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  • Level: GCSE
  • Subject: Maths
  • Word count: 1567

T shapes. Once I have all of the results, I shall work out the nth term and investigate the relationship between the T number and the T total.

Extracts from this document...

Introduction

Kate Stewart

Explanation for task 1.

I am going to draw several T shapes on a 9 by 9 number grid and get the total of the numbers inside the T shape, which is called the T total, get the T number, which is the bottom number in the T shape and note them down in a table of results. I will repeat this a few times and note down the other results I get in the same table.

...read more.

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Table of results.

T number

T total

20

37

        +5

21

42

        +5

22

47

        +5

23

52

        +5

24

57

n

5n-63

5n-63 is the general rule.

Predict and test.

T25 = 57 + 5 = 62.

You get 57 from the table and you +5 because the pattern goes up in 5. It is just an easier way of working out a prediction.

62 is my prediction for the answer.

I chose T25 because it is the next consecutive number in the sequence.

I am now going to test it to see if my prediction was correct.

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T25 = 6+7+8+16+25 = 62

My prediction was correct. This means that the general rule is correct. However, I am going to try again with another T shape just to make sure the general rule actually works.

T68 = (68x5) – 63 = 277.

277 is my prediction and 68 is my T number.

I am now going to test it out to see if my prediction is correct. If it is correct, then the general rule is correct.

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51

58

59

60

67

68

69

T68 = 49+50+51+59+68= 277

Therefore, as my prediction was correct, the general rule is also correct.

In general.

n-19

n-18

n-17

n-9

n

T number = n

T total = n+n-9+n-18+n-17+n-19

        =5n-63.

You have 5n because there are 5 squares and it is -63 because all of the – numbers added together = -63.

Explanation for task 2.

I am going to draw several T shapes on several random number grids of different sizes to translate the T shapes to different positions and then when I have the results, I will investigate the relationships between the T total, the T number and the grid size.

8 by 8 number grid.

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...read more.

Conclusion

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T50=33+34+35+42+50=194

As my second prediction was also correct, this means that my general rule is also correct.

In general.

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T number = n

T total = n+n-8+n-17+n-16+n-15

                = 5n-56.

It is 5n because there are 5 squares and it is -56 because all the minus numbers added together make -56.

6 by 6 number grid.

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T number

T total

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28

        +5

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        +5

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n

5n-42

5n-42 is the general rule.

Predict and test.

T20=100-42=58

58 is my prediction.

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T20=7+8+9+14+20=58.

My prediction was correct so that means that my general rule may also be correct but I will try it out again just to be sure.

T35= (35x5)-42=133

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T35= 35+29+23+22+24=133

My prediction was correct again and so therefore is my general rule.

In general.

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n-6

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Grid size = g

T total

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5n-63

        +7

8

5n-56

        +14

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5n-42

g

5n-7g

...read more.

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