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Stair investigation

has anyone done the investigation where you investigate different size stairs on a 10 by 10 grid? Can you give me a quick summary of what you've done?? PLEASE! :biggrin:

Reply 1

Jonny W

Im_here

has anyone done the investigation where you investigate different size stairs on a 10 by 10 grid? Can you give me a quick summary of what you've done?? PLEASE! :biggrin:

I'll try to help if you tell me the questions.

Reply 2

Im_here

Hey, thanks! I'm usually pretty good at investigations but we just had this one thrown at us and we haven't been given long to do it!

The sheet i got says... part 1
for other 3 step stairs, investigate the relationship between the total stair position of the stair shape on the grid ( i think i understand that bit, but i dnt no how to write it up :confused:

)

Part 2
Investigate further the relationship between the stair totals and other step stairs on other number grids.

any help would be greatly appreciated!! :smile:

Reply 3

Jonny W

I haven't done this investigation, so I can't help without more details.

Reply 4

Im_here

well ive basically told you all i know. I have a sheet, it has a a 10 by 10 square grid on it. starting at the bottom left with 1. It has a 3-step stair shaded in.. the numbers 25,26,27 then 35,36 and finally 45. underneath it then says...

this is a three step stair
the total of numbers inside the stair shape is
25+26+27+35+36+45=194
the stair total for this 3-step stair is 194.
then it has the question part 1 and 2 as i typed b4.

I don't nesacerily need answers... jus some help!! :redface:

PLZ!

Reply 5

Jonny W

This is the example (right?):

91 92 93 94 95 96 97 98 99 100
81 82 83 84 85 86 87 88 89 90
71 72 73 74 75 76 77 78 79 80
61 62 63 64 65 66 67 68 69 70
51 52 53 54 55 56 57 58 59 60
41 42 43 44 45 46 47 48 49 50
31 32 33 34 35 36 37 38 39 40
21 22 23 24 25 26 27 29 29 30
11 12 13 14 15 16 17 18 19 20
01 02 03 04 05 06 07 08 09 10

The score in the example is 25 + 26 + 27 + 35 + 36 + 45 = 194.

Let's use the variable N to mean the number under the bottom-left square in the stairs. In the example, N = 25. Then the numbