35 Maths Questions Year 6: SATs Reasoning Questions And Answers With Worked Examples

Maths questions in Year 6 assess pupils’ ability to apply their knowledge of key maths topics from KS2 to new and unexpected contexts. Year 6 maths questions are designed to move past mere knowledge recall, instead requiring pupils to demonstrate problem solving skills, critical thinking and reasoning.

This is why the KS2 SATs reasoning papers 6 are often a challenge for Year 6 pupils, even for classes with strong subject knowledge. Examiners are skilled at crafting questions that can confuse even the most prepared Year 6 pupil, revealing a clear gap between topic understanding and SATs readiness.

The most effective way to bridge this gap is through practice and increasing pupils’ familiarity with different SATs question types. This comprehensive collection of maths questions for Year 6 is designed by Third Space Learning’s expert team of teachers. Drawing on over 10 years’ experience preparing Year 6 pupils for the KS2 SATs through one to one tutoring and teaching resources, it provides essential practice to help you confidently prepare your class for success.

These practice SATs questions for Year 6 are based on a mix of:

• Questions from past SATs papers;
• Free Year 6 maths SATs papers;
• Collections of Year 6 reasoning questions from Third Space Learning’s Rapid Reasoning resource collection.

All questions include answers and are organised by question type to familiarise pupils with the most common question types they are likely to encounter in the KS2 SATs.

Why focus on maths SATs reasoning questions? 

The KS2 maths SATs are designed to test pupils’ knowledge and understanding of:

• Arithmetic: confidence with core calculations like addition, subtraction, multiplication, and division, including fractions, decimals, and percentages.
• Reasoning: mathematical fluency, logic and problem-solving.

In Year 6, pupils will take a total of 3 maths papers for the KS2 SATs:

• Paper 1: Arithmetic (30 minutes)
• Paper 2 & Paper 3: Reasoning (40 minutes each)

There is a greater emphasis on reasoning across the three papers, and reasoning is often considered to be more challenging than arithmetic.

As in-school maths tutoring providers, Third Space Learning works closely with primary schools and teachers across the country who consistently report that their Year 6 pupils find the reasoning papers the hardest. That’s why the Third Space Learning curriculum focuses heavily on developing pupils’ KS2 maths reasoning skills.

Our primary maths experts found that when reasoning questions were only at the end of a tutoring session, the level of challenge was too high. As a result, they restructured the SATs tutoring lessons to introduce maths reasoning earlier. This allows pupils to apply new knowledge immediately and start to embed problem solving skills gradually.

Drawing on over a decade of experience of SATs tutoring, this article provides you with a sample of the different types of KS2 SATs reasoning questions and ideas on how to teach the reasoning and problem solving skills needed to answer them.

The questions cover all major content areas from the KS2 maths curriculum:

1. Number and Place Value
2. Addition and Subtraction, Multiplication and Division (The Four Operations)
3. Fractions KS2
4. Decimals and Percentages KS2
5. Ratio KS2 and Proportion
6. Algebra KS2
7. Measurement
8. Geometry KS2

35 SATs maths questions for KS2 Year 6 SATs

There are seven types of maths reasoning questions likely to appear in the Year 6 SATs:

1. Single step worded problems
2. Multiple step worded problems
3. Problems involving measures
4. Problems involving drawing
5. Explanation questions
6. Sequence questions
7. Ordering questions

For each of these 7 question types, we’ll:

• Provide further examples taken from Third Space Learning’s Rapid Reasoning resource with worked examples and an explanation for each.
• Examine an example from a previous SATs paper: looking at the question, the correct answer, and advice on how to approach it.

For more word problems, check out this collection of 2-step and multi-step word problems and tips on how to use the bar model for maths problem solving to answer Year 6 word problems.

SATs maths question type 1: Single step worded problems

The simplest type of reasoning question Year 6 pupils are likely to encounter in the reasoning papers: single step problems. Single step problems ask pupils to interpret a written question and carry out a single mathematical step to solve it.

