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  • Level: GCSE
  • Subject: Maths
  • Word count: 1065

Number stairs.

Extracts from this document...

Introduction

Number Stairs

Aim

        The intention of this investigation is to find the stair total of a stair shape when I know the stair number, I should endeavour to know this stair total in any size number grid.

Introduction

        Here is an example of a stair shape;

This particular stair shape would be described as a 3-step stair, as it has three tiers; there are 3 levels hence 3-step stair.

Adding all the digits within the stair shape together can identify the stair total,

        I.e. the stair total in the diagram above would be 45+35+36+25+26+27= 194  

                                        This number is the stair total

To calculate the position of the stair shape I must select a particular stair number (this is what I have named it.) I have decided to use the bottom left- hand digit, which in my diagram (above) is 25 (and circled.)

I am now going to investigate how the position of the stair shape (stair number) effects the stair total, I intend to do this by systematically moving the stair number, horizontally.

...read more.

Middle

3

62

4

68

I have noticed from the results that the stair total goes up by 6 each time, making it a linear sequence. From this I can predict that if the stair number was 5 the stair total would be 74 (68+6). Although I can also use this sequence to find the rule that will enable me to find the stair total in any stair shape, provided I know the stair number. This rule, when x is the stair number, is

6x  + 44

Now that I have found the rule for any 3-step stair in a 10x10 number grid. I will deepen this investigation by attempting to find the rule for any size number grid. I will do this by systematically finding the rule in a 9x9 grid then 8x8 etc but to speed up my investigation I will find this rule by using an algebraic technique (Shown below). After this I will, as before, analyse my results for a pattern.

Here is an example of the type of algebraic technique I will be using;

...read more.

Conclusion

any number step stair in any number grid.

I will continue to use my algebraic technique.

4-step stair in a 10x10 number grid

x+30+x+20+x+10+x+21+x+11+x+12+x+1+x+2+x+3+x=  10x+110

4-step stair in a 9x9 number grid

x+27+x+18+x+9+x+19+x+10+x+11+x+1+x+2+x+3+x=  10x+100

4-step stair in a 8x8 number grid

x+24+x+17+x+16+x+8+x+9+x+10+x+1+x+2+x+3+x=  10x+90

4-step stair in a 7x7 number grid

x+21+x+14+x+7+x+15+x+8+x+9+x+1+x+2+x+3+x=  10x+80

4-step stair in a 6x6 number grid

x+18+x+12+x+13+x+6+x+7+x+8+x+1+x+2+x+3+x=  10x+70

Results Table for a 4-step stair

Number grid

Rule when x is stair no.

6x6

10x+110

7x7

10x+100

8x8

10x+90

9x9

10x+80

10x10

10x+70

I can see that there is a visible linear sequence the constant in the rule increases each time by 10 so I can predict that the rule for a 5x5

 BETHAN WHAT HAPPENED TO  THE

...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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