Table of results.
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.
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.
T68 = 49+50+51+59+68= 277
Therefore, as my prediction was correct, the general rule is also correct.
In general.
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.
5n-56 is the general rule.
Predict and test.
T23 = 54 + 5 = 59
59 is my prediction.
T23=6+7+8+15+23=59.
My prediction was correct so the general rule must also be correct. However, I am going to test it out again just to make sure.
T50 = (50x5) – 56 = 194
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.
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.
5n-42 is the general rule.
Predict and test.
T20=100-42=58
58 is my prediction.
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
T35= 35+29+23+22+24=133
My prediction was correct again and so therefore is my general rule.
In general.
