150 Mental Maths Questions And Answers For Year 3 to Year 6
If you’re like most teachers, you have an almost unending appetite for mental maths questions that you can bring out at any time of day for some rapid recall and mental maths practice.
Whether it’s adding three numbers or rapid recall of multiplication and maths facts, as a primary school teacher it always helps to have a bank of mental maths questions and teaching resources available at your fingertips.
We’ve brought together an easy to use powerpoint of 150+ mental maths problems. Here’s a sample of what to expect and some mental maths questions for you to get started on with your pupils right away.
- Mental maths for primary school
- Why introduce mental maths?
- Choosing between mental and written methods
- The Ultimate Mental Maths Pack: 150 mental maths questions
- Addition and subtraction questions
- Multiplication and division questions
- BIDMAS questions
- Money questions
- The perfect resource for improving mental maths in KS1 and 2
Mental maths for primary school
When discussing mental maths, the focus is not only recalling facts quickly but also applying known facts. A pupil may be able to recall number bonds to ten, for example, but they also need to know how to apply this knowledge to a question they are solving.
Mental maths should be introduced once pupils have a secure understanding of the abstract maths concept of numbers and security in key facts (see our blog on mental maths strategies for more).
At Third Space Learning, we understand the importance of mental maths in the mathematics curriculum. During our online maths tuition lessons, tutors start with a quick warm up question that usually involves mental maths. This helps them to gauge the pupil’s understanding of a topic, or just as an icebreaker activity. Our tutors understand that some questions are best solved using mental strategies and encourage pupils to verbalise their mental strategies in the problem solving.
The Ultimate Mental Maths Pack
Download free our Ultimate Mental Maths Pack containing over 150 mental maths questions for Years 1-6
Why introduce mental maths?
Some questions can be solved far quicker using mental strategies compared to written strategies. Mental maths is also essential in everyday life; consider how much more difficult it would be to calculate monetary totals in real life without the ability to quickly add approximate totals mentally.
When tackling more complex mathematical problems, such as multi-step problems or order of operations calculations, using mental strategies to solve parts of the calculation can also reduce the perceived complexity of the task, making it far more manageable.
However, it is important that pupils understand that completing calculations mentally is not always the best strategy. They need to become adept at analysing a calculation to decide if it is best to complete it using a mental or a written strategy.
In arithmetic tests, many pupils will take a long time using written methods when they could find the correct answer mentally. If a question is best solved using mental methods, pupils then need to select the most efficient method to solve the given calculation. This may seem a lot for pupils to grasp, which is why regularly practising mental maths tasks is important.
Choosing between mental and written methods
When introducing mental methods, we recommend drawing the pupils’ attention to the most efficient method they could use for a question, and then explaining why in that case, it is the best choice.
Third Space Learning’s Fluent in Five resource focuses on arithmetic questions for key stage 1 and 2 (in slides and/ or SATs style printable worksheet form). For each question, we give guidance on whether it should be solved using a written or mental arithmetic method. These suggestions can lead to interesting discussion with pupils around the method they use and why it is efficient. If you haven’t yet downloaded the free version of this resource – 6 weeks of daily arithmetic questions for Years 1 to 6 – we recommend doing so now.
While a question might suggest using a mental method, an inefficient method could confuse the pupil and take them far longer than necessary to solve. If when adding 9 to a number, for example, the pupil counts in ones instead of adding 10 and adjusting, they are using an inefficient and slow method.
By encouraging discussion around different methods, pupils will not only be exposed to a range of methods, they will also develop their verbal reasoning skills. Additionally, by exposing pupils to a range of mental maths skills and methods they will develop their understanding that the most efficient method for one calculation may not be the most efficient method for the next. Daily questions and mental maths games are a great way to introduce more mental maths into your classroom.
The Ultimate Mental Maths Pack: 150 mental maths questions
Third Space Learning has developed a set of 150 mental maths questions – The Ultimate Mental Maths Pack – to facilitate mental maths teaching. The pack includes an editable PowerPoint with a wide variety of mental maths questions appropriate for KS1 and KS2.
