GCSE Mathematics

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GCSE Mathematics

Coursework

Number Grid

By Gareth Davies

Introduction

For this task I was presented with a 10x10 number grid (see below). Within this grid was a box drawn around four numbers. I was asked to find the product of the top left and the bottom right numbers or corners in that box. And again with the top right and bottom left numbers. Finally I was asked to calculate the difference.

To calculate the product difference, firstly I must multiply.

So firstly                 12 x 23  =  276

                                13 x 22  =  286

Secondly I would simply subtract the smaller number from the larger one.

Secondly                  286-276

                               =10

To investigate this task further I decided to find out if the product difference varied if the box was drawn around another four numbers.

I chose:

                    Therefore product difference = 34 x 45 = 1530

                                                                   = 35 x 44 = 1540

                                                                   = 1540-1530

Join now!

                                                                                  = 10

As illustrated the product difference didn’t change.

At this stage I made an hypothesis and stated that wherever the 2x2 box was drawn within the 10 x 10 grid the product difference wouldn’t vary.

To verify this claim, I tested another three boxes. I would use the same technique throughout ie. the same as ...

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