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# number grid....help me, please. watch

1. hello, i'm new to this forum, so please be kind.

anyway, my name's india and my maths teacher set us some really hard course work called 'number grid', which i'm really struggling with. like, you have a 10x10 grid and you have to work out an algebra formula using a 2x2 box, where you times the top left by the bottom right number, then times the top right by th bottom left number, finding the product by taking each number away.

i'm doing a 2x2 box, which i make longer. like, the width. so it goes 2x2, then 2x3, then 2x4 etc

then i do a height of 3, which goes 3x2, then 3x3, then 3x4 etc

i've know how much it goes up by - it goes up by 10 each time. so a height of 2 gives a product of 10, a height of 3 gives a product of 20, a height of 4 gives a product of 30, but i don't know how to find a formula that will work for a box of any size on any set of numbers on the whole grid.

i'm sorry, but this is really stressing me out.

please help me.
2. (Original post by India)
hello, i'm new to this forum, so please be kind.

anyway, my name's india and my maths teacher set us some really hard course work called 'number grid', which i'm really struggling with. like, you have a 10x10 grid and you have to work out an algebra formula using a 2x2 box, where you times the top left by the bottom right number, then times the top right by th bottom left number, finding the product by taking each number away.

i'm doing a 2x2 box, which i make longer. like, the width. so it goes 2x2, then 2x3, then 2x4 etc

then i do a height of 3, which goes 3x2, then 3x3, then 3x4 etc

i've know how much it goes up by - it goes up by 10 each time. so a height of 2 gives a product of 10, a height of 3 gives a product of 20, a height of 4 gives a product of 30, but i don't know how to find a formula that will work for a box of any size on any set of numbers on the whole grid.

i'm sorry, but this is really stressing me out.

please help me.

height of 2 gives a difference of 10
height of 3 gives a difference of 20
height of 4 gives a difference of 30

if you notice you have to take away 1 from the height of the box, and then times it by 10.

e.g. a height of 3, take away 1 gives 2, and then times by 10, which gives 20. Then state this formula and do a test for it to confirm.

After you have stated this formula try a 2x2 box, then 3x3 box, then 4x4 box.
Work out the difference and you will notice for an "n x n" box, you take away 1, then square that, and then times by 10 and this will give the difference for an n x n box. If i remember correctly for when i did this coursework the difference for an n x n box was 10(n-1)^2 ( ^ means power).

Remember after you state this formula test it with a size box that haven't already done, for example a 6 x 6 box should give a difference of:

10 (6-1)^2
= 10(25)
= 250

Hope this helps. Maybe after this you can add another variable such as the gap size of each square so instead of a gap size of 1 you can have a gap size of 2 or 3, or you could just state a gap size of "g" or any other letter and just do it by algebra. Then state the formula that you find for the difference and then test it.
3. thank you, you're very kind.

i'm quite dumb at maths though. what does 'power' and 'square' mean?

i understand the formula - very clever, but i don't understand what those terms means. can that formula be used anywhere on the grid, like a 7x6 for example?
4. Code:
```____ ____
|    |    |
|a+10|a+11|
|____|____|
|    |    |
| a  |a+1 |
|____|____|```
The above represents any 2x2 box on a 10x10 grid

TL x BR = (a+10)(a+1) = a2 + 11a + 10
TR x BL = a (a+11) = a2 + 11 a
(TL x BR) - (TR x BL) = 10

Now consider a 3x3 box (ignoring the boxes between the corners)

Code:
```____ ____
|    |    |
|a+20|a+22|
|____|____|
|    |    |
| a  |a+2 |
|____|____|```
TL x BR = (a+20)(a+2) = a2 + 22a + 40
TR x BL = a (a+22) = a2 + 22 a
(TL x BR) - (TR x BL) = 40

Using this technique try a general case of a box of width w and height h
Code:
```_______________ _______________
|               |               |
|a+10(h-1)      |a+10(h-1)+(w-1)|
|_______________|_______________|
|               |               |
| a             |a+(w-1)        |
|_______________|_______________|```
Or even a grid of width w, height h, on a grid of size n x n going up in increments of i
Code:
```_______________ _______________
|               |               |
|a+n(h-1)       |a+n(h-1)+i(w-1)|
|_______________|_______________|
|               |               |
| a             |a+i(w-1)       |
|_______________|_______________|```
After looking over this I realise I might have made it even more confusing ...
But I hope I gave you a general gist of how you might approach it algebraically
5. (Original post by India)
thank you, you're very kind.

i'm quite dumb at maths though. what does 'power' and 'square' mean?

i understand the formula - very clever, but i don't understand what those terms means. can that formula be used anywhere on the grid, like a 7x6 for example?
Square - times a number by itself, e.g. 4^2 = 4 x 4 = 16
Power - number times itself that many times, e.g. 2^4 = 2 x 2 x 2 x 2 = 16

Just out of interest, how can you be doing coursework like this and learning a gcse syllabus without knowing what these are or how they work?
6. pls can u help me with my coursework.......number grid....
how do i show my working using diagrams....
i first did 2x2...3x3...2x4 ............and so
7. (Original post by elizabethdavisdemol)
pls can u help me with my coursework.......number grid....
how do i show my working using diagrams....
i first did 2x2...3x3...2x4 ............and so
Ok, you're on the right track. I did this a couple weeks ago! look at the formulae for your 2x2, 3x3, and 4x4 grids. Look for a pattern that links them all then try to translate the formula into variable terms. Once you have the formula for an nxn grid, you're done!
8. This is one of the coursework tasks set by AQA for this year's exam. It is open to both Foundation and Higher level candidates. We need to be careful here.

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