I'm going to investigate the difference between products on a number grid first I'm going to draw a box round four numbers then I will find the product of top left, bottom right numbers, and then

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I'm going to investigate the difference between products on a number grid first I'm going to draw a box round four numbers then I will find the product of top left, bottom right numbers, and then I'm going to do the same with the top right, bottom right numbers in the box. I'll will then calculate the difference between these products. Not only I am going to investigate squares, but also rectangles, I'll use algebra to try and find a formula or a general rule that will give me this difference for any size shape.

I'm going to draw a box round four numbers then I will find the product of top left, bottom right numbers, and then I'm going to do the same with the top right, bottom right numbers.                        

                               The difference between 286 and 276 is 10 because  286 - 276 = 10                                 13 x 22 = 286     
12 x 23 = 276

 

                              The difference between 2950 and 2940 is 10 because 2950 - 2940 = 10
50 x 59 = 2950   
49 x 60 = 2940  

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                             The difference between 90 and 80 is 10 because 90 - 80 = 10  
6 x 15 = 90
5 x 16 = 80

 

I predicted that the difference for all 2x2 spares will be 10, I'll do another 2 by 2 grid to confirm that my prediction is correct.

The difference between 7636 and 7626 is 10 because 7636 - 7626 = 10

83 x 92 = 7636
82 x 93 = 7626

This shows that my prediction is correct, that all 2 by 2 will equal to 10.


3 by 3

I'm going to draw a ...

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