# Sample Maths SATs Questions and Answers: Reasoning

Table of Contents

## Introduction

The second part in our series on Maths SATS questions and answers, this post looks at the Reasoning part of the exam. Alongside our sample SATs arithmetic questions, these examples can be used to help your child prepare for their Maths SATs tests.

The following examples have been chosen to provide a general overview of the types of reasoning questions that your child may come across on exam day. We’ve also included sample answers and full explanations to help you understand what the examiners are looking for. All questions are taken from the most recent tests, which were administered this year.

**Maths SATs Reasoning Sample Question 1**

The SATs reasoning papers are designed to test a child’s ability to apply their understanding of all areas of mathematics. They also aim to test their ability to select relevant information and present answers in a correct context. The question above expects the student to be able to add and subtract numbers in the thousands, once they have recognised that there are two stages to the question. They should show their working out as a mark may be awarded for doing so, even if the answer provided is incorrect.

In most cases, it’s usually the student’s inability to extract the key information that results in them giving an incorrect answer for this type of question.

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**Maths SATs Reasoning Sample Question 2**

This question focuses on equivalent fractions. Children may easily recognise 3 | 4 when the shape is divided into four equal parts and three are shaded. What they should also recognise, is that six out of eight, nine out of twelve and twelve out of sixteen all have the same value as three out of four. They should also recognise that those shaded sections do not necessarily need to be next to each other.

One thing to watch out for here is the shape in the top right-hand corner – although three sections are shaded, it is three out of six, not three out of four.

**Maths SATs Reasoning Sample Question 3**

This question is a straightforward test of the student’s understanding of the language of geometry. ‘Faces’ are the flat surfaces that make up a three-dimensional shape, and ‘vertices’ are the points where two or more edges meet. If that knowledge is secure, this is a fairly straightforward question!

**Maths SATs Reasoning Sample Question 4**

This is a question about scale and proportion. Again, it is a multi-step question. The child should first recognise that 1cm on a map represents 20km. They should then demonstrate evidence of an appropriate method, such as 250 ÷ 20 to achieve an answer of 12.5cm.

Other indications that the child has understood what the question is asking of them may include the following: 20km is 1cm, 100km is 5cm, 50km is 2.5cm. 5cm + 5cm + 2.5cm = 12.5cm. Once again, showing the method is important, as it may achieve a mark even if the answer is incorrect. It’s worth noting however, that a correct answer provided without any method would achieve the full two marks.

**Maths SATs Reasoning Sample Question 5**

The ability to extract information from charts and graphs is an important skill, and one area that many children find extremely difficult. This may have something to do with the way the data is presented and could also link to how relevant the information is to the child. This example is all to do with temperature changes over a period of time. Although many children may understand the concept, it isn’t perhaps a daily feature of a Year 6 child’s life.

There is a lot of information here, with the two axes showing the time and change in temperature. The expectation is that the student can pinpoint the temperature at certain times during the period shown, and use the data they identify to answer the questions.

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**Maths SATs Reasoning Sample Question 6**

This is another example of a question set in context, although this time using a timetable. Although children will be taught how to read timetables accurately, this question not only relies on their ability to read the timings, but also their ability to make a decision based on factors.

William needs to arrive in Paris by 5.30pm and therefore the 14.01 train is the latest he should take. The potential stumbling block here would be if the child cannot translate times between twelve hours and twenty-four hours – although the question is asked using ‘pm’ the timetable is written using the twenty-four-hour clock.

**Maths SATs Reasoning Sample Question 7**

This is perhaps one of the most difficult questions in both reasoning papers. It relies on the child’s ability to manipulate numbers and, in actual fact, use algebraic equations to solve a problem.

If the child recognises that 18 + 9 + 2 widths = 34 + 1 width, or that 27 + 2 widths = 34 + 1 width (or even that 27 + 1 width = 34), then they should be able to conclude that 34 – 27 = 7, which is the width of one tile. In effect, they are using algebra: 34 + w = 18 + w + 9 + w or 34 + w = 27 + w + w.

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