# Investigate the differences of the products

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Now that I have come to realize that the difference of the squares, I need to now try and find out a formula to the graphs. H=Height D=Difference L=Length Some test formulas I have been working on: L-1*5H This Formula will work on the shape 2*2; however it does not work on n any other shapes. The problem I found was that I could find the answer, with out looking at the square board, but I couldn’t write the formula down. So after thinking about the formula this is what I came up with. L-110=D.

To test this out I will be working on a 29, so 9-1=8 and 8*10=80 and looking at the table I have drawn above this is correct. After working out the formula for that type of square, I now wanted to investigate further. I realized that I have changed the length, I now needed to change the height of the squares. This would also be a good chance to see if my formula works on other types of squares. However what will be the difference when I change the length?

I can see a pattern starting to form, it seems to be going up by twenty, every time two is added to the area. Will my formula ‘L-1*10=D’ work will this type of square? I need to test it out. 2*5 5-1=5, 5*10=50 by looking at my previous answer fifty does not seem to be the correct answer. I now needed to work out a different equation. In the previous the formula that worked was L-1*10=D, the answer now is greater so I need to add on some numbers to get a larger number. I did this by changing the formula.

As the size of the square goes up so does the multiply number, so I could have done this by adding ten on each time. To give L-1*20 +10 (the ten is added on as the square changes) Conclusion I think that I have completed my aims and achieved my goals that I set out. I have found out a formula to work out the square problem. I feel that I could have done a little more work investigation the problem but time was against me in this case. If more time would have been allowed I would have liked to investigate into more depth, this may involve working on 3d squares or a larger number grid.