Investigating how the numbers worked on a number grid.

Maths GCSE Coursework Kaleigh Mills Investigation I was given the task of investigating how the numbers worked on a number grid. This is what I did to find out: I chose a grid of four numbers and I multiplied the Top Left (TL) by the Bottom Right (BR) then I did the same with the Top Right (TR) and the Bottom Left (BL). I then found out the difference between the two outcomes. n n+1 n+10 n+ 1 E.g. 2 3 22 23 44 45 54 55 After trying a few 2 x 2 grids I then went on to do some 3 x 3 grids. n n + 2 n + 20 n + 22 E.g. 61 62 63 71 72 73 81 82 83 5 6 7 5 6 7 25 26 27 n n+3 n+ 30 n+ 33 n(n + 33) = n2 + 33n (n + 3) (n + 30) = n2 + 33n + 90 The difference between these two equations is 90. In order to test the rule I tried a few more 4 x 4 grids. 35 36 37 38 45 46 47 48 55 56 57 58 65 66 67 68 5 6 7 8 5 6 7 8 25 26 27 28 35 36 37 38 5 by 5 n n+4 n+40 n+44 53 54 55 56 57 63 64 65 66 67 73 74 75 76 77 83 84 85 86 87 93 94 95 96 97 5 6 7 8 9 5 6 7 8 9 25 26 27 28 29 35 36 37 38 39 45 46 47 48 49 After testing a lot of grids I have discovered that the rule for a square of any size is (n-1)2x10. To prove this I am going to test it for a 6 x 6 grid. Prediction I predict that for a 6 x 6 grid the difference will always be 250. For a 6 x 6

  • Word count: 882
  • Level: GCSE
  • Subject: Maths
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Maths Grids Totals

I am going to investigate squares of different sizes and on different grids. I am going to draw a square around numbers on a grid, and find the product of the top-left and bottom-right numbers, and the top-right and bottom-left numbers. I will then calculate the difference. 0 x 10 grids 2 x 2 squares 2 3 22 23 2 x 23 = 276 3 x 22 = 286 286 - 276 = 10. 55 56 65 66 55 x 66 = 3630 56 x 65 = 3640 3640 - 3630 = 10. 25 26 35 36 25 x 36 = 900 26 x 35 = 910 910 - 900 = 10 I have found that that there is a difference of 10 on any 2 x 2 square, on a 10 x 10 grid. 3 x 3 squares 36 37 38 46 47 48 56 57 58 36 x 58 = 2088 38 x 56 = 2128 2128 - 2088 = 40. 77 78 79 87 88 89 97 98 99 77 x 99 = 7623 79 x 97 = 7663 7663 - 7623 = 40. 4 x 4 squares 25 26 27 28 35 36 37 38 45 46 47 48 55 56 57 58 25 x 58 = 1450 28 x 55 = 1540 540 - 1450 = 90. 5 x 5 squares 32 33 34 35 36 42 43 44 45 46 52 53 54 55 56 62 63 64 65 66 72 73 74 75 76 32 x 76 = 2432 36 x 72 = 3592 3592 - 2432 = 160. I have now found out the differences for 2x2, 3x3, 4x4 and 5x5 squares on a 10x10, which will be shown in the following table: Size Difference 2 x 2 0 3 x 3 40 4 x 4 90 5 x 5 60 All the differences are square numbers of the previous number multiplied by 10 (e.g. 3 x 3 = 10 x 22 = 10 x 4 = 40). This gives me the

  • Word count: 5017
  • Level: GCSE
  • Subject: Maths
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Number grids. In this investigation I have been attempting to work out a formula that will find the difference between the products of the top left and bottom right of a number grid and the top right and bottom left of a number grid.

2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 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 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 00 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 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 71 72 73 74 75 76 77 78 79 80 81 In this investigation I have been attempting to work out a formula that will find the difference between the products of the top left and bottom right of a number grid and the top right and bottom left of a number grid. 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 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 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 00 A 10x10 number grid If you choose any 2x2 box on a 10x10 number grid then the difference should equal 10...

