondering how to do it without calculators as Mr Gove doesn’t seem to agree with them at KS2?

Great ideas, I’ll try these out!

Hi JBurt. Thanks for your comment. Doing it without a calculator is reasonably easy, if not completely accurate as long as the students can estimate fractions of a unit. With the circumference activity, just count how many string diameters can be made out of the string circumference. Round your divisor up or down to the nearest whole number for the area activity or multiply both numbers until the divisor is a whole number or nearly a whole number in which case you can round it then the division should be easier on paper without a calculator.