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35 SATs Maths Questions And Answers With Worked Examples: Essential Maths Reasoning Practice For Year 6 [FREE]

Anantha Anilkumar

For Year 6, the toughest of their SATs maths questions are the reasoning questions. 

No matter how good pupils’ subject knowledge is or how effective your SATs revision lessons are, the examiners always manage to come up with maths questions that can baffle and flummox even the hardiest year 6 pupil.

To mitigate against this for SATs 2024 your pupils need plenty of exam practice and more specifically exam question practice to be familiar with both the types of SATs reasoning questions that can come up and the skills needed to answer them.

So to make life easy for you we’ve put together here a comprehensive collection of 35 SATs maths questions, organised by the sorts of question that pupils can expect to encounter.

All these practice SATs questions have been based on a mix of questions from past SATs papers , our own free year 6 maths SATs papers , and our collections of year 6 reasoning questions from the Rapid Reasoning resource collection. The answers are all taken from the answer sheets we provide for each test paper.

Other useful SATs revision resources

Before we get into the year 6 maths questions you might find it helpful to know that we have hundreds of other free KS2 SATs revision resources, including free SATs papers , and SATs intervention packs for those wanting to use the Year 6 SATs revision lessons we use in one to one tutoring in their own boosters.

You should also make sure you’re up to date with the latest analysis on the 20 most ‘valuable’ topics to study for SATs this year and also this analysis of the KS2 SATs Maths Papers Question Breakdown in 2023 .

You may also wish to read this guide to SATs first to give you some background information about the tests.

Why the focus on maths reasoning questions for SATs? 

Ever since the new national curriculum Key Stage 2 SATs in 2016, the emphasis in the all SATs papers has been very much on SATs reasoning questions. While there is one arithmetic paper, there are two reasoning papers; and the variety, breadth and level of challenge in the reasoning paper continues to impress us.

Most Year 6 pupils find the reasoning SATs maths questions the hardest part of these maths papers. Unsurprisingly! We teach thousands of pupils every week in the run up to SATs, and teaching them maths reasoning skills at KS2 is a big part of what we do.

We even recently took the decision to restructure our SATs lessons to introduce maths reasoning questions earlier in the learning journey as the level of challenge just at the end of the lesson was too high. So we feel the Year 6 teacher’s pain!

Whatever level pupils go on to perform at in maths, maths reasoning questions and numerical reasoning tests (such as those used by grammar and private schools) are likely to be a part of the practice they require.

If you find you have children in your class with much further to catch-up than the others then we we would be happy to support them with some personalised online one to one maths tuition .

35 SATs maths questions for KS2 year 6 SATs

For the KS2 SATs tests, there are 7 types of maths reasoning question that are likely to come up:

• Single step worded problems
• Multiple step worded problems
• Problems involving measures
• Problems involving drawing
• Explanation questions
• Sequence questions
• Ordering questions

For each of these types we’ll examine an example SATs maths question from a previous SATs paper, looking at the question, the correct answer, and how to go about answering this question.

We’ll also look at further examples of each type of maths reasoning questions and answers from Third Space’s Rapid Reasoning resource, again with worked examples and an explanation of how to answer each.

Finally, at the end of this article we provide links to further Year 6 maths questions, assessments and other SATs papers that you may find useful including plenty of arithmetic practice too.

Our aim is to provide you as part of your SATs practice with a sample of the types of KS2 SATs questions pupils can expect in the reasoning papers and how to teach the reasoning and problem solving  skills they’ll need to answer them.

For more word problems like this, check out our collection of 2-step and multi-step word problems for you as well as tips on how to use the bar model to answer Year 6 word problems . For advice on how to teach children to solve problems like this, check out these maths problem solving strategies.

SATs Maths Question Type 1: Single step worded problems

The simplest type of reasoning question pupils are likely to encounter in the reasoning papers, single step problems are exactly that: pupils are asked 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 – the first step is to recognise £2 and £1.35 as equivalent to 200 and 135. From here the simple mathematical step is subtraction i.e. 200-135=65.

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 cm 3

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

A more complex version of the single step worded problem, multi-step problems require 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 – adding the two values together, and subtracting the total from £5.

