# Maths GCSE Coursework: T-Total Investigation

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Introduction

Maths GCSE Coursework

T-Total investigating monitoring cover sheet

Introduction

In this investigation we have to find a relationship between the numbers in the T and the T-Total number.

We are using a nine by nine grid and we will move the T is a systematic way to see if wee is able to find a relationship between the numbers across the grid.

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 |

The total of the numbers inside the T are:

1 + 2 + 3 + 11 + 20 = 37

The number at the bottom of the T is called the T number:

1 | 2 | 3 | 4 |

10 | 11 | 12 | 13 |

19 | 20 | 21 | 22 |

28 | 29 | 30 | 31 |

To make sure you get a different T number each time, you need to move the T shape around the number grid.

2 | 3 | 4 |

12 | ||

21 |

4 | 5 | 6 |

14 | ||

23 |

7 | 8 | 9 |

17 | ||

26 |

T- Number T – Total

20 37

21 42

22 47

23 52

24 57

25 62

Middle

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

1 | 2 | 3 |

10 | ||

18 |

1 | 2 | 3 |

10 | ||

18 |

2 | 3 | 4 |

11 | ||

19 |

3 | 4 | 5 |

12 | ||

20 |

T-Number T-Total

18 34

19 39

20 44

21 49

The pattern in these tables is plus one every time in the T – Number and for the T – Total it is plus five very time.

5 | 6 | 7 |

14 | ||

N |

The nth term = 5N – 56

To find the nth tern I looked at the T – Number value and times it by the gap which is 5 and then subtracted by the first T-number to get the gap which in this case was 56.

Prediction

I predict that when the t - number is 23 the T – total will be 59, and also in an equation the T –number will be 24 and the T-Total will be 64 this is shown in the table below.

22 x 5 – 56 = 54

23 x 5 – 56 = 59

24 x 5 – 56 = 64

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 |

1 | 2 | 3 |

10 | ||

16 |

2 | 3 | 4 |

10 | ||

17 |

Conclusion

Prediction

I predict that when the t - number is 18 the T – total will be 48, and also in an equation the T –number will be 19 and the T-Total will be 53 this is shown in the table below.

17 x 5 – 42 = 43

18 x 5 – 42 = 48

19 x 5 – 42 = 53

Formulas

3 x 3 = 19 + (5 x (r-8)

8 x 8 = 34 + (5 x (r–18)

9 x 9 = 37 + (5 x (r – 22)

10 x 10 = 40 + (5 x (r-22)

11 x 11 = 43 + (5x (r-24)

12 x 12 = 46 + (5 x (r-26)

These grids are to work out certain sizes; if you want to work out any size grin you can use the formula below.

(19 + 3 x (r – 3) + (5 x *t – 2 x (T + 1)

What I found out

In this investigation I have found out that this formula above will work out the sizes for any size grid.

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

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