The Ultimate Mental Maths Pack aims to strengthen children’s mental maths skills by encouraging them to think about different methods for maths problem solving. The pack includes answers as well as key questions to ask pupils to deepen their understanding and spark conversation about different strategies in mental maths. A break down of the resource is as follows:
- Addition and subtraction – Slides 3 to 20
- Times Tables – Slides 21 to 24
- Multiplying and dividing by 10 (and multiples of 10) – Slides 25 to 37
- Multiplying and dividing by 100 (and related calculations) – Slides 38 to 50
- Multiplying to make 100 – Slide 51
- Multiplying three numbers – Slides 52 to 58
- BODMAS/BIDMAS – Slides 59 and 62
- Money (including rounding, adding and subtracting) – Slides 63 to 77
We’ve organised the mental maths questions in the PowerPoint to gradually increase in difficulty. When there are multiple questions on a page, they have generally been designed so there is a connection between the questions. This connection will help pupils find and check their answers.
The questions have also been clearly grouped into different topics so that you can easily navigate to the type of question you are looking for. Within the PowerPoint, we have also included notes that identify the relevant content domain for the question and any key questions that could be asked when tackling the given question(s). Below are some examples of the mental maths questions you’ll find – for the full 150+, download the attached PowerPoint to use in class.
Addition and subtraction questions
In this section we will start with some basic number bonds questions then move on to addition, subtraction and then combined addition and subtraction questions.
Mental maths questions: number bonds example
Pupils should learn number bonds within 20 in Year 1. This should then become part of their rapid recall and enable them to complete related calculations easily in subsequent years.
If pupils know 3 + 7 = 10, they should recognise that 70 and 30 are ten times larger than 3 and 7, therefore the answer should be 10 times larger than 10.
Year 2 children are expected to add three one-digit numbers. With question d, pupils should look for number bonds first. If they can see that 7 + 3 = 10, solving the rest of the calculation becomes much easier. When solving this calculation, it is essential that pupils understand that addition is commutative.
Mental maths questions: addition and subtraction example
There are several different mental strategies that can be used for addition and subtraction, depending on the question pupils are answering.
With the question above, the suggestion is to find the nearest multiple of 10 and adjust. Subtracting 30 from 55 is far easier than subtracting 29. This method relies on pupils understanding that subtracting 30 and adding 1 is the same as subtracting 29.
An alternative method is to count on to find the difference. This method involves starting from 29 and counting on in ones and tens until you reach 55. Some pupils may struggle with this method as they may not understand the meaning of ‘difference’ and the ways of finding the difference. They may also not understand the relationship between addition and subtraction.
Until pupils are confident with a range of different methods and explaining their method, it is often useful to provide them with a range of concrete and pictorial representations. Eventually, these can be removed and pupils can work with the abstract concepts alone, as is exemplified with the second question. Pupils should be able to use the information gained in the first question to help them solve the second question.
To solve this calculation, pupils could use their rapid recall of number bonds to 10 and 100. They could also use the inverse operation to calculate 100 subtract 60 = ?. An alternative method is to count on in tens from 60 to 100. Some pupils might use their fingers to help them keep track of their process while others might imagine a number line.
Mental maths questions: addition and subtraction decimals example
Adding decimals mentally can be difficult. This is the type of question where estimating, using whole numbers and jottings can be helpful. By estimating the answer first, pupils will get a good idea of what their answer should be. If, when finding the exact answer, the two are vastly different, pupils will know they have made a mistake. This does rely on pupils understanding how to estimate accurately.
When finding the exact answer, pupils could use number bonds, partitioning and jotting to help them. For example, adding the pence first and identifying that 3p + 7p = 10p then adding the 10p to 90p to make £1. Without jottings, such as crossing off digits, writing 10p etc, they may become confused as to what they have added.
Multiplication and division questions
In this section we look at times table questions and multiplying three numbers together, before moving on to multiplying and dividing by 10 and 100.
