# In this piece course work I am going to investigate opposite corners in grids

Mathematics Course Work

## Introduction

In this piece course work I am going to investigate opposite corners in grids. I will start by investigating a 7x7 grid. Within this grid I will use 2x2, 3x3, 4x4, 5x5, 6x6 and a 7x7 grid. I will do this to find whether I can find a pattern. I will do this by multiplying the two opposite corners together then subtracting them. I will try to find the patterns and do a formula that will work for all grid sizes and shapes. I will experiment shapes and sizes of all different grids.

### Prediction

I predict that in a 7x7 grid all the opposite corners will be a multiple of 7 and in an 8x8 grid they will be a multiple of 8 and so on. They will only do this if I multiply the two opposite corners then subtract the two from each other.

To check my hypothesis I will use 6x6, 7x7, 8x8 and maybe if I have time I will do a 9x9 and 10x10 grid. Also I will be looking at all different shapes and sizes. I hope to find a formula for all grids and all shapes and sizes.

## 7x7 Grid

Here is a grid of numbers in sevens. It is called a seven grid. In this section I will multiply the opposite corners and then subtract them.

2x2

In my 7x7 grid I have highlighted three 2x2 grids. I will multiply and subtract the opposite corners now.

As you can see from my three examples they all have a difference of 7. The main grid size is the same of the difference, 7. All ready I can start to see a pattern.

3x3

Now I am going to see if a 3x3 grid gets the same out come as a 2x2 grid.

I don’t have the same outcome as my last examples but if I divide 28 by 4 I will get 7. This means I have a multiple of 7.

Again I have 28. I have a multiple of 7 again.

Again all the answers are at least a multiple of 7.

4x4

I am going to see what a 4x4 grid gives ...

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

This is a reasonably well structured investigation. It uses a wide variety of experimental examples to support a discovered pattern. To improve this more algebraic expressions to represent the differences need to be included.