Proportion is basically a problem-solving element of multiplication and division. The term is used to refer to questions such as:

If I need 250g of flour to make 10 biscuits, how much flour will I need to make 15 biscuits?

The difficulty for the child is not usually the actual number work but the concept; they need to work out exactly what is going on and then carry out the appropriate sum. This is where a bit of preparation is crucial so that they are fully aware of what needs to be done.

In the example question there are different techniques that will help. One approach would be to work out how much flour is needed for one biscuit (divide 250g by 10 to get the amount of flour for a single biscuit). Once you have this figure you can multiply it by whatever number you like to give the amount of flour for that number of biscuits.

250g ÷ 10 = 25g (one biscuit)

25g x 15 = 375g (fifteen biscuits)

An alternative method could be to say that the difference between 10 biscuits and 15 is 5; that is half the quantity again. If we were to add half as much flour again to the 250g we'd have the amount needed for 15 biscuits.

Questions could be asked the other way round - how many biscuits could be made from 500g of flour?

This would mean you would have to work out the amount in one biscuit, then divide 500g by this amount. Alternatively, as 500g is double the 250g that we need for ten biscuits, the number of biscuits must also be doubled.

Ratio is very similar to proportion but it uses a formal notation with a colon ( : ) between the relevant figures. Ratios can be expressed in terms of two figures, for instance 2 : 1, or more, such as 3 : 2 : 5. It is unusual at KS2, but perfectly acceptable, to use decimal numbers in a ratio.

A question on ratio might look like this:

A farmer has many animals in a field. They are in the ratio of three sheep to every two cows. If there are 80 cows, how many sheep are there?

The steps to answer this question are as follows. Divide the number of cows by two as the ratio refers to TWO COWS for every three sheep. This tells us how many of the 'base units' there are. I think of a base unit as the minimum number of things needed to fulfil the ratio. There are two cows and three sheep in our 'base unit'.

Given that 80 ÷ 2 is 40, there are forty lots of two cows. There must therefore be forty of the 'base units', meaning forty lots of three sheep, or 40 x 3 = 120.

An alternative way of doing this would be to give the total number of things and a ratio, then ask for the numbers of individual elements. For example:

The ratio of red beads to yellow beads on a necklace is 3 : 5. If there are 32 beads altogether, how many are red?

Once again it's worth thinking of 'base units' here. Our base ratio is 3 : 5 so the 'base unit' contains 8 beads - 3 red and 5 yellow. If there are 32 beads altogether then it is the same as four 'base units'. Four lots of the three red beads is ( 4 x 3 ) = 12. There must be 12 red beads (and 20 yellow ones) in the necklace.