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  • Level: GCSE
  • Subject: Maths
  • Word count: 1104

T totals. By drawing 4of these t-shapes I have noticed that the T-total increases by 5. When I moved my T-shape 1 place to the right, my T-number increased by 1.

Extracts from this document...

Introduction

T-Totals

        T=3+4+5+13+22=47

        T-Total=47

        T-number=22

        T=4+5+6+14+23=52

        T-Total=52

        T-number=23

        T=5+6+7+15+24=57

        T-Total=57

        T-number=22

        T=6+7+8+16+25=62

        T-Total=62

        T-number=25

Comment

By drawing 4of these t-shapes I have noticed that the T-total increases by 5. When I moved my T-shape 1 place to the right, my T-number increased by 1.

Comment

T=m+ (m-9) +(m-18)+ (m-17) + (m-19)             Comment

  =5m-63        

CheckT=Total

47=5(22)-63                   m=T-number

47=110-63

47=47

8 by 8 grid

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I am now going to do the same method but by using an 8 by 8 grid.

        T=17+18+19+26+34=114

        T-Total=114

        T-number=34

        T=18+19+20+27+35=119

        T-Total=119

        T-number=35

        T=19+20+21+28+36+124

        T-Total=124

        T-number=36

        T=6+7+8+16+25=62

        T-Total=62

        T-number=37

Comment

By drawing 4of these t-shapes I have noticed that the T-total still increases by 5.

...read more.

Middle

Comment

  T=m+ (m-7) + (m-14) + (m-15) + (m-13)             Comment

  =5m-49        

CheckT=Total

                   m=T-number

9 by 9

T=5m-63

8 by 8

T=5m-56

7 by 7

 T=5m-49

I have noticed that all multiples of 7. The numbers on top of the T-number increase by 1.

Grid Size

Comment

Check

9 by 9

Comment

        T=Total

        T-number=21

        T=5(21)-7(9)

           105-63

Comment

I am now going to do the same method but I will put the T-shape in different positions.

9 by 9

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        T=3+12+21+11+10=54

        T-Total=57

        T-number=10

        T=4+13+22+12+11=62

        T-Total=62

        T-number=11

        T=5+14+23+13+12=67

        T-Total=67

        T-number=12

        T=6+15+24+14+13=72

        T-Total=72

        T-number=13

Comment

By drawing 4of these shapes I have noticed that the T-total increases by 5.

...read more.

Conclusion

                         T-number=32

Comment

By drawing 4 of these shapes I have noticed that the T-total increases by 5. When I moved my shape 1 place to the right, my T-number increased by 1.

Comment

T=m+ (m+9) +(m+18)+ (m+17) + (m+19)             Comment

=5m+63        

CheckT=Total

47=5(22)-63                   m=T-number

47=110-63

47=47

I am now going to do the same method but put it in another position again.

9 by 9

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                         T=3+12+13+14+21=63

                         T-Total=63

                         T-number=14

                         T=4+13+14+15+22=68

                         T-Total=

                         T-number=15

                         T=5+14+15+16+23=73

                         T-Total=73

                         T-number=16

                         T=6+15+16+17+24=78

                         T-Total=78

                         T-number=17

Comment

By drawing 4 of these shapes I have noticed that the T-total increases by 5. When I moved my shape 1 place to the right, my T-number increased by 1.

Comment        

T=m+ (m+1) +(m+2)+ (m-7) + (m+11)             Comment

 =1+2=3

=3+11=14

=14-7=7

=5m+7        

CheckT=Total

47=5(22)-63                   m=T-number

47=110-63

47=47

...read more.

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