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PART1 This is an investigation to find the relationship between the T-total and the T-number. A T-total is the numbers inside the T-shape added together and the T-number is the number at the bottom of the T-shape. 1 2 3 4 5 10 11 12 13 14 19 20 21 22 23 28 29 30 31 32 37 38 39 40 41 This is a 9x9 grid but I have cut it down because there is no need for me to draw all of it. T-number = 20 T-total = 1+2+3+11+20 ‘T’ Numbers T-total 1+2+3+11+20 37 2+3+4+12+21 42 3+4+5+13+22 47 4+5+6+14+23 52 5+6+7+15+24 57 6+7+8+16+25 62 7+8+9+17+26 67 After adding all of the T’s up the T-totals all have a difference of 5. T-Number 20 21 22 23 24 25 26 T-total 37 42 47 52 57 62 67 This table shows that it is +5 every time so we now know that this involves the 5 times table or 5n where n is the T-number. T-total 37 42 47 52 57 62 67 5n 100 105 110 115 120 125 130 5n means 5 times the T-number. For example when the T-number is 20 the 5n is 100. (20x5) When I look at and compare each T-total and 5n, the T-total increases by 63 each time. 37+63=100 42+63=105 47+63=110 etc. So for each expression it would be: T=5n-63, where n is the T-number and T is the T-total. This is a generalisation For any T-shape on a 9x9 grid to show Why T=5n –63.
Approximate Word count = 1000
Approximate Pages = 4
(250 words per page double spaced)
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