• 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
  11. 11
    11
  12. 12
    12
  13. 13
    13
  14. 14
    14
  15. 15
    15
  16. 16
    16
  17. 17
    17
  18. 18
    18
  19. 19
    19
  20. 20
    20
  21. 21
    21
  22. 22
    22
  23. 23
    23
  24. 24
    24
  25. 25
    25
  26. 26
    26
  27. 27
    27
  28. 28
    28
  • Level: GCSE
  • Subject: Maths
  • Word count: 3274

Maths Number Stairs

Extracts from this document...

Introduction

Maths Investigation Introduction This investigation is called number stairs. I am going to investigate the relationship between the stair total and the position of the stair shape on the grid. Secondly I will do this by finding formula's for each step stair on a 10x10 grid. I will then look for a general formula to work out the position. I will then see if my general formula works on other grids, and then I will try to find one whole general formula to work out anywhere on any step stair or grid. I will now begin to find out the relationship I will start by looking for patterns on a 2 step stair and then moving on. 2 Step Stair Total = 14 Total = 58 Total = 47 Total = 113 Finding the formula I will now try to find the formula for my 2 step stair. I have noticed patterns. So I have decided to change my numbers into letters and making my smallest number n. Like this. Now I will take all my n's and add them together, to hopefully give me a formula. So n(n+1)+(n+10) = Hopefully my formula for a 2 step stair is 3n+11. I will check if my formula is correct by predicting the 5th term total. I will do this by substituting any value with n. 1 will use this stair. As an example Total = 152 one I have already used 3n+11 3 x 1 + 11 = total or 14 3 x 47 + 11 = total 14 = total or 14 152 = Total So I am correct my formula works. 3 step stair Total = 50 Total = 116 Total = 230 Total = 362 Finding the formula As before I will do the snme method to find my formula. So n+(n+1)+(n+2)+(n+10)+(n+11)+(n+20) = is my formula I will check to see if it works in same way as before. ...read more.

Middle

+ (n +2)+(n+3)(n+12)+ (n+13)+(n+14)+(n+24)+(n+25)+(n+36) = Total = 220 5 Step stair = n + (n+1) + (n +2)+(n+3)+(n+4)+(n+12)+ (n+13)+(n+14)+(n+15)+ (n+24)+ (n+25)+(n+26)+(n+36)+(n+37)+(n+48) = Total = 845 The formulas 2 Step Stair 3n + 13 3 Step Stair 6n +52 4 Step Stair 10n+130 5 Step Stair 15n + 260 I have noticed that the first part follows the same sequence as when on the 10x10 grid. 3, 6, 10, 15, follow the rule of the triangular numbers so there would be no need to find a formula for a them. So I can move straight to the other part. 0 12 52 130 260 13 39 78 130 26 39 52 13 13 Because of the three level of difference, again I will use the cubic formula N = step stair My list of formulas 1)a + b + c + d = 0 2)8a + 4b + 2c + d = 13 3)27a + 9b + 3c + d = 52 4)64a + 16b + 4c + d = 130 5)125a + 25b + 5c + d = 260 6)216a + 36b + 6c + d = 455 Take away 2) from 1) Take away 3) from 2) 2) 8a + 4b + 2c +d =13 3)27a + 9b + 3c + d = 52 1) a + b + c + d = 0 2) 8a + 4b + 2c +d =13 a) 7a + 3b + c = 13 b)19a + 5b + c = 39 Take away 4) from 3) Take away 6) from 5) 4)64a + 16b + 4c + d = 130 6)216a + 36b + 6c + d = 260 3)27a + 9b + 3c + d = 52 5)125a + 25b + 5c + d = 130 c)37a + 7b + c = 78 d)61a + 9b + c = 130 Take away b) from a) Take away d) ...read more.

