• 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

# Number Grid

Extracts from this document...

Introduction

N ATWELL-MANSINGH

GCSE MATHS

COURSE WORK

Number Grid

 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 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 70 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 90 100

Fig. A

To solve this problem I have broken down the table as much as possible starting with the first query given in the problem.

Ex (1) first box

Highlighted box: the product of the top right hand number and the bottom left hand

number minus the product of the top left hand number and the bottom right hand number

2*13= 26

12*3= 36

36-26= 10

Ex (2) second box

45*56=2520

55*46= 2530

2530-2520= 10

The product of the top right hand number and the bottom left hand number in each      square of numbers minus the product of the top left hand number

Middle

I tried using the formula for what I have found before in table Fig. B below but this time I added more columns to the problem

 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 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 70 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 90 100

Fig. B

The first column grid only 7 columns were highlighted and the following was taken into consideration

6 first number is n

7 the second number is n +1

By trying to find the formula for the number of columns used I introduced c in the formula

Therefore when 7 columns were used

The number below n =n+c

The number next to is as  n +c=1

Conclusion

Investigation 1:

The product of any square regardless of it’s location in the grid is 10.

Investigation 2:

n+c+1 (c being the number of columns) the answer is always equal to the number of columns used in the grid.

Investigation 3:

The total of numbers in the top row of a grid subtract the total of numbers below is always equal to the number of columns used in the grid multiply by ten (10) which is the product of any square.

In conclusion I found that the general formula for a grid with c columns multiply by the general formula in a square is equal to the sum of numbers in the grid square and grid column.

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 Investigation.

Width of grid (width of box - 1)� Only if squares are 2 X 2, 3 X 3, 4 X 4 etc Say the grid was 108 wide, the formula would be 108 (n-1)� What next? I am now going to see if my 2nd and 3rd formulas work in the same way as mentioned before and above.

2. ## Open Box Problem.

10 0 40 0 As you can see, the table above shows the volume of an open box for different measurements for cut x for a rectangle with the measurements of 20cm by 60cm, which is in the ration of 1:3.

1. ## For other 3-step stairs, investigate the relationship between the stair total and the position ...

The results are conclusive and consistent, proving the theory to be accurate and reliable. Using any of the algebra equation from the above table, e.g. 21x-315 or 21x-385 we can prove the results for any 6-step grid: 1 Formula: 21x-315 11 12 1: 21x51-315= 756 21 22 23 1+11+21+31+41+51+12+22+32+42+52+23+33+43+ 2:

2. ## Maths - number grid

To ensure my calculations are right I will use algebra: (r+4)(r+48) - r(r+52) r(r+48) +4(r+48) - r - 52r r +48r +4r +192 - r - 52r =192 As can be seen my calculations are correct, I will now continue to further my investigation.

1. ## Number Grid Investigation

The next square number is 25 so the difference should be 250. 14 15 16 17 18 19 24 25 26 27 28 29 34 35 37 37 38 39 44 45 47 47 48 49 54 55 56 57 58 59 64 65 66 67 68 69 14 x

2. ## number grid

4 X 4 Grid Now I will look at 4 X 4 grids within a 10 X 10 grid. Again I will work this out algebraically. Here is the algebraic grid for a 4 X 4 grid within a 10 X 10 grid.

1. ## Mathematics - Number Stairs

it will always be T = n because the n is the bottom left number and the formula is not accumulating anything but the bottom left number which is the only term in the formula. 8 9 10 11 12 1 T = n T = n T = n

2. ## Mathematical Coursework: 3-step stairs

Therefore I will take the pattern number of the total: > 54-6=48 > b= 48 To conclusion my new formula would be: > 6n+48 12cm by 12cm grid 133 134 135 136 137 138 139 140 141 142 143 144 121 122 123 124 125 126 127 128 129 130

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