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• Level: GCSE
• Subject: Maths
• Word count: 1355

# T-totals. I have realised that the number above any T-number is the T-number minus the Grid size, in other words, N-G. To work out the T-total, just simply add everything in the T-shape.

Extracts from this document...

Introduction

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Example 1:

 T-number T-total 21 42 51 192 75 312

Example 2:

Example 3:

T-structure:

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T-structure for a 7x7 Grid

Example 1:

Example 2:

General T-structure for any Grid size:

N= T-number

G= Grid size

I have realised that the number above any T-number is the T-number minus the Grid size, in other words, N-G.

To work out the T-total, just simply add everything in the T-shape.

T-total= n+ (n-g) + (n-2g-1) + (n-2g) + (n-2g+1)

T-total= 5n-7g

I will check that this formula works for any size grid:

 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

T-total = 1+2+3+6+10= 22

Using the formula: 5x10=50 – (7x4) = 22

The formula works for this grid size.

 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

T-total = 7+8+9+13+18 = 55

Using the formula: 5x18=90 – (7x5) = 55

The formula works for this grid size as well.

Middle

N+A

Variable = A

A= the number of times T is moved across

Translations: down

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When you move the T-shape down one square the number increases by the size of the grid. For example, in this grid, every number increases by 9.

When the T-shape is moved 2 squares down, the number increases by 2x size of the grid.

The same rule applies: When T-shape is moved 3 squares down, the number increases by 3x size of the grid.

Formula:

N= T-number

D= the amount of times the T-shape is moved down.

G= Grid size

The formula which works for any grid size is: N+DG

Translation: across and down

Formula for T-number:        N+A+DG

Formula for T-total:

T-total = N+A+DG-2G-1+N+A+DG-2G+N+A+DG-2G+1+N+A+DG-G+N+A+DG

Conclusion

Therefore, N’ = N+A+DG+H+VG+V-HG.

The T-total for a shape which has been translated then rotated is as follows:

Therefore the T-total would be all the boxes added together.

T-total = 5N+5A+5DG+5H+5VG+5V-5HG+7

This can be factorised to get

T-total = 5(N+A+DG+H+VG+V-HG) +7

Now I will test this for the above grid to check if this works.

 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

Formula:

5(N+A+DG+H+VG+V-HG) +7

Therefore: - 5(16+1+21+1+7+1-7) +7 = 207

T-total = 40+41+42+35+49 = 207

The formula works!

In conclusion to work out the T-number for a new shape after it has been translated and rotated you use the formula:

N’= N+A+DG+H+VGV-HG

And the formula for the T-total after the shape has been translated and rotated is:

N’= 5(N+A+GD+H+VG+V-HG)+7

This student written piece of work is one of many that can be found in our GCSE T-Total section.

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