Conclusion

You can also rearrange the formula to find which ever variable you want. Now I will prove that my formula works On a 3x3 grid 3 step stair N = 3 g = 3 x = 1 4 x 27 + 1 x 9 - 1 x 3 6 2 6 18 + 9 - 1 = 22 Total = 22 My formula seems to be working 2 step stair = 4 x 8 + 5 x 4 + 15 - 3 - 1 x 2 6 2 6 = 16 + 10 +11 3 3 Total = 19 = 19 I am correct both times my formula works Proving it on a 5x5 4 step stair using same method again T = 5+ 1 4 + 2 4 + 3(2) - 5 - 1 4 6 2 6 T = 6 x 64 +2 x 16 + 1 x 4 6 2 6 T = 64 + 18 + 0 Total = 80 T = 80 I am correct as you can see I have proved that my formula works three times. Proving it on a 7x7 grid 3 step stair T = 7+1 3 + 3 3 + 3(3) - 5 -1 3 6 2 6 T = 8 x 27 + 3 x 9 + 3 x 3 6 2 6 T = 36 + 27 + 3 2 2 Total = 51 Total = 51 As you can see again the formula works. Conclusion In this coursework there were two parts to it. I have successfully completed both parts. In part 1 I approached it in a different way to part 2. I found that my formula for a 10x10grid only works for 10x10. 1 also found patterns within the step stairs g = grid size = This increases by grid size Smallest Number This diagram above shows the patterns and variables which are grid size, smallest number, total, step number. These patterns helped together by using the cubic and quadratic function helped me and so together I found my general formula. By Mohamed Ibrahim 11h ...read more.

The above preview is unformatted text

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. GCSE Maths Sequences Coursework

    Shape 2 in the cube sequence is made up off two "start shapes", two stage one's and stage 2 from the square sequence. I believe this pattern will continue. Using this information I will be able to get the total number of cubes for the first five stages of this sequence using the information from the squares tables.

  2. Number Grids Investigation Coursework

    the algebraic expression for the difference between the products of opposite corners would be: (top right x bottom left) - (top left x bottom right) = (a + 2) (a + 20) - a (a + 22) = a2 + 2a + 20a + 40 - a2 - 22a =

  1. For other 3-step stairs, investigate the relationship between the stair total and the position ...

    the calculations are 9, 10 & 11 i.e: 9 x 4 = 36 10 x 4 = 40 11 x 4 = 44 We can now use 4 as the constant number and [n] as the grid size in our algebra equation.

  2. Number Stairs Maths Investigation

    we can call the number of each block going along the side of the grid (the coefficient of w in the formulae) "y" and call the number of each block going along the bottom (the number after the addition sign in the formulae)

  1. Number Stairs

    in the stair quickly. by just adding the numbers. x+40 x+30 x+31 x+20 x+21 x+22 x+10 x+11 x+12 x+13 x +1 x+2 x+3 x+4 In this 5-Step stair I know the first part of it is formula is x(5(5+1)/2) =15x So to get the value of (n)

  2. Number Grid Coursework

    the location of the box upon the grid. 2) Method Varying values and combinations of p and q will be tested to give different lengths and widths of sides for the boxes. Simultaneously, varying values of z will be tested to give different widths of grids.

  1. Algebra Investigation - Grid Square and Cube Relationships

    answers begin with the equation n2+100dn+100n+nsw+ghns-gns-ns, which signifies that they can be manipulated easily. Because the second answer has +100dghs-100ghs-100dgs+100gs+ghws2-ghs2-gws2+gs2 at the end, it demonstrates that no matter what number is chosen to begin with (n), a difference of 100dghs-100ghs-100dgs+100gs+ghws2-ghs2-gws2+gs2 will always be present.

  2. Number stairs

    so for this 3-step stair the stair total is 553 On the right is a portion of the 12 x 12 grid squares and there is 6 boxes which are representing the numbers 109, 97, 98, 85, 86, 8 and these are the 3-step stair From this diagram of the

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