• Join over 1.2 million students every month
  • Accelerate your learning by 29%
  • Unlimited access from just £6.99 per month

To investigate the relationship between the T-total and the T-number. The problem of the question is based on a 9 by 9 number grid.

Extracts from this document...

Introduction

Kimberly Wong 10F MATH COURSEWORK T-Totals Part I: Aim: To investigate the relationship between the T-total and the T-number. The problem of the question is based on a 9 by 9 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 T-shape drawn on a 9x9 grid: A T-shape is drawn on the 9 by 9 grid and all the numbers the T-shape are added together, and the sum is the T-total. This 'T-total' is known as T. The problem is to figure out the relationship between the T-total and the position of the T-shape (the position of the T-shape is the number in the bottom part of the T-shape). This position of the T-shape is known as p. ...read more.

Middle

Proving the Formula: 1. * Because it is a 9 x 9 grid, the difference between the three numbers is 9 * Each level increased means a decrease in 9 T = p (p - 9) + (p - 18) + (p - 17) + (p - 19) decrease by 9 each time This is shown in the equation. P represents the position of the T-shape, which can be shown as 0 because every other number has a relationship on some way with this number. This can be described as (9 x 0). 9 is because it is on a 9 x 9 number grid and zero is because it is the starting level of the T-shape. The next box above is (p - 9) because it has increased one level on the 9 x 9 grid, and therefore the number is 9 less than before. So, since the number is 9 less than the p number, it is therefore (p - 9). Another way I got the 9, is from (9 x 1). 9 is because it is a 9 x 9 number grid, and 1 because it has increased one level. ...read more.

Conclusion

Therefore, the equation is just p, because 8 x 0 is just 0. * 8 x 1 is because it is on an 8 x 8 number grid, and 1 is because it has increased one level. 8 x 1 is 8, but because it has increased one level, the number has decreased by 8, so it is p - 8. * 8 x 2 is because it is on an 8 x 8 number grid and 2 is because it has gone up 2 levels. 8 x 2 is 16, but because it has increased 2 levels, the number has decreased by 16, so it is p - 16. * The top two side numbers are figured out using the middle top number. Since they are consecutive, the number on the left would be p - 17 (this is found from 8 x 2 +1, and the number on the right would be p - 15 (this if found from 8 x 2 - 1). Also, since I know that T= 5p - 63, I now also know what p would be if I only knew T. If T= 5p - 63 P= T + 63 5 ...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

See related essaysSee related essays

Related GCSE T-Total essays

  1. T Total and T Number Coursework

    The translations will be done using vectors. I will use this to represent the vectors in my work. The top will be (x) And the bottom (y) Vector Tables for 9x9, 8x8 and 7x7 Grid Sizes. I will now find the t-total of the new shape and the change in

  2. The T-Total Mathematics Coursework Task.

    71 385 36 210 72 390 Analysis of a L-shape rotated 270 degrees clockwise on a 9 by 9 number grid From this table and the two number grids above we are now able to work out a formula for this particular type of L-shape by only having the two variables of the L-number and the grid size.

  1. T-Total Investigation

    Clockwise with the centre of rotation being 58, the original T-Total is 187 and the rotated T-Total is 347. We need to find the difference from the original Middle number the centre of rotation then, reverse the differences (i.e. horizontal amount = vertical amount and vice versa), then use the

  2. Given a 10 x 10 table, and a 3 steps stair case, I tried ...

    the formula the number of term, then the formula becomes: Where: "n" = bottom left number of staircase, e.g 3 n(1/2s2 + 1/2s) "s" = number of stairs in staircase e.g 3 stairs = 3 So, looking at my table in more depth I found two cubic sequences: 0, 11, 44, 110, 220, ...

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

    } +7 = 272 1 -1 55 292 5 {55+1+1(10)+1-1(10) } +7 = 292 -1 -1 55 382 5 {55-1+1(10)+1+1(10) } +7 = 382 Rotation of 180� about an external point g n T T = 5 (n + 2c - 2dg )+ 7g c d 9�9 1 1 40 183 5 {40+2-2(9)

  2. Objectives Investigate the relationship between ...

    I will use the T-shape, T19 to test if this works. 5x21 - 7 = 98 The formula works, just as expected. I will now show ALL the formulas that can be used in a 9x9 grid to calculate the T-total: Formula(8x8)

  1. T-Shapes Coursework

    25 60 105 160 225 Mean of Tail Boxes 25 30 35 40 45 Sum of Tail Tail Length 25 30 35 40 45 Fig 4.2 From Fig 4.2, it is possible to see a very useful pattern: 1) The Sum of the Tail divided by the Tail Length equals

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

    Middle number (v) T-Total (t) Equation used Difference 49 225 t = (5 x 49) + ( 2 x 10 ) 5 (225 - 220) 48 220 t = (5 x 48) + ( 2 x 10 ) 5 (220 - 215)

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