10x10 number grid

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Stephanie Evans – 20002303

GCSE Maths Coursework

Ma 1 Number Grids

Aim:

 My task is to look at a 10x10 number grid and take a box of numbers from within that grid. I will then find the products of the numbers in opposite corners of the box and calculate the difference between the products.

I will start with a box of 4 numbers from the grid, and then change the size of the box to see what the variation may be and record my results as I progress.

Hypothesis:

Based on the example given in the original question (12x23= 276 13x22=286 difference = 10) I predict that the results for other number groups with a square or rectangle of the same size will have the same difference. i.e. a group of 4 numbers where the products of the numbers in opposite corners are subtracted to find the difference will always have a difference of 10.

I predict that if I investigate this theory further using varying sizes of square that providing the same method is used the difference between products will remain the same for that size square. E.g. a group of 4 numbers the difference is always 10. A group of 9 numbers will always have a difference that is the same as another group of 9 numbers and so on.

12 x 23=276

13 x 22=286

Difference = 10

36 x 47=1692

37 x 46=1702

Difference= 10

To extend this theory further I will look at rectangular groups of numbers e.g. 3 numbers along the top and 2 down. I predict that a similar result will emerge. Once all the data is collected I predict that a pattern in the difference between products and box sizes will also become apparent e.g. a 2x2 square, 3x3 square, 4x4 square will have a noticeable pattern in the product differences.

Stephanie Evans – 20002303

Method

So let start with the number grid below:-

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The product of the numbers in the first grid is

12 x 23= 276

13 x 22= 286

This means that the products have a difference of 10.

The products of the second grid are

36 x 47= 1692

46 x 37= 1702

Another product difference of 10

I will try looking at some other grids

The products for the first number grid are

32 x 43= 1376

33 x 42= 1386

Again a product ...

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