To calculate the radius of each rainbow, we halved the diameter. We used the part-part-whole method to help with our halving.

## Resources

- 3 hoops: Grimms concentric circles
- 2 lollipop sticks
- Base Ten blocks

Some of our rainbows:

## Method

Ioan set up the rings as he had done previously for the part-part-whole method. It can demonstrate the relationship between a number (whole) and it’s components (parts). To work out the radius, we took our measurement for the diameter then halved it, or split it into two equal parts.

Ioan explained to Finn that, “Radius is half of diameter,” then went on to work out the radius:

He worked it back to check that his radius of 13cm, was half of the diameter (26cm).

The diameter was an even number and easy to halve. I asked Ioan what the problem would be if he needed to halve an odd number:

The diameter of Ioan’s water colour rainbow was an easy one, he knew half of 20 was 10.

After watching Ioan’s previous examples, Finn worked out the radius of his paint stick rainbow independently.

We had saved the largest rainbow until last. I went upstairs to put Cian down for a nap and came back to find the tray set out in first image below. I asked Ioan to explain all his working out, step by step:

- He knew 100 was made up of 2 lots of 50.
- He knew 10 was 5 + 5.
- The number 7 was trickier because it was an odd number, so he had set it out as 3 + 3 + 1. He drew round a ‘one’ and cut it in half to make two halves.

Finn found the term ‘2 lots of 50’ confusing, especially with so many steps involved in halving 117. I asked Ioan if he could think of another way of explaining what ‘2 lots of 50’ meant. He suggested 50+50.

This video was Ioan explaining his working out to Finn:

## DfES Outcomes for EYFS and National Curriculum (2013)

### Numeracy Year 1 programme of study

#### Number – measurements

- compare, describe and solve practical problems for lengths and heights
- measure and begin to record lengths and heights

#### Number – fractions

- recognise, find and name a half as one of two equal parts of an object, shape or quantity

### Numeracy Year 6 programme of study

#### Geometry – properties of shapes

- illustrate and name parts of circles, including radius, diameter and circumference and know that the diameter is twice the radius