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

Step Stairs

Extracts from this document...

Introduction

Number squares

In this investigation I will be looking at ‘square step shapes’. These are shapes such as the one pictured below:

image00.png

These shapes are put onto a grid such

...read more.

Middle

5

6

7

8

9

10

When placed on one of these grids the numbers inside of each box of the step shape are added to give you a total. The number in the bottom left-hand corner of the step shape is the number for that step shape.

        E.g.image01.png

This is shape placed on a 10x10 grid. It is shape number one, the first shape, as the number in the bottom left hand corner is 1. All the numbers in the shape added together equals 81. So the total for stair shape 1 on a 10x10 grid is 81.

I am going to begin my investigation by trying to find the rule that allows you, if you are given a shape number, to work out the total for a shape on a 10x10 grid. I will begin by putting the shape numbers, numbers inside that shape and shape totals onto a grid. I already know number one from my example and I will use the method I used in my example to work out the subsequent numbers and totals. However, for times’ sake I will not draw out each shape.

10x10 grid:

Shape number

Numbers in shape

Shape total

1

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

11

11,12,13,21,22,31

110

12

12,13,14,22,23,32

116

...read more.

Conclusion

8 x 8 grid:

An 8 x 8 grid will use this pattern:

image05.png

Giving this formula:

6n+36

I know this formula is correct so I wont test it.

7 x 7 grid:

A 7 x 7 grid will use this pattern:

image06.png

Giving this formula:

6n+32

6 x 6 grid:

A 6 x 6 grid will use this pattern:

Giving this formula:

6n+28

5 x 5 grid:

A 5 x 5 grid will use this pattern:

image07.png

Giving this formula:

6n+24

I am now going to try and find out a formula that, given the shape number, will allow you to work out a shapes total on any size grid.

Shape size

Grid Size

Formula

6

10

6N +44

6

9

6N +40

6

8

6N +36

6

7

6N +32

6

6

6N +28

6

5

6N +24

From this I have noticed that the number is always 6N for a 6-box stair shape and that the ‘plus’ number is always the grid size times 4 plus 4. So if this were written into a rule it would be:

6N +4G+4

(G =the grid size)

        I have also noticed that the 4 in the four G relates to the following:

In each case G repres-

ents 10.

...read more.

This student written piece of work is one of many that can be found in our GCSE T-Total 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 T-Total essays

  1. Number Stairs

    I have both times got the same formula 3n+11. Now I will see if this gives me the value of position 5. Formula = 3n+11 Position 5 = 3 x 5 + 11 = 26 This is correct as in the total for position 5, which I worked out previously and I got the answer 26.

  2. Number Stairs

    now going to investigate the fifth row, 41=290, 42=296, 43=302, 44=308, 45=314, 46=320, 47=326, 48=332 I am now going to investigate the sixth row, 51=350, 52=356, 53=362, 54=368, 55=374, 56=380, 57=386, 58=392 I am now going to investigate the seventh row, 61=410, 62=416, 63=422, 64=428, 65=434, 66=440, 67=446, 68=452 I

  1. T-Total Investigation

    2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 Firstly, we can see our T-Shape (with a T-Total (t) of 52), then a rotation of our T-Shape, rotated 90 degrees clockwise, with v

  2. T totals. In this investigation I aim to find out relationships between grid sizes ...

    1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 The T-Total for this middle number (12) is 67, using the same method of substitution: t = v + (v -1) + (v - 2)

  1. 3 Step Stairs

    Number added = 50 Number of squares = 6 Squares right = 0 Squares up = 0 Abbreviations: Total = n Number of squares = s Squares right = r Squares up = u For this position, in 3 step stairs, the formula would be: n = 50 + ( ( s x r )

  2. For this task we were required to create a model that can be used ...

    It also saves a huge amount of time, which is needed for this task. Cell protection is another one of Excel's advantages that I used. By protecting a cell, the data or formula of a cell can't be changed. This is useful because some cells don't need to be changed

  1. 'T' Totals Investigation.

    T = 5X-56 Check T = 5X-56 T = 5x50-56 T = 194 Formula to find 'T' Total if you have the 'T'? (X) in a 8x8 grid: =5X-56 Table of Results for a 10x10 Grid See next page X 1 2 3 4 5 6 7 8 9 10

  2. Investigating the links between the T-number and the T-total on a size 9 grid

    15 16 17 18 19 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 I think that, if the differences are the same throughout

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