Year 6 maths · Key Stage 2 · Ratio and proportion

Year 6 ratio, proportion and percentages: a guide for parents

Ratio and proportion is a new strand that first appears in Year 6. Children compare the sizes of two quantities, use multiplication and division to find missing values, calculate percentages of amounts, enlarge shapes using a scale factor, and share amounts unequally. Underneath, it is all about multiplicative thinking: keeping the relationship between quantities the same as the numbers get bigger or smaller.

Ratio, percentages and scale factors, explained

A ratio compares two quantities. A recipe that needs 3 spoonfuls of flour for every egg is in the ratio 1 egg to 3 spoonfuls of flour, written 1 : 3. If the recipe uses 4 eggs, the flour is 4 × 3 = 12 spoonfuls. Children find missing values by multiplying or dividing both quantities by the same whole number, often using a ratio table. Schools may introduce the a : b notation, and many also keep to phrases like “for every”.

Proportion describes a part in relation to the whole, using fractions or percentages. If 3/5 of a class are boys, then 2/5 are girls, and in a class of 30 there are 18 boys and 12 girls. Ratio and proportion are different ways to say related things: the ratio of boys to girls is 3 : 2, while the proportion of boys is 3 out of 5. Many problems use both, so children practise saying which one a question is asking for.

Percentages come from fractions out of 100. To find 15% of 360, children work out 10% by dividing by 10 (36), 5% by halving that (18) and add them to get 54. They also use 50%, 25% and 1% to build up other amounts. Percentages allow fair comparison: 18 correct out of 24 is 75%, while 30 correct out of 50 is 60%, so the first score is better even though the second has more marks. Percentages and 360° link up in pie charts, where 25% is a quarter turn, 90°.

Similar shapes are the same shape in a different size, with all lengths multiplied by the same scale factor and all angles unchanged. A triangle with sides of 3 cm, 4 cm and 5 cm enlarged by a scale factor of 3 has sides of 9 cm, 12 cm and 15 cm. Children also work backwards, finding the scale factor by dividing one length by its matching length. Maps, models and photographs follow the same idea.

Unequal sharing and grouping brings fractions and multiples together. To share 48 sweets in the ratio 3 : 5, add the parts (3 + 5 = 8), find the value of one part (48 ÷ 8 = 6), then multiply. Children see it first as a bar of equal pieces. This is where times tables and fractions of amounts, such as finding 5/8 of 48, pay off. In Year 6 the numbers are usually chosen so that every step uses whole-number multiplication and division facts and works out neatly.

Words your child will hear

Ratio: A comparison of the size of two quantities, such as 1 : 3 for 1 egg to every 3 spoonfuls of flour.
Proportion: A part compared with the whole, such as 3 out of 5, 3/5 or 60%.
Percentage: A number out of 100, written with the % sign. 15% means 15 out of every 100.
Scale factor: The number each length is multiplied by when a shape is enlarged.
Similar shapes: Shapes with the same angles and with matching lengths all multiplied by the same scale factor.
For every: The phrase used to describe a ratio, as in “for every 2 red counters there are 3 blue ones”.
Part: One share in a ratio problem. In a 3 : 5 ratio there are 8 equal parts in all.

What the National Curriculum says

In Year 6, pupils should be taught to:

Solve problems involving the relative sizes of 2 quantities where missing values can be found by using integer multiplication and division facts
Solve problems involving the calculation of percentages [for example, of measures and such as 15% of 360] and the use of percentages for comparison
Solve problems involving similar shapes where the scale factor is known or can be found
Solve problems involving unequal sharing and grouping using knowledge of fractions and multiples

Objectives from the National Curriculum in England, © Crown copyright, used under the Open Government Licence v3.0.

A worked example

Mia and Tom share 48 sweets. For every 3 sweets Mia gets, Tom gets 5. How many sweets does each of them get?

Think of the sweets in equal groups. Mia’s share is 3 parts and Tom’s share is 5 parts. Draw a bar split into 3 + 5 = 8 equal parts.
Mia 3 of 8 parts
All 8 parts together are 48 sweets, so one part is 48 ÷ 8 = 6 sweets.
Mia has 3 parts: 3 × 6 = 18 sweets. Tom has 5 parts: 5 × 6 = 30 sweets.
Check: 18 + 30 = 48, so no sweets are missing. And Tom has more than Mia, which fits with 5 parts to her 3. Also 18 = 3 × 6 and 30 = 5 × 6, so the shares really are in the ratio 3 : 5.

Mia gets 18 sweets and Tom gets 30 sweets.

Common mistakes and how to help

Adding instead of multiplying to scale a recipe or ratio

A recipe for 2 people uses 4 eggs and 6 spoonfuls of flour. To make it for 5 people, a child adds 3 to everything, getting 7 eggs and 9 spoonfuls, because adding feels like “making more”.

What helps: Find what one person needs by dividing by 2 (2 eggs and 3 spoonfuls), then multiply by 5: 10 eggs and 15 spoonfuls. Test the answer: there should still be 2 eggs for every 3 spoonfuls of flour, and 7 eggs to 9 spoonfuls breaks that. A ratio table with “÷ 2” and “× 5” arrows helps.

Reading the ratio 1 : 3 as “one third”

The numbers 1 and 3 are in the ratio, so it is natural to think of 1/3. But the whole is 1 + 3 = 4 parts, so the part is 1/4.

What helps: Always draw the bar and count the total number of parts. For 1 : 3 there are four boxes and one is shaded. Compare it with “1 out of 3”, which really is a third.

Adding the same length to each side when enlarging a shape

To enlarge a 2 cm by 3 cm rectangle “by 2”, the child makes it 4 cm by 5 cm, which looks stretched, not enlarged.

What helps: A scale factor means multiplying. The rectangle becomes 4 cm by 6 cm. Ask the child to draw both on squared paper and see that the sides keep their relationship. The 4 cm by 5 cm shape is a different shape altogether.

Comparing raw scores instead of percentages

30 out of 50 and 18 out of 24 are compared by looking at 30 and 18, so the larger number seems to win.

What helps: Convert to the same scale. 18/24 is 3/4 or 75%, and 30/50 is 60/100 or 60%. Using “out of 100” makes any two results comparable.

How to help at home

Scale a recipe up or down. Choose a simple recipe and work out the amounts for twice as many or half as many people. Then ask what the ratio of flour to sugar is. Your child multiplies or divides every amount by the same number. The cooking should be adult-supervised.
Percentages in the shops. When you see “10% off” or “25% off”, ask your child to find the saving on a sensible price. Using 10%, 50% and 25% as building blocks (for example 15% = 10% + 5%) matches how it is taught.
Mix a drink by ratio. Mix squash with water in a ratio like 1 : 4. How much squash is needed for 500 ml of drink? The drink is 5 parts, so each part is 100 ml: 100 ml of squash and 400 ml of water. Using real measuring jugs makes the parts easy to see.
Draw and enlarge. On squared paper, draw a simple shape such as a house outline and then redraw it with every length doubled or tripled. Measure the angles of both: they stay the same. This is a good way to see a scale factor.
Spot ratios in everyday life. Ask questions like “For every 2 red cars, there are 3 blue ones. If there are 10 red cars, how many blue?” or use a class, a team or a pack of cards. Making up your own ratio puzzles is as good as solving them.

Leads on to

Key Stage 3: Units, scale and fractions of quantities
Key Stage 3: Ratio and sharing in a ratio
Key Stage 3: Percentage change, proportion, compound units

Everything in Year 6 maths

Updated 20 October 2026.