Number stairs

MATHEMATICS COURSEWORK- NUMBER STAIRS My investigation is based on number stairs. An example of a number stair is below: This is a 3 step stair because both the length and the width of the stair are 3 steps For the first part of my investigation this 3-step stairs (above is) is going to be placed on different number grids such as a 10 by 10 or 9 by 9 Number Grid etc Secondly for my first part of my investigation I also need to find a formula for each grid. These formulas must be able to work out the stair total for the 3-step on a number of different size grids such as 10 by 10 or 9 by 9 etc A stair total is all the values added together in the 3-step stairs After I have found a formula for a couple of number grids I am going to work out a general formula for any grid size possible. Below is a stair drawn on a 10 by 10 Number Grid: On the 10 by 10 Number Grid (on the previous page) a 3-step stair is highlighted The total of the numbers inside the stair shape is: 91+81+82+71+72+73=470 The stair total for this 3-step stair is 470 PART 1 For other 3-step stairs, investigation the relationship between the stair total and the position of the stair shape on the gird To start my investigation I am going to start by using a 10 by 10 Number grid below: I have highlighted a 3-step stair above on my 10 by 10 Number Grid The total of the numbers inside the stair shape is:

  • Word count: 4419
  • Level: GCSE
  • Subject: Maths
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Number Stairs

Number Stairs +2+3+11+12+21=50 8+9+10+18+19+28=92 48+49+50+58+59+68=332 71+72+73+81+82+91=470 5+16+17+25+26+35=161 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 the stairs numbers and I add all the stair number and every time I got different totals. E.g. 50, 92, 332, 470 and 161 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 71+72+73+81+82+91=470 72+73+74+82+83+92=476 73+74+75+83+84+93=482 74+75+76+84+85+94=488 I am finding out different totals, but going up by set amount. Every time it goes up by 6. Stair Number: 71 72 73 74 Stair total: 470 476 482 488 Difference: 6 6 6 Now I know

  • Word count: 2022
  • Level: GCSE
  • Subject: Maths
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Number stairs.

GCSE MATHEMATICS COURSEWORK: NUMBER STAIRS NAME: PRATEEK BHANDARI FORM: 11C DATE: 7TH MARCH 2004 PART 1: For the other 3-step stairs, investigate the relationship between the stair total and the position of the stair shape on the grid. As described in the question I will be investigating the relationship between stair total and the position of the stair shape on a 10 by 10 grid. To find that out, I have decided to take three stairs on different positions on the grid and find their stair total. After that, I will find a formula through which I can calculate the stair total of any stair number. Below is a three level stair shape on a 10 by 10 grid. If we write the same stair in terms n (stair number) then it It will be: Stair number up by 20 stair number up by 10 stair number up by 11 stair number stair no. up by 2 stair number up by 1. This shows that: * Every time we move to the right we increase by 1. * Every time we move up we increase by 10. Mainly because of the grid size. * Similarly if we move 1 to the left it will decrease by 1. * By moving down one square it will decrease by 10. The diagram shows: * n to n+1 is increased by one * n to n+2 is increased by two * n to n+10 is increased by ten * n to n+11 is increased by eleven * n to n+20 is increased by twenty. Therefore it can be written as: n+n+1+n+2+n+10+n+11+n+20= 6n+ 44 To

  • Word count: 1640
  • Level: GCSE
  • Subject: Maths
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Number Stairs

I have been given a number grid that counts in ascending order from one to a hundred, beginning at the bottom left hand corner to end at the top right corner with the number one hundred. With this grid I have been given the task of investigating the relationship/s between the grid size, the stair size, the stair total and the 'n' number. 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 35 6 7 8 9 20 2 3 4 5 6 7 8 9 0 The step shape given above is a 3-step stair, simply because it consists of 3 steps. The stair total is labelled as being the sum of all of the numbers in the stair shape: 24 + 25 + 26 + 34 + 35 + 44 = 212 The Stair total for this 3-step shape is 212 The 'n' number is defined as being the smallest number of the stair shape, in the grid above it is specified as ' 24'. I will systematically work my way through this problem to find appropriate algebraic solutions to simplify the workings of the stair totals. In doing so, I will use different size grids and use different size stairs. Again, investigating relationships and discovering formulae for each problem I

  • Word count: 3711
  • Level: GCSE
  • Subject: Maths
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Number Stairs

GCSE Coursework - Number Stairs Investigation Part 1 This is a 10 x 10 size grid with a 3-stair shape in gray. This is called the stair total. The stair total for this stair shape is 25 + 26 + 27 + 35 + 36 + 45 = 194. To investigate the relationship between the stair total and the position of the stair shape, I will use the far-left bottom square as my stair number: This is always the smallest number in the stair shape. It is 25 for this stair shape. Now , I'm going to translate this 3-stair shape to different positions around the 10 x 10 grid: The stair-total for this stair shape is 24 + 25 + 26 + 34 + 35 + 44 = 188 The stair-total for this stair shape is 26 +27 + 28 + 36 + 37 + 46 = 200 The stair-total for this stair shape is 27 + 28+ 29 + 37 + 38 + 47= 206 The stair-total for this stair shape is 3 + 4 + 5 + 13 + 14 + 23 = 62 The stair-total for this stair shape is 4 + 5 + 6 + 14 + 15 + 23 = 68 This table summarizes these results : Stair number 24 25 26 25 3 4 Stair Total 88 94 200 206 62 68 In order to find a formula which give the stair total when I am given the stair number, I am going to put the stair number as the position and the stair total as the term for the sequence: Position 24 25 26 27 3 4 Term 88 94 200 206 62 68 Difference +6 +6 +6 I have noticed that there is an increase of 6 between two consecutive terms

  • Word count: 587
  • Level: GCSE
  • Subject: Maths
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Number stairs.

