Out of the hat! Magic with maths

Can there be anything more exciting than combining maths with magic? They are natural partners and go together like Ant and Dec, copy and paste, eggs and bacon, strawberries and cream.

Maths magic tricks are an underused slice of maths life yet they are an inventive, enjoyable and fascinating way of bringing numbers to life. They have the power to motivate, inspire and amaze children, help children to understand maths concepts and develop their maths skills. Children delight in performing them.

Research by Richard Wiseman has found that teaching children magic can boost their self-discipline and social skills as well as develop their self-esteem, confidence, empathy and interaction. Whilst it might be pushing the talents of most teachers to teach Harry Potter-style lessons, what they can do is teach some simple tricks that have the wow factor.  

Professor Wiseman’s study found that an hour’s lesson studying magic did more good for a group of 10 to 12-year-olds than their normal PSHE classes. It also elevates their playground status!
Here’s a classic magic trick using binary arithmetic, the basis of all computer logic.


What to do:

Select a number without telling me but point to the card or cards it appears on.

I will tell you the number you have in your mind!

For example, if someone chooses the number 5 and they point to the two cards this appears on, simply look in the top left hand corner of the cards and add the numbers (4 +1).

Maths magic tricks can energise any maths class and create a sense of wonder and curiosity about maths. You can introduce them as problem-solving tasks and challenge children to demystify them so they are valuable activities for developing critical thinking skills. THOANs are probably the easiest to start with (THink Of A Number).

Share the following 10 tricks with children and explain how they are done.

Encourage them to practise with family and friends but remember to tell them that a magician never reveals their secrets! 

Trick 1: Think of a number
  • Pick a whole number between 1 and 10.
  • Add 2.
  • Multiply by 2.
  • Subtract 2.
  • Divide by 2.
  • Subtract your original number.
  • Everyone’s final answer will be 1
Trick 2: Think of a number
  • Choose a number from 1 to 8.
  • Multiply it by 2.
  • Now multiply by 5.
  • Subtract 5.
  • Finally add 7.
  • The first digit is the number you chose and the second digit is the number 2.
Trick 3: Think of a number
  • Think of any number.
  • Double the number.
  • Add 9 with result.
  • Subtract 3 with the result.
  • Divide the result by 2.
  • Subtract the number with the first number started with.
  • The answer will always be 3.
Trick 4: Think of a number
  • Ask someone to pick a number.
  • Add the next higher number to it.
  • Add 9 and divide by 2, and then subtract the original number.
  • The answer will be 5.
Trick 5: Think of a number
  • Write down a number.
  • Add 5.
  • Multiply by 3.
  • Minus 15.
  • Divide by your original number.
  • Add 7.
  • Your answer is 10.
Trick 6: Think of a number between 20 and 100
  • Pick a number between 20 and 100.
  • Now add your digits together.
  • Now subtract the total from your original number.
  • Finally, add the digits of the new number together.
  • Your answer will always be 9
Trick 7: Think of a 3 digit number
  • Pick a 3 digit number with 3 different digits.
  • Now reverse the digits to get a new number.
  • You now have two numbers. Subtract the smaller number from the larger number.
  • Now add up the digits of the result.
  • The answer will always be 18
Trick 8: Think of a 3 digit number
  • Pick a 3-digit number with all three digits different.
  • Reverse the digits and subtract to get another 3-digit number.
  • Reverse the digits of the difference and add it to the difference.
  • Your sum will be 1089.
For example, start with 845. Then 845 – 548 = 297 and 297 + 792 = 1089.
Trick 9: Pick a number between 1 and 14
  • Ask someone to think of a number between 1 and 14.
  • Look at the 5 cards below and ask them to point to the card their secret number appears on.
  • To work out what their secret number is look at the centre number on the card(s) they have chosen and add them together.
  • For example, if they chose 10 then they would point to card 2, 3 and 5. Looking at the centre numbers on these cards that would be 2 + 3 + 5 = 10 
12 6 11
13 7 8
11 9 10
12 7 14
13 9 10
11 8 14
13 9 12
14 7 8
12 6 11
14 10 13
Trick 10: Dicey
  • Ask someone to roll two dice without telling you the numbers thrown, e.g. 4 and a 6.
  • Ask them to multiply the number on the first die by 2 (4 x 2 = 8).
  • Add 5 (8 + 5 = 13).
  • Multiply by 5 (13 x 5 = 65).
  • Add the number on the second die (65 + 6 = 71).
  • You can now predict the numbers on the two dice by subtracting 25 (71 - 25 = 46).
  • 4 = first die and 6 = second die.

Just as every teacher should have a collection of jokes at the ready, every teacher should also have a collection of maths tricks up their sleeve to show children.    

Encourage children to practise and personalise a couple of tricks with a maths partner, building up to a performance in front of a small group; add a bit of performance theatre to it as confidence grows.

Within a whole-class session ask children to take on the role of a mathemagician - ready to impress everyone with marvellous memory feats and spell-binding maths wizardry!
John Dabell is a teacher with over 20 years teaching experience across all key stages. He has worked as a national in-service provider and is a trained OfSTED inspector.

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