Multi-step problems are particularly valuable to include in practice tests because they 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. The first is to work out how much money is made per day – 92 x £15. This sum is then multiplied by 4 – the number of days – to get to the solution.

Reasoning Question 8

Answer : 2,160 km

Another two step problem. The first step is to work out 10% of 5400 km. Then multiply this by 4 to solve 40%.

Reasoning Question 9

Answer : £43.50

There are three steps involved in solving this problem: multiplication (doubling £51 and £36 to find the cost of two adult and two child tickets), addition (putting the two costs together) and division (dividing 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.

Read more: Mean median mode

Reasoning question 10.

Answer : 11.45 kg

A two-step problem again: multiplying 3.45 kg by 4, then subtracting 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.

Year 6 Rapid Reasoning (Weeks 1-6)

Download 6 weeks of Rapid Reasoning slides for your Year 6 pupils and help them get a head start on preparing for the SATs reasoning papers.

SATs Maths Question Type 3: Problems involving measures

As their name suggests, 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 1 1

Answer: 40 washes

This is a two step problem; pupils must first be able to read and convert kilograms to grams (and therefore know the relationship between the two units), then divide 2600 by 65 to work out the number of washes possible.

Questions involving measures tend to be few in number in the KS2 exam papers, but they often provide an excellent way to couch key maths skills such as 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 – multiplying 500 by 4 to get the total mass of the four melons, multiplying 300 by 3 to get the total mass of the remaining three melons, and then subtracting 2000 from 900 to obtain the mass of the fourth melon.

It’s worth noting that 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 : 216cm

Interesting to note that in this problem (unlike the previous example), the units for the answer are specified – an answer given in metres will be marked as wrong, since cm is specified in the answer box. This is why we encourage pupils to keep an eye on whether units are provided in the answer box.

Reasoning Question 15

Answer : 170g

As with the melon question there are three steps involved to solve this problem: working out the mass of the four cars (4 x 80), working out the mass of the remaining three cars (3 x 50) and subtracting 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 1 6

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 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

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 skills  as well as their mathematical ones. Here pupils must articulate either in words or (where possible) numerically that they understand that Q to R is 1/5 of the total, that therefore P to Q is 4/5 of the total distance, and then calculate what this is via division and multiplication.

Further examples from TSL’s Rapid Reasoning resources:

Reasoning Question 22

Answer : No; 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 (as in this case) 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.

Reasoning Question 2 7

Answer(s) : 5/8 and 2 1/8 (OR 17/8)

Both answers must be correct to receive the mark. Pupils must recognise that 3/4 is the same as 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

A slightly more complex variation of the sequence question, 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: 3/5, 3/4, 6/5

This question throws a stick in the wheels by including an improper fraction, but this is hardly unusual. These sorts of questions are just the place to find other ‘curveballs’ such as equivalent fractions, mixed numbers and decimals and fractions combined.

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.

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.
• In a similar vein, 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.

More free SATs questions (all with answers)

• 75 KS2 SATs maths questions Reasoning and Arithmetic practice questions by topic – includes fractions, decimals, percentages; place value; addition and subtraction.
• 250+ SATs questions
• Year 6 algebra questions
• Year 6 arithmetic questions
• Year 6 ratio questions
• Year 6 fractions questions
• Free year 6 maths test

If you’re looking for even more free and premium maths resources join 80,000 teachers using the resources in the Third Space Learning Mathshub (free to sign up).

Online 1-to-1 maths lessons trusted by schools and teachers Every week Third Space Learning’s maths specialist tutors support thousands of pupils across hundreds of schools with weekly online 1-to-1 lessons and  maths interventions  designed to plug gaps and boost progress. Since 2013 we’ve helped over 80,000 primary and secondary school pupils become more confident, able mathematicians.  Learn more  or  request a personalised quote  to speak to us about your school’s needs and how we can help.

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Since 2013 these personalised one to 1 lessons have helped over 150,000 primary and secondary students become more confident, able mathematicians.

Learn about the SATs revision programme or request a personalised quote from your school to speak to us about your school’s needs and how we can help.

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FREE KS2 Maths SATs Practice Papers (Set of 6)

Get ready for KS2 SATs tests with this set of 6 maths SATs practice papers.