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  • Level: GCSE
  • Subject: Maths
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Investigating the number of patterns in a certain grid.

COURSEWORK (PAGE 1) Introduction This piece of coursework is about investigating the number of patterns in a certain grid. The grid I am starting off with is 10x10. The rule or pattern I have to investigate is whether when you multiply the opposite corners in a 2x2 box, you can find a pattern or link between the two answers. I will also investigate to see if there are any patterns when I multiply the opposite corners of a box but using a larger grid (increase the row length) or increase the size of the square (3x3etc.). I will always use algebra to check if my assumptions are correct. I will also see what happens if I do not use a square but use other shapes such as a rectangle or a T-shape. I will see whether the rule still applies and I will generalise the rule by using algebra. Finally I will invent my own rule and if it is successful I will generalise using algebra Here is a list, in order, of the plans of my investigation: check if the rules are universal Do the arithmetic 2 generalise using y y+1 Do the algebra y +7 y+8 3 change the size of the grid (e.g. row 1-10) Do arithmetic Do algebra (row 1-n) 4 change the size of the square y y+1 y+2 Do the arithmetic y+7 y+8 y+9 Do the

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  • Level: GCSE
  • Subject: Maths
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I am going to investigate the difference between the products of the numbers in the opposite corners of any rectangle that can be drawn on a 100 square (10x10) grid

Opposite Corners Opposite Corners * Throughout this piece of work, the horizontal side will be referred to as the length, whilst the vertical side will be referred to as width. Introduction/Aim I am going to investigate the difference between the products of the numbers in the opposite corners of any rectangle that can be drawn on a 100 square (10x10) grid. I am going to investigate different rectangles, of different areas, lengths, widths and positioning on a grid. After finding a pattern, I will try and prove that it will work for other cases by using algebra and making an algebraic formula. As I go along, I will have to record any ideas I have or patterns I see. Afterwards, I will go on to investigate how this rule may differs on a different sized grid. 2x2 Square, 10x10 Grid 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 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 This is a 10x10 grid. On it (outlines in red) is a 2x2 square. Firstly, I’m going to see what the difference between the products of the corners is (D): 55x64=3520 54x65= 3510 3520-3510=10, D=10 Now: What

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  • Level: GCSE
  • Subject: Maths
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Investigate the size of the cut out square, from any square sheet of card, which makes an open box of the largest volume.

Maths Coursework- The Open Box Problem Mary-Louise Duffy 11R Part 1 I am going to investigate the size of the cut out square, from any square sheet of card, which makes an open box of the largest volume. Firstly, I am going to do two investigations, using exact numbers, of this box so I can establish a connection between the size of the sheet and the size of the cut-out square. Then if I found out a similarity between the two, then I will use another example to prove my theory. This is a diagram of the of the box: C= Cut-out square size X= original length of card This is a formula to work out any volume, and I'm going to change it, so it's shows how to work out the volume of the card above: Volume = length x width x height V= (X-2C) x (X-2C) x C V= (X - 2C) Squared x C So the final formula to work out the volume of this box is: V= C(X-2C) squared This is my first investigation: 30cm by 30cm piece of card. As you can see, the largest volume present in the table is 2000cm cubed, which is what you end up with if have 5cm by 5cm square cut-out. At the bottom of the table, you should see that I have checked if the volume can get any higher. That is why I have checked to see 5.1 by 5.1 and 4.9 by 4.9 might have a higher volume than 5cm by 5cm. Clearly, the highest is 5 by 5. I'm going to do a few calculations to see if there are any similarities between this

  • Word count: 1264
  • Level: GCSE
  • Subject: Maths
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Investigate different shapes in different sized number grids.