Have a look at the question below:

Reasoning question 1

Answer: 65p

A relatively easy question to interpret and solve in two steps:

1. Recognise that £2 and £1.35 are equivalent to 200 and 135. 
2. Subtract 200 from 135.

The most crucial skill for primary school pupils in this question is a solid understanding of money as relating to place value. If this understanding is present, the mathematical step itself is quite easy.

Below are several more examples, taken from Third Space Learning’s Rapid Reasoning resources:

Reasoning question 2

Answer: 7 hours 24 minutes

Pupils need to understand that one hour is equal to 60 minutes. From here the single mathematical step is short division: 444/60, with a remainder.

Reasoning question 3

Answer: 48 cm³

Pupils must calculate length by breadth by height, using the figures provided by the question.

Reasoning question 4

Answer: 124 cm

A simple enough calculation (doubling) if pupils are aware that the diameter is twice the radius.

Reasoning question 5

Answer: 7,590

A single, relatively simple rounding problem – pupils should recognise that ’94’ is the operative part of this figure.

SATs maths question type 2: Multiple step worded problems

Multi-step problems require Year 6 pupils to interpret a written problem, but solving it then requires the use of two or three maths skills.

For example, consider this question from the 2019 KS2 maths SATs:

Reasoning question 6

Answer: £1.85

This question encompasses three different maths skills: multiplying (and dividing) mixed numbers, addition and subtraction. Pupils can choose to work out the multiplication or division first, but must complete both before moving on.

Once these values have been worked out the next steps are relatively simple:

1. Add the two values together.
2. Subtract the total from £5.

Multi-step problems require children to apply their knowledge of maths language and their reasoning skills several times across the course of a single question, usually in slightly different contexts.

More examples:

Reasoning question 7

Answer: £5,520

There are two steps to this problem, but both are multiplications:

1. Multiply this sum by 4 – the number of days – to get to the solution.
2. Work out how much money is made per day – 92 x £15. 

Reasoning question 8

Answer: 2,160 km

Another two step problem: 

1. Multiply this by 4 to solve 40%.
2. Work out 10% of 5400 km. 

Reasoning question 9

Answer: £43.50

There are three steps involved in solving this problem: 

1. Multiplication: Double £51 and £36 to find the cost of two adult and two child tickets.
2. Addition: Put the two costs together.
3. Division: Divide the total by four to obtain the mean cost.

Given the number of steps involved it can be easy for pupils to make arithmetic mistakes, and the mark scheme accounts for this by allowing for one mistake – but no more.

Reasoning question 10

Answer: 11.45 kg

A two-step problem again: 

1. Multiply 3.45 kg by 4.
2. Subtract 2.35 kg from the total. 

As with the previous problem, the mark scheme again allows for at most one arithmetic error, assuming the method is correct.

SATs maths question type 3: Problems involving measures

These questions ask pupils to solve a problem that includes one or more units of measurement.

Take a look at this question from 2018’s Reasoning Paper 3:

Reasoning question 11

Answer: 40 washes

This is a two step problem:

1. Pupils must first be able to read and convert kilograms to grams (and therefore know the relationship between the two units).
2. Divide 2600 by 65 to work out the number of washes possible.

Measure questions are usually limited in the KS2 exam, however they are often used to test core skills like the four operations.

Further examples:

Reasoning question 12

Answer: 50g

A relatively simple division problem, relying on pupils having knowledge that 200g is one fifth of a kilogram.

Reasoning question 13

Answer: 1.1kg

Another three step problem:

1. Multiply 500 by 4 to get the total mass of the four melons.
2. Multiplying 300 by 3 to get the total mass of the remaining three melons.
3. Subtract 900 from 2000 to obtain the mass of the fourth melon.

The mark scheme allows either 1.1kg or 1,100g as acceptable answers – the units of measurement are not as important as obtaining the current figure.

Reasoning question 14

Answer: 216 cm

In this problem, the units for the answer are specified and an answer given in metres will be marked as wrong as cm is specified in the answer box. This is why it’s important to encourage pupils to check whether units are provided in the answer box.

Reasoning question 15

Answer: 170 g

As with the melon question there are three steps involved to solve this problem: 

1. Work out the mass of the four cars (4 x 80).
2. Work out the mass of the remaining three cars (3 x 50).
3. Subtract 150 from 320 to get the mass of the fourth car.