Includes 2 Arithmetic and 4 Reasoning Papers, with mark schemes and answer booklets, that follow the National Curriculum Assessments.

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Free SAT Practice Questions

Doesn't everyone love the word "free"? This could not be truer—especially in the world of test prep. Practice makes perfect—or at least that's how the old saying goes—and free SAT practice means the world to ambitious students with high-scoring goals. If you're looking for a thorough breakdown of how to solve particular SAT question types, then we've got the free practice that could be a real game-changer in your course of study. Our step-by-step explanations illustrate for you what to expect from what each SAT question, revealing question-specific hurdles and common test-related traps.

Each of our free 60 practice questions is accompanied with a detailed explanation to clarify why a particular answer is correct, but even taking it one step further and entailing why the others are incorrect. We believe a well-rounded approach to understanding the SAT is crucial for success, which is why our breakdowns of important sample questions facilitate more than one way to arrive at the right choice. In the end, the only way to find out your trouble spots and successes is to practice, practice, practice—so why not get cracking on what we have to offer so you can ensure your destiny with a high score.

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1 . Question

What percentage does 90 represent in relation to 360?

2 . Question

7 added to 4 times a quantity y is equal to 62. Which equation represents this condition?

• a. 7(4y) = 62
• b. 7 – 4y = 62
• c. 7 + 4y = 62
• d. 4y – 7 = 62

3 . Question

For a cost of $57, how many pounds of avocados were bought at a rate of $19 per pound?

4 . Question

The table displays three sets of values for x and their corresponding f(x) values for a linear function f. What equation accurately represents the definition of f(x)?

• a. f(x) = 6x + 65
• b. f(x) = 8x + 65
• c. f(x) = 65x + 73
• d. f(x) = 73x + 81

5 . Question

If \frac{x}{15}=20 , what is the value of \frac{15}{x} ?

6 . Question

What is the equation that defines line p in the xy-plane, given that it passes through the point (-4, 6) and has a slope of 6?

• a. y = 6x + 30
• b. y = 6x – 30
• c. y = 6 + 30x
• d. y = 6x – 30x

7 . Question

2.5b + 5r = 80

The provided equation expresses the connection between the quantity of biscuits (b) and raisins (r) that a reviewer business can handle in a single day. If the business is tending to 16 raisins on a specific day, what is the capacity for biscuits that it can manage on the same day?

8 . Question

In a specific rectangular area, the length-to-width ratio is 45 : 15. If the width of the region grows by 8 units, how should the length be adjusted to uphold this ratio?

• a. It must decrease by 24.5 units.
• b. It must increase by 24.5 units.
• c. It must decrease by 24 units.
• d. It must increase by 24 units.

9 . Question

In a circle with center O, the arc XY measures 105°. What is the degree measure of the angle XOY that corresponds to this arc?

10 . Question

In a right triangle, the side lengths are 3\sqrt3 , 2\sqrt3 ,and \sqrt{70} units. What is the area of the triangle in square units?

*Enter in just the number for your answer.

All SAT Practice Tests

If you want some more in-depth prep, use a free SAT practice test listed below.

• Practice Exams = Timed and Full-Length
• Practice Sets = Not Timed and Smaller Sets of Questions

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SAT Math Practice Sets

SAT Reading & Writing Practice Sets

If you want some additional help with prepping for the SAT, consider using  SAT prep courses .

Official SAT PDF Practice Exams

If you want to study using PDFs, use the links below. These are full-length practice exams provided by the CollegeBoard.

Overview of the SAT

The SAT is an entrance exam used by colleges and universities to help make decisions about admissions.

The SAT is administered by the CollegeBoard and is given 7 times per year. The exam is a timed, mainly multiple-choice exam, taken by students in high school.

Beginning in the spring of 2024, the SAT will be going fully digital. The digital SAT (DSAT) will have some formatting and content changes to it, along with some other changes. You can review those changes below.

New SAT (Digital SAT)

This exam will be given to students starting in spring of 2024.

Old SAT (Written Exam)

This exam will be given to students up until spring of 2024.

The biggest difference between the old SAT and the digital SAT is that the digital SAT is taken completely online and has combined some sections to streamline the exam.

Scoring of the SAT

You will receive a score for math and a score for reading/writing. Each of those scores will be between 200 and 800 .

