• 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
8. 8
8
9. 9
9
10. 10
10
11. 11
11
12. 12
12
13. 13
13
14. 14
14
15. 15
15
16. 16
16
17. 17
17
18. 18
18
19. 19
19
20. 20
20
21. 21
21
22. 22
22
23. 23
23
24. 24
24
• Level: GCSE
• Subject: Maths
• Word count: 5603

# Number Grid

Extracts from this document...

Introduction

Higher Tier Task - 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 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 Use the following rule: find the product of the top left number and the bottom right number in the square. Do the same thing with the bottom left and the top right numbers in the square. Calculate the difference between these numbers. INVESTIGATE! I will begin with 2x2 windows on a 10x10 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 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 34 x 25 = 850 49 x 58 = 2842 24 x 35 = 840- 48 x 59 = 2832- 10 10 88 x 97 = 8536 63 x 72 = 4536 87 x 98 = 8526- 73 x 62 = 4526- 10 10 3 x 12 = 36 6 x 15 = 90 2 x 13 = 26- 5 x 16 = 80- 10 10 For all of these windows you can see ...read more.

Middle

When multiplied outside of the brackets: n�+ 8n + n + 8 - n�- 9n This can be simplified to: n�+ 9n + 8 - n� - 9n = 8 The n� and 9n cancel each other out therefore you are left with 8. I will now substitute a random 2x2 window size into this equation. n n+1 n+8 n+9 44 45 52 53 44�+ (9 x 44) + 8 - 44�-(44 x 9) = 8 1936 + 396 + 8 - 1936 - 396 = 8 2340 - 2332 = 8 n n+1 n+8 n+9 I predict that when doing 3x3 window on an 8x8 grid the difference will 32 because the sum of the opposite corners subtracted from each other in 2x2 window on the 8x8 grid was 4/5 of the difference for a 2x2 window on a 10x10 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 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 26 x 12 = 312 57 x 43 = 2451 10 x 28 = 280- 41 x 59 = 2419- 32 32 39 x 53 = 2067 21 x 7 = 147 37 x 55 = 2035- 23 x 5 = 115- 32 32 I was correct, it was 32, therefore the difference for a 4x4 window size should be 72. ...read more.

Conclusion

Therefore if you put 5x5 windows anywhere on a 10x10 grid with an increment of 3 the difference will be equal to 1440. We can again show the algebraic method of working out the difference. n n+3 n+6 n+9 n+12 n+30 n+33 n+36 n+39 n+42 n+60 n+63 n+66 n+69 n+72 n+90 n+93 n+96 n+99 n+102 n+120 n+123 n+126 n+129 n+132 We can change this into an equation: (n+12)(n+120)-n(n+132) When multiplied out of the brackets: n�+ 120n + 12n + 1440 - n�- 132n= 1440 This can be simplified to: n�+ 132n + 1440 - n�- 132n = 1440 Again the n� and 132n cancel each other out therefore you are left with 1440. This is the pattern I have seen. Window size Difference First Difference Second Difference 2x2 90 270 3x3 360 180 450 4x4 810 180 630 5x5 1440 180 810 6x6 2250 180 990 7x7 3240 180 1170 8x8 4410 180 1350 9x9 5760 This is a formula I have recognised for grids with an increment: The increment� multiplied by the difference for the same size window on a 10x10 grid with an increment of 1, for example: On a 10x10 grid with an increment of 1 anywhere a 2x2 window was placed the difference was 10. On a 10x10 grid with an increment of 2 anywhere a 2x2 window was placed the difference was 40. 2�= 4 4 x 10 = 40 And, on a 10x10 grid with an increment of 3 anywhere a 2x2 window was placed the difference was 90. 3�= 9 9 x 10 = 90 Therefore, a 2x2 window placed anywhere on a 10x10 grid with an increment of 4 the difference would equal 160. 4�= 16 16 x 10 = 160 Conclusion This is the formula to find the difference for any window size on any size grid with any increment. (n - 1)(n - 1) x w x i� = difference 'w' means width of the grid i� means the increment squared This could be simplified to: (n - 1)�x w x i�= difference Robert Bland Maths Coursework January 2004 ...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 Aim: The aim of this investigation is to formulate an algebraic equation ...

3 star(s)

I will now use the algebraic formula, using 11 in place of 'g' to prove that this is correct. n n + 1 n + g n + g + 1 n(n + g + 1) = n2 + ng + n n + 1(n + g)

2. ## Number Grid Coursework

d = [p - 1], and e = [q - 1]): Difference = (a + d)(a + 10e) - a(a + 10e + d) a2 + 10ae + ad + 10de - {a2 + 10ae + ad} a2 + 10ae + ad + 10de - a2 - 10ae - ad

1. ## Investigation of diagonal difference.

I will now convert the cutout into its algebraic form Converting the cutout into its algebraic form. n n + 3 n + 3g n + 3g + 3 Step 1 Step 2 Step 3 n N + 3 n + 30 n + 33 61 62 63 64 71

2. ## Maths - number grid

I will again increase the size of my rectangles and aim to come up with a major pattern. I will increase the size of my rectangles to 7x4, and with any luck this will help me reach my aim. 8x32 - 2x38 f 256 -76 Difference = 180 58x82 -

1. ## Maths-Number Grid

the product difference, because the answer always comes to a certain number 10. 3 � 3 Grid: - (A + 72) (A + 74) (A + 92) (A + 94) This algebra method, is once again correct because the product difference always came to 40 in all the 3 � 3 grids and has now appeared above in the algebra.

2. ## Number Stairs

= 24 By substitution stair total= 24+24+1+24+2+24+3+24+9+24+10+24+11+24+18+24+19+24+27= 340 = T Now that I have accomplished my investigation on the 9x9 grid with 4 step stair case, I am going to the 4 step stair investigation on the 8x8 grid. Here we can see that, stair number=1 Stair total= 1+2+3+4+9+10+11+17+18+25= 100

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

The criterion of why I haven't explained what B stands for is because I haven't found it yet. Nevertheless using the annotated notes on the formula my formula would look like this now: > 6N =6n x 1= 6 > 6+b=42 Now I would need to find the value of b in order to use my formula in future calculations.

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