SATs maths question type 4: Problems involving drawing

Problems involving drawing require pupils to construct an accurate drawing by following a set of instructions, or through reflection, translation, or scaling.  

This type of question is quite rare, but there are some notable exceptions, such as the infamous Question 21 in Paper 2 of the 2019 Reasoning SATs:

Reasoning question 16

Answer: Any pair of lines that make a square of 4 units, a rectangle of 6 units, and a square of 25 units.

This question is considerably more complex than it appears, and incorporates aspects of multiplication as well as shapes and spatial awareness. One potential solution is to work out the area of the card (35), then work out the possible square numbers that will fit in (understanding that square numbers produce a square when drawn out as on a grid), and which then leave a single rectangle behind.

A lot of work for a single mark!

Some further examples:

Reasoning question 17

Answer: Any quadrilateral made by joining the dots that has 3 acute angles e.g. an arrowhead shape.

Reasoning question 18

Answer: An accurately drawn angle.

The mark scheme here allows some room for error – “between 34 and 36 degrees” is acceptable.

Reasoning question 19

Answer: An accurately drawn angle.

As with the question above, a small amount of room for error is given – “between 139 and 141 degrees”.

Reasoning question 20

Answer: A new triangle drawn with points at (2,1), (5,1) and (2,4).

Translation can be tricky for pupils. Encourage them to look at the triangle as three points, and to translate each point separately rather than trying to move ‘the whole triangle’.

SATs maths question type 5: Explanation questions

An early form of the ‘Prove X’ questions that come up in GCSEs, these problems ask children to explain a mathematical statement or error.

As an example:

Reasoning question 21

Answer: If the distance from P to R is 800m and the distance from P to Q is (Q -> R x 4), it must be 4/5 of 800 = 640m. Therefore Olivia is wrong.

More than most problems, this type requires pupils to actively demonstrate their reasoning skillsas well as their mathematical ones. Here, pupils must articulate either in words or, where possible, numerically that they understand that Q to R is \frac{1}{5} of the total, that therefore P to Q is \frac{4}{5} of the total distance, and then calculate what this is via division and multiplication.

Further examples from Third Space Learning’s Rapid Reasoning resources:

Reasoning question 22

Answer: No; \frac{20}{100} is the same as 20 divided by 100, which equals 0.2.

Reasoning question 23

Answer: No; multiplication and division have the same priority, so in a problem like 40 x 6 ÷2, you would carry out the multiplication first as it occurs first.

The mark scheme notes that vague answers or any answers with a mathematical error are unacceptable.

Reasoning question 24

Answer: No.

Any explanation that provides a counter-example is acceptable e.g. “Not if the number is 1”, “Not for 0” etc.

Reasoning question 25

Answer: Any answer that refers to the fact that there is a 5 in the hundreds place, AND a 9 in the thousands place, so that the number has to be rounded up as far as the ten-thousands place.

SATs Maths Question Type 6: Sequence questions

Another relatively simple kind of reasoning question, sequence problems involve pupils completing mathematical sequences.

Consider this example:

Reasoning question 26

Answer: 35, 42, 49, 56, 63, 70

Number sequence questions, particularly those that involve linear sequences or times tables, come up relatively frequently in the SATs maths tests. The question’s instructions point clearly to the solution: work out what the increase between numbers is, then apply this via addition or subtraction to find the missing numbers.

Higher attaining pupils might quickly pick up that this is in fact the 7 times table and rely on their knowledge of multiplication facts to obtain the answer. This should be encouraged, so long as they then check their answer in the normal method to ensure they haven’t made a mistake.

More examples:

Reasoning question 27

Answer(s): \frac{5}{8} and 2\frac{1}{8} (Or \frac{17}{8})

Both answers must be correct to receive the mark. Pupils must recognise that \frac{3}{4} is the same as \frac{6}{8}, so the following number must be three eighths higher.

Reasoning question 28

Answer(s): -19 and 9

Reasoning question 29

Answer(s): 128, 135 and 156.

