Opposite Corners
In this piece course work I am going to investigate opposite corners
in grids. I will start by investigating a 7x7 grid. Within this grid I
will use 2x2, 3x3, 4x4, 5x5, 6x6 and a 7x7 grid. I will do this to
find whether I can find a pattern. I will do this by multiplying the
two opposite corners together then subtracting them. I will try to
find the patterns and do a formula that will work for all grid sizes
and shapes. I will experiment shapes and sizes of all different grids.
Prediction
I predict that in a 7x7 grid all the opposite corners will be a
multiple of 7 and in an 8x8 grid they will be a multiple of 8 and so
on. They will only do this if I multiply the two opposite corners then
subtract the two from each other.
To check my hypothesis I will use 6x6, 7x7, 8x8 and maybe if I have
time I will do a 9x9 and 10x10 grid. Also I will be looking at all
different shapes and sizes. I hope to find a formula for all grids and
all shapes and sizes.
7x7 Grid
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Here is a grid of numbers in sevens. It is called a seven grid. In
this section I will multiply the opposite corners and then subtract
them.
2x2
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On the second day of class, the Professor Judit Kerekes developed a short chart of the Xmania system and briefly explained how students would experience a number problem. Professor Kerekes invented letters to name the quantities such as “A” for one box, “B” for two boxes. “C” is for three boxes, “D” is for four boxes and “E” is for five boxes. This chart confused me because I wasn’t too familiar with this system. One thing that generated a lot of excitement for me was when she used huge foam blocks shaped as dice. A student threw two blocks across the room and identified the symbol “0”, “A”, “B”, “C”, “D”, and “E.” To everyone’s amazement, we had fun practicing the Xmania system and learned as each table took turns trying to work out problems.
6x6x6 cube and see if I can find a pattern. When I have found a
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I will use arithmetic and algebra to investigate the relationships between the grid and the stair further. The variables used will be: Position of stair on grid = X Sum of all the numbers within the stair = S Step Size= n Grid size= g 91 92 93 94 95 96 97 98 99 100 81 82 83 84 85 86 87 88 89 90 71 72 73 74 75 76 77 78 79 80 61 62 63 64 65 66 67 68 69 70 51 52 53 54 55 56 57 58 59 60 41 42 43 44 45 46 47 48 49 50 31 32 33 34 35 36 37 38 39 40 21 22 23 24 25 26 27 28 29 30 11
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I am going to begin by investigating a square with a side length of 10
Text Box: In the square grids I shall call the sides N. I have colour coded which numbers should be multiplied by which. To work out the answer the calculation is: (2 x 3) – (1 x 4) = Answer Then if I simplify this: 6 - 4 = 2 Therefore: Answer = 2
out square length I can cut out will be 9cm else I will have no box
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