Number Grid.

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Maths coursework.

Number Grid.

Introduction

I have a number grid that ranges from 1 to 100 in rows and columns of ten.

I have been given a box of four numbers, I was told to multiply the top left and then the bottom right then the bottom left and the top right. Below are the numbers that I choose.

2

3

22

23

I have been asked to find the products of:

2

23

3

22

.

Then calculate the difference between the two results

I have then been asked to investigate further.

Plan

. I plan to try some more boxes of 4 numbers to see how the results compare.

2. I am then going to try some bigger squares, rectangles, and different size number grids to see if I can find any number patterns emerging.

3. I will then put my answers and try to find the formulas for the boxes.

4. When I find the formulas I intend to test them out to see if they are correct.

5. I will then the formulas into algebraic form.

2 x 23 = 276

3 x 22 = 286

The difference between the products is 10.

I will now try some more:

55

56

65

66

55 x 66 = 3630

56 x 65 = 3640

The difference is 10 again.

I am going to try one more:

7

8

27

28

7 x 28 = 476

8 x 27 = 486

The difference is 10 again!

I am now going to try and work out a formula, and try another one using the formula:

n

n+1

n +10

n +11

If this formula is correct I should be able to pick any number from the grid and use the formula to get the right answer

If n =77 then:

(n) (N +11) = n2 + 11n. & (n + 1) (n + 10) = n2 + 11n +10.

(77) (77+11) = 772 +11x77 (77 + 1) (77 + 10) = 772 +11x77 + 10.

77 x 88 =6776. 78 x 87 =6786.

If n=50 then:

N (n + 11) = n2 +11n. & (n + 1) (n +10) =n2 +11n + 10.

50 (50 +11) = 502 + 11x 50. (50 + 1) (50 +10) = 502 +11n + 10.

50 x 61 = 3050. 51 x 60 =3060.

The formula works the difference is 10.

I am going to try some bigger squares. Like 3 by 3 and 4 by 4

I will also make up a formula grid to help me make a formula.

2

3

1

2

3

21

22

23
Join now!


S

S+1

S+2

S+10

S+11

S+12

S+20

S+21

S+22

x 23 = 23

3 x 21 = 63

The difference is 40

S (S+22) =S2 +22S & (S+2) (S+20) =S2+22S+40.

I will now try my formula.

If S=27.

272 + (22x27) =1323 272 + (22x27) +40=1363

The difference is 40. I found this from looking at the simplified second half of the formula.

I am now going to try a 4x4 square.

S

S+1

S+2

S+3

...

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