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  • Level: GCSE
  • Subject: Maths
  • Word count: 1956

Opposite Corners

Extracts from this document...

Introduction

Simon Bevan                

Opposite Corners

Maths Coursework

Investigation

The aim of this investigation is to find out the difference between the products of numbers in the opposite corners of any rectangle that can be drawn on a 100 square. I shall start off researching the 2x3 rectangle and then working onto bigger ones.

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100

2x3 Rectangle                    

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100

1x13=13                          88x100=8800                           7x19=133                                                                                                        

11x3=33                          98x90=8820                             17x9=153                              

          20                                          20                                          20

Prediction

I predict that when I multiply a 2x3 rectangle the opposite corners will have a difference of 20.

2x2 Rectangle (square)

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4x15=60                        33x44=1452                     72x83=5976

14x5=70                         43x34=1462                    82x73=5986

           10                                       10                                      10

Prediction

I predict that when I multiply a 2x2 rectangle (square)

...read more.

Middle

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54x76=4104                                         71x93=6603

74x56=4144                                         91x73=6643

  1. 40

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Prediction
I predict that when I

10x32=320                                                   multiply a 3x3 30x12=360                                                   rectangle (square) the

                                                                               Opposite corners will

                                                               Have a difference of 40.

3x4 Rectangle

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42x65=2730                                                 17x40=680                                                      

62x45=2790                                                 37x20=740                                                      

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           68x91=6188

           88x91=6248

                            60

Again I have noticed a pattern occurring each time the width increases by 1 the difference increases by 20.

Prediction

Using the theory I predict that when I multiply a 3x4 rectangle the opposite corners will have a difference of 60.

3x5 Rectangle

Prediction

I predict that when I multiply a 3x5 rectangle the opposite corners will have a difference of 80.

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1x25=25                                                   73x97=7081

21x5=105                                                 93x77=7161

  1. 80

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40x64=2560

60x44=2640

               80

3x6 Rectangle

Prediction

I predict that when I multiply a 3x6 rectangle the opposite corners will have a difference of 100.

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18x43=774                                             61x86=5246

38x23=874                                             81x66=5346

  1. 100  

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8x33=264

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            100

Pattern  Difference

                                            3x2    20image01.png

                                            3x3    40

                                            3x4    60

                                            3x5    80

                                            3x6    100

A Graph to Show the Difference within the Rectangle 3n

image05.png

X

X+1

X+2

X+3

X+4

X+10

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X+12

X+13

X+14

X+20

X+21

X+22

X+23

X+24

3x5

X(X+24)                            (X+4) X+20)

X² +24X                               X(X+20) +4(X+20)  

X² +24X                               X² +20X+4X+80

X² +24X                               X² +24X+80

 X² +24X

-X² +24X+80

        80

I shall now move on and investigate 4x4 Rectangle (square) and more Rectangles in the same way.

4x4 Rectangle (square)

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56x89=4984                                        19x52=988

86x59=5074                                        49x22=1078

  1. 90

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...read more.

Conclusion

L-1(G (H-1)) = L-1 x (Grid Width) x (H-1) = Difference

Evaluation

I have completed this piece of coursework and succeeded in my aims I set out to do. I have found the rule to work out the difference for any Rectangle of any size on any grid. I have done this by progressive investigation and the use of algebraic methods.

    I have taken the coursework as far as I can in the amount of time I had been allotted. I am happy with the amount of work that I have done on this bit of coursework and can’t think of anything I could of carried out better or improved upon.

...read more.

This student written piece of work is one of many that can be found in our GCSE Number Stairs, Grids and Sequences section.

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Here's what a teacher thought of this essay

3 star(s)

This is a fairly well structured report that covers a wide variety of experimental examples. To improve this the minor errors need to be revised and more emphasis placed on the algebraic analysis of the patterns. There are specific strengths and limitations suggested throughout.

Marked by teacher Cornelia Bruce 18/04/2013

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