GCSE Mathematics T-Totals

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GCSE Mathematics T-Total C/W

I have been given mathematics coursework on T-totals; the coursework has been set in three tasks. The question is about T-shapes on different grids. The bottom number in the T is called the T-number. All the numbers in the T-shape added together are called the T-total. For each part of the coursework I have to translate the T-shape to different positions on the grid.

Key:

T-total = T

T-number = n

Grid Size = G

Part 1

For the first part of the coursework, I have to investigate the relationship between T-total and T-number.

I will use a 9x9 number grid and start off with the T-shape beginning at the number 1.

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To understand the relationship between the T-total and T-number we can look at the T-shape drawn on the 9x9 number grid. The total of the numbers inside the T-shape is 37 this is called the T-total. The number at the bottom of the T-shape is called the T-number. The T-number for this T-shape is 20.

In order to investigate the relationship between the T-total and T-number I will translate the T-shape by the vector (1, 0). In order to achieve accurate results I will carry this out 3 times. Here are the three T-shapes I end up with.

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20

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22

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21

I then tabulated the results to look for patterns.

n

20

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T

37

42

47

52

9x9 Grids

I did a prediction for the next T-shape.

I predict this because the T-number is increasing by 1 and the T-Total is increasing by 5. From my findings I concluded a formula linking the T-Number and T-Total which is T=5n-63.

I got this formula when I seen that the difference between each T-Total
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is 5 so the formula had to contain 5n.i used the 5n on my first of n in my table and I got 100. Then I subtracted 37(T-Total) from 100 which gave me 63.

Part 2

For the second part of the coursework, I have to investigate relationships between the T-total, the T-numbers and the grid size, using grids of different sizes.

I will use the following grid sizes to find the relationships:

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0

1

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