Reasoning question 30

Answer(s): -10 and 22

This question can be a little tricky; pupils need to work out that the marks on the line represent increments of 4, and count backwards and forwards in 4s to obtain the missing numbers.

SATs maths question type 7: Ordering questions

Ordering problems require pupils to put a set of numbers, fractions or measures in the correct order.

A good example is this question from Paper 2 of the 2018 SATs:

Reasoning question 31

Answer: \frac{3}{5}, \frac{3}{4}, \frac{6}{5}

The improper fraction is a typical complication here. Look out for similar ‘curveballs’ in these questions, including equivalent fractions, mixed numbers, and combined decimals and fractions.

A good knowledge of the fundamentals of fractions is essential here: pupils must understand what a larger denominator means, and the significance of a fraction with a numerator greater than its denominator.

Further examples:

Reasoning question 32

Answer: D, C, A, B

Encourage pupils to convert all the fractions to one denominator value to make ordering easier.

Reasoning question 33

Answer: (descending down the ‘Place’ column) 3rd, 5th, 2nd, 4th

As with the example above, pupils should be encouraged to convert the fractions to make it easier to order them.

Reasoning question 34

Answer: C, B, D, A

Reasoning question 35

Answer: D, A, C, B

7 top tips for answering SATs questions

Now that we’ve covered how to answer some specific types of reasoning questions, here are some more generic tips for success in the reasoning papers. They may not all be applicable to every single question type, but will apply to at least two, usually more.

• Get pupils in the habit for any practice paper of identifying what information they’re given in a question, and what they need to know to solve the problem. This helps them start to form the steps needed to find the solution.
• Ask pupils to ‘spot the maths’ in a question – which calculations or skills do they actually need to use to solve the problem? This is useful even for arithmetic questions – it’s no surprise how often children can misread a question.
• Check the units! Especially in questions involving multiple measures, it can be easy to give the answer in the wrong one. The answer box might give a specific unit of measurement, so pupils should work to give their answer in that unit.
• Remind pupils to convert different units of measurement in a question into the same unit to make calculations easier, e.g. kg to g.
• Encourage numerical answers where possible. Even in explanation questions, demonstrating the mathematical calculation is a better explanation than trying to write it out.
• The bar model can be a useful way of visualising many different types of questions, and might make it easier to spot the ‘steps’ needed for the solution.
• Check your working out! Even if the working is ultimately irrelevant to the question, you can lose marks if it is wrong.

5 common teacher misconceptions when teaching Year 6 reasoning

Misconception 1: Pupils will automatically transfer knowledge from arithmetic to reasoning.

Fluency in Paper 1 (Arithmetic) doesn’t guarantee success in Papers 2 & 3 (Reasoning). Pupils need targeted practice in interpreting written problems to understand what maths they need to use.

Misconception 2: Reading comprehension is separate from maths.

Pupils often struggle with reasoning questions because of complex language, not lack of mathematical skill. Pupils need explicit practice in deconstructing lengthy word problems and identifying key mathematical vocabulary.

Misconception 3: All multi-step problems require different operations.

Some multi-step problems (like Reasoning Question 7) require the same operation repeated. Teachers should ensure pupils read the context to determine the structure, not just look for multiple keywords.

Misconception 4: If the unit isn’t given in the question, any unit in the answer is acceptable.

While some mark schemes are lenient (e.g., Reasoning Question 13 allows 1.1kg or 1,100g), pupils should still use the context to infer the required unit (e.g., height in cm or m) and they must check the answer box for a specified unit.

Misconception 5: Year 6 pupils no longer need manipulatives or visual models.

To tackle abstract concepts like volume and ratio, visual models act as a bridge, allowing pupils to deepen their understanding. When problem solving, using the bar model or similar visual aids provides a practical way for pupils to structure their reasoning, especially when faced with multi-step problems.

Comprehensive SATs revision resources

There are hundreds of other free SATs revision resources on the Third Space Learning Maths Hub that can you can view online, download and print, including free SATs papers and SATs intervention packs:

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Maths questions Year 6 and SATs reasoning FAQ