KS2 Mathematics: Ratio, Proportion and Algebra

Almost every question in this set turns on the same habit: work out what one of something is worth before you do anything else. One part of a ratio, one biscuit's worth of butter, one pen, one centimetre on the map. Get that number and the rest follows; reach straight for the answer and you end up scaling the wrong way round or pricing eight pens instead of seven. The ten questions cover sharing an amount in a ratio and simplifying one, scaling a recipe up, working out a price from a different quantity, reading a map scale, and the algebra Year 6 actually meets: a missing number in a multiplication, a two-step one where you undo the steps backwards, a formula given in words with a fixed charge plus an hourly rate, and the tenth term of a sequence — where the trap is counting ten steps when there are only nine, because the first term is already there before any stepping starts. The last question asks for the difference between two shares rather than either share itself, which is the shape that catches pupils who have done all the work correctly and then answered the wrong question. Zestly is an independent study tool. It is not affiliated with any exam board and it is not an exam centre.

• Share an amount in a given ratio by finding the value of one part first
• Write a ratio in its simplest form and recognise an equivalent ratio that is not yet simplified
• Scale a recipe and work out a price for a different quantity by finding the unit value
• Use a map scale to turn a map distance into a real one, and know which way the multiplication goes
• Find a missing number in one step and in two, undoing the operations in reverse order
• Use a formula given in words with a fixed part and a repeated part
• Continue a sequence to a later term by counting the steps rather than the terms

A sequence begins 4, 7, 10, 13 and carries on in the same way. What is the tenth term? — 31. Getting from the first term to the tenth means taking nine steps, not ten, because the first term is already there before any stepping starts: 4 plus 9 times 3.