= 5t-63
T Total= 13+14+15+23+32=97
32x5=160-63=97
My investigation turned out to be exactly what I predicted it to be. From my this experiment I can identify that 5t- t- numbers added together will always give you the
T total.
8 Grid
T total= (t) + (t-8) + (t-16) + (t-15) + (t-17)
=5t-56
T total=1+2+3+10+18=34
18x5=90-56=34
I am now going to draw 3 more T shape moving to the right across one on the grid
T total=2+3+4+11+19=39
19x5=95-56=39
T total=3+4+5+12+20=44
20x5=100-56=44
T total=4+5+6+13+21=49
21x5=105-56=49
From the table I have noticed that when that when you move a T shape across each time all the numbers go up by one, as they are five numbers the total goes up by five.
I am now to investigate the total by moving the T shape down the grid
T total=9+10+11+18+26=74
26x5=130-56=74
T total=17+18+19+26+34=114
34x5=170-56=114
T total=25+26+27+34+42=154
42x5=210-56=154
I have noticed that each time I move the T shape down the grid each number increases by eight, as they are five numbers the total increase by 40.
10 Grid
T total= (t) + (t-21) + (t-20) + (t-19) + (t-10)
=5t-70
T Total= 1+2+3+12+22=40
22x5=110-70=40
I am now going to draw 3 more T shape moving to the right across one on the grid
T Total= 2+3+4+13+23=45
23x5=115-70=45
T Total=3+4+5+14+24=50
24x5=120-70=50
T Total=4+5+6+15+25=55
25x5=125-70=55
From the table I have noticed that when that when you move a T shape across each time all the numbers go up by one, as they are five numbers the total goes up by five.
I am now to investigate the total by moving the T shape down the grid
T Total= 11+12+13+22+32=90
32x5=160-70=90
T Total=21+22+23+32+42=140
42x5=210-70=140
T Total=31+32+33+42+52=190
52x5=260-70=190
I have noticed that each time I move the T shape down the grid each number increases by ten, as they are five numbers the total increase by 50.
I will now put my results for all different grid sizes into a table to compare them
I predict that a 7 grid will be like this
I will now check this
7 Grid
T total= (t) + (t-7) + (t-14) + (t-13) + (t-15)
=5t-49
T Total=1+2+3+9+16=31
16x5=80-49=31
Add 5
Moved across one square to the right
T Total=2+3+4+10+17=36
17x5=85-49=36
T Total=3+4+5+11+18=41
18x5=90-49=41
Add 5
Moved down one square
T Total=8+9+10+16+23=46
23x5=115-49=46
My teacher told me that I could the bottom number ‘t’.
I can now work out some algebra for each box.
10 Grid
T total= (t) + (t-10) + (t-20) + (t-19) + (t-21)
=5t-70
(This only works on a 10 grid)
9 Grid
T total= (t) + (t-9) + (t-18) + (t-17) + (t-19)
=5t-63
(This only works on a 9 grid)
8 Grid
T total= (t) + (t-8) + (t-16) + (t-15) + (t-17)
=5t-56
(This only works on a 8 grid)
7 Grid
T total= (t) + (t-7) + (t-14) + (t-13) + (t-15)
=5t-49
(This only works on a 7 grid)
I have noticed that the algebra changes because the grid size is different each time.
I call the size ‘g’ I can work out some algebra for each box.
(This is now a ‘g’ grid)
T total= (t) + (t-g) + (t-2g) + (t-2g-1) + (t-2g+1)
=5t-7g
So to work out the total of a t shape anywhere on a grid I can multiply the t number by 5 and subtract 7 lots of the grid size.
I will now check this on this T shape a 10 grid with 26 as the T number.
T total= 5+6+7+16+26 = 60 T number= 26
T total= 5x26=130-70=60 Grid size= 10