Your total score will be the sum of those two scores. You can receive a total score between 400 and 1600 on the SAT.

The average SAT score is 1060. Learn more about good SAT scores .

Registering for the SAT and Test Dates

You can register for the SAT online via the CollegeBoard site .

You will need to do the following when registering for the SAT:

• Have a Valid Photo ID
• Upload a Photo of Yourself When Registering Online
• Pay Registration Fees
• Print Your Admission Ticket

It will cost your $60 to take the SAT. There may be some additional fees like canceling, changing test center, etc..

The SAT is typically given 7 times per year. The exam is given on Saturdays. You can expect the exam to be given in these months:

• Early March
• Late August
• Early October
• Early November
• Early December

You can find exact dates on the official website .

Steps for Using SAT Practice

When using our free SAT practice tests, we recommend the following steps to get the most out of your time:

• Take 1 practice exam from each subject.
• Determine which subject you struggled the most with.
• Focus on that 1 subject moving forward. Take additional practice exams in that subject, study important concepts, and invest in a SAT prep course if need be.
• Take a practice exam on that subject again and see where you stand. Continue to focus on that subject if you need more help or move on to another subject if you did well on this practice exam.
• Repeat steps 3 and 4 for other subjects.

Benefits of Using SAT Practice Questions

There are many benefits to using SAT questions during your prep process. Some of those benefits include:

Help With Timing

The SAT exam is a timed test. Keeping a steady pace is critical to achieving a high score.

You can improve your decision making and your time by taking practice exams.

Test Familiarity

All standardized tests, including the SAT, have their own unique way of presenting questions and answer choices.

You will gain more familiarity and comfort with the SAT question style as you take more practice quizzes. On the real exam day, there will be no surprises.

Efficient Studying

When you take many practice exams, you will get a sense of your test strengths and weaknesses.

Many students mistakenly spend time working on their strengths while ignoring their weaknesses.

Knowing which subjects you struggle with will help you focus your study time.

Work On Problem Solving

Tests like the SAT measure your ability to solve problems, not just memorize information. It is critical to have strong problem-solving abilities.

The answer explanations provided in our score reports can help you understand how to solve problems that you may be struggling with.

Frequently Asked Questions

When is the sat going to the digital format.

The SAT will be switching to the digital format in the spring of 2024.

How many questions are on the SAT?

There are 154 questions on the old SAT (written version).

There are 98 questions on the new SAT (digital version).

How much time do you have to take the SAT?

You will have 3 hours and 15 minutes to take the old SAT (written version).

You will have 2 hours and 14 minutes to take the new SAT (digital version).

Can I use a calculator on the math section of the SAT?

There will be 1 math section in which you can use a calculator and 1 math section in which you cannot use a calculator on the old SAT (written version).

You will be permitted to use a calculator on all math modules on the new SAT (digital version).

What is a good way to practice for the SAT?

We recommend taking 1 practice exam for each subject. You can then determine which subject gave you the most trouble and focus your studies on that subject.

• Authored By: Adam Groden
• Last Updated: January 19, 2024

Year 6 Maths SATs Past Papers and Solutions

On this page you will find all the past papers and solutions for the maths SATs papers that students in the UK sit in Year 6 (age 10 and 11). I hope they are useful to anyone revising for or teaching this exam. 

Even if you are not a primary school teacher/student, these are incredibly useful for those in secondary education. They give a great insight into the level of work students have covered at primary school, and are a great source for extra questions

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Help your child succeed in their SATs

The sats paper guide - free advice and help for the sats.

• KS1 Year 2 SATS PAPERS
• KS2 Year 6 SATs
• Level 6 SATs Papers
• Phonics Screening Test
• SATS PREPARATION GUIDES & BOOKS
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• SATs Information
• SATs Papers Forum
• Contents of KS1 English SATS Tests
• Contents of KS1 Maths SATS Test

Maths Reasoning Worksheet and Explanation

We’ve structured this information to help children with their education. It is targeted at children in years 5 and 6 and the questions for the worksheet have been stripped from past papers. Having an understanding of maths reasoning is part of the primary school curriculum and children will deal with maths reasoning in both KS1 and KS2.

