• 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
  • Level: GCSE
  • Subject: Maths
  • Word count: 1289

The Relationship between the T-number and T-total

Extracts from this document...

Introduction

Mathematics coursework by Nanjie Lu

The Relationship between the T-number and T-total

Question One

  • Investigate the relationship between the T-total and the T-number.

First of all I want use letter n for T-number, use letter T for T-total, use letter g for size of number-grid.

This question already told me that the size of number-grid is nine. So I am copied a size nine number-grid below:image08.png

In this table I chose a group of numbers to compare them and try to find out a relationship between one number and the total amount of this group, the numbers are below:

1

2

3

10

11

12

I chose the number ten for basic number, I am going to use letter X for this basic number. Also I am going to use letter Y for the total amount of this group.

So the result is showing below:

X-9

X-8

X-7

X

X+1

X+2

Next step is work out the how much Y is (the total amount of this group).

Add them all together equals:

image00.png

So the relationship between the Y and X is:

...read more.

Middle

62 = 5 × 25 – 63

The result of T-shape three:

  • n = 78
  • T = 59 + 60 + 61 + 69 + 78 = 327
  • 327 = 5 × 78 – 63

These two T-shapes are both correct; I used same formula as T-shape one.

So this means this relationship can be used for anywhere of a size 9 by 9 number-grid.

Key point – the formula of the size 9 number-grid is showing below:

image01.png

Question two:

  • Use grids of different sizes. Translate the T-shape to different position. Investigate relationships between the T-total, T-number and the grid size.

I chose two different sizes of number-grid to see the relationships between the T-number, T-total and the grid size.

The first one is size of 6 number-grid.

image09.png

 First of all I chose three T-shapes are showing below:

19

20

21

26

32

1

2

3

8

14

22

23

24

29

35

I am still using letter n for T-number, letter T for T-number try to find the relationship between the T-number and T-total in size six number-grid.

The result is showing below:

n – 11

n – 12

n – 13

n – 6

n

Now I am going to work out the T-total of this T-shape.

I found the relationship between the T-total and T-number is:

T = 5n – 42

The next thing is check the answer see if it is really can used for these T-shapes.

The results are showing below:

In T-shape one:

  • n = 14
  • T = 1 + 2 + 3 + 8 + 14 = 28
  • 28 = 5 × 14 – 42

In T-shape two:

  • n = 32
  • T = 19 + 20 + 21 + 26 + 32 = 118
  • 118 = 5 × 32 – 42

In T-shape three:

  • n = 35
  • T = 22 + 23 + 24 + 29 + 35 = 133
  • 133 = 5 × 35 – 42
...read more.

Conclusion


image08.png

From the table above I found out that we could not use some numbers next to the edge of number-grid, the reason for this is showing below:image11.png

The diagram above shows some numbers that I chose from the size nine number-grid, all these numbers could not be T-numbers. That is because we cannot use these numbers to form a complete T-shape. For example, I chose number one as a T-number, the meaning of T-number is the number at the bottom of the T-shape. But the problem is the number one is the top row of the whole number-grid so we cannot find any line above it to form a T-shape. Next we try the number ten as a T-number, still could not get a whole T-shape out, if we use ten the shape just like this:image12.png

Same problem as all the number in the last right hand-side column we cannot make a T-shape out use this numbers.

Now I found out that all the number in the first two rows across, the first column and last column cannot be a T-number.

...read more.

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

See related essaysSee related essays

Related GCSE T-Total essays

  1. T Total and T Number Coursework

    The final formula is 5n-7g+5x-5gy+14g, this will simplify to; 5n+7g+5x-5gy. I must now repeat this for -90 and +90 degrees. Then I will prove that my formulas are correct. +90 degree general formula for Rotation and Translation I will now have to repeat what I did above but for +90 degrees.

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

    - (d - b) (g+1) + a - bg } + 7 * Translate and rotate 180� T = 5 {n + 2 (c - a) - 2g (d - b) + a - bg } + 7g * Translate and rotate 270� clockwise T = 5 { n + (c - a)

  1. Objectives Investigate the relationship between ...

    5n+7 Works out the T-total of any T-shape translated in a 90� angle 5n+63 Works out the T-total of any T-shape translated in a 180� angle Rotating 270� I will now find out a formula for finding the T-total of any T-shape rotated by 270� 1 2 3 4 10

  2. T-Shapes Coursework

    Since all these variables have been tested before, it should be easy to spot the earlier patterns using previous knowledge that should remain true. 3) Data Collection 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23

  1. T-shapes. In this project we have found out many ways in which to ...

    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 Red t-shape 5tn- (7*G)

  2. T-Shapes Coursework

    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

  1. T totals. In this investigation I aim to find out relationships between grid sizes ...

    a is the number by which to translate vertically and b is the number by which to translate horizontally. It is also apparent that this equation can be used for any singular vertical or horizontal translation, as the other value (vertical or horizontal)

  2. T-Totals. We have a grid nine by nine with the numbers starting from 1 ...

    If we rotated the t-shape 180 degrees, The same will happen, as what happened when the t-shape was turned 180 degrees from it is first original position. This is proven below. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

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