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

Number Stairs investigation.

Extracts from this document...

Introduction

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.

-

...read more.

Middle

6                                80                                                6

7                                86                                                6

Each time the stair total increases by 6.  This takes the previous total to the next total.

To get the formula I multiplied each stair total by 6.  I noticed that after each multiplication the only difference between the number and the ST was 44.

Therefore the formula is Dn+(A-D)

                                    6n+(50-6)

                                    6n+44

The stair number is multiplied by 6 and 44 is added to make the stair total.

The formula allows the stair total to be obtained from only the star number.

Part 2

As said in my plan I intend to try different step sizes on the same 10 x 10 grid.  I will try a 2-step stair.

From my previous investigation I figured that

...read more.

Conclusion

The total of the difference is 20 + 10 + 11+ 1 +2 = 44

The difference when added together makes the number that must be added at the end of the formula (i.e.6n + 44).

I will see if this applies to all stair sizes.

11

1

2

Sn+10

Sn

Sn+1

The total of the differences is 11.  This is also the end of the rule(3n + 11).

41

31

23

21

22

23

11

12

13

14

1

2

3

4

5

Sn+40

Sn+30

Sn+31

Sn+20

Sn+21

Sn+22

Sn+10

Sn+11

Sn+12

Sn+13

SN

Sn+1

Sn+2

Sn+3

Sn+4

Total difference = 220

Formula = 15n +220

The rule for finding the differences works.

I will try to find the rules for larger stair numbers.

51

41

42

31

32

33

21

22

23

24

11

12

13

14

15

1

2

3

4

5

6

Sn+50

Sn+40

Sn+41

Sn+30

Sn+31

Sn+32

Sn+20

Sn+21

Sn+22

Sn+23

Sn+10

Sn+11

Sn+12

Sn+13

Sn+14

SN

Sn+1

Sn+2

Sn+3

Sn+4

Sn+5

As there are 21 squares I will say the start of the rules is 21n.  The total of the differences is 385.  The formula can is 21n + 385.

...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.

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