• Join over 1.2 million students every month
  • Accelerate your learning by 29%
  • Unlimited access from just £6.99 per month
Page
  1. 1
    1
  2. 2
    2
  3. 3
    3
  4. 4
    4
  5. 5
    5
  6. 6
    6
  7. 7
    7
  8. 8
    8
  9. 9
    9
  10. 10
    10

Opposite Corners.

Extracts from this document...

Introduction

Opposite Corners

Introduction

Ellie Birch

image41.pngimage01.pngimage00.pngimage01.png

Opposite corners are really simple. Basically, you choose any number between 1 – 100. The only numbers that you won’t be able to choose are the numbers along the bottom row (91 – 100) and the ones running down the right hand side (the multiples of 10). Look at the green lines on the diagram and you’ll see that only rectangles can be made, and as they are only half squares, image02.pngimage00.pngimage03.pngimage39.pngimage19.pngimage29.pngimage02.pngimage11.pngimage04.pngimage11.pngimage04.pngimage03.pngimage08.png

image05.png

2x2 Squares

image41.pngimage01.pngimage01.pngimage00.png

1x12= 12 difference = 10

11x2= 22 difference = 10image00.png

57x68= 3876 difference = 10

67x58= 3886 difference = 10image00.pngimage01.pngimage01.png

81x92= 7452 difference = 10image00.png

91x82= 7462 difference = 10image00.pngimage06.pngimage06.png

image00.png

Number in left hand corner of the box = n

L)[n(n+11)] + [n+1(n+9)]

En          n+1  image07.pngimage09.png

N

n+10      n+11

The formula

...read more.

Middle

1x13= 13

11x3= 33image10.pngimage10.png

18x10= 180

8x20= 160image10.pngimage12.pngimage12.png

image10.png

66x58= 3828

56x68= 3808

The difference is always 20.

Nn          n+1      n+2      n+3

image14.pngimage13.png

Ln+10   n+11    n+12    n+13

Hn(n+13)                Difference is 20image15.png

(n+3) (n+10)

3x3 Squares

image10.pngimage16.pngimage16.pngimage41.png

1x23= 23

21x3= 63

image10.png

43x65= 2795image10.pngimage17.pngimage17.png

63x45= 2835

image16.pngimage10.pngimage16.png

68x90= 6120image10.png

88x70= 6160

image10.png

The difference is always 40.

n          n+1          n+2

image18.pngimage20.png

n+10   n+11        n+12

n+20    n+21       n+22

Hn(n+22)                Difference is 40image15.png

(n+2) (n+20)

2(w)xL    DifferenceThe numbers step up in 10image21.png

2         10

3                            20    >10

4                        30    >10

I predict that a 2x5 square will have a difference of 40.

4x4

  1.    2    3    4                         1x14=44image22.pngimage23.png

                11x4=44

11  12  13  14

The difference is 40. Now I need to test out my prediction:

1       2      3      4    5            1x15= 15

        11x5=55image25.pngimage24.png

11    12    13   14    15

The prediction was correct, the difference is 40.

So that means that if you want

...read more.

Conclusion

Square number         (w) _        Formulaimage37.png

2                                (wx10) –10  = difference

3                                (wx20) – 20 = difference

4                                (wx30) – 30 = difference

5                                  (wx40) – 40 = difference

I predict that a 5x5 square will have a formula of:

(wx40) – 40

This is because I have made a formula to work out the general formula, and tested it out:

w[10(w – 1)] – [10(w – 1)]

image38.png

w – 1

 Square number = 2 (w)

  1. – 1 = 1

 x 10 = 10

x 2 = 20

– 1 = 1

x 10 = 10

20 – 20 = 10

divided by 2 – 1 = 10

All you do is write out this equation: (wx__) - __ and replace the two blank spaces with the number that you have found

That proves to be correct, so now I will see if the theory for the 5x5 square is correct.

I predicted that the formula would be:

 (wx40) – 40 = difference

5[10(5 – 1)] – [10(5 – 1)]

image38.png

5 – 1

5(4x10) – (4x10)

        4image40.png

40x5 = 200 – 40 = 160

160 divided by 4 = 40

The formula proves to be correct.

...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.

Found what you're looking for?

  • Start learning 29% faster today
  • 150,000+ documents available
  • Just £6.99 a month

Not the one? Search for your essay title...
  • Join over 1.2 million students every month
  • Accelerate your learning by 29%
  • Unlimited access from just £6.99 per month

See related essaysSee related essays

Related GCSE Number Stairs, Grids and Sequences essays

  1. Marked by a teacher

    Opposite Corners. In this coursework, to find a formula from a set of numbers ...

    4 star(s)

    � Where: y = numbers arranged in y Columns or in a y grid and n = size of square. Unit 2- Testing the rule, y (n-1) �, on larger squares: In a 8�8 square: y (n-1) � = difference 10 (8 - 1)� = difference 10 � 7� =

  2. Marked by a teacher

    Opposite Corners

    3 star(s)

    84 90 91 92 93 94 80x94=7520 90x84=7560 40 2x6 Rectangle Prediction I predict that when I multiply a 2x6 rectangle the opposite corners will have a difference of 50. 52 53 54 55 56 57 62 63 64 65 66 67 1 2 3 4 5 6 11 12

  1. Marked by a teacher

    Opposite Corners.

    60 61 62 63 64 65 66 67 68 69 70 71 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 1.

  2. Investigate the difference between the products of the numbers in the opposite corners of ...

    = 8910 8910 - 8900 = 10 I can now also see that no matter where the shape is on the diagonal axis the difference remains the same. I will now try a random position on the grid to finalise my results so far.

  1. Mathematical Coursework: 3-step stairs

    67 68 69 70 71 72 49 50 51 52 53 54 55 56 57 58 59 60 37 38 39 40 41 42 43 44 45 46 47 48 25 26 27 28 29 30 31 32 33 34 35 36 13 14 15 16 17 18 19 20

  2. I am doing an investigation to look at borders made up after a square ...

    4 4 4 4 5 5 5 5 5 5 Border Number=B Number of numbered squares=N 1 12 2 16 3 20 4 24 5 28 Using my table of results I can work out a rule finding the term-to-term rule.

  1. "Multiply the figures in opposite corners of the square and find the difference between ...

    The number generated will be the number in the top left hand corner of the square. 89 90 99 100 90 x 99 = 8910 89 x 100 = 8900 The difference yet again is 10; this is no mere coincidence and therefore is a constant pattern within all the 2 by 2 squares that I have tested so far.

  2. "Multiply the figures in opposite corners of the square and find the difference between ...

    The number generated will be the number in the top left hand corner of the square. 89 90 99 100 90 x 99 = 8910 89 x 100 = 8900 The difference yet again is 10; this is no mere coincidence and therefore is a constant pattern within all the 2 by 2 squares that I have tested so far.

  • Over 160,000 pieces
    of student written work
  • Annotated by
    experienced teachers
  • Ideas and feedback to
    improve your own work