Number Grid Coursework

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Number Grid Coursework

My task is to investigate a 2x2 box on a 100 square

I will take a 2x2 square on a 100 square grid and multiply the two

corners together. I will then look at the relationship between the two

results, by finding the difference.

Test 1

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54 55 54 x 65= 3510

64 65 55 x 64= 3520

3520-3510= 10

DIFFERENCE = 10

Test 2

======

5 6 5 x 16= 80

15 16 6 x 15= 90

90-80= 10

DIFFERENCE = 10

Test 3

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18 19 18 x 29= 522

28 29 19 x 28= 532

532-522= 10

DIFFERENCE = 10

Prediction

==========

I predict that in a two by two square the difference will always be 10

Proof

=====

83 84 83 x 94= 7802

93 94 84 x 93= 7812

7812-7802= 10

DIFFERENCE = 10

Algebraic Explanation

=====================

[IMAGE]I will assign a letter to the first number in the 2 x 2 square,

n.

The next number to the right will therefore be n+1

The number directly below it will then be n+10

The number diagonally across from it will be n+11

I will then times the corners together, like In did on the above

examples.

Top Left hand corner x bottom right hand corner = n(n+11) = n² + 11n

Top right hand corner x bottom left hand corner = n² +1n+10n+10

n² +11n+10

(n² +11n+10) - (n² + 11n) = 10

Therefore the difference between the corners multiplied together will

always be 10.

Expanding the Task

==================

I now feel it will be interesting to look at a 3x3 number square on a

100 grid. I will take a 3x3 square on a 100 square grid and multiply

the two corners together. I will then look at the relationship between

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