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Investigation tips
By Rachelle Najman (T4009) on Monday, April 2, 2001 - 06:05 am:

Consider some squared paper with lines 1 cm apart and dots where the lines cross. Place squares whose sides are whole numbers of centimetres on the paper in such a way that the sides of the squares always lie along the lines of the paper. For each square, find (a) the number of points inside the square; (b)the number of points on the square and; (c) the area of the square. How are these quantities related? Any patterns?

By Emma McCaughan (Emma) on Tuesday, April 3, 2001 - 12:41 pm:

What have you done so far?

By Rachelle Najman (T4009) on Wednesday, April 4, 2001 - 06:15 am:

I really haven't done much except for drawing the diagrams and identifying how many dots are found in the centre of the squares. I am trying to look for some sort of pattern, but as you can see I am stumped. I would greatly appreciate some guidance and explanations...thanks.

By Emma McCaughan (Emma) on Thursday, April 5, 2001 - 10:36 am:

Try building up a table of your results. It might start like this:

Side length Points inside Points on edge Area
1 0 4 1

Fill in the results you have. Can you see any patterns? (These aren't too difficult to spot, in this case.)
Try and predict what the table would read for side length 10, or 100. Then you might be able to go into algebra, by saying what the table would say for side length n.

If this doesn't help, you'd better post your results so far, in case there's a problem there.