Investigation: T-Shaped Investigation

Originally I was unsure on which investigation to pick however after looking at each in detail the T-Shaped investigation seemed more logical to me. At the beginning, I took a very random approach in picking the different T-Shapes (10, 20, 39, 5) I could not draw much of a conclusion (see figure one.) After reevaluating, I decided to take a more systematic approach, going along number by number to work out the T total. I was unable to start at T1 because of the number grid, therefore the first starting point was T2 and so on (see figure two.)
Recording my results in a table, I noticed that each T total increased by five (see figure 3 for working out each T total.) Therefore, it must be related to the 5 times table, multiplying by five. This was my first step in creating a formula, multiplying the T number (otherwise known as N in the formula) by 5 though, at the time I thought I was just using trial and error. However, by multiplying the T number by five, it did not give the T number total (see figure 4) therefore …show more content…
Having a shape of five numbers also relates to why multiple by 5. Knowing this it then gave me an idea on how to extend the investigation on for children. By changing the shape, could children work out the formula based on the knowledge found from this investigation? Can they work out the formula by just looking at the shape?
Therefore, changing shape from a T-shape to a square, it changes the amount of numbers but also the relationship between surrounding numbers and N number.

Another way in which to extend the problem is a smaller grid. Rather than having 7 numbers across and having 5, it once again changes the dynamics as the relationship between the numbers are