T Shapes - T total coursework for maths

GCSE: Maths

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T-Total Investigation

Tasks 1 and 2:

Introduction:

This coursework involves the use of algebraic techniques to
investigate the relationship between the T-Total, the T-Number and the
grid size. I will be using different sized grids such as the one
below.

This is a grid sized 9 x 9, (g = 9)

where g = the grid size

image of grid

On this grid, I will start by drawing a shape, highlighted in blue.
This will be known as the T-Shape.

The number at the bottom of the T-Shape, (in this case 20), will be
known as the T-Number.

The total of all the numbers within the T- Shape will be known as the
T-Total.

For Example - For this T-Shape on the 9 x 9 grid above, the T-Number
is 20 and the T-Total is 37, (1 + 2 + 3 + 11 + 20 = 37).

In this coursework I will be drawing and using grids of 5 different
sizes and in each of these I will be drawing T-Shapes and calculating
the T-Number and T-Total for each, as shown above. Furthermore, in
each grid I will be moving the T-Shape along by 1 square, a minimum of
5 times if possible. This will help me find a pattern and investigate
the relationship between the T-Total, the T-Number and the Grid Size.

6 x 6 Grid (g = 6)

image of grid

From this grid I will tabulate the results of the T-Number and the
T-Total, starting from the top left and moving along by one block:

T-Number

T-Total

14

1 + 2 + 3 + 8 + 14 = 28

15

2 + 3 + 4 + 9 + 15 = 33

16

3 + 4 + 5 + 10 + 16 = 38

17

4 + 5 + 6 + 11 + 17 = 43

From the grid it can be seen that the centre column in the T-Shape
increases by 6 as you go down. This is because of the grid size (g =
6)
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