Squares and Next-door Squares
Here are some squares I have cut from centimetre-squared paper.
If I cut squares of all sizes from one centimetre to ten centimetres arrange them in order they will look like this:
I am going to take two squares which are next door neighbours and put the smaller one on top of the larger one, keeping one corner and two sides together. This bit is the difference between the two squares.
To make it easier to see I have coloured the squares.
Now I am going to cut off the extra piece to make the two the same size and this is what I get:
This can be arranged like this:
How many squares long is it?
Now the job for you to do is to find the differences between all the next-door squares from one to ten and to arrange the differences in lines like the one above.
You can use squared paper to do this or you can download this sheet with all the squares on it. You will probably need two copies.
If you would like the coloured version you can find that here.
This means you need to find the differences between one and two squared, two squared and three squared all the way up to the difference between nine and ten squared.
Now arrange the differences you have cut off neatly in order of size so you can compare them.
Now look at the differences in order.
What can you say about them?
Write down the length of each one in order.
What do you notice?