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• Level: GCSE
• Subject: Maths
• Word count: 2521

# In this investigation I will be finding out the relationship between the T-total and the T-number.

Extracts from this document...

Introduction

Coursework.

## T-Totals

In this investigation I will be finding out the relationship between the        T-total and the T-number.

The first table will be a 9 x 9 table.

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• The T-total is: 1+2+3+11+20=37

The T-number is 20.

• The T-total is: 2+3+4+12+21=42

### The T-number is 21

• The T-total is: 3+4+5+13+22=47

### The T-number is 22

The relationship between each T-total is that they go up in 5’s.  Eg 37+5=42 etc

The relationship between each T-number is that they go up in 1’s.  Eg 20+1=22 etc

I have now decided to translate the T by 2cm to the left.

 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 81
• The T-total is: 1+2+3+11+20=37

The T-number is 20.

• The T-total is: 3+4+5+13+22=47

### The T-number is 22

• The T-total is:5+6+7+15+24=57

### The T-number is 24

The relationship between each T-total is that they go up in 10’s.  Eg 37+10=47 etc

The relationship between each T-number is that they go up in 2’s.  Eg 20+2=22 etc

I have decided to make a prediction.

• My prediction is that when I translate the shape by 3cm to the left the T-total will go up by 15 and that the T-number will go up by 3.
 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 81
• The T-total is: 1+2+3+11+20=37

The T-number is 20.

• The T-total is: 4+5+6+14+23=52

The T-number is 23.

• The T-total is: 7+8+9+17+26=67

The T-number is 26.

• My prediction is correct.

I predicted that the T-total would go up by 15.  Eg 52-37=15 etc

I also predicted that each T-number would go up by 3.  Eg 20+3=23 etc

I am now going to translate the shape 1cm down.

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• The T-total is 37.

The T-number is 20.

• The T-total is 172.

The T-number is 47.

• The T-total is 307.

The T-number is 74.

The prediction I made was incorrect.  The T-total actually goes up by 135 and the T-number by 27 each time.

I am now going to change the size of the grid to an 8x8 table to see if I can spot any changes or similarities.

 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 34 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
• The T-total is: 1+2+3+10+18=34

The T-number is 18

• The T-total is 39.

The T-number is 19.

• The T-total is 44.

The T-number is 20.

The relationship between each T-total is that they go up by 5 each time.  Eg 34+5=39 etc

The relationship between each T-number is that they go up by 1 each time.  Eg 18+1=19 etc

I am now again going to be translating the ‘T’ 2cm to the left.

 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 34 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
•  The T-total is: 1+2+3+10+18=34.

The T-number is 18.

• The T-total is 44.

The T-number is 20.

• The T-total is 54.

The T-number is 22.

The relationship between each T-total is that they go up in 10’s.  Eg 44+10=54 etc

The relationship between each T-number is that they go up by 2 each time.  Eg 187+2=20 etc

I am now going to make a prediction.

• I predict that by moving the ‘T’ by 3cm each time the T-total will go up by 15 and that the T-number will go up by 3.
 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 34 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
• The T-total is 34.

The T-number is 18.

• The T-total is 49.

The T-number is 21.

Looking back at my results I can see that my prediction is correct.

The relationship between each T-total is that they go up in 15’s and each T-number goes up by 3 each time.  Eg 34+15=49 and 18+3=21.

I am now going to continue by translating the ‘T’ 1cm down.

 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 34 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
• The T-total is 34.

The T-number is 18.

• The T-total is 74.

The T-number is 26.

• The T-total is 114.

The T-number is 34.

The relationship between each T-total is that they go up by 40 each time.  Eg 74+40=114 etc

The relationship between each T-number is that they go up by 8.  Eg 26+8=34 etc

I am now moving on to move the ‘T’ shape 2cm down.

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Conclusion

I am now continuing by making the grid to a 10x10 grid to see if I can spot any changes.

 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 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100
• T-total = 40 and T-number = 22.
• T-total = 45 and T-number = 23.
• T-total = 50 and T-number = 24.

I have noticed that all 3 T-totals go up by 5 each time and that each T-number goes up by 1.  Eg 40+5=45 and 22+1=23 etc

I am now translating the shape 2cm to the left.

 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 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100
• T-total = 40 and T-number = 22.
• T-total = 50 and T-number = 24.
• T-total = 55 and T-number = 26.

I am now beginning to see a big similarity by using a 10x10 grid.  I have noticed that however many cm you move the ‘T’ to the left the T-total goes up by 5 and the T-number goes up by however many cm you move the shape.

I am now going to continue by moving the shape down by 1cm.

 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 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100
• T-total = 40 and T-number = 22.
• T-total = 90 and T-number = 32.
• T-total = 140 and T-number = 42.

The relationship between each T-number is that they go up by 50.

Eg 90-40=50 etc

The relationship between each T-number is that they go up in 10’s.

Eg 22+10=32 etc

I am now going to translate the shape 2cm down.

 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 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100
• T-total = 40 and T-number = 22.
• T-total = 140 and T-number = 42.
• T-total = 240 and T-number = 62.

I have noticed that each T-total goes up by 100.  Eg 40+100=140 etc

I also have noticed that each T-number goes up by 20.  Eg 22+20=42.

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

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