• 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
• Level: GCSE
• Subject: Maths
• Word count: 2629

# Maths GCSE Investigation - T Numbers

Extracts from this document...

Introduction

Maths GCSE Investigation - T Numbers Introduction In a number grid, a T-shape can be drawn outlining five numbers. The sum of all the numbers within the T-shape is the T-total, and the number at the base of the T is the T-number. 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 In this 5 by 5 grid example, the T-number is 12, and the T-total is 1+2+3+7+12, which is 25. My task is to investigate the relationship between the T-number and the T-total for T-shapes within the number grid. The factors I can change which might change the pattern of numbers are: * Grid size * Direction of T-shape (with the T pointing N/S/E/W) * Translating the T-shape within a number grid to investigate patterns. Investigation#1-upright T-shape First of all, I am going to focus on the T-shape pointing S, the upright T: 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 I first thought that any T-shape could be created if the T-number was known, as the rest of the numbers in the T-shape are related to the T-number. For example, in the above 6 by 6 square, a T-shape is selected: T-number=21 T-total=21(T-number) ...read more.

Middle

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 The upright T-shape and the upside-down T-shape had an opposite in their formulas: -7Z and +7Z. Due to this fact, I predict that the formula for a sideways T-shape pointing W would be 5X+7, opposite to the sideways T-shape pointing E's formula of 5X-7. To test my prediction, I will apply it to the above 9 by 9 grid: T-total = 5X+7 = 5*51+7 = 262 51+52+53+44+62 = 262 My formula works, so 5T+7 is the formula for a sideways T-shape pointing W. Summary From the above four investigations, I can summarise that: * The formula for an upright T-shape in ANY grid size is: T-total = 5X-7Z * The formula for an upside-down T-shape in ANY grid size is: T-total = 5X+7Z * The formula for a sideways T-shape pointing E in ANY grid size is: T-total = 5X-7 * The formula for a sideways T-shape pointing W in ANY grid size is: T-total = 5X+7 Further investigations There are several different variables which I can change to extend this investigation: * Investigate in 3 dimensions * Translation of T-shape * Rotation of T-shape * Reflection of T-shape * Enlargement of T-shape 3D investigations A basic 3D cube can be made from small cubes, each representing one number. ...read more.

Conclusion

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 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 Applying the rules previously, the T-number in the above shape should be 35. The T-total is 105. The formula is: T-total = X(35) + X-Z+1(25) + X-2Z+2(15) + X-3Z+1(3) + X-Z+3(27) = 5X-7Z+7 = 5*35 - 7*11 + 7 = 105 3+15+25+27+35 = 105 From the derivation of my formula, I have proved that the T-shape and its number are in a fixed position, so it will work wherever it is placed. Test formula for 6 by 6 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 T-total = 5X-7Z+7 = 5*20-7*6+7 = 65 3+10+15+17+20 = 65 My formula works for the 6 by 6 grid. So the formula for a T-shape rotated through 45� is: T-total = 5X-7Z+7 N.B. Since this investigation is based on patterns derived from a diagram, ALL the formulas derived only apply in cases which the T-shape itself fits into the grid. ?? ?? ?? ?? Qiming Liu 10SM 09/05/2007 ...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 T-Total 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 T-Total essays

1. ## Connect 4 - Maths Investigation.

11L - 27 Test Rule: If the length is 7: [11L - 27] 11 x 7 - 27 = 50. I predict that the total number of connect 4 for the 5 x 7 grid will be 50. From this I can see that my prediction is correct.

2. ## T-Totals Investigation.

172 217 262 307 +45 +45 +45 +45 +45 +45 These T-totals have an addition of 45. With this I can see that 45�9=5. Next I will try and see if these are similar to the results from an 8 by 8 grid.

1. ## T-Shape investigation.

this sequence perfectly 5n - 63 I will check this by placing a T in the middle of the grid. 29 30 31 32 33 34 35 38 39 40 41 42 43 44 47 48 49 50 51 52 53 56 57 58 59 60 61 62 65 66

2. ## T-total Investigation

Using expressions I found out that my formula 5T - 70 is correct. I will now work out the formula for the given 3by2 T on a 9by9 grid. I placed the 3by2 T on the beginning of my 9by9 grid.

1. ## T-totals. I am going to investigate the relationship between the t-total, T, and ...

= 343 8�8 1 1 28 126 5 {28+2-2(8) } +7(8) = 126 -1 1 28 106 5 {28-2-2(8) } +7(8) = 106 1 -1 28 286 5 {28+2+2(8)} +7(8) = 286 -1 -1 28 316 5 {38-2+2(8) } +7(8) = 316 10�10 1 1 55 255 5 {55+2-2(10) } +7(10) = 255 -1 1 55 235 5 {55-2-2(10)

2. ## Objectives Investigate the relationship between ...

rotated in a 180� angle 5n-7 5n-7 5n-7 Works out the T-total of any T-shape rotated in a 270� angle What pattern can you notice? Looking at the table above, I can see that the formula for calculating the horizontal and vertical translations increase by an increment of '-7' every

1. ## In this section there is an investigation between the t-total and the t-number.

+ 70 = t-total 5*41-63+ 70 = 212 The formula has worked. We now want to work out the difference in the t-total of the first t-shape we started with to the rest of the other six t-shapes. The next two are the below t-shapes.

2. ## T-Total. I will take steps to find formulae for changing the position of the ...

information: 5 x 40 + 7 Answer: 207 Checking: 33 + 42 + 51 + 41 + 40 Answer: 207 Another example Substituting in the relevant information: 5 x 64 + 7 Answer = 327 Checking: 64 + 65 + 66 + 57 + 75 Answer: 327 My formula is correct.

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