• Join over 1.2 million students every month
• Accelerate your learning by 29%
• Unlimited access from just £6.99 per month
Page
1. 1
1
2. 2
2
3. 3
3
4. 4
4
• Level: GCSE
• Subject: Maths
• Word count: 1153

# Number Grids

Extracts from this document...

Introduction

Number Grids

Introduction

I have a10x10 grid. The task is to select various size squares and rectangles, I will then be multiplying the opposite corners together then subtracting the results to get the difference between the two answers. I hope to find patterns and rules in the results, if I can find patterns I will use algebra to describe them. My aim is to find the general rule for any size rectangle on any size grid.

Plan

• investigate different squares on a 10x10 grid.
• Find an algebraic rule.
• Repeat for rectangles on a 10x10 grid.
• Adapt the rule for squares to fit rectangles.
• Change the size of the grid
• Find an overall rule for any rectangle on any grid.

25 26                   25 x 36 = 900

35 36                   26 x 35 = 910

910 – 900 = 10

The difference between the two answers is 10.

1   2                   1 x 12 = 12

11 12                   2 x 11 = 22

22 – 12 = 10

Middle

91 92 93 94

The difference between the two answers is 90.

1   2   3   4      1 x 34 = 34

11 12 13 14      4 x 31 = 124

21 22 23 24      124 – 34 = 90

31 32 33 34

The difference between the two answers is 90.

67 68 69 70       67 x 100 = 6700

77 78 79 80       70 x 97 = 6790

87 88 89 90       6790 – 6700 = 90

97 98 99 100

The difference between the two answers is 90.

Now that I have my results from each of the different size squares I done, I will put them into the table.

 Size of Square The difference 2 x 2 3 x 3 4 x 4 104090

I now need to look for a pattern which is within the results.

After looking at the results I notice that if I ignore the noughts on the results, for example 1, 4, 9 . . . . . these numbers are all square numbers.

For the nth term, squaring must be involved.

When I square the number in the first column, I get the answer in the second column but on the line below. So instead of squaring n,  I need to square (n – 1).

Conclusion

2 – 1 = 1         1 x 5 = 5

6 – 1 = 5

5 x 10 = 50  using the formula I predict the the difference will be 50.

10(2 -1)(6 -1) = 10 x 5 = 50

This proves my formula works.

I have a theory that the reason I have to times by 10 is because I am usining a 10 x 10 grid. So I am going to test this theory by changing the size of the grid to a 5 x 5 grid, to see if the number I have to multiply by is 5.

I am going to test this theory on a 2 x 3 rectangle.

7   8

12 13

17 18

By using my previous formula I am going to guess what the difference is going to be.

2 – 1 = 1

3 – 1 = 2

1 x 2 = 2

2 x 5 = 5. I predict the number 5 will be the difference.

7 x 18 = 126

8 x 17 = 136

136 – 126 = 10    this provesmy theory was correct.

I have noticed the number you times it by is the size of the grid, so therefore to work out any rectangle on any size grid the formula would be:

g(n-1)(m-1)

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

## Found what you're looking for?

• Start learning 29% faster today
• 150,000+ documents available
• Just £6.99 a month

Not the one? Search for your essay title...
• Join over 1.2 million students every month
• Accelerate your learning by 29%
• Unlimited access from just £6.99 per month

# Related GCSE Number Stairs, Grids and Sequences essays

1. ## Investigation of diagonal difference.

So in the case of a 7 x 8 grid, the grid stops at 56 as it is not a perfect square, and this the product of 7 x 8, but in the case of a 7 x 7 grid, the grid stops at 64 as this is the product of 7 x 7 and it is a perfect square.

2. ## Maths Grids Totals

7 8 17 18 27 28 8 x 27 = 216 7 x 28 = 196 216 - 196 = 20. All 2 x 3 rectangles have a difference of 20, regardless of whether they are bigger horizontally or vertically.

1. ## Number Grids

Result 2 10 3 40 4 90 5 160 Using nth term I can tell that the formula is 10(n-1) Example (2x2 grid) n=2 10(n-1)2=10(2-1)2 =10(1)2 =10 Therefore I predict that a 6x6 grid would result in the following: 6x6= 10(6-1)2 =10(5)2 =10x25=250 I will now test my prediction.

2. ## Investigate The Answer When The Products Of Opposite Corners on Number Grids Are Subtracted.

- (1 x N�) 5(25- 5 + 1) - (1 x 25) (5 x 21) - 25 105 - 25 =80: Which is correct. However the starting number might not always be one. So I need to find an expression for it. If the bottom left square is 'N� - N + 1' then the top left square

1. ## Number Grids

This formula does show what happens with the grids before, so therefore I can say this is a definite rule. I am now going to investigate further with these types of rules, to see if there is a common link between different corners and the area of the grids we use.

2. ## The patterns

- (X�+44X)=160 This proves my equation correct! Now I shall try to answer the question "does this differ with a different size grid?" I shall try to fill the table shown underneath to get a clear view on all the data and try to see a formula from this data.

1. ## Algebra Investigation - Grid Square and Cube Relationships

of the box using a formula that remains constant: Formula 3: Bottom Left (BL) = (Width (w) - 1) x 10 The formulas stated above can be used to calculate these terms in any given table: TL: n ~ TR: Formula 2 ~ ~ ~ BL: Formula 3 ~ BR:

2. ## Number Grids

49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98

• Over 160,000 pieces
of student written work
• Annotated by
experienced teachers
• Ideas and feedback to