Ratio and Proportion
Ratio and proportion is brand new in Year 6, and it is one of the ideas children lean on most when they reach secondary school. Here they learn to write and simplify a ratio, and to use a fraction to describe how big one quantity is compared with another. None of it is as daunting as it sounds once it feels like sharing something real rather than shuffling numbers.
Practise Ratio and Proportion
Have a guess, even if you're not sure. Get one wrong and we'll show you why, so every miss is a chance to learn.
Timed practice
The same practice, just with a gentle clock. Pick a length and see how many you can answer.
Good to know
Sharing in a ratio
To share in a ratio, the bar splits into that many equal parts. Here 20 pounds is split in the ratio 2 to 3, which is 5 equal parts of 4 pounds.
20 pounds shared in the ratio 2 to 3 (2 + 3 = 5 parts of 4 pounds)
For grown-ups
Year 6 ratio work centres on sharing an amount unequally in a given ratio and on the unitary method, where you find the value of one part first and then multiply, which is exactly how a recipe is scaled up or down. Children also compare quantities using percentages, and work out the missing measurements of similar shapes that have been enlarged by a known scale factor. This is proportional reasoning, the thinking that sits under so much of secondary maths, from algebra to scale drawings, so a calm, confident start in Year 6 makes the move to Year 7 far smoother.
What is in this topic
- Writing and simplifying ratios
- Using a fraction to compare the size of two quantities
- Sharing an amount unequally in a given ratio
- The unitary method, and scaling recipes up and down
- Comparing quantities using percentages
- Similar shapes by a whole-number scale factor
How to help at home
Ratio clicks when it feels like sharing something real, not shuffling numbers. Reach for jugs, coins and recipes at home, and let your child say each step out loud so the reasoning, not just the answer, becomes the habit.
- Anchor every ratio in real sharing first. To split 20 pounds between two children in the ratio 2:3, add the parts to find the shares (2 + 3 = 5), find one share (20 divided by 5 = 4 pounds), then hand out 2 shares and 3 shares: 8 pounds and 12 pounds.
- Practise the unitary method on recipes, scaling both up and down. If 6 fairy cakes need 300g of flour, find one cake first (300 divided by 6 = 50g), then multiply for any batch: 9 cakes need 9 x 50 = 450g.
- Turn ratios into fractions out loud to compare two quantities. In a 2:3 mix there are 5 parts in total, so the first quantity is 2/5 of the whole and the second is 3/5: say 'two fifths and three fifths' to check they add back to one whole.
- Simplify ratios the same way you simplify fractions, by dividing both sides by a common factor. For 12:18, both numbers divide by 6, so 12:18 becomes 2:3.
Where children get stuck
The most common slip is sharing the amount into the wrong number of parts, often dividing by one of the ratio numbers (here 2 or 3) instead of by the total. The fix is to make adding the parts the very first move, every single time: for 20 pounds in the ratio 2:3, write 2 + 3 = 5 before touching anything else, then divide 20 by 5 to find one share is 4 pounds. No division happens until the total number of shares is on the page.
The other frequent wobble is with similar shapes: children sometimes add to the lengths instead of multiplying by the scale factor. If a shape is enlarged by a scale factor of 3, a 4cm side does not become 4 + 3 = 7cm, it becomes 4 x 3 = 12cm. Ask 'how many times bigger, not how much bigger?' so they reach for multiplication, and check by confirming every side has grown by the same number of times.