Mental maths

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Mental mathematics :

Mental mathematics Presented by Umaira Bukhari

Warm up activity:

Warm up activity

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Two of the several different way of Making 100 are 12+35+46+7=100 15+47+36+2=100

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The ability to calculate in your head is an important part of mathematics. It is also an essential part of coping with society’s demands and managing everyday events.

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Why Focus on Mental Mathematics? It is the form of calculation used by numerate people. It makes sense. It develops number sense. It promotes thinking and reasoning skills. It provides an insight into student’s thinking and understanding. When students use the written algorithm they often get the wrong answer.

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In the National Strategies’ suite of publications: Securing levels in mathematics (for example Securing level 4 in mathematics Ref: 00065-2009BKT-EN) They have identified six key points to remember when planning and teaching mathematics:

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Revisiting mental work at different times in the daily mathematics lesson, or even devoting a whole lesson to it from time to time, helps children to generate confidence in themselves and a feeling that they control calculations rather than calculations controlling them. Look out too for opportunity to introduce short periods of mental calculation in other lessons or outside lessons when queuing for some activity . Regular short practice keeps the mind fresh. Mental calculation is one of those aspects of learning where – if you don’t use it you will end up losing it!

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The mental calculation publication has been adapted from Teaching mental calculation strategies – guidance for teachers at Key Stages 1 and 2 , produced in 1999 by the National Numeracy Strategy and Qualifications and Curriculum Authority (now QCDA).

Progression in mental calculation skills :

Progression in mental calculation skills All teachers need to review, consolidate and build on children’s developing mental calculation skills throughout Key Stages 1 and 2. To help your planning, the progression in mental calculation with whole numbers, including the recall of number facts, and fractions, decimals and percentages, is set out for you on the next few slides.

The following tables provide further details to exemplify the expectations in the Primary Framework for mathematics. :

The following tables provide further details to exemplify the expectations in the Primary Framework for mathematics .

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Research shows that learning key facts ‘by heart’ enables children to concentrate on the calculation which helps them to develop calculation strategies. Using and applying strategies to work out answers helps children to acquire and so remember more facts. Many children who are not able to recall key facts often treat each calculation as a new one and have to return to first principles to work out the answer again

What’s special about mental calculations?:

What’s special about mental calculations? Calculating mentally may involve ‘seeing’ objects, images or quantities that help you manage the process. But this is not the same as just picturing in your head how to do the calculation using a traditional paper and pencil method.

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A feature of mental calculation is that a type of calculation can often be worked out in several different ways. Which method is the best will depend on the numbers involved, the age of the children and the range of methods that they are confident with.

Can mental calculations involve practical equipment? :

Can mental calculations involve practical equipment? Hands-on learning is important Mental calculations involve visualising, imagining and working things out in your head.

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Activity time

The 7-11-13 trick! : :

The 7-11-13 trick! :  The 7-11-13 trick! write down ANY three digit number such as 231 or 884. Now multiply the number by: x 7 x 11 x 13 ...


THE SECRET: all you do is write out the starting number twice! So 231 will become 231231 and 884 will become 884884. You don't believe it? Well try it on this calculator and see for yourself! You work this calculator by clicking the mouse on the buttons. Go on, put in ANY three digit number then x7 x11 x 13 and see what you get!

The 3367 trick! :

The 3367 trick! Pick any 2 digit number e.g. 74 x 3367 .

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To work out the final answer you have to imagine the original number written out three times e.g. 747474 then divide it by three. 249158 This one takes practice, but unlike the others, it's very hard to see how it's done!

The missing digit trick! :

The missing digit trick! write down ANY number (at least four digits long). e.g. 78341 .NOW add up the digits... e.g. 7+8+3+4+1 = 23 ... and then subtract the answer from the first number. e.g. 78341 - 23 = 78318.Now crosses out ONE digit from the answer. reads out what digits are left .e.g. 7-3-1-8 Even though you haven't seen any numbers,


THE SECRET EIGHT THE SECRET This great trick relies on the power of 9. After your friend has added up the digits and subtracted them, the answer will ALWAYS divide by 9. If a number divides by nine, then when you add the digits up, they will also divide by 9. If you check our example 7+8+3+1+8 = 27 which does divide by nine. When your friend crosses a digit out, he then reads out the digits that are left. You add them up. In the example we had 7+3+1+8 = 19 All you do now is see what you have to add on to your answer to get the next number that divides by nine! The next number to divide by 9 after 19 is 27. So you need to add on EIGHT. This is the number that was crossed out!

The Prime Number Trick :

The Prime Number Trick to pick any prime number bigger than 5. Square it. Add 17 Divide by 12


Answer There will be a remainder of 6.

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Fill the numbers 1,2,3,4,5,6,7,8,9 so that the sum of numbers on each side of triangle is 17.

The six R’s of oral and mental work:

The six R’s of oral and mental work Rehearse Recall Refresh Refine Read Reason


Rehearse Practise and consolidate existing skills. (usually mental calculation skills, including using and applying) Vocabulary and language of number Properties of shapes or describing and reasoning.


Recall To secure knowledge of number facts, (developing speed and accuracy) Recall quickly names and properties of shapes Recall quickly units of measure or types of charts or graphs to represent data.


Refresh To draw on and revisit previous learning To assess, review and strengthen children’s previously acquired knowledge and skills Return to aspects of mathematics with which the children have had difficulty Draw out key points from learning.


Refine To sharpen methods and procedures Explain strategies and solutions Extend ideas; develop and deepen the children’s knowledge Reinforce their understanding of key concepts Build on earlier learning so that strategies and techniques become more efficient and precise


Read To use mathematical vocabulary To interpret images, diagrams and symbols correctly To read number sentences and provide equivalents To describe and explain diagrams and features involving scales, tables or graphs To identify shapes from a list of their properties To read and interpret word problems and puzzles To create their own problems and lines of enquiry.


Reason To use and apply acquired knowledge, skills and understanding To make informed choices and decisions To predict and hypothesise To use deductive reasoning to eliminate or conclude To provide examples that satisfy a condition always, sometimes or never and say why.

Sample Paper:

Sample Paper Work out 19 x 3 Add together £3.52, £5.00 . If I get 6 out of 10 on a spelling test what is this score as a percentage. How many millilitres in 3 ½ litres ? Work out 3 2 + 3 3 Write 0.43 as a fraction Shade in ¼ of the square Work out 13 squared What is the square root of 36? How many centimetres in 68.2 metres ?

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