# Year 5 Mental Maths: Consolidating Known Number Facts And Introducing New Concepts

By Year 5 mental maths, children will have already taken their multiplication tests (administered in the summer term of Year 4) so we should expect them to know their times tables off by heart with a reasonable degree of fluency.

It is still worth informally assessing times tables early in the year to pick up those children who struggled or have learning loss from the long summer holidays. It is also important to check the understanding behind the fluency of multiplication table recall. If they have learnt them by rote but struggle with the actual mental arithmetic, this is an important time to unpick any misconceptions before moving forward into the Upper Key Stage 2 mathematics content.

Mental maths tests do not need to be formal at this stage but planning should be systematic at the start of the year to enable some sort of gap analysis of the cohort.

Concepts introduced in Year 5, plus the larger numbers expected in Years 5 and 6, rely on solid foundations.

### What the national curriculum says about Year 5 mental maths

In Upper Key Stage 2 “The principal focus of mathematics teaching in upper key stage 2 is to ensure that pupils extend their understanding of the number system and place value to include larger integers. This should develop the connections that pupils make between multiplication and division with fractions, decimals, percentages and ratios. At this stage, pupils should develop their ability to solve a wider range of problems, including increasingly complex properties of numbers and arithmetic, and problems demanding efficient written and mental methods of calculation.”

Fluent in Five Years 1-6 (Weeks 1-6)

Download this free resource pack of daily maths questions for KS1 and KS2. Help cement your class' mental maths knowledge with these practice questions

Together with the 1-12 x multiplication, division facts and basic addition facts, children should be able to answer the following Year 5 mental maths questions:

• Addition and subtraction of multiples of 10 (e.g. 60 + 40= 100, 40 + 70 = 110, 30 + 40 = 70)
• Addition and subtraction of multiples of 100 (e.g. 200 + 500 = 700, 300 + 700 = 1,000, 800 + 600 = 1,400)
• Addition and subtraction of multiples of 1000 (e.g. 4000 + 5000 = 9000)
• Double and halves of multiples of 10 to 100 (e.g. double 70 = 140, half 40 = 20)
• Quadruples (x4) of all numbers to 10 (e.g. 7 x 4 = 28)
• Multiplying two-digit number by 10 (e.g. 34 x 10 = 340)
• Halves of any number up to 100 (e.g. half of 24 = 12, half of 51 = 25.5)
• Multiplying and dividing any number by 10 and 100 (e.g. 24 x 100 = 2,400, 45 ÷ 100 = 0.45, 3.4 x 10 = 34)
• Multiplication of multiples of 10 and 100 based on known facts (e.g. 40 x 40 = 1,600)
• Squares of all number up to 12
• And cubes of 2,3,4 and 5

#### Year 5 mental maths: place value

In year 5 pupils will be expected to know place value going into decimal places, and into much higher numbers. A firm understanding of the place value, helped by some interactive practice using manipulatives and activities, will ensure pupils are ready to apply this knowledge to a range of methods such as long multiplication and long division.

For maths practice and consolidation, place value games can form a good part of recap at the beginning of KS2 maths lessons.

#### Year 5 mental maths: addition and subtraction

As they use bigger numbers in their addition and subtraction, often going higher than 4 digit numbers, children will be consolidating their skills with columnar methods of addition and subtraction.

Physical resources and pictorials may still be used to help children to gain a more solid understanding of the numbers they are dealing with and the methods to both work out and check their answers.

Ideally, pupils are gaining confidence in maths and are able to choose the operations to apply to word problems and explain their reasoning. Pupils will start to solve more complex problems related to real world scenarios, and this should include discussion, as well as written methods alongside application of their mental maths skills.

Pupils will also be getting used to numbers and operations being missing or replaced with symbols – this will lay the groundwork for algebra in Year 6.

#### Year 5 mental maths: multiplication and division

By Year 5 pupils should be confident in their understanding of division as the inverse of multiplication and be able to apply their known multiplication tables to problems involving division.

Most children will now be able to move on to division questions where the answer includes a remainder rather than simply whole numbers. However, some students may require a little extra support to gain understanding of these new concepts.