The Information below will give an overview of the topic and we have included a detailed worksheet with full answers. The worksheet includes 30 maths reasoning questions and is relevant for KS2 pupils approaching their SATS test.

Download Free Maths Reasoning Worksheet – Questions

Download free maths reasoning worksheet – answers.

If you are not ready to download the worksheets yet, then read on for some information about maths reasoning. This has provided to introduce the topics covered in the worksheet for those that might be unfamiliar but also as a quick revision tool for those that would like a quick refresher before accessing the worksheet.

Maths Reasoning Explained

The purpose of maths reasoning.

Reasoning allows us to make sense of the world around is and problems we might face on a day-to-day basis. Maths reasoning is part of this ability and helps us to use maths in meaningful ways and in applied settings. The question sheet uses examples that we might come across in everyday life where we need to use our maths skills to make an informed decision, such as the correct train to catch or how much money I will have remaining after I have been to the shops.

How do I Develop my Maths Reasoning?

Maths reasoning is dependent on the core skills learnt in the primary curriculum and is essentially utilising these in applied scenarios. In order to improve your maths reasoning skills, it is therefore important that you continue to develop your core skills. It is also important that students are able to explain their maths reasoning using the correct terminology wherever possible.

Where Maths Reasoning is Used?

As mentioned above reasoning is something we use every day, usually without thinking. These groups describe most of the situations where we will most likely be using our maths reasoning skills:

• The first encounter of a new challenge
• When a range of starting locations are possible
• When there is missing information
• When selecting a problem-solving skill
• When evaluating a solution in context
• When there is more than one solution
• When logical and critical thinking are required
• When there are multiple ways of solving a problem
• The basis for mathematical proof

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SATs (Year-6) Maths Questions By Topics

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KS2 Maths (Problem Solving)

Subject: Mathematics

Age range: 7-11

Resource type: Worksheet/Activity

Last updated

16 January 2019

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These topic-focused SATs questions at the end of a unit will help to test and extend students’ understanding as well as helping them to prepare for SATs next year. These questions have fully-worked solutions which can be displayed on a whiteboard making feedback with students more efficient. Click 👉 tes.com/…/KS2-Maths-Questions… for similar-style compilations on the other KS2 topics. <hr> This particular compilation is mainly from the ALGEBRA strand and contains questions which require students us problem solving techniques . In the solutions, I have often used algebraic notation to show how an answer has been obtained, but most of the solutions actually use logic rather than formal algebraic methods. <hr> I have designed this compilation to be printed as an A4 or A5 booklet which is in the style of the actual SATs papers and is convenient for use in class or as homework. It can even be given to individual students if a parent is asking for ‘some more work’!

KEY POINTS:

• I have provided full answers, with comments and working where helpful.
• I have maintained the style of the actual SATs questions so that students can become comfortable with the way that SATs questions are presented.
• Most of the questions are from actual SATs papers, but I have also added questions so that this resource matches the requirements the current curriculum better than the older resources that are still in common use (note that many of the older resources of this type contain questions on topics which are no longer examined).
• I have spent a lot of time arranging the questions so that there is a general increase in difficulty as students work through them, and so that they fit on the pages better – this means less wasted space and significant paper-saving when printing 😃 <hr> 👍If you like this resource, then please rate it and/or leave a comment💬. If the rate-resource button on this page doesn’t work, then go to your ratings page by clicking 👉 www.tes.com/…/rate-resources…

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Thank you so much for putting the time and effort into all of your resources - so helpful.

Absolutely fabulous, exactly what I needed to help my son at home now. Thank you sooo much!!

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SATs Resources and Worksheets

About these resources.

Assessments written with SATs style questions and papers for primary teachers of Year 6 children. Fluency, reasoning and problem solving questions for maths, as well as arithmetic papers . All SATs subjects and question styles are covered, including grammar, punctuation and spelling papers , and reading . SATs questions are mapped to the SATs sample paper, as well as past papers, to give your children the opportunity to practice specific question styles in bulk.

Arithmetic SATs Practice Resources & Worksheets

Grammar, punctuation and spelling sats practice resources & worksheets, key stage 2 boost timetable, reading sats practice resources & worksheets, reasoning sats practice resources & worksheets.

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