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• Level: GCSE
• Subject: Maths
• Word count: 1364

# Number Grids - Algebra

Extracts from this document...

Introduction

Number Grid Coursework

I am doing this experiment to see if there are any patterns in squares on a 1 - 100 grid. I will then see if I can make a formula to express these patterns.

2 x 2 Squares

My 2 x 2 square is 14, 15, 24 and 25. The top left times by the bottom right is 14 x 25, this equals 350. The top right multiplied by the bottom left is 15 x 24 = 360. To finish I will take the smaller of the two numbers from the larger. This is 360 – 350 = 10.

My 2 x 2 square is 84, 85, 94 and 95. The top left times by the bottom right is 84 x 95, this equals 7980. The top right multiplied by the bottom left is 85 x 94 = 7990. To finish I will take the smaller of the two numbers from the larger. This is 7990 – 7980 = 10.

My 2 x 2 square is 27, 28, 37 and 38. The top left times by the bottom right is 27x 38, this equals 1026. The top right multiplied by the bottom left is 28 x 37 = 1036. To finish I will take the smaller of the two numbers from the larger. This is 1036 – 1026 = 10.

Middle

X + 2

X + 10

X + 11

X + 12

X + 20

X + 21

X + 22

(X2 + 2X + 20X + 40) – (X2 +22X) = 40

FORMULA = (X2 + 22X + 40) - (X2 +22X) = 40

4 x 4 Squares

My 4 x 4 square is 17, 18, 19, 20, 27, 28, 29, 30, 37, 38, 39, 40, 47, 48, 49 and 50. The top left times by the bottom right is 17 x 50 = 850. The top right multiplied by the bottom left is 20 x 47 = 940. The difference between the smaller and bigger numbers is 940 – 850 = 90.

My 4 x 4 square is 1, 2, 3, 4, 11, 12, 13, 14, 21, 22, 23, 24, 31, 32, 33 and 34. The top left times by the bottom right is 1 x 34 = 34. The top right multiplied by the bottom left is 4 x 31 = 124. The difference between the smaller and bigger numbers is 124 – 34 = 90.

My 4 x 4 square is 62, 63, 64, 65, 72, 73, 74, 75, 82, 83, 84, 85, 92, 93, 94 and 95. The top left times by the bottom right is 62 x 95 = 5890. The top right multiplied by the bottom left is 65 x 92 = 5980. The difference between the smaller and bigger numbers is 5980 – 5890 = 90.

My 4 x 4 square is67, 68, 69, 70, 77, 78, 79, 80,87, 88, 89, 90, 97, 98, 99 and 100. The top left times by the bottom right is 67 x 100 = 6700. The top right multiplied by the bottom left is 70 x 97 = 6790. The difference between the smaller and bigger numbers is 6790 – 6700 =90.

I have found that for any 4 x 4 square on a 1-100 grid the difference between the two numbers is 90.

Algebra – 4 x 4

 X X + 1 X + 2 X + 3 X + 10 X + 11 X + 12 X + 13 X + 20 X + 21 X + 22 X + 23 X + 30 X + 31 X +32 X + 33

Conclusion

My 5 x 5 square is 51, 52, 53, 54, 55, 61, 62, 63, 64, 65, 71, 72, 73, 74, 75, 81, 82, 83, 84, 85, 91, 92, 93, 94 and 95. The top left times by the bottom right is 51 x 95 = 4845. The top right multiplied by the bottom left is 55 x 91 = 5005. The difference between the smaller and bigger numbers is 5005 – 4845 = 160.

My 5 x 5 square is 56, 57, 58, 59, 60, 66, 67, 68, 69, 70, 76, 77, 78, 79, 80, 86, 87, 88, 89, 90, 96, 97, 98, 99 and 100. The top left times by the bottom right is 56 x 100 = 5600. The top right multiplied by the bottom left is96 x 60 = 5760. The difference between the smaller and bigger numbers is 5760 – 5600 = 160.

I have found that they all end out that the difference between the two numbers of any 5 x 5 squares on a 1 – 100 grid is 160.

Algebra - 5 x 5

 X X + 1 X + 2 X + 3 X + 4 X + 10 X + 11 X + 12 X + 13 X + 14 X + 20 X + 21 X + 22 X + 23 X + 24 X + 30 X + 31 X +32 X + 33 X + 34 X + 40 X + 41 X + 42 X + 43 X + 44

(X2 + 40X + 4X + 160) – (X2 + 44X) = 160

FORMULA = (X2 + 44X + 160) – (X2 + 44X) = 160

Algebra for All

The algebra for all the equations is 10(n-1)2. This formula can be used to find out any size square on a 10 x 10 grid.

This student written piece of work is one of many that can be found in our GCSE Number Stairs, Grids and Sequences section.

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# Related GCSE Number Stairs, Grids and Sequences essays

1. ## Number Grids Investigation Coursework

products of opposite corners in all 2 x 4 rectangles in 10 x 10 grids, I will now move on to 2 x 5 rectangles. 1 2 3 4 5 11 12 13 14 15 The difference between the products of opposite corners of this rectangle would equal: (top right x bottom left)

2. ## Investigation of diagonal difference.

1 From calculating the diagonal difference of these 2 x X cutouts I can now produce a table of results. I will start by producing a table of results for the horizontally aligned cutouts, and then I will produce a further table of results for vertically aligned cutouts.

1. ## Maths Grids Totals

5 x 6 16 17 18 19 20 26 27 28 29 30 36 37 38 39 40 46 47 48 49 50 56 57 58 59 60 66 67 68 69 70 20x 66 = 1320 16 x 70 = 1120 1320 - 1120 = 200.

2. ## Number Grids

= 250 35 36 37 38 39 40 45 46 47 48 49 50 55 56 57 58 59 60 65 66 67 68 69 70 75 76 77 78 79 80 85 86 87 88 89 90 40 x 85 = 3400 35 x 90 = 3150 3400 - 3150 = 250 The same result keeps occurring.

1. ## Number Grids

32 33 34 72 73 74 82 83 84 92 93 94 38 39 40 48 49 50 58 59 60 51 52 53 61 62 63 71 72 73 51 52 53 61 62 63 71 72 73 The rule explaining this is the same as the rule for the two by two grid.

2. ## Number Stairs

This will lead to the fact that the nth term has to have 6n in the formula, the extra is calculated by working out what is left over this will be +32.Therefore, the formula has to be T =6n + 32.

1. ## Mathematical Coursework: 3-step stairs

60 61 62 63 46 47 48 49 50 51 52 53 54 37 38 39 40 41 42 43 44 45 28 29 30 31 32 33 34 35 36 19 20 21 22 23 24 25 26 27 10 11 12 13 14 15 16 17 18 1

2. ## The patterns

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