Third Space Learning’s one-to-one online interventions are designed to give students that little bit of extra assistance. We aim to build confidence and fluency in maths and help children to reach their target level.

Low stakes maths activities and practice questions can help build confidence. For example, offering a multiple choice for answers, before expecting children to offer a single answer, can be less intimidating. Fun mental maths games are also helpful, as are real world chances to practise, for example sharing out sweets to give out on a birthday.

Applying mental maths strategies to long multiplication and written methods can help pupils find answers quicker and enable them to check their answers in a maths test scenario. Mental arithmetic tests can help children to build confidence. When tests are low stakes, they can help build confidence as children become familiar with the layout and structure of questions.

#### Year 5 mental maths: fractions, percentages and decimals

In year 5 pupils will need to know how to order fractions with denominators which are all multiples of the same number. They will also compare fractions and write equivalent fractions.

Pupils will also convert fractions into decimals in KS2 and vice versa, i.e. know that 58/100 is the same as 0.58. Teaching resources can help children to ‘hold’ the equivalent value in their hands.

Year 5 is also when percentages are introduced and pupils will start to know the equivalence of decimals, fractions and percentages, i.e. know that 50% = ½ = 0.5.

Being able to move between fraction, decimals and percentages relies on strong knowledge of the place value elements which help us to know when we must have roughly the right answer when we check our work.

### The importance of mental maths skills in Year 5 problem solving

When pupils are moving through primary school towards their Year 6 SATs, the Year 5 curriculum is a key time to check for understanding and misconceptions.

Mental maths worksheets can help to build fluency alongside maths practice with physical manipulatives and pictorials. Then weave through opportunities to apply that into problem solving and reasoning.

Across the ‘maths year’ you will want to have a range of practice questions which tackle the mental maths strategies and application of them, alongside columnar methods of written arithmetic, and some more physical lessons involving educational resources and maths manipulatives which give children the opportunity to make sense of  the numbers as they get bigger.

### Year 5 mental maths challenges

Stretch Year 5 mentally with maths challenges to give children the opportunity to discuss their maths as well as explore various problem solving methods.

They may feel confident in multiplication in a multiplication lesson, or even rapid recall as a starter to a lesson, but do they know how multiplication can help them with an ‘All Possibilities’ problem, for example? Year 5 maths gives the opportunity to really ‘play’ with the maths they already know.

Year 5 pupils usually love the chance to solve the impossible and have paired and grouped discussions about how you might go about planning big maths such as roller coaster design or a Formula 1 race. Encourage discussions about maths and the use of maths vocabulary

Year 5 really like “real” problems to solve and testing their skills in multiple areas of maths. Challenges in Year 5 can include all four operations. A popular challenge is the theme park plan. Give each child a sheet of squared paper and ask them to design their own theme park with different lands. Except that they have rules to abide by. You might say, for example, that only 1/4 of the park can contain rides. A maximum of 1/6 can be for cafes/food stalls. At least 1/8 must be seating. The biggest rollercoaster must cover a certain area. The carousel must have a certain perimeter. And so on. You can relate this to anything you are studying so instead of a theme park it might be a city plan.

Essentially what they will have to be constantly checking is the area of each thing they add, and then checking this against the allowed fraction. To make it accessible to all you can say that for each of the rules they adhere to they get extra points so that if they break a rule it isn’t a massive problem but they get fewer points than someone who really sticks to them all. This can be insightful as during the lesson you can assess who is working out mentally and who is physically counting up each square and doing lots of working out on paper. You can also see those who plan ahead and work out their number of squares at the start. Insights gained from this challenge can help to lead into future lessons.

### Year 5 mental maths resources

The Third Space Learning maths hub offers a wealth of maths resources across topics and year groups.

In a year where the SATs start to play a part in planning the teaching and interventions you may find a mixture of resources are required. You will want a bank of flexible resources – from blogs about methods and pedagogy, to a powerpoint to use in class, to online resources you can use on the whiteboard in class or print for homework. Our teachers-written content is ideal for teachers and support staff working with Year 5. We have teaching resources suitable for all lessons.

Take a look at some of our most popular free mental maths resources:

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All you need to know to successfully implement a mastery approach to mathematics in your primary school, at whatever stage of your journey.

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