• Join over 1.2 million students every month
  • Accelerate your learning by 29%
  • Unlimited access from just £6.99 per month

Investigating three step stairs.

Extracts from this document...


Aim I am set the task of investigating three step stairs (which I will go into some more detail on later on) and how their position on the number grid and the step total corresponds to the step number. Prediction My basic prediction is that... Definitions Step total - the total of all the numbers in the stair added up Stair number - this is the lowest number in the stair and is found in the bottom left hand corner of them Number grid - this is a ten by ten square with the numbers from one to one hundred in it as ten time ten is 100. The ten by ten grid is the grid we will be using in the first part of the investigation but in the second stage of the investigation other smaller and larger number grids will be tested. Step number - this is the number of steps the stair is comprised of. As I have stated the step number I will be using for the main part for this investigation will be a three step stair, with a three step number there will be six numbers within the stair. ...read more.


Lets say I am given the task of finding out the rest of a three step stair where the n=5. In order to do this I would like at the pattern that all three step stairs follow (see left) all that is required for me to do is to fill in n as 5 and do the appropriate calculations for each box in the three step stair. My finished three step stair with all the calculations done looks like this: By using the pattern grid I have accurately found the missing numbers. However this is not exactly a formula and whilst it may be useful for a question like the one I just answered its uses are limited. A formula to calculate the step total from just the stair number would be ideal and so I began to experiment and using trial and error. To start with I looked at the number of numbers in a three step stair and began to look back on the pattern that was found to be behind all three step stairs. I looked at what was actually done to n and how much overall was added to n in a three step stair. ...read more.


I based my theory that the source of the problem would be easier to spot with lower stair numbers on that with lower numbers those that are unnecessary would be removed and I would be able to look and spot any problem more easily dealing with a stair number of one. Much like if I had to draw a cross on the exact centre of a circle it would be easier for me to do it holding the pencil at a close distance away from the circle rather than doing it with a metre long pencil and holding it by the end and at arms length. Things have a tendency to get exaggerated the further they are from the actual problem and the problem is often hidden better when surrounded by a larger problem than by a small problem. In order to stop a problem it must be stopped at the root or source (where it most vulnerable and exposed). Anyway, I went back and looked at stair number one and looked how far off I was from the stair total; I was six off the stair total. I then moved along to stair number two and saw how far off I was from its stair total; I was ...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. Number stairs

    I am going to add the value inside the 3-step stair above so: Total= X + (x+24) + (x+13) + (x+11) + (x+1) + (x+2) = 52 In conclusion the algebra formula to find the total inside the 3-step stairs for a 12 by 12 Number Grid is: T=6x +

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

    values we get -220 If we closely examine the results from the 5-step stairs from the 3 numbered grid boxes, i.e. 10x10, 11x11 and 12x12 we can see there is a constant number that is consistent, which is [20] We can then complete the rest of the table by using

  1. Number Stairs

    Since1- Step stair has nothing to investigate because it has only 1 number, i will start by the smallest stair possible (in this case 2-Step Stair) and then try to make a formula that works for any 2-Step Stair. Then make a formula for 4Step Stair, Then 5, 6, 7, 8, 9and lastly 10-Step Stair.

  2. Algebra Investigation - Grid Square and Cube Relationships

    Increment Size: 3 3 6 9 12 15 18 21 24 27 30 33 36 39 42 45 48 51 54 57 60 63 66 69 72 75 Experimental number box: Algebraic box: n n+3(w-1) n+3g(h-1) n+3(w-1)+3g(h-1) Simplifies to: n n+3w-3 n+3gh-3g n+3w+3gh-3g-3 Stage A: Top left number x Bottom right number = n(n+3w+3gh-3g-3)

  1. Number Stairs

    +6 It is clear that the difference between the numbers is 6. This means that the formula, to solve the total, must include a multiple of 6. This will lead to the fact that the nth term has to have6nin the formula, the extra is calculated by working out what

  2. Mathematics - Number Stairs

    it will be: T = 3n + 12 2-Step Staircase/ Grid Width 11 12 1 2 n 1 2 3 4 5 T 15 18 21 24 27 Suspected formula: T = 3n + 12 Prediction / Test: 3 x 20 + 12 = 72 31 20 21 20 +

  1. number stairs

    74 6, 7, 8, 16, 17, 26 6 80 From this information, you can see that; 1. Each 3-step stair can be divided evenly by 2 2. Each step-total increases by 6 starting from 50 3. The step-number goes up by 1 and the step-total goes up by 6.

  2. Maths Coursework: Number Stairs

    using 1 as the base number on a 10 by 10-number grid is 644 as 1 + 2 + 3 + 4 + 5 + 6 + 7 + 11 + 12 + 13 + 14 + 15 + 16 + 21 + 22 + 23 + 24 + 25

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