• 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
5. 5
5
6. 6
6
7. 7
7
• Level: GCSE
• Subject: Maths
• Word count: 1050

# Number Grid.

Extracts from this document...

Introduction

GCSE Mathematics Coursework Number Grid Prepared by: Scott Bayfield This investigation relates to the product differences in different sized areas within a 10 x 10 number grid. For example: A 2 x 2 grid has been selected inside of the above grid. The objective of the investigation is to find the product of the bottom right and the top left numbers in the selected area. To calculate the product I must: Multiply the number in the bottom right cell with the number in the top left cell. The product difference is 10. This figure remains the same no matter where I carry out the above sum when used on a 2 x 2 grid within a 10x10 matrix. For example: Example 1 (75 x 86) - (76 x 85) = 10 Example 2 (1 x 12) - (2 x 11) = 10 Example 3 (17 x 28) - (18 x 27) = 10 These examples prove that the answer remains the same regardless of where we complete the sum with in the grid. ...read more.

Middle

term formula. The formula that I found effective was this: Total grid size x NTh term 2 = product difference i.e. NTh. term 1st 2nd 3rd 4th 5th Grid size 2 x 2 3 x 3 4 x 4 5 x 5 6 x 6 NTh. term calculation 10n2 Product difference 10 40 90 160 250 Note that the NTh. term is always 1 less than the grid size To see if this formula would work with a different size number grid I used the same formula as before only this time worked from a 10 x 8 matrix. Within the grid I tried the same variations as above i.e. 2 x 2, 3 x 3 etc. and discovered that the results remained exactly the same. I continued to investigation further, only this time I experimented using the 8 x 8 grid that can be seen below: When calculating the product from the above selection I encountered different results than found using the 10 x 10 matrix. ...read more.

Conclusion

I experimented with three individual 3 x 2 grids to prove my results remained constant. Example 1 (12 x 24) - (14 x 22) = 20 Example 2 (44 x 56) - (46 x 54) = 20 Example 3 (88 x 100) - (90 x 98) = 20 I found that the product differences remained the same however, in an effort to once again, further the investigation I carried out several more individual tests, increasing the size of the internal grid on each occasion. My results were as follows: Grid Size Product Difference 3 x 2 20 4 x 3 60 5 x 4 120 6 x 5 200 7 x 6 300 And again, I worked out a formula to find the product difference. Formula: Grid size x internal grid length -1 x internal grid height -1 or: 10(L-1)(H-1) NTh. term 1st 2nd 3rd 4th 5th Grid size 3 x 2 4 x 3 5 x 4 6 x 5 7 x 6 NTh. term calculation 10(L-1)(H-1) Product difference 8 32 72 128 200 Note that the NTh. term is always 1 less than the grid height ...read more.

The above preview is unformatted text

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. ## Number Grid Coursework

Justification The formula can be proven to work with the following algebra (where d = [p - 1], and e = [q - 1]): Difference = (a + d)(a + ze) - a(a + ze + d) a2 + zae + ad + zde - {a2 + zae +

2. ## Number Grids Investigation Coursework

between the numbers in the grid, I can come up with this formula: D = w (m - p) (n - p) I will try putting one of my examples into this to see if it is correct: D = w (m - p) (n - p) (w = 10)

1. ## Number Grid Investigation.

Product difference = 128. Justifying my results. A pattern has emerged from my calculations. Large Grid Square size Product difference 8 X 8 2 X 2 8 8 X 8 3 X 3 32 8 X 8 4 X 4 72 8 X 8 5 X 5 128 8 32 72 128 ?

2. ## Investigation of diagonal difference.

But can I apply g to the equation as well? Earlier on in the investigation G represented the length of the grid and it was common in the bottom 2 corners. In the case of a 2 x 3 cutout on a 10 x 10 grid G would be equal to 10.

1. ## Maths - number grid

These will be randomly selected from the 10x10 number grid, my aim being to find a pattern in my results. I feel unable to make a prediction of a defined difference at this point; I hope to make able to predict some type of trend or pattern further on.

2. ## Number Grid Investigation

I will now go on to investigate 5 x 5 squares on the grid, using the same process I used for the 4 x 4, 3 x 3 etc. I predict that the difference will be 160 because so far it has been all the square numbers multiplied by 10 in ascending order.

1. ## number grid

I am now going to repeat my investigation again so that my results are more reliable and so I can create a table with them. _3640 3630 10 For this 2 X 2 grid I have done the exact same thing as I did for the first one.

2. ## Mathematical Coursework: 3-step stairs

Therefore I will take the pattern number of the total: > 42-6=36 > b= 36 To conclusion my new formula would be: > 6n+36 11cm by 11cm grid 111 112 113 114 115 116 117 118 119 120 121 100 101 102 103 104 105 106 107 108 109 110

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