Mental maths questions: times tables example
By the end of Year 4, pupils are expected to know all the times tables up to 12 x 12. If pupils are not yet confident with all of their times tables, there are methods they can use to help them mentally calculate the answer.
With the nine times tables, they can calculate the answer to the associated ten times table and subtract one lot of the multiplier. For example for 3 x 9, pupils can complete 3 x 10 – 3. Another method to solve this calculation is to count in multiples of 3 or 9, although this method may not be the most efficient or accurate.
To solve the division calculations, pupils may find it easier to complete the inverse, for example 72 ÷ 9 is the same as 9 x ? = 72. They can then use a multiplication method to find the answer.
Mental maths questions: multiplying and dividing by 10 (and multiples of 10)
Multiplying and dividing by 10 and 100 can cause some confusion with pupils. When completing these calculations mentally, encourage pupils to avoid thinking they are adding or subtracting zeros as this will embed misconceptions.
When multiplying by 10 mentally, there are several methods pupils could use. When multiplying a one-digit number by 10, they may be able to recall the answer (e.g. 8 x 10). They could also count in tens, although this method could be inaccurate. Pupils could also imagine a place value grid and mentally move the digits one column to the left. This method would also work for multiplying two-digit numbers by 10.
When dividing by 10, pupils could also use the method of imagining a place value grid and moving the digits one place to the right. If the pupil is confident multiplying by 10 using different methods, they could also use their understanding of inverse operations to find the answer. If, for example, they struggle with 30 ÷ 10, they could instead complete ? x 10 = 30.
When multiplying by a multiple of 10, pupils can partition the multiple of ten to make the calculation easier to solve. In this example, the pupil could partition 40 into 10 x 4. This makes the calculation far easier to solve as they can multiply 4 by 5, then multiply the product by 10.
Mental maths questions: multiplying and dividing by 100 (and related calculations)
The methods pupils will have developed when multiplying by 10 can be applied to multiplying by 100. Another method that can be used is multiplying the multiplier by 10 then multiplying the product by 10. This would rely on the pupil understanding that x 10 x 10 is the same as x 100.
When dividing by 100, the methods are similar to dividing by 10. Pupils could imagine a place value grid and move the digits two places to the right. They could also use the inverse operation if they are more comfortable with multiplying by 100, or to simply check their answers. Similarly to multiplying by 100, pupils could also divide the dividend by 10 then divide the quotient by 10.
Mental maths questions: multiplying three numbers
A question involving multiplying three numbers may look intimidating at first, however, when pupils use their known number facts, they become far easier to solve.
When completing 2 x 4 x 5, pupils could identify that 2 x 5 = 10 and multiply this by 4 or complete 4 x 5 and multiply the product by 2. By identifying easier calculations to multiply, they can find more manageable numbers to work with. There are times where pupils may struggle with this. For example, with the second question, if pupils first complete 9 x 2 = 18, they may then struggle to answer 5 x 18.
In this section we look at order of operations and recalling number facts.
Mental maths questions: oder of operations
With questions involving the order of operations, rapid recall of number facts becomes very useful. While we have set out all the steps pupils would take to complete the calculations, they could use jottings to help them.
In this calculation, pupils can quickly recall the product of 5 and 5 then subtract 3 from this, which has then significantly simplified the calculation. A quick jotting of 22 would then allow the pupil to solve 4 cubed without forgetting their previous answer.
In this section we look at real life uses for mental calculations.
Mental maths questions: word problem example
This real world word problem is a good example of when mental calculations are used in everyday life. First, pupils will need to decide how they are rounding (the answer shows rounding to the nearest £1). They can then add the rounded numbers mentally. These numbers are fairly easy to add as one is a multiple of 100, one is a multiple of 10 and one is a one-digit number. This sum can then be compared to the amount he has in his bank.
The perfect resource for improving mental maths in KS1 and 2
The example questions above provide only a brief overview of the mental maths questions on offer in our Ultimate Mental Maths Pack. Download the resource for the full selection of 150+ questions and watch your pupils’ mental maths capabilities grow as they explore and discuss a wide range of mathematical methods and how and when to deploy them.
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