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
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