# Opposite Corners

Simon Bevan

## Opposite Corners

Maths Coursework

## Investigation

The aim of this investigation is to find out the difference between the products of numbers in the opposite corners of any rectangle that can be drawn on a 100 square. I shall start off researching the 2x3 rectangle and then working onto bigger ones.

2x3 Rectangle

1x13=13                          88x100=8800                           7x19=133

11x3=33                          98x90=8820                             17x9=153

20                                          20                                          20

Prediction

I predict that when I multiply a 2x3 rectangle the opposite corners will have a difference of 20.

2x2 Rectangle (square)

4x15=60                        33x44=1452                     72x83=5976

14x5=70                         43x34=1462                    82x73=5986

10                                       10                                      10

Prediction

I predict that when I multiply a 2x2 rectangle (square) the opposite corners will have a difference of 10.

2x4 Rectangle

24x37=888                             1x14=14                        67x80=5360

34x27=918                             11x4=44                        77x70=5390

30                                       30                                       30

I have noticed a pattern occurring each time the width increases, the difference increases by 10, by 1.

Prediction

Using the theory I predict that when I multiply a 2x4 rectangle the opposite corners will have a difference of 30.

2x5 Rectangle

Prediction

I predict that when I multiply 2x5 rectangle the opposite corners will have a difference of 40.

10x24=240                                                   48x62=2976

20x14=280                                                   58x52=3016

40                                                                    40

80x94=7520

90x84=7560

40

2x6 Rectangle

Prediction

I predict that when I multiply a 2x6 rectangle the opposite corners will have a difference of 50.

52x67=2484                   ...

#### Here's what a teacher thought of this essay

This is a fairly well structured report that covers a wide variety of experimental examples. To improve this the minor errors need to be revised and more emphasis placed on the algebraic analysis of the patterns. There are specific strengths and limitations suggested throughout.