+ = 2
2= 2
Formula:
Middle number multiplied by 2 = (First number) + (Last number)
Case.2:
To see if “Case.1” applies for horizontal and diagonal rectangles.
Testing:
Conclusion:
The original formula (Case.1) also works for Variable.2.
Case.3:
Investigate what happens when Mary draws a rectangle around five numbers.
Testing:
I first tried to see if the formula for Case.1 applied for Case.3:
Conclusion:
The formula for Case.3 also works for rectangles with 5 squares whether it is diagonal, horizontal or vertical.
Case.4
Investigate if the formula also works for any amount of rectangle squares:
Testing:
Conclusion:
After doing the previous scenarios I have realised that by adding the first and last numbers together and then dividing by 2 makes the middle number (see formula in Case.4.) This works for any amount of rectangle squares in any direction.
Formula:
n.b. Error! Not a valid link. = Middle number
= First number
= Last number
= Error! Not a valid link. + Error! Not a valid link. 2
Case 3:
To investigate if there is any relationship between the middle number of a square and it’s parameter:
Testing:
n.b.
“Corners” are each corners of a square e.g.
71,73,93,91=
Conclusion:
We found out that it is possible to find out the middle number by finding the sum of the parameter and then dividing it by the parameter (squares on the outside.) Another way of finding the middle number was to take two diagonally opposite corners and divide by 2. This works as it is the same as diagonal rectangles (see case.2)
Formula:
n.b = parameter.
= Sum of parameter.
Error! Not a valid link. = Middle number.
Error! Not a valid link. =
Or
Error! Not a valid link. = Two diagonally opposite corners 2
