Year 6 Ratio and Proportion: Recipes, Sharing and Scale Drawings
Help your Year 6 child understand ratios, unequal sharing, recipes, scale drawings and percentage comparisons with original examples.
By Math School Editorial Team
What is ratio, and why does Year 6 teach it?
Ratio compares the relative amounts of two quantities. It helps us scale recipes, read drawings, mix ingredients and divide amounts into unequal shares. England's Year 6 mathematics curriculum explicitly covers relative sizes, percentages, similar shapes and unequal sharing. These topics connect multiplication and division with fractions and prepare pupils for secondary-school proportional reasoning.
The important change is from additive thinking (“add the same amount”) to multiplicative thinking (“multiply both quantities by the same factor”).
1. Read the ratio in the correct order
A box contains 4 red counters and 6 blue counters. The red-to-blue ratio is 4:6, which simplifies to 2:3. That means for every two red counters there are three blue counters.
However, the fraction of all counters that are red is 4/10 = 2/5, not 2/3. The ratio 2:3 compares red with blue, whereas the fraction 2/5 compares red with the total.
This distinction between part-to-part and part-to-whole comparisons is a frequent source of errors. Ask your child to say aloud what each number represents.
2. Scale a recipe using multiplication
A recipe uses 3 eggs for 12 muffins. How many eggs are needed for 20 muffins, assuming the recipe scales proportionally?
First, 12 ÷ 3 = 4 muffins per egg. Then 20 ÷ 4 = 5 eggs.
Alternatively, the scale factor from 12 muffins to 20 is 20/12 = 5/3. Multiply 3 eggs by 5/3 to obtain 5 eggs.
Check: 3:12 = 1:4 and 5:20 = 1:4.
A common error is to add eight eggs because the number of muffins increases by eight. That would give eleven eggs, which does not preserve the original relationship. Proportional scaling uses the same multiplier, not the same addition.
3. Share £84 in the ratio 2:5
Two siblings share £84 in the ratio 2:5. How much does each receive?
There are 2 + 5 = 7 equal parts. One part is £84 ÷ 7 = £12.
The first sibling receives 2 × £12 = £24. The second receives 5 × £12 = £60.
Check both conditions: £24 + £60 = £84, and 24:60 = 2:5.
A bar model is especially helpful. Draw two equal-sized boxes for the first sibling and five for the second. All seven boxes represent the total. The boxes have equal value, but the two shares are unequal.
4. Interpret a scale drawing
On a simple drawing, 1 cm represents 3 m. A path measures 8 cm on the drawing. Its real length is 8 × 3 = 24 m. Working backwards, a real path of 15 m would be 15 ÷ 3 = 5 cm on the drawing.
Always write units. If a map gives a scale such as 1:1000, the quantities must first be expressed in consistent units. A scale factor for length does not automatically give the same scale factor for area.
5. Compare percentages and actual numbers
At one school, 30% of 120 pupils choose football. At another, 25% of 160 pupils choose football.
First school: 0.30 × 120 = 36 pupils. Second school: 0.25 × 160 = 40 pupils.
The first school has the larger percentage, but the second has the larger number. This is why percentages should be interpreted alongside group sizes. Ask: “Which proportion is greater?” and “Which number of pupils is greater?”
6. Not every relationship is proportional
A taxi charges a £4 fixed fee plus £2 per kilometre. A 2 km trip costs £8, while a 4 km trip costs £12.
Distance doubles, but cost does not: £12 is not twice £8. The fixed charge means total cost is not directly proportional to distance. This contrasts with the recipe, where doubling all ingredient quantities doubles the intended yield under the proportional model.
Recognising when a relationship is not proportional is as valuable as calculating a ratio.
Four original practice questions
Q1: Fifteen pencils are shared in the ratio 3:2. How many does each person receive?
Answer: Five parts, each worth three pencils. Shares are 9 and 6.
Q2: Six biscuits need 150 g of flour. How much for ten biscuits?
Answer: 150 ÷ 6 = 25 g per biscuit, so 250 g.
Q3: A drawing uses 1 cm for 4 km. How far does 7 cm represent?
Answer: 28 km.
Q4: Find 20% of 85.
Answer: 10% is 8.5, so 20% is 17.
A ten-minute practice routine for parents
Use counters for two minutes to describe part-to-part and part-to-whole comparisons. Spend three minutes scaling a recipe, three minutes drawing equal-part bars for sharing, and two minutes comparing percentages from different-sized groups.
When your child makes a mistake, identify whether the difficulty comes from multiplication facts, ratio order, finding the total number of parts, or understanding scaling. Each needs a different explanation.
Official source: Department for Education — National curriculum in England: mathematics programmes of study, Year 6 “Ratio and proportion”.
