Year 6 maths reasoning: how the papers work and how to answer

England's key stage 2 maths test at a glance

Source: Standards and Testing Agency, key stage 2 mathematics test framework; GOV.UK, scaled scores at key stage 2. Schools in the Gulf are not part of England's statutory tests but many use papers in this format.

What 'reasoning' means in these papers

Reasoning questions test whether a child can choose and use the maths, not just carry it out. Expect multi-step problems, questions with missing numbers or shapes, simple formulae and pairs of unknowns, ratio and scaling, reading tables and graphs, and questions that ask a child to explain, show or prove. The test framework allows partial marks for correct working on some questions where the final answer is wrong, so showing working matters.

Calculators are not on the equipment list; children need a pencil, ruler, protractor and mirror. That means efficient written methods and secure times tables are what make the reasoning papers manageable in the time.

Worked example 1: an 'explain' question

Sami says 0.6 is smaller than 0.45 because 6 is smaller than 45. Explain why he is wrong.

1. A good answer uses place value, not just 'because it is bigger'.
2. Write both with two decimal places: 0.6 = 0.60. Then 60 hundredths is more than 45 hundredths.
3. Or: 0.6 has 6 tenths and 0.45 has only 4 tenths, so 0.6 is bigger.
4. Marks come from a reason a reader can check. 'Because 0.6 is bigger' earns nothing; '0.6 is 6 tenths but 0.45 is 4 tenths and 5 hundredths' does.

Worked example 2: two unknowns

a + b = 20 and a - b = 6. Find a and b.

1. Two numbers add to 20 and differ by 6.
2. Take the difference away from the total: 20 - 6 = 14. That is two lots of the smaller number, so b = 7.
3. Then a = 7 + 6 = 13.
4. Check: 13 + 7 = 20 and 13 - 7 = 6. Both are true.

Worked example 3: ratio and percentages

(a) A recipe uses 3 eggs for every 200 g of flour. How much flour is needed with 9 eggs? (b) Find 35% of 240.

1. (a) 9 eggs is 3 times as many as 3 eggs, so use 3 times the flour: 3 × 200 = 600 g.
2. (b) Build from 10%: 10% of 240 = 24, so 30% = 72.
3. 5% is half of 10%: 12.
4. 35% = 30% + 5% = 72 + 12 = 84.

Worked example 4: area of a compound shape

A rectangle 12 cm by 8 cm has a 3 cm by 3 cm square cut from one corner. What is the area of the shape that is left?

1. Area of the full rectangle: 12 × 8 = 96 cm².
2. Area of the square removed: 3 × 3 = 9 cm².
3. Area left: 96 - 9 = 87 cm².
4. Watch the units: area is in square centimetres. Writing 87 cm instead of 87 cm² can lose the mark.

Common mistakes

• Leaving answer boxes empty. Correct working can still earn a partial mark on some questions, and a sensible attempt costs nothing.
• Answering part of a multi-step question and stopping.
• Explanations that restate the answer instead of giving a reason.
• Misreading scales on graphs and measuring instruments.
• Forgetting units, or giving cm when the question asks for m.
• Spending too long on one hard question. Every question in a paper is worth trying, so move on and come back.

How one-to-one lessons help in Year 6

A tutor starts with a reasoning paper under timed conditions and marks it with your child, sorting lost marks into three kinds: not knowing the maths, misreading the question, and running out of time. Each kind needs a different fix. Gaps in content are taught directly; misreading is tackled with the read, draw, estimate routine; timing improves with practice on short sets. Your child explains their reasoning aloud on the shared whiteboard, which is exactly the skill the 'explain' questions reward. A lesson or two a week in the months before the Year 6 assessments is a common pattern.

Self-check

• Order from smallest: 0.7, 0.65, 0.072. (0.072, 0.65, 0.7)
• y = 3x + 4. What is y when x = 5? (19)
• A map uses 1 cm for 5 km. Two towns are 7 cm apart on the map. How far apart are they? (35 km)
• The mean of 4, 7, 9 and 12 is? (8)
• Explain why every multiple of 6 is also a multiple of 3.