Number Grids

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Number Grids

Introduction

I have a10x10 grid. The task is to select various size squares and rectangles, I will then be multiplying the opposite corners together then subtracting the results to get the difference between the two answers. I hope to find patterns and rules in the results, if I can find patterns I will use algebra to describe them. My aim is to find the general rule for any size rectangle on any size grid.

Plan

  • investigate different squares on a 10x10 grid.
  • Find an algebraic rule.
  • Repeat for rectangles on a 10x10 grid.
  • Adapt the rule for squares to fit rectangles.
  • Change the size of the grid
  • Find an overall rule for any rectangle on any grid.

25 26                   25 x 36 = 900

35 36                   26 x 35 = 910

                            910 – 900 = 10

The difference between the two answers is 10.

  1   2                   1 x 12 = 12

11 12                   2 x 11 = 22

                            22 – 12 = 10

The difference between the two answers is 10.

72 73                   72 x 83 = 5976

82 83                   73 x 82 = 5986

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                            5986 – 5876 = 10

The difference between the two answers is 10.

49 50                   49 x 60 = 2940

59 60                   50 x 59 = 2950

The difference between the two answers is 10.

12 13 14             12 x 34 = 408

22 23 24             14 x 32 = 448

32 33 ...

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