Introduction In this piece of course work I will investigate different shapes in different sized number grids. The shapes I will look at will be the square, the rectangle, the rhombus and the parallelogram. I will investigate these shapes in two different number grids, one a 10x10 grid and the other a 5x5 grid. I will draw these shapes on the number grids at random points and take the corner numbers and then multiply the opposite corners. From these results I will attempt to work out a formula for how the size of shape affects the result taken from the table. I will take the number from the bottom left corner of the shape and the top right corner of the shape and multiply these numbers together. This set of numbers will be represented by the colour RED. I will then take the top left corner and the bottom right corner and multiply these two numbers together. This set of numbers will be represented by the colour BLUE. I will then subtract the RED result from the BLUE which will give me the number I need to work out my formula. The number gained from the subtraction will be called the difference. All my results will be taken from either a 5x5 grid like this: 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 20 21 22 23 24 25 Or a 10x10 grid like this: 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34

  • Word count: 6562
  • Level: GCSE
  • Subject: Maths
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I will attempt to discover a general formula that will find the difference between the product of the top left number and the bottom right and the product of top right and bottom left (diagonals) of any size square and any size grid.

Maths Coursework In this investigation I will attempt to discover a general formula that will find the difference between the product of the top left number and the bottom right and the product of top right and bottom left (diagonals) of any size square and any size grid. I will start on a 10 by 10 grid and a square of 4 numbers, by picking a square of 4 numbers and multiplying the top left number with the bottom right and then finding the difference between this and the product of top right and bottom left. Eg. 3 3 4 3 13 14 In this case, it would be the difference between 3 x 14 and 4 x 13, which is 10. 2x2 square 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 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 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 00 2 1 2 x 12 = 12 2 x 11 = 22 Difference between the product of the diagonals is 10 44 45 54 55 44 x 55 = 2420 45 x 54 = 2430 Difference = 10 77 78 87 88 77 x 88 = 6776 78 x 87 = 6786 Difference = 10 8 9 28 29 8 x 29 = 522 9 x 28 = 532 Difference = 10 Pattern: As you can see, the difference between the product top left number with the

  • Word count: 1864
  • Level: GCSE
  • Subject: Maths
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My investigation will be on 3 - step stairs where I will be: Trying to investigate the relationship between the stair total and the position

Introduction My investigation will be on 3 - step stairs where I will be: > Trying to investigate the relationship between the stair total and the position of the stair shape on the grid 91 92 93 94 95 96 97 98 99 00 81 82 83 84 85 86 87 88 89 90 71 72 73 73 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 1 2 3 4 5 6 7 8 9 20 2 3 4 5 6 7 8 9 0 > Further investigating the relationship between the stair totals and other step stair on other number grids e.g. 5 x 5 grid and 4 - step stairs 21 22 23 24 25 6 7 8 9 20 1 2 3 4 5 6 7 8 9 0 2 3 4 5 31 21 22 1 2 3 2 3 4 Prediction As my investigation unfolds I believe I will find a pattern connecting the all Plan During my investigation on stairs I will: . do the horizontal 3 - step stairs and find out whether there is a formula to locate another 3 - step stair horizontally on the 10 x 10 grid 2. test the formula to see if it works 3. repeat the same process for vertical and diagonal 3 - step stairs on the 10 x 10 grid and find a formula for both 4. test both formulae and see if they achieve their purpose 5. compare the formula found for horizontal, vertical, and diagonal 3 -

  • Word count: 3997
  • Level: GCSE
  • Subject: Maths
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Investigate the diagonal difference of a 2 by 2 grid inside a 10 by 10 grid

Maths Coursework-Diagonal Difference Introduction I am given a 10 by 10 grid. I am going to find the diagonal difference of different size grids (For e.g. 3 by 3, 4 by 4) within the 10 by 10 grid, by multiplying the opposite corners which results in two answers, we then deduct these two to get a final answer for that size. This is the grid that I will use to help me investigate. 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 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 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 00 Aim I am going to investigate the diagonal difference of a 2 by 2 grid inside a 10 by 10 grid. I will then try to find a formula which relates to the diagonal difference of each square, I will then further this investigation by trying to find the diagonal difference of an 11 by 11 grid and a 12 by 12 grid and find the formula and see if it is the same. I will also do an extension by doing a rectangle and a square and then find the diagonal difference and the formula for this. I am going to find the formula by finding the diagonal difference of all the sizes within the 10 by 10 grids, and then try to find any patterns,

  • Word count: 1769
  • Level: GCSE
  • Subject: Maths
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