• 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

Number Grid Investigation.

Extracts from this document...

Introduction

Number Grid Investigation I was first given A 10x10 grid, counting from 1-100. Inside the grid was A 2x2 box surrounding the numbers, 12, 13, 22 and 23; 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 was asked to; * Find the product of the top left number and bottom right number in the box. * Do the same with the top right and bottom left numbers n the box. * Calculate the difference between these numbers. ...read more.

Middle

= M Top of box = N Side of grid = X Bottom of grid = Y Difference = L I now had to start by trying to work out the sequence of the numbers: M = 2 3 4 5 L = 10 40 90 160 30 50 70 20 20 To work out A sequence, we first see how many times we have to look for an equal difference, in this case we have to go look twice, this means that M will be squared; M2 We next look at the difference, in this case 20, we halve it, this will be multiplied by M; M2 x 10 This should be the formula, I will test it; 42 x 10 = 160 This is clearly wrong, as this is the answer for the next part, but I can see what's wrong, so I can fix it. The problem is that I am going to have to take 1 away from M before it is multiplied by 10 to get the correct formula; (M - 1)2 x 10, or factorised, 10(M - 1)2 This will now work, (4 ...read more.

Conclusion

86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 I will not write here all of my working, as it would take up too much space, so I will just write the results; N x M = L 2x2 = 10 3x2 = 20 4x2 = 30 5x2 = 40 6x2 = 50 There is A certain pattern here, as each time we add 1 to N, the difference goes up by 10. Instead of taking M to be the variable in this formula, I will use N as it is the one changing; N --> 2 3 4 5 6 L --> 10 20 30 40 50 10 10 10 10 As I only had to look once for A common difference, N will not have to be squared. The formula turned out like this: 10 (N - 1) I tested this for the 7th part of the 'sequence', 10 (7 - 1) = 60, which, as you can see from the numbers above, is the next part of the sequence, I have found A formula for rectangles where M = 2. ...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 Consecutive Numbers 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 Consecutive Numbers essays

1. GCSE Maths Coursework - Maxi Product

Product of number 12 6 and 6 6+6 6x6 36 13 6.5 and 6.5 6.5+6.5 6.5x6.5 42.25 14 7 and 7 7+7 7x7 49 15 7.5 and 7.5 7.5+7.5 7.5x7.5 56.25 16 8 and 8 8+8 8x8 64 What I notice: I notice that the Maxi product is retrieved when the two halves of the selected number are multiplied together.

2. Maths Investigation - Pile 'em High

I now have to use the cubic standard sequence t0 find the formula for the number of tins Term Number 1, 2, 3, 4, 5 N= 1, 5, 14, 30, 55 a+b+c= 4 9 16 25 7a+3b+= +5 +7 +9 12a+2b= +2 +2 The standard cubic formula is an� +

1. Investigate calendars, and look for any patterns.

Ex.5.14 Starting 1st February 1 2 3 1 x 24 = 24 3 x 22 = 66 Difference = 42 8 9 10 15 16 17 22 23 24 Finally, I decided to test a box of 14 numbers. Ex.5.15 Starting 1st August 1 2 3 4 5 6 7

2. Nth Term Investigation

x2 and for the third lot (n +2) x2 Plus with any rectangle at all will always be 4. So with this bit of information I predict: When t = 5, is n = 4, is (n + 3) x2 and + is (n - 1) x4 When t = 10, is n = 4, is (n + 3)

1. Borders and squares

'n' indicates the position in the sequence. an4 +bn3 +cn2+dn+e position of sequence: an4 +bn3 +cn2+dn+e n=1 a+b+c+d+e= 1 n=2 16a+ 8b+4c+2d+e=7 n=3 81a+27b+9c+3d+e=25 n=4 256a+64b+16c+4d+e= 63 n=5 625a+125b+25c+5d+e= 129 Now I am going to subtract n=2 from n=1, n=4 from n=3 and n=5 from n=4.

2. In this investigation I will explore the relationship between a series of straight, non-parallel, ...

and 3, when every line in the diagram crosses over every other line, there are in fact a maximum of six crossover points and a total of 11 regions. Diagram 4: (all 4 lines cross each other, regions are depicted with numbers, crossover points are high-lighted with red circles)

1. I'm going to investigate the difference between products on a number grid first I'm ...

3 by 3 spares will be 40, I'll do another 3 by 3 grid to confirm that my prediction is correct. 16 17 18 26 27 28 36 37 38 The difference between 648 and 608 is 40 because 648 - 608 = 40 18 x 36 = 648 16

2. I am to conduct an investigation involving a number grid.

x2 + 33x [image012.gif] 47 x 20 = 940 (x + 3) (x + 30) x2 + 30x + 3x + 90 =(x2 + 33x + 90) - (x2 + 33x) = 90 940 - 850 = 90 The difference between the two numbers is 90 Box 2 1 2

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