# I am going to investigate by taking a square shape of numbers from a grid, and then I multiply the opposite corners to find the difference of these two results. Firstly I am going to start with a 10x10 grid

Natalien nasir

Gcse Math's – number grid coursework

I am going to investigate by taking a square shape of numbers from a grid, and then I multiply the opposite corners to find the difference of these two results.

Firstly I am going to start with a 10x10 grid and pick up 4 different squares, I will start with the 2x2 square. Then I move on and use the 3x3, 4x4 and the 5x5 square.

I have noticed that the products difference of 2x2 squares in a 10x10 grid equal to 10. I predict if I move the 2x2 square to the right or down I will get the same answer.

My prediction is right. I am going to use algebra to test my results.

(n+1)(n+10)=n²+10+11n

n(n+11)=n²+11n

Products difference is equal to (n²+10+11n) – (n²+11n) =10

In the same grid I will now work out a 3x3 square.

I have noticed that the products difference of 3x3 squares in a 10x10 grid equal to 40. I predict if I move the 3x3 square to the right or up I will get the same answer.

My prediction is right. I am going to use algebra to test my results.

(n+2)(n+20)=n²+40+22n

n(n+22)=n²+22n

Products difference is equal to (n²+40+22n) – (n²+22n) =40

In the same grid I will now work out a 4x4 square.

I have noticed that the products difference of 4x4 squares in a 10x10 grid equal to 90. I predict if I move the 4x4 square up, I will get the same answer.

My prediction is right. I am going to use algebra to test my results.

(n+3)(n+30)=n²+90+33n

n(n+33)=n²+33n

Products difference is equal to (n²+90+33n) – (n²+33n) =90

In the same grid I will now work out a 5x5 square.

I have noticed that the products difference of 5x5 squares in a 10x10 grid equal to 160. I predict if I move the 5x5 square to the left I will get the same answer.

My prediction is right. I am going to use algebra to test my results.

(n+4)(n+40)=n²+160+44

n(n+44)=n²+44n

Products difference is equal to (n²+160+44n) – (n²+44n) =160

I have put my results in a table and I am now going to try to predict the 6x6 square in a 10x10 grid.

10,       40,       90,       160,      250,

+30       +50       +70      +90

+20       +20       +20

nth term= 10n²

The n is not the box size because for example if I put the 2x2 square in a 10x10 grid I will get 40. Unfortunately, this formula does not work but if I minus the box size by one I will then get 10 which is the right answer.

10(b-1) ²           this is my new formula.

I will test this formula on two box sizes I already have the results for:

E.g. 3x3 and 4x4 box size (see page 2).

10(3-1) ² = 40

10(4-1) ² =90       my new formula works.

I predict that the 6x6 square in a 10x10 grid will be 250 by using this formula:

• 10(b-1) ²
• =10(6-1) ²
• =10x25
• =250

My prediction is right.

I predict that the result for an 8x8 square in a 10x10 grid will be 490 by using this ...

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

**** This is a very well structured investigation. All mathematical working is correct and appropriately tested throughout. Specific strengths and improvements are suggested throughout. This is a good example of this coursework task.