Lastly, I have to show how patterns have been used and to test my conclusions by providing proof of my results using mathematical models and new results from work previously done, using clear reasoning to prove my results.
How I can get started.
I could start by by drawing different T-shapes and using 12 different grid-sizes. I could explore as many aspects of the task as possible, explaining why and how, and develop the task into new areas.
Which connection is possible?
The connection between the graphs and the tables of my results. I had to find-out the type of pattern which would show-up if I used the data I placed in my tables.
Is there a result to help me?
Yes, the tables which I constructed by collecting a number of t-numbers and then working out their T-totals. For each different number-grid I used, I had to start a new table in order to identify the different patterns found in the t-numbers and T-totals.
Is there a pattern?
I have done a table for each of my 12 grid-sizes, which show the t-numbers and T-totals that I recorded. Taking the table for Grid 1 as an example, the t-number is going up in 3's while the T-totals are going up by 24.
I can make a prediction for the T-totals that don't show in the table, by creating a line graph to prove my theory. Then again, the other pattern I discovered during my investigation is the one on 5t's.
6 times table - 5t = 70
7 times table - 5t = ?
8 times table - 5t = ?
9 times table - 5t = 100
10 times table - 5t = ?
11 times table - 5t = ?
I could predict the 4 missing numbers by plotting a graph and showing the corresponding pattern accurately and straight and present it as my proof.
Conclusion*
This task has made me realise that there are so many patterns to be discovered in mathematics and they are all leading to a clear reasoning which just shows up once you have taken the steps needed to reach that point.
Using algebra also has an effect in helping me understand more about the work and also has it's pattern charactristics, which are complicated but still make sense once you focus on the formulae; Algebra makes the answers get squeezed up into a shorter explanation . For example, instead of writing 62+50+38+26+14+3+2+1= 196 you could just express it as T= 8t - 300, when t = 62. This coursework just gets my full reasoning, accuracy and draws upon the evidence I have presented.