Year 6 Maths: How to Solve Ratio and Scale Problems in SATs Questions

Ratio and scale problems ask Year 6 pupils to compare amounts, enlarge or reduce measurements, and explain how quantities are connected. They can look unfamiliar in a SATs paper, especially when the question is presented as a word problem, but most rely on a small number of clear ideas. With regular practice, children can learn to spot what is being compared, choose an efficient method and check whether their answer makes sense.

What Year 6 pupils need to know

The National Curriculum for mathematics in England expects pupils in upper Key Stage 2 to solve problems involving the relative sizes of two quantities, using appropriate notation. They should recognise the relationship between fractions, decimals and percentages, and apply their knowledge of multiplication and division to a range of problems. Pupils also work with scale drawings and interpret information presented in different ways.

In practice, this means children need to understand that a ratio describes a relationship between quantities, rather than simply giving two separate numbers. In the ratio 2:3, for example, there are two equal parts of one quantity for every three equal parts of another. The actual amounts could be 2 and 3, 4 and 6, or 10 and 15; all share the same relationship.

Scale problems use a related idea. A scale drawing represents a real object or distance at a different size. A scale of 1 cm to 5 m means that each centimetre on the drawing represents five metres in real life. Pupils need to keep track of units and apply the scale consistently.

Start by identifying what the ratio compares

Before calculating, encourage your child to read the question carefully and name the quantities in order. If a recipe uses flour and sugar in the ratio 4:1, the 4 refers to flour and the 1 to sugar. Reversing the order changes the meaning, so writing labels beside the numbers can prevent a common mistake.

A useful first step is to draw a simple bar model or write the ratio with labels. For example, if red and blue counters are in the ratio 2:5, draw two equal boxes for red and five equal boxes for blue. The model makes it clear that there are seven equal parts altogether, and that blue counters make up five of those parts.

This visual approach is especially helpful when a question gives the total. If there are 28 counters altogether in the ratio 2:5, the seven parts share 28, so each part is worth 4. There are 8 red counters and 20 blue counters. Ask pupils to check by adding the answers and comparing them with the original ratio.

Use the “parts” method for sharing problems

Many SATs-style questions ask children to divide an amount in a given ratio. The reliable method is to add the ratio parts, divide the total by that number, then multiply by the parts for each quantity.

For example, two friends share £36 in the ratio 1:3. There are four parts altogether, so each part is £9. The shares are £9 and £27. This method works whether the ratio has two terms or more, provided the quantities are in the order stated in the question.

Children should notice whether the question asks for the value of each share or just one of them. Encourage them to write down the intermediate steps, especially in multi-part problems. Showing that 36 ÷ 4 = 9 makes it easier to spot and correct an error than jumping straight to an answer.

Find equivalent ratios by scaling both parts

An equivalent ratio is made by multiplying or dividing every term by the same number. If the ratio of cats to dogs is 3:4, then 6:8 and 12:16 describe the same relationship. Multiplying only one part does not preserve the ratio.

For a question such as “A drink is mixed in the ratio 2 parts cordial to 7 parts water. How much water is needed for 6 parts cordial?”, pupils can see that 2 has been multiplied by 3. They must also multiply 7 by 3, giving 21 parts water. A ratio table can help children organise these steps and is useful when the scaling factor is not immediately obvious.

Practise asking, “What has happened to the first number?” and “What must happen to the second number?” This encourages pupils to understand the relationship, rather than memorising a procedure without knowing why it works.

Solve scale questions with units in view

Scale drawings can involve length, maps, plans or models. The main challenge is often managing units, not the multiplication itself. If 1 cm represents 4 m, a drawing length of 6 cm represents 24 m. If the question gives a real distance and asks for the drawing length, pupils need to work backwards: a 20 m distance at this scale is shown as 5 cm.

Encourage children to write the units at every stage. They should check that the scale and measurement are expressed in compatible units before calculating. For example, if a scale is given in centimetres but the real distance is in metres, the question may require a conversion. A quick estimate can help: a longer real distance should usually correspond to a longer drawing measurement, while a reduced scale drawing will be smaller than the object it represents.

For more demanding problems, pupils may need to compare two measurements or use a scale factor. If a model is three times the length of a small figure, each relevant measurement must be multiplied by three. If it is reduced to one quarter of its original size, each measurement must be divided by four.

Help children interpret SATs-style wording

Ratio questions may use everyday contexts such as recipes, money, teams, paint mixtures or journeys. Scale questions may refer to maps, room plans, models or diagrams. The context can distract pupils from the maths, so encourage them to underline the information they need and identify exactly what they are asked to find.

Look out for wording such as “in the ratio”, “for every”, “share in the ratio”, “scale of” and “actual distance”. These phrases indicate different relationships. A question asking for the total number of parts is not the same as one asking for the value of one part. Likewise, a scale question may ask for the real measurement or the measurement on the drawing.

After solving, children should use an inverse check where possible. If they have shared an amount, the parts should add back to the total. If they have scaled a ratio, dividing both new terms by the same factor should recover the original ratio. For a scale drawing, applying the scale backwards should return the measurement they started with.

Build confidence through short, varied practice

A few carefully chosen questions are often more useful than a long page of repetitive calculations. Mix straightforward equivalent-ratio tasks with sharing problems and scale conversions. Once your child is comfortable, include word problems that require them to decide which method to use before calculating.

Worksheets can provide structured practice and revision, but ask your child to explain their reasoning aloud as well as record their working. A parent or teacher might ask, “How many parts are there altogether?”, “Which quantity does this number represent?” or “How could you check that answer?” These questions reveal whether a pupil understands the relationship or is relying on guesswork.

If a mistake occurs, focus on the step where the reasoning changed. Was the ratio reversed? Were the parts added incorrectly? Did a unit conversion get missed? Correcting one misconception at a time helps children feel capable and makes revision more purposeful.

A practical conclusion

Ratio and scale problems become manageable when pupils label the quantities, represent the relationship clearly and keep units visible. Encourage your Year 6 child to use bar models, ratio tables and written calculations, then check that the answer fits the question. Regular, low-pressure practice with worksheets and SATs-style problems will build both accuracy and confidence, while helping children apply their National Curriculum maths knowledge to unfamiliar situations.