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

Investigation - stair shape on a 10x10 numbergrid

Extracts from this document...


Investigation-stair shape on a 10x10 number grid


     For this investigation I will be investigating the relationship between no. total and stair no. on a 10x10 number grid. I will also be comparing results when the stairs are moved around the grid, finding patterns that may occur.


A diagram of the stair shape is shown below. There are three numbers on the bottom layer, two on the second and one on the top, starting from left. The stair no. will be identified by the number in the bottom left hand corner of the stair. The grid starts from one in the bottom left hand corner and ascends to 100 in the top right. This is done so the stairs are in an up-right position rather than up side down. As shown below.

I began by planning the first set of stairs…

I shaded in no.s 1,2, 3, 4 and 5 to make the outline of the stair case clear. The no.

...read more.





Stair total






                                           +60                 + 60                 + 60                 +60

As you can see the pattern increases by 60 every time

Therefore we can conclude that the rule

6n + 44 definitely does not work

Although it seems to work for  stair no. 1

The horizontal rule does cannot be applied to the vertical rule

60n -10

Instead I will test the formulae  60n – 10

I was lead to this formulae as the pattern increases by 60; therefore 60n seems correct

The second half of the equation is – 10 as

110 – 60 = 50

The first stair total works using this formulae!

I  will now try 11

11 x 60 =660

660 – 10 = 650

This formulae definitely does not work

After much consideration , I have come to the conclusion that  working out the formulae is beyond my mathematical knowledge.Although I can see a pattern

Re- ocurring.The totals increase by 60 every time.

To expand the investigation further I will now be using a 7 x 7 grid …

7 x 7 Grid

The 7 x 7 grid will look something like this…..


I will take the stair no.s  3, 4 , 5, 6, and 7

The totals are as follows…

Stair no.






Stair total






                                           6                        6                      6                    6

As the difference is 6 the formula will be 6n

...read more.


T= 6n + 24

Now I will try to find the vertical rule


I will take the sequence 5 , 12 , 19 , 26 , and 33

Stair no






Stair total






                                            42                     42                  42                    42

The pattern shows an increase of 42

The equation should use 42 to multiply the subject


If 5 x 42 = 210

To get to 54 we need to subtract 54 from 210

210 – 54=156

The formulae could be  T= 42 n – 156

I will test the formulae using stair no. 12

It should total 96

12 x 42 = 504

504 – 156= 348

The formulae does not work

I will try another formulae using another sequence…

Sequence 6 , 13 , 20, 27 and 34

I will take stair no.s 6,13,20,27 and 34.

I then add up the totals for each stair no. and record it in the table below.

These were the results I found…

Stair no.






Stair total






                                             42                   24                   60                   42  

                                                        18                  36                 18

                                                                  18              18

The difference is 18

I will check to see if the horizontal formulae applies to the vertical as well.


Stair no. 6

6 x 6 +24= 60

The formulae works for stair no.6

I will now check, using the other stairs in the sequence.

13x 6 +24=102

The formulae works for stair no. 13

20 x 6 + 24 =144

The formulae does not work

Therefore it is not the formulae

Although I can identify the patterns I cannot see a formulae that works.

...read more.

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. Marked by a teacher

    I am going to investigate by taking a square shape of numbers from a ...

    4 star(s)

    4 52x61=3172 53x60=3180 8 My prediction is right. I am going to use algebra to test my results. n n+1 n+8 n+9 (n+1)(n+8)=n�+8+9n n(n+9)=n�+9n Products difference is equal to (n�+8+9n) - (n�+9n) =8 In the same grid I will now work out a 3x3 square.

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

    We continue to proceed with the exercise to complete our formula (The General Formula). In the algebra equation we need to include the value of the grid size, i.e. is it a 4x4 [4] or 16x16 [16] represented as algebra to give us the total of the numbers added together.

  1. What the 'L' - L shape investigation.

    8 L-16 L-8 L L+1 L+2 5L - 21 I am now going to find a formula to find the L-Sum given just the L-Number and grid size. The formula must also be able to be used in any size grid.

  2. Algebra Investigation - Grid Square and Cube Relationships

    h: The height of the cube in question. d: The depth of the cube in question. g: The overall gridsize contained in the cube. s: The increment (step) size between numbers in the grid. Top Face (TF) n n+sw-s n+ghs-sg n+sw-s+ghs-sg Bottom Face (BF) n+100d-100 n+100d-100+sw-s n+100d-100+ghs-gs n+100d-100+sw+ghs-gs-s Difference in Cube: Stage A: (TF)

  1. Number stairs

    3, 16, 17 and 31 these are the 3-step stair I am going to test my formula for this portion of a 3-step stair: T=6x + 4n + 4 T= (6 x 1) + (4 x 15) + 4 T= 66+6 T=70 The total for all the stair values added

  2. Step-stair Investigation.

    5 step stairs: X+4g X+3g X+3g+1 X+2g X+2g+1 X+2g+2 X+g X+g+1 X+g+2 X+g+3 X X+1 X+2 X+3 X+4 By adding all the Xs, all the gs and all the numbers together I got: X+X+1+X+2+X+3+X+4+X+g+X+g+1+X+g+2+X+g+3+X+2g+X+2g+1+X+2g+2+X+ 3g+X+3g+1+X+4g = 15X+20g+20. This is the formula for all 5-step stairs on any size grid.

  1. Maths Grid Investigation

    b + 8(a - 1) + (a - 1) G =b x b + 8(a - 1) + (a - 1) = b + a - 1 x b + 8(a - 1) =b x b + 8(a - 1)

  2. Number Stairs

    As we can see here n=stair number, and the 3x3 stair case from the 8x8 grid can be substituted in to the formula staircase for the 8x8 grid. Total for algebraic staircase= n+n+1+n+2+n+8+n+9+n+16= 6n+36 We can also evaluate that Stair number (n)

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