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• Level: GCSE
• Subject: Maths
• Word count: 1711

# To investigate how the T number moves across And down effects the T total.

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Introduction

To investigate how the T number moves across

And down effects the T total.

8 by 10 grids

 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

I have colored numbers inside the grid so it looks like a letter T.

I have also done this on a 9 by 10 grid and a 10 by 10 grid.

To investigate how the T number moves across

And down effects the T total.

In this investigation I had to find out how the T number moves across and down, effects the T total. I used grid sizes of 8 by 10, 9 by 10 and 10 by 10.

The T number is the number at the bottom of the T.

18 = the T number

Middle

18

34

21

49

42

154

45

169

66

247

69

289

I found out that going across the grid once, and adding 5 to the last t-total gives you the next t–total.

Then I found out that going down the grid once, and adding 40 to the last t–total gives you the next t–total.

If you multiply the difference going across by the gridsize you get the difference going down.

5 * 8 = 40

9 by 10 grid going down and across.

 T – Number T – Total 20 37 23 52 26 67 47 172 50 187 53 262 74 307 77 322 80 337

I found out that going across the grid once and adding 5 to the next t-total gives you the next t-total.

Then I found out that going down the grid once, and adding 45 to the last t–total gives you the next t–total.

If you multiply the difference going across by the gridsize you get the difference going down.

5 * 9 = 45

10 by 10 grid going down and across.

 T – Number T – Total 22 40 25 55 28 70 52 190 55 205 58 220 82 340 85 258 88 370

I found out that going across the grid once and adding 5 to the next t-total gives you the next t-total.

Then I found out that going down the grid once, and adding 50 to the last t–total gives you the next t–total.

Conclusion

=        =

=

=

Multiples

I drew a 10*10 grid going up in the three times table. I took a T out of the grid and then done the algebra for it. Here are my results:-

 T – Number T – Total 75 165

Algebra

=

In this T is equal to 75 so 75 – 45 is equal to T – 30.

Then I did the equation using G for the grid size.

=        =

In my equation I used G for the gridsize so T-30 is equal to T-3g because G is equal to 10 and 10 is the gridsize.

Then I put M into the algebra. M meaning multiple. I am using a multiple of 3 because that is what the grid was going up in.

=        =

=

I looked at both equations for the grids going up in 2’s & 3’sand found out a pattern. The pattern is that on the multiple equations it is the same for both of them apart from the number at the end. On the 2 equation it is + 2 & - 2 and on the 3 equation it is + 3 & - 3.

The equation here is 5T because I added all the T’s and then I got 7MG because I added up MG + 2MG + 2MG + 2MG. Therefore the equation is 5T – 7MG.

Maths Coursework                T - Totals

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