Philip Spicer Maths coursework: Number Stairs 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 49 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 The problem: I have to find a theory that links the relationship between the stair total and the position of the stair shape on the grid. I plan to do this is by comparing the grid width against the stair number (for this stair the bottom left hand square) to find an equation that relates it to the stair total ( the sum of all the numbers in the stair). e.g. stair number 55: 55+56+57+65+66+75 = 374 (stair total) I will then proceed not to just rotate the stair but change its size and see from these results if I can find one general equation which sums up the project. Then I will plot these results onto a table and look to find an equation to solve them. Stair no. 55 56 57 58 59 Stair total 374 380 386 392 398 To find an equation from this I will have to translate a stair into algebraic form: Proof: (6x55) + (4x10) +4 = 374 This shows that this equation is correct for at least a grid of this size and with a three-step stair. To prove this

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  • Level: GCSE
  • Subject: Maths
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Number Stairs investigation.

Number Stairs investigation The task of this coursework is to investigate the relationship between the total of a 3-step stair and the position of it on a 10 x 10 grid. The three step stair is made up of 6 squares. X = Stair number or Sn I will carry out the investigation in the following steps: - On a 10 x 10 grid move the 'stairs' 1 square to the right and find the stair total, by adding all the numbers in the stair together. - Put the information into a table and look for any pattern or rules. - Describe any patterns or rules using words and/or algebra. - Try to explain any patterns found. - Move the 'stairs' up a row and move it 1 to the right, same as before. - Change the position of the 'stairs' and size of the grid. - Try and explain any links between figures and anything that has been found. 0x 10 grid 91 92 93 94 95 96 97 98 99 00 81 82 83 84 85 86 87 88 89 90 71 71 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 21 1 2 1 2 3 SN = 1 ST = 50 22 2 3 2 3 4 SN = 2 ST = 56 23 3 4 3 4 5 SN = 3 ST = 62 24 4 5 4 5 6 SN = 4 ST = 68 SN Total

  • Word count: 1054
  • Level: GCSE
  • Subject: Maths
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opposite corners

GCSE Maths Coursework Opposite Corners I have been given the task to investigate the differences of the products of the diagonal opposite corners of a square on a 10x10 Grid with the numbers 1 to 100 to start with. I will start with a 2 x 2 square on a 10 x 10 grid and discover the rule for it, then I will progress onto a 3 x 3 square on the same grid. I will then keep on going until I eventually find the rule for any sized square on a 10 x 10 grid. 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 (2 x 11) - (1 x 12) = 10 (14 x 25) - (15 x 24) = 10 (8 x 17) - (7 x 18) = 10 (20 x 29) - (19 x 30) = 10 I have discovered that the answer is always 10 I will now use algebra to see if the answer is once again 10. n n+1 n+10 n+11 (n+1)(n+10) - n(n+11) (n2+11n+10) - (n2+11n) 0 As the algebraic equation also gives the answer of 10 I know it must be right. As I believe I can keep on learning throughout the investigation I will now move onto a 3x3 square on the same grid. I predict that once again all answers will be the same. 3 X 3 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 (3 x 21) - (1 x 23) = 40 (6 x 24) - (4 x 26) = 40 (10 x 28) - (8 x 30) = 40 I believe the answer will always be 40 for a 3 x 3 square on this grid. So I will now use algebra

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  • Level: GCSE
  • Subject: Maths
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Opposite Corners

Opposite Corners This piece of coursework uses a grid of numbers and a x by x box drawn around a set of numbers. I am trying to see if there is a pattern between the differences of the products. Aim: My task is to investigate the differences of the products of the diagonally opposite corners of a rectangle, drawn on a 10x10 grid, with the squares numbered off 1 to 100. I will aim to investigate the differences for rectangles and squares of different lengths, widths. I plan to use algebra to prove any rules I discover which I will hopefully find by analysing my results that I will display in tables. I will test any rules, patterns and theories I find by using predictions and examples. I will record any ideas and thoughts I have as I proceed. Plan: Firstly use a 2x2 box on a 10x10 grid in 5 positions Move on to 3x3 in 3 positions. Then 4x4 in 3 positions. Then predict what the difference will be for a 5x5 box. Test the prediction. Prove using algebra why the difference is always the same. Find formula for a square on a 10x10 grid. Prove formula works Investigate rectangles(with same method). Change grid size. Squares: I started by calculating the differences for 2x2-4x4 boxes and then predicting the difference for a 5x5. 2x2- 1x12=12 2x13=26 3x14=42 4x15=60 5x16=80 2x11=22 3x12=36 4x13=52 5x14=70 6x15=90 (diff.)10 10 10 10 10 3x3- 1x23=23 2x24=48

  • Word count: 786
  • Level: GCSE
  • Subject: Maths
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Opposite Corners.

Opposite Corners Investigation: Given a 100 Square, I am to investigate the difference between the products of the numbers in the opposite corners of any rectangle that can be drawn on the 100 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 2x3 A rectangle has been highlighted in the 100 square 1 and 13/11 and 3 are the numbers in the opposite corners product of the number in these opposite corners are x13=13 1x3=33 The difference between these products is 33-13= 20 A rectangle has been highlighted in the 100 square 4 and 16/14 and 6 are the numbers in the opposite corners product of the number in these opposite corners are 4x16=64 4x6=84 The difference between these products is 84-64= 20 A rectangle has been highlighted in the 100 square 7 and 19/17 and 9 are the numbers in the opposite corners product of the number in these opposite corners are 7x19=133 7x9=153 The difference between these products is 153-133=20 Conclusion: I have Concluded that my prediction was correct and that a 2 by 3 rectangles have a

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  • Word count: 1921
  • Level: GCSE
  • Subject: Maths
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