KS2 Maths Paper 2: Reasoning (SATs Practice)
The reasoning papers put the arithmetic inside problems, so the difficulty is in deciding what to calculate rather than in the calculation itself. They cover word problems with several steps, measures and unit conversion, time, money, shape and angles, position and direction, perimeter, area and volume, ratio and proportion, scaling, averages, and reading information from tables, bar charts, pie charts and line graphs. Marks are usually split, with a mark for a correct method and a mark for the answer, which is why showing working matters more on the reasoning papers than on the arithmetic paper. Explanation questions appear too, where a child has to say WHY an answer is right or where someone has gone wrong.
Before you start
Make sure you're comfortable with these topics first:
Method
- Read the question twice. On the second read, underline the numbers, the units and the words that say what to find.
- Decide what the question is asking before touching the numbers, and write down the calculation you are going to do. For a multi-step problem, write the steps in order first.
- Draw something whenever it would help: a bar model for a ratio or fraction problem, a quick sketch for a shape problem, or a table for information given in prose.
- Watch the units. Convert everything into the same unit before calculating, and check whether the answer must be in a different unit from the numbers in the question.
- Show your working for every step, since method marks are awarded for a correct approach even when the arithmetic slips.
- Check the answer in context at the end: an answer of 3.5 buses, or a perimeter smaller than one of the sides, means something is wrong. For explanation questions, write a full sentence naming the reason, not just a number.
Worked example
A rectangular garden is 12 m long and 7 m wide. A path 1 m wide runs all the way around the INSIDE edge of the garden. What is the area of the grass left in the middle?
- Sketch the garden and mark the path around the inside edge, so the grass is a smaller rectangle in the middle.
- The path takes 1 m off each side, so it takes 2 m off the total length and 2 m off the total width.
- Find the dimensions of the grass: length = 12 - 2 = 10 m, and width = 7 - 2 = 5 m.
- Find the area of the grass: 10 x 5 = 50 square metres.
- Check by another route: the whole garden is 12 x 7 = 84 square metres, so the path covers 84 - 50 = 34 square metres, which is a believable amount for a 1 m path around a garden that size.
- Answer with the unit: the area of grass is 50 square metres.
Practice questions
Type your answer and press Check to be marked straight away, or reveal the answer and mark yourself.
Q1A train leaves at 14:35 and arrives at 16:10. How long is the journey?Show answer
Answer: 1 hour 35 minutes.
Q2Convert 3.4 kilometres into metres.Show answer
Answer: 3400 m.
Q3Sweets are shared between Ali and Ben in the ratio 2 to 3. There are 45 sweets. How many does Ben get?Show answer
Answer: There are 5 parts, so one part is 9. Ben gets 3 parts, which is 27 sweets.
Q4A rectangle has perimeter 30 cm and length 9 cm. Find its width.Show answer
Answer: The two lengths total 18 cm, leaving 12 cm for the two widths, so the width is 6 cm.
Q5Find the mean of 4, 7, 9 and 12.Show answer
Answer: The total is 32, and 32 divided by 4 = 8.
Q6Why is a bar model useful for a ratio problem?Show answer
Answer: It shows how many equal parts there are and which parts belong to whom, so the value of one part can be found and then scaled.
Q7A question asks you to explain why an answer is wrong. What must your answer include?Show answer
Answer: The specific mistake made, written as a sentence, rather than just the correct answer.
Exam-style questions
Written in the style of a KS1 and KS2 SATs exam paper, with a full mark scheme.
A shop sells pencils in packs of 12 for 2.40 pounds and singly for 25p each. Mrs Kaur needs 40 pencils and wants to spend as little as possible. Work out the cheapest total cost, showing your working.
Show mark scheme
Tick each line you got. Your score builds from the marks on the scheme.
Nothing ticked yet - 4 available
Josh says: 'A shape with four equal sides must be a square.' Explain why Josh is wrong.
Show mark scheme
Tick each line you got. Your score builds from the marks on the scheme.
Nothing ticked yet - 2 available
Free printable worksheet
Want more practice on paper? Download the ks2 maths paper 2: reasoning (sats practice) worksheet pack - 8 pages of exam-style questions with a full mark scheme. One email opens every download in this browser for 14 days - no account, no card. Print it for personal and classroom use.
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