Investigate the differences between products in a controlled sized grid.

Aim I am going to investigate the differences between products in a controlled sized grid. Method I am going to keep the grid size the same. Keeping the number of rows and columns the same. I am going to change the position of the box and the size of the size of the box altering the number of rows and columns. Investigation on 2by 2 boxes in a 10 by 10 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 I am now going to multiply opposite numbers together in the box. This is to show the differences. 2 1 2 *12=12 1*2=22 DIFFERENCE=10 9 0 9 20 9*20=180 9*100=190 DIFFERENCE=10 36 37 46 47 36*47=1692 37*46=1702 DIFFERENCE=10 Table of results 2 1 2 9 0 9 20 A B A B C D C D 36 37 46 47 A B C D I have called these numbers A, B, C, D so that it will be easier to see the results in the table. It will also be easier to see which numbers I am going to multiply together. Number A Number B Number C Number D Product of A*D Product of B*C Product of A*D- product of B*C 2 1 2 2 22 0 9 0 9 20 80 90 0 36

  • Word count: 5808
  • Level: GCSE
  • Subject: Maths
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Number Grids Investigation

Sophie Johnson 10A6 Maths Coursework Number Grids The diagram shows a 10*10 grid, a rectangle has been shaded on the 10*10 grid. I will find the diagonal difference between the products of the numbers in the opposite corners of the rectangle. 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 Opposite numbers in the rectangle are:- 54 and 66 56 and 64 56*64=3584 54*66=3564 .·. The Diagonal Difference = 3584 - 3564 = 20 Study I have studied some more 3*2 rectangles and I have found this:- 2 3 4 22 23 24 74 75 76 84 85 86 27 28 29 37 38 39 So from this I conclude that all 3*2 rectangles have a diagonal difference of 20. After doing this I wondered if this theory would work if I used a 2*3 rectangle. 27 28 37 38 47 48 34 35 44 45 54 55 So I then from this I wondered if larger rectangles had the same diagonal difference from this I found: - Rectangle Rows * columns Diagonal difference 2*3 20 3*4 60 4*5 20

  • Word count: 1721
  • Level: GCSE
  • Subject: Maths
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Number stairsMy aim is to investigate the relationship between the stair total and the position of the stair shape on the grid for 3 step

Number stairs My aim is to investigate the relationship between the stair total and the position of the stair shape on the grid for 3 step stairs and to investigate further the relationship between the stair totals and other step stairs on other number grids. 91 92 93 94 95 96 97 98 99 00 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 1 2 3 4 5 6 7 8 9 20 2 3 4 5 6 7 8 9 0 To begin I will try to identify a pattern. Taking my example I will take all the three stair steps on the bottom row and see if there are any similarities between the results. ) 1+2+3+11+12+21=50 2) 2+3+4+12+13+22=56 3) 3+4+5+13+14+23=62 4) 4+5+6+14+15+24=68 5) 5+6+7+15+16+25=74 6) 6+7+8+16+17+26=80 7) 7+8+9+17+18+27=86 8) 8+9+10+18+19+28=92 Therefore I can now find a formula. The general term for an arithmetic sequence is Un=ab+c. The terms go up in sixes and this tells me that the nth term will include 6 lots of n or 6n. For the first term n=1, so 6n=6. But the first term is 50 which is 44 more than 6n. This suggests that the formula is 6n+44. Trying a few values of n will help prove that my formula is correct. (6 multiplied by 1) +44

  • Word count: 2734
  • Level: GCSE
  • Subject: Maths
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For this coursework - stair shape - I am going to investigate the relationship between the stair total and the position of the stair shape on the grid. To do this I am going to create tables, charts, graphs, algebra equations and try to find the n'th ter

GCSE Maths Coursework. 'Stair shape' Introduction For this coursework 'stair shape' I am going to investigate the relationship between the stair total and the position of the stair shape on the grid. To do this I am going to create tables, charts, graphs, algebra equations and try to find the n'th term. I am also going to investigate the relationship between the stair totals and other step stairs on the other number grids. Plan I plan to draw different stair shapes on a grid, and then show my finding in a table format. I also plan to show my working outs, and my method of my data capture. Once I have done this I will predicate the n'th term then test to see if my formula works. Data This data that I have collected was from a 10, by 10 grids. The data is presented in a table below. Number inside stair Shape Stair Total +2+3+11+12+21 21 1 2 2 3 50 6 2+3+4+12+13+22 56 22 2 3 2 3 4 6 3+4+5+13+14+23 62 23 3 4 3 4 5 6 4+5+6+14+15+24 68 24 4 5 4 5 6 *Number in Red is the different that the Stair total is going up in. Conclusion From the data I have collected I found that if the stair shape moves across the bottom of the grid the stair total will increase by 6. If I move the stair shape across the middle of the 10, by 10 grid the stair total should also increase by 6. Number inside stair Shape Stair Total 33+34+35+43+44+53 53 43

  • Word count: 672
  • Level: GCSE
  • Subject: Maths
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My Investigation is called 'Number Stairs'

Mathematics Coursework Number stairs My Investigation is called 'Number Stairs' Task Statement I have been set the task of working out the relationship between a three-stair total and the position of the stair shape on the prearranged grid and other stair totals. For further investigation other stair totals could be worked out on different grids of our own and also different numbers of stairs other than three. The rules for my investigation are: . Each stair is labelled as a number; this number is the bottom left hand number of that stair. This is known as the keystone. 2. You will work horizontally across the grid from square number one. 3. If you come to a stair total on the edge of a grid this is what you should do: 91 92 93 94 95 96 97 98 99 00 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 1 2 3 4 5 6 7 8 9 20 2 3 4 5 6 7 8 9 0 This is, if it was not on the edge: 40 30 31 20 21 22 Aim As I work through this task I hope to find a formula that will help me to work out any stair total on any grid. Method To start with I will work out the stairs going across. This, after working a few stairs a pattern

  • Word count: 1945
  • Level: GCSE
  • Subject: Maths
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Mathematics Layers Coursework

Mathematics Layers Coursework Chris Grindrod 11SRH Introduction: In this investigation I will be investigating the amount combinations there are when there is a set sized grid with x number of squares on it, one cube can fit In to each square but there must also be one empty square. Then another layer of squares can be placed on top of the first layer of squares but the same rules apply and there must be one square that does not have another square placed on top of it. This applies to any number of layers until you are made to or required to stop. On each new layer you have to use one cube than the layer before until you have to stop or are asked to stop at a certain layer. The rules of the investigation are as follows: The number of cubes on the bottom layer is always one less than the number of squares on the grid unless stated otherwise. Each new layer is made with one less cube than the layer underneath it. Each cube must fit exactly in to a square or a cube underneath it. Part One For part one of the investigation I will investigate how many different arrangements of five cubes there are on a six square grid. Method: I am going to draw all the combinations for the specifications above to find out how many combinations there are. Results: There are six combinations for the specifications, this is because no matter were you put the five cubes on the six

  • Word count: 2679
  • Level: GCSE
  • Subject: Maths
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Investigate the relationship between different stairs placed in different places in a number square, which is numbered from one to one hundred.

Introduction In this project I am going to investigate the relationship between different stairs placed in different places in a number square, which is numbered from one to one hundred. I will be trying to find a formula to get a total of any stair any place. Example 91 92 93 94 95 96 97 98 99 00 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 20 1 2 3 4 5 6 7 8 9 20 2 3 4 5 6 7 8 9 0 This is a 3-step stair The total of the numbers in side the stair is 25+26+27+35+36+37+45=194 I will start on a 2-step stair 38 28+29+38=95 28 29 37 37+27+28=92 27 28 36 36+26+27=89 26 27 I have found out that every time you move the two-step stair one to the left the product of the two-step stair goes down by three. This also means that every time you move the two-step stair one to the right the product will go up by three. 23 23+13+14=50 3 14 33 33+23+24=80 23 24 43 43+33+34=110 33 34 I have found out that when you move the stairs up by one the product of the two-step stair goes up by 30. This also means that when you move the two-step stair down by one the product will go down by -30. I have also found out the

  • Word count: 1631
  • Level: GCSE
  • Subject: Maths
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Algebra Investigation - Grid Square and Cube Relationships

Algebraic Investigation 1: Square Boxes on a 10x10 Grid In this first investigation, the difference in products of the alternate corners of a square, equal-sided box on a 10x10 gridsquare will be investigated. It is believed that the products and their differences should demonstrate a constant pattern no matter what dimensions are used; as long as they remain equal. In order to prove this, both a numeric and algebraic method will be used in order to calculate this difference. The numeric method will help establish a baseline set of numbers for testing, and to help in the establishment of a set of algebraic formulae for use on an n x n gridsquare. In the example gridsquare below, the following method is used in order to calculate the difference between the products of opposite corners. (a) (b) (c) (d) Stage A: Top left number x Bottom right number = (a) multiplied by (d) Stage B: Bottom left number x Top right number = (c) multiplied by (b) Stage B - Stage A: (c)(b) - (a)(d) = The difference The overall, 10 x 10 grid that is used for the first investigation will be a standard, cardinal gridsquare, which progresses in increments of 1. The formulae calculated will mainly be applicable to this grid, as other formats of gridsquares will require others formulae to provide valid results. 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 20 21 22 23 24 25

  • Word count: 8966
  • Level: GCSE
  • Subject: Maths
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Investigate the difference between the products of the numbers in the opposite corners of any rectangles that can be drawn on a 100 square.

Tom Gowing 11A GCSE Maths Coursework Opposite Corners Investigate the difference between the products of the numbers in the opposite corners of any rectangles that can be drawn on a 100 square. During the investigation my aim is to find a formula to work out the difference of these products for any size rectangle on any size grid. I will start off by working out the difference on different shapes and looking for a basic pattern. I will try moving the shapes around the grid to see how this affects the difference. I am going to use the following 5 shapes during this part of the investigation: A 2x2 square A 3x3 square A 2x3 rectangle A 2x5 rectangle A 3x5 rectangle A 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 For the 2x2 I have decided to try 3 different positions along the horizontal, 3 along the vertical and 3 along the diagonal this should tell me if the difference alters depending on which way you move the shape around the grid. I have done 3 along each axis to provide accurate results by highlighting any anomalous ones.

  • Word count: 5216
  • Level: GCSE
  • Subject: Maths
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The purpose of this investigation is to look at diagonal differences on different sizes of grids

Number grid The purpose of this investigation is to look at diagonal differences on different sizes of grids. I am going to do this by multiple the numbers in the corners of the grids and then subtracting there answers to get the over all difference. To carry out this investigation I will start by extracting a 2 by 2 grid by my original 10 by 10 grid. I will then carry out by multiplying the corner numbers and subtracting the smaller number by bigger the number so I can gain an answer. To further this investigation I will extend the grid size to a 3 by 3 grid and I will be doing exactly the same method as the other grid. I will then continue this by extending the grid size to a 4 by 4, 5 by 5, 6 by 6 and so on. 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 by 2 grids . 1x12=12 2x11=22 22-12=10 2. 17x28=476 8x27=486 486-476=10 3. 24x35=840 25x34=850 850-540=10 4. 31x42=1302 32x41=1312 312-1302=10 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

  • Word count: 2529
  • Level: GCSE
  • Subject: Maths
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