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Mental Strategies

Practise your mental arithmetic skills and learn some new strategies with this self marking exercise.

Level 1 Level 2 Level 3 Level 4 Description Help More...
No calculator

This is level 3: mental strategies for multiplication. Click on the blue question mark buttons for strategy suggestions.

34 × 5

Correct Wrong

17 × 49

Correct Wrong

40 × 2

Correct Wrong

6 × 49

Correct Wrong

300 × 120

Correct Wrong

14 × 91

Correct Wrong

19 × 32

Correct Wrong

14 × 16

Correct Wrong

0.8 × 1

Correct Wrong

17 × 121

Correct Wrong

3 × 1.2

Correct Wrong

13 × 8

Correct Wrong

1.1 × 5

Correct Wrong

0.9 × 2

Correct Wrong

8 × 400

Correct Wrong

80 × 3

Correct Wrong

18 × 199

Correct Wrong

0.3 × 0.06

Correct Wrong


This is Mental Strategies level 3. You can also try:
Level 1 Level 2 Level 4


Try your best to answer the questions above. Type your answers into the boxes provided leaving no spaces. As you work through the exercise regularly click the "check" button. If you have any wrong answers, do your best to do corrections but if there is anything you don't understand, please ask your teacher for help.

When you have got all of the questions correct you may want to print out this page and paste it into your exercise book. If you keep your work in an ePortfolio you could take a screen shot of your answers and paste that into your Maths file.

This web site contains over a thousand free mathematical activities for teachers and pupils. Click here to go to the main page which links to all of the resources available.

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Mathematicians are not the people who find Maths easy; they are the people who enjoy how mystifying, puzzling and hard it is. Are you a mathematician?

Comment recorded on the 19 June 'Starter of the Day' page by Nikki Jordan, Braunton School, Devon:

"Excellent. Thank you very much for a fabulous set of starters. I use the 'weekenders' if the daily ones are not quite what I want. Brilliant and much appreciated."

Comment recorded on the 11 January 'Starter of the Day' page by S Johnson, The King John School:

"We recently had an afternoon on accelerated learning.This linked really well and prompted a discussion about learning styles and short term memory."

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Learning and understanding Mathematics, at every level, requires learner engagement. Mathematics is not a spectator sport. Sometimes traditional teaching fails to actively involve students. One way to address the problem is through the use of interactive activities and this web site provides many of those. The Go Maths page is an alphabetical list of free activities designed for students in Secondary/High school.

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Are you looking for something specific? An exercise to supplement the topic you are studying at school at the moment perhaps. Navigate using our Maths Map to find exercises, puzzles and Maths lesson starters grouped by topic.


If you found this activity useful don't forget to record it in your scheme of work or learning management system. The short URL, ready to be copied and pasted, is as follows:

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Description of Levels



Level 1 - Mental strategies for addition

Level 2 - Mental strategies for subtraction

Level 3 - Mental strategies for multiplication

Level 4 - Mental strategies for division

More Mental Methods including lesson Starters, visual aids, investigations and self-marking exercises.

Answers to this exercise are available lower down this page when you are logged in to your Transum account. If you don’t yet have a Transum subscription one can be very quickly set up if you are a teacher, tutor or parent.

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Curriculum Reference

See the National Curriculum page for links to related online activities and resources.

Extension Activity

Make up a ten-question mental arithmetic exercise for a friend. For each question you should secretly write down your prediction of which strategy they will use. You should include addition, subtraction, multiplication and division questions and your ten predictions should all be different.

Multiplication Strategies

Knowing multiplication facts to 12 × 12

Knowing that 7 × 8 = 56
will help work out
0.7 × 8
= 5.6

Repeated doubling

Multiply by 8 by doubling three times
17 × 8
=34 × 4
= 68 × 2 = 136

Multiplying by multiples of 10

120 × 700
=12 × 7 × 1000
=84 × 1000

Partitioning one number

34 × 7
= (30 + 4) × 7
= 30 × 7 + 4 × 7
= 210 + 28
= 238

Rounding then adjusting

23 × 19
= 23 × 20 - 23
= 460 - 23
= 437

Factorising then rearranging

14 × 15
= 2 × 7 × 3 × 5
= 2 × 5 × 7 × 3
= 10 × 21
= 210

Adapted from The National Primary Strategies, UK Department for Education

Don't wait until you have finished the exercise before you click on the 'Check' button. Click it often as you work through the questions to see if you are answering them correctly. You can double-click the 'Check' button to make it float at the bottom of your screen.

Answers to this exercise are available lower down this page when you are logged in to your Transum account. If you don’t yet have a Transum subscription one can be very quickly set up if you are a teacher, tutor or parent.

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