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  • Level: GCSE
  • Subject: Maths
  • Word count: 1581

Number grid algebraic course work

Extracts from this document...

Introduction

Number grid algebraic course work

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Firstly I was given this number grid, the intrusions were…

  • A box is drawn round four numbers.
  • Find the product of the top left number and the bottom left in this box.
  • Do the same with the top right and bottom left numbers.
  • Calculate the difference between these products.
  • Investigate further.

The first thing I did was follow these instructions. Then I changed the box size and looked for patterns.

A two by two box…

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12×23=276                 286-276= 10

13×22=286                

I tested a two by two box two more times to ensure each time I got the answer of 10, also to ensure that the answer was the same in different areas of the grid. I will do this for each different size boxes.

78×89=6942

79×88= 6952

9×20=180               10×19= 190

6952-6942 =10

190-180=10

...read more.

Middle

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12×56=672

16×52=832

1×45=45

5×41=205

96×60=5760

100×56=5600

832-672=160

205-45=160

5760-5600=160

I have noticed that all these numbers are divisible by ten. I’m going to divide by 10 to see what answers I get…

box

Difference

Divide by 10

answer

2×2

10

10÷10=

1

3×3

40

40÷10=

4

4×4

90

90÷10=

9

5×5

160

160÷10=

16

I have notice that when I divide by 10 I get all square numbers as my answers. These answers are all less than the box size chosen. Eg 2×2    2-1=1     1²

box

Difference

Divide by 10

answer

Square no

2×2

10

10÷10=

1

3×3

40

40÷10=

4

4×4

90

90÷10=

9

5×5

160

160÷10=

16

So from this I can make an equation to test any box…

10 (n-1)(n-1)=10 (n-1)²

Now I will test rectangle boxes to further my investigation. I predicted that this formula would not work on the rectangles. I will have to alter the formula later.  

A three by two box…

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  12×24=288               308-288=20

  22×14=308

I tested the three by two box twice more in different places to see if it would be the same answer…

5×17=85

7×15=105

67×79=5293

69×77=5313

105-85=20

5313-5293=20

Now I will test the box as a two by three and see if this will alter my answer…

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...read more.

Conclusion

128

4293-4165=128

I can use the same formula on this grid except I have to change it slightly… this was my formula for the 10 grid

10(c-1)(r-1)

as this is a 8 grid and all my difference are divisible by 8 I will change my formula to

8(c-1)(r-1)

I can check my answers using this formula

8(5-1)(5-1)=128                  8(2-1)(2-1)=8

I now know that I can use my formula to find my difference of rectangles in this grid. Eg.

A two by three grid…

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11x21=231           247-231=16

13x19=247

 8(2-1)(3-1)=16

The answers are the same so I think it is more efficient to use the formula to find the answers…

8(2-1)(4-1)=24        8(4-1)(2-1)=24

8(2-1)(5-1)=32        8(5-1)(2-1)=32

I will now further my investigation using algebra…

If I know that it’s a two by grid…

            2

X    

2

TL=X  TR=X+1

BL=X+10   BR=X+11

TL X BR         TRXBL

(X)(X+11)        (X+1)(X+10)

X²+11X         X²+10+X+10X   X²+10+11X           

This helps to p

...read more.

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