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Introduction

Mariela Mezquita 10ª

Math, Mr Bhoja

30 April 2008

COURSEWORK

Aim: To find out a formula for rectangles on different grid sizes.

That is done by multiplying the corners of the rectangle and then we subtract them.

Hypothesis:

Eg. (on a 10x10 grid size with a 2x3 rectangle)

 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 72 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100

3 x 11= 33

1 x 13=13

33-13 = 20

Then, move on the rectangle.

A 2 x 3 cube… 1 2 3 11 12 13 2 3 4 12 13 14 3 4 5 13 14 15

As we can see, when we have a 2 x 3 rectangle, the final result will always be 20.

Explanation:

If we substitute the

Middle

 1 2 3 4 11 12 13 14 21 22 23 24
 2 3 4 5 12 13 14 15 22 23 24 25 It will always be 60..

Explanation:

 x x+3 x+20 x+23

x(x+23)

x+3(x+20)

expand

x(x+23) = x²+23x

x+3(x+20) = x²+20x+3x+60

x²+23x  x²+20x+3x+60

=60 x² and 23x cancel each other out, leaving us with a result of 60. If we change the

Conclusion

3 X 4 RECTANGLE ON ANY GRID SIZE So:

3x4 = 6n

FORMULA ABOVE ONLY APLLIES FOR A 4 X 5 RECTANGLE ON ANY GRID SIZE So:

4x5= 12n

FORMULA ABOVE ONLY APLLIES FOR A 5 X 6 RECTANGLE ON ANY GRID SIZE So:

5x6= 20n

FORMULA ABOVE ONLY APLLIES FOR A 6 X 7 RECTANGLE ON ANY GRID SIZE So:

6x7= 30n

Overall Formula:

N(H-1)(L-1)     Extension:

In my extension I will draw crosses instead of rectangles. Multiply the opposite sizes and try to find out a formula.

Hypothesis: I think it will be similar to the rectangle formula but a little bit more complicated.

Example:

 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 72 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100  This student written piece of work is one of many that can be found in our GCSE Open Box Problem section.

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