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Number board magic

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By John Dabellteacher, writer and Ofsted-trained inspector

Squeeze every last bit of learning out of simple number boards with these mathematics investigations for KS2 children

Crystal ball

Number boards are puzzles that are full of maths magic, if you know where to look and know what questions to ask.

Using number boards

Take a look at the number boards on the Activity sheet, ‘Number boards’ and think of ‘I spy’ questions you could ask children about them. Board 1 contains a top row of the numbers 1, 3, 5 and 7, and a bottom row with numbers 9, 11, 13, 15. Can you see any square numbers? (1 and 4) Or prime numbers less than 7? (3 and 5)

You could ask children to use the numbers differently and add all the numbers in the top row and subtract these from total of the numbers in the bottom row (48 – 16 = 32). Alternatively, ask children to combine all the numbers in the top row to make any one number in the bottom row using the four operations – for example, 5 × 3 = 15, 15 – 7 = 8, 8 + 1 = 9.

Another idea to try would be to make a target number using all the numbers in the board. Can you make 100 using all the numbers on the board? (15 × 5 = 75, 11 + 9 = 20, 75 + 20 = 95. 13 – 7 = 6, 6 –1 = 5. 95 + 5 = 100).

Guess my number

Finally, play ‘Guess my number’. Say that you are thinking of a number from Board 1 and children have to ask questions to guess that number. Provide some sample questions such as
Is it more than 7?
Is it divisible by 3?
Is it a prime number?
and so on.

Encourage children to find alternative ways of asking questions.

How about playing ‘Mystery number’? This is a game where clues are given. For example: Which number on the board is the product of two prime numbers, has two digits that add up to 6, and has 4 factors? (15). Can children think of their own clues?

Number magic

Now combine Board 1 with Boards 2 to 4 for some ‘number magic’ to impress your class.

Ask someone to choose a number from one of the boards (without telling you what that number is) and then to point to that board and any other board that the number appears on. When all the pointing has been done, read that person’s mind and magically reveal their number!

How? Well, for each of the boards pointed to, add the numbers that appear in the top left hand corner. For example, if a child pointed to Boards 1, 2 and 4, then you need to look at the top left corner numbers and add them together (1 + 2 + 8) to reveal that the number selected was 11.

More complex number boards

You could move on to more complicated number boards to develop children’s mathematical thinking, such as Board 5 on Activity sheet, ‘Number boards’. It is an unusual board because it contains double digit numbers above a seven-digit number. What’s the connection? What can children think of? Can the individual digits of the big number be combined in some way to make the two-digit number? Can you separate the numbers using commas and read the big number?

Now for some more magic. Tell children that you have memorised all the numbers on the number board. With the board hidden from you, ask a child to select a number in bold, then offer to tell them the seven-digit number underneath.

To reveal the seven-digit number follow these steps:
  1. Add 11 to the chosen number.
  2. Reverse the result. Now start writing down the digits.
  3. Keep on adding the two previous numbers, leaving out the tens.
  4. Say the number.
For example, say that the chosen number is 26:
  1. Add 11 to 26 to get 37.
  2. Reverse 37 to get 73.
  3. Add 7 and 3 to get 10; (omit 1 and just write down the 0); add 0 and 3 to get 3; add 3 and 3 to get 6, then add 3 and 6 to get 9
  4. So, the number is 7303369.

The trick basically involves adding neighbouring numbers. If you make a number 10 or more then always ignore the tens part of the number and just add the units digit.

How about creating your own number boards? They can come in all shapes and sizes and numbers can be big, small, integers, fractions, decimals, and percentages. You can include numbers with different units of measurement too. Number boards can be used with the whole class, group or pairs of children and they provide some great opportunities for posing open and closed questions.

Image © 2011 Images