Consecutive numbers in a 3 by 3 square

This is really a mini version of investigating a 100 number square, but many children will feel more confident when faced with a less daunting starting point.

Choose any nine consecutive numbers and place them in order (from left to right) in a 3 x 3 square. Add the diagonals. What do you notice?

A whole class introduction could concentrate on what consecutive numbers are, how the square is set out and the initial addition of rows and diagonals. The language used to describe parts of the square could also be reinforced – diagonal, row and column.

There are plenty of opportunities to explore this idea, beginning with other sets of numbers, then perhaps moving to numbers in a multiplication table – 2, 4, 6 etc or 3, 6, 9 and seeing if the same ambien online pharmacy patterns emerge.

Children may well try random numbers where a pattern does not emerge – this could help them see why a pattern does occur with consecutive numbers.

Some children may notice that the middle number is always four more than the first number and four less than the end number.

By adding rows or columns different answers are found, but the important thing is to look at the differences to see the pattern.

Encourage children to ask “What would happen if?” questions and try to explain why the diagonals come to the same answer.

Similar questions can be asked on a larger square, 4 x 4 or 5 x 5.

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