• 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: 1612

# rectangles. I will be trying to develop a formula that will enable me to calculate the sum of all the numbers in a rectangle given

Extracts from this document...

Introduction

 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 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100

 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 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100

The value of the rectangle is 132.

We would get the value by calculating the sum of all the numbers.

A way we could find this value out could be by using a formula. But what formula could we use?

 n n+1 n+2 n+10 n+11 n+12
 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 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100

The sum of the values in the turquoise box adds up to 132.

To find this, we could try n and n+12.

16+16+12=44

132÷44=3

3 are equal to the width.

So far we have w (2n + 12).

Middle

 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 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100

This time, the width of each shaded square is 4.

For the first shaded square, the values come up to 180.

4(2n+12): 4(44): 4x44= 176.

As you can see, we have changed the width, but have not changed the n+12 to n+13. If we tried this, we would get 180.

To do this so our formula is correct we would have to alter it.

W (2n+r). ‘R’ stands for the range. To make sure this formula is correct, I will try it on the remaining two squares and then on one with a completely different width.

The sum of the rose coloured box comes up to 380.

Conclusion

R(LxW)+(LxW)

2

14(2x5)+(2x5)

2

14(10): 140. 140÷2=70. 70+(10)=80. So far this formula has been correct, but would happen if initial term changes from 1 to a different number.

R(LxW)+(LxW)

2

12(2x3)+(2x3)

2

12(6)=72. 72÷2=36. 36+6=42.

 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 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100

I could now try to split the height from 2 to 1 and adding both rows to get the final product.

w(in+1). I can change in which is the initial term to n, which will stand for the lowest number.

Width(n+1). 3(4+1)=3(5)=15. 4+5+6=15.

For the second row we will have 3(14+1)=3(15)= 45. 14+15+16=45.

45+15+60.

4+5+6+14+15+16=60.

54+55+56+57+64+65+66+67=484.

4(54+1) 4(55)= 220.

4(64+1) 4(65) 195. 220+260=480. This answer is incorrect. So instead of it being w(n+1), I am going to change it to w(n+(r-1)) for each row.

4 (54+(2))= 4(56)= 224

4(64+2)=4(66)=264. 224+264= 488. this answer is also incorrect.

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. ## Investigate the difference between the products of the numbers in the opposite corners of ...

x 20 = 160 10 x 18 = 180 180 - 160 = 20 1 2 3 11 12 13 1 x 13 = 13 3 x 11 = 33 33 - 13 = 20 81 82 83 91 92 93 81 x 93 = 7533 83 x 91 =

2. ## Mathematical Coursework: 3-step stairs

131 132 109 110 111 112 113 114 115 116 117 118 119 120 97 98 99 100 101 102 103 104 105 106 107 108 85 86 87 88 89 90 91 92 93 94 95 96 73 74 75 76 77 78 79 80 81 82 83 84

1. ## Investigate Borders - a fencing problem.

needed for border number 6 using the formula, I found out, above: nth term = 4 x 6 + 10 = 34 Common Difference nth Term Results My prediction was 34 which is the correct answer, for the number of squares needed for border number 6, and which also proves that the formula is in working order.

2. ## I will try to find a formula linking P (perimeter), D (dots enclosed) and ...

is obvious with all these tables that as P increases, D decreases. The two values are inversely proportionate. As t remains constant, I suspect that some combination of P and D will give T, on account of one going up and the other going down.

1. ## Investigate the relationships between the numbers in the crosses.

- (d+11)(d-9) = (d +2d) - (d -9d+11d-99) = (d +2d) - (d +2d-99) = -99 * If x is known: = (x-1)(x+2) - (x+10)(x-10) = (x +1x-1x-1) - (x -10x+10x-100) = (x +x-1) - (x +x-100) = 99 * This also implies that the outcome of the sum (d x b)

2. ## My investigation will be on 3 - step stairs where I will be: ...

15 16 5 6 7 Stair Number Addition Total Pattern 1 1 + 2 + 3 + 11 + 12 + 21 50 6*1 + 44 2 2 + 3 + 4 + 12 + 13 + 22 56 6*2 + 44 3 3 + 4 + 5 + 13

1. ## Open Box Problem.

The scatter diagram on the next page also shows us that the maximum value is 6. Notice that the shape of the scatter diagram is the same as the two scatter diagrams done for the other two squares.

2. ## For my investigation I will be finding out patterns and differences in a number ...

All the differences are underlined and in bold. 1 2 3 4 5 6 11 12 13 14 15 16 21 22 23 24 25 26 31 32 33 34 35 36 41 42 43 44 45 46 51 52 53 54 55 56 1 x 56 = 56 51

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