For 3-step stairs, investigate the relationship between the stair total and the position of the stair shape on the grid. Investigate further the relationship between the stair totals and other step stairs on other number grids.

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Maths Coursework

By Tom Nixon

10HS

THE QUESTION

This is a 3-step stair.

The total of the numbers inside the stair shape is

25+26+27+35+36+45 = 194

The stair total for this 3-step stair is 194.

PART 1

For other 3-step stairs, investigate the relationship between the stair total and the position of the stair shape on the grid.

PART 2

Investigate further the relationship between the stair totals and other step stairs on other number grids.

PART 1

The total of the squares inside the stair is all the squares added together. The stair number is the number in the bottom left hand corner of the stair. We can call this number n.

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In order to see a pattern between the totals of the shapes, we can arrange information in a table.

 

As you can see from the above table we can come to a formula of:

T = 6n + 44

T is the stair total, n the stair number and 44 is the remaining number.

T = n + (n+1) + (n+2) + (n+10) + (n+11) + (n+20)

T = 6n + 44

I have tested the formula above on other stairs on a 10 x 10 grid but not ...

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