Investigating the relationship between the T-totals and the T-number.

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Mathematics

G.C.S.E.

Course Work

T-Totals

By: Bharatjit Basuta

10kw

07/04/2004

Part One: I’ll be investigating the relationship between the T-totals and the T-number.

To show the relationship between T-totals and the T-numbers I will use a nine by nine grid to explain. There is a shape in the grid called the T-shape. This is shown below highlighted in the colour red.

The number 20 at the bottom of the T-shape, this is called the T-number. All the other numbers highlighted in the T-shape are called the T-total.

For this T-shape

T-number = 20

T-total = 37

For this T-shape

T-number = 21

T-total = 42

After viewing the information that every time the T-number goes up one the T-total goes up by five. So in this case the ratio between the T-number and the T-total is 1:5. This can help me because when I want to translate a T-shape that is in another position. For instance when I the T-shape here.

For red T-shape

T-number = 20

T-total = 1+2+3+11+20 = 37

For Orange T-shape

T-number = 74

T-total = 55+56+57+65+74 = 307

I all ready know the answer to the red T-shape from the previous work that I did. To work out the orange T-shape I will have to work out the difference of the T-number. In this case it is 54 (74-20). Then I will times the 54 by 5 because the T-total rises by 5 ever time the T-number goes up by one. Then I will add the T-total from the original T-shape and I will come out with the T-total for the Orange T-shape. To make it clear I will show it below

74-20 = 54

54x5 = 270

270+37 = 307

 This is just another way to work out the T-total.

I have found a formula for the relationship between the T-total and the T-number. The formula is 5T-number-63 = T-total

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How I got the formula

The formula starts with 5x the T-number. This is because The T-total rises by 5 for every T-number. For example look at the chart below. As the T-number rises by 1 the T-total rises by 5

Then I minus 63 which I got from by working out the difference between the T-number and another number in the T-shape. This has to be done wit all 4 numbers in the T-shape. After getting the difference of each number in the T-shape I then added them together and got 63.

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