# Maths and magic

18 December 2009

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Amaze your class with these ‘mathemagical’ tricks and teasers

Maths tricks can woo and wow children’s imaginations. They have a magical feel to them and can breathe mystery and fun into your classroom. This article contains a selection of tried and tested recreational activities to add a little zip to your maths teaching and inspire and deepen children’s interest. They offer a wide variety of classroom uses and are prime candidates for mathematical ‘milking’. Use them alongside formal maths teaching in starter and plenary sessions, within focus groups, as brain breaks or to end the day. They also provide excellent material for maths clubs.

It’s a good idea to start a file of your favourite tricks so you can use them year after year. Each time you introduce a new one to the class, give the children time to explore it and practise the maths for themselves. They can then prepare demonstrations to perform to you and the rest of the class.

## Activities

- The number 11 sandwich
- Recurring number magic
- Postal number
- That’s original
- Number line magic
- The magic number
- Guess two nunbers
- A head full of numbers

### 1. The number 11 sandwich

A very neat trick for multiplying a two-digit number by 11 is to write down the number you are multiplying by, leaving a space between the two numbers. For example, to work out 35×11, leave a space between the 3 and 5 = 3_5. Now, add these two digits and place the answer in between. So 3 + 5 = 8, then place the 8 in between the 3 and 5 to make 385. Check this on a calculator to see that 35×11 is 385.

This method works if the total of the two digits is less than ten. If they add up to ten or more, you will need to add the 1 to the first digit and place just the second number in the space. For example, to do 67×11 you would separate the 6 and 7, add 6 and 7 to make 13, but rather than place 13 in between, place the 3 in the space and add the 1 to the 6, so the answer is 737.

### 2. Recurring number magic

Write down the following eight-digit number on a piece of paper: 1 2 3 4 5 6 7 9 Then ask someone to circle one of the digits. Say that they circle number 6. You then ask them to multiply the eight-digit number by 54, and magically the result is 66666666 – the number they originally created recurring.

To do this trick keep the way you work this out a secret. For every number they circle, multiply it by 9 in your head. So, if 2 was chosen, you would work out 2×9 = 18. Then you need to ask someone to multiply the eight-digit number by the answer to your multiplication. In the case of 2 being chosen, you would ask someone to multiply 12345679 by 18 and you magically get the answer 22222222.

### 3. Postal number

Write the number 23 on a piece of paper, and place it in a sealed envelope before the lesson. When the children arrive, ask for a volunteer and give them the envelope. Ask your volunteer to write down any three-digit number, say 645. They must now do the following series of calculations:

a Add 25. (645 + 25 = 670)

b Multiply by 2. (670×2 = 1340)

c Subtract 4. (1340 – 4 = 1336)

d Divide by 2. (1336 ÷ 2 = 668)

e Subtract the original number (668 – 645 = 23)

Invite your volunteer to open up the envelope to reveal the number 23. Amazing!

### 4. That’s original

Ask someone to write down any four-digit number. When they have done that, tell them that they have selected a very magical number. Explain why as follows:

a Write down the number. (4829)

b Write down the first digit. (4)

c Write down the first two digits. (48)

d Write down the first three digits. (482)

e Add these together. (4 + 48 + 482 = 534)

f Multiply this answer by 9. (534×9 = 4806)

g Add up the original four digits. (4 + 8 + 2 + 9 = 23)

h Add these last two results. (4806 + 23 = 4829)

Following this process means the original number will always appear at the end!

### 5. Number line magic

Write out the following numbers:

Ask someone to choose any number from the lines. They should not tell you the number, but just tell you all the lines it appears on. You can astound your class by quickly saying what number was chosen. The secret to this trick is to look at the first number on each line the number appears on and add them together. This will give you the number the person chose. For example, if your volunteer chose number 6, they would tell you that it appears on lines two and three. The first two numbers from these lines are 2 and 4 – add them together to make 6.

### 6. The magic number

This is a simple one, but impressive. The answer is always 3. a Think of a whole number bigger than zero. (Say, 4)

b Square it. (4² = 16)

c Add the original number. (16 + 4 = 20)

d Divide by the original number. (20 ÷ 4 = 5)

e Add 17. (5 + 17 = 22)

f Take away the original number. (22 – 4 = 18)

g Divide by 6. (18 ÷ 6 = 3)

### 7. Guess two numbers

Ask a volunteer to pick a number from 1 to 9. (Say, 8) They then need to:

a Double it. (8×2 = 16)

b Add 5. (16 + 5 = 21)

c Multiply by 5. (21×5 = 105)

Now, ask them to pick another number from 1 to 9 and add it to their answer. (2 + 105 = 107) To guess the two numbers, subtract 25 from the total (107 – 25 = 82). The first digit of this answer is the first digit of your volunteer’s numbers and the second digit is the second number.

### 8. A head full of numbers

This number trick is quite a winner and, when practised, can be performed with real finesse and flair. Give children a copy of the grid on the **Activity sheet**, ‘A head full of numbers’ and tell them that you have memorised every single number in the table. Point out that there are 49 key numbers that are in bold and under each bold number is a seven-digit number.
Without looking at the table yourself, ask one of the children to choose a number in bold and confidently declare that you will be able to recall the number underneath. For example, if the number 41 was chosen, slowly reveal each of the numbers but remember to add plenty of performance and theatricals such as: The first number is coming to me. I can see it now… it’s a prime number… it’s an even number… it’s the number 2! Then go on to say and write down the other numbers: My mental powers are weak, but I think the next number is also a prime number. I think it’s the square root of 25. It’s the number 5!

Repeat this for several more bold numbers as children try to work out how you can recall all the numbers so readily. Now, tell the children how it’s done and let them have a go with a partner. Say the number 14 is chosen:

a Add 11 to the chosen number. (14 + 11 = 25)

b Reverse the result so the number is 52. These are the first two numbers of your long number.

c Add these two numbers together to get the third number. (5 + 2 = 7)

d Continue adding each pair of consecutive numbers, leaving out the ‘tens’ if necessary, until you reach a seven-digit number. This is easier if you write down the numbers on a whiteboard as you do it. (2 + 7 = 9; 7 + 9 = (1)6; 9 + 6 = (1)5; 6 + 5 = (1)1.)

e When you have finished, say the number aloud in true magician style. (Hey presto – 5279651!)