Maths-Number Grid

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                                                                                              Ranvir Kandola 10.5

                               Maths Coursework-Algebra!

Objective: - I will carry out an investigation to reveal the relationship

                    between the differences of products found in different sized

                    square grids.  

I will be using this 10 x 10 grid above, during the time of this coursework.

I will begin this investigation by starting off with a 2 × 2 grid and extend it

gradually, until I have reached a 10 × 10 square grid. I will use a highlighted

grid in each investigation, to show an example and prediction for the other

square grids of the same size.

Method:-

1. I will multiply the bottom left number by the top right number, to give

    me the product of these 2 numbers.

2. I will then multiply the bottom right number by the top left number,

    to give me the next product.

3. I will get the 2 products found and subtract the smaller product away

    from the larger product, to give me the product difference.

4. I will use this result found, to investigate further and find out if the same

    product difference occurs in each and every grid of the same size.

5. Finally, I will use the algebraic method, to test if my predictions were

    correct.

     

2 × 2 Grid Example:-

I have highlighted above the 2 × 2 grid I will be using for this example. I will

now use this grid to come up with a prediction for the other grids of the same

length and width. I will do this by multiplying 63 and 54 together to give me a

product of 3402. Afterwards, I will multiply 64 and 53 to give me a product of

3392. Lastly, I will subtract 3392 from 3402 to give me a product difference of

10. I will draw up 3 other grids, to test if my prediction is correct.    

 

 

2 × 2 Grids:-

 

       

   

From the following 2 × 2 grids, I have found

out that the difference between the products

is always 10. I have also uncovered that the

different numbers present in the box does

not affect the product difference of 10.

3 × 3 Grid Example :-

I have highlighted above a 3 × 3 grid, I will be using for the duration of this

time. I will now use the grid below to help me make a prediction for the product differences in other 3 × 3 grids. I will do this by multiplying the bottom left

number which is 93 by the top right number which is 75 to come up with a

product of 6975. I will then proceed to multiply the bottom right number which

is 95 by the top left number which is 73 to come up with a product of 6935.

Finally, I will subtract 6975 away from 6935 to come up with a product difference

of 40.

3 × 3 Grids:- 

 

From the above grid I have found out that

my prediction was correct because in each

of the 3 × 3 square grids the product difference

always came to 40. I have also found out

changing the numbers in the 3 × 3 square grid

does not affect the product difference of 40.  

4 × 4 Grid Example:-

I have highlighted above a 4 × 4 grid, which will help me make a prediction

for the other grids of the same length and width. I will use the square grid

highlighted above to help me make a prediction for the product differences

for the 4 × 4 grids. I will begin this by multiplying 46 by 19 to give me a

product of 874. I will continue to multiply the next 2 multiples which are 49

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by 16 to give me a product of 784. Finally, I will subtract 874 away from 784 to

give me a product difference of 90.

4 × 4 Grids:-

I have learnt from the above 4 × 4 grids that the difference between the

products has not changed throughout the following 3 cases I have completed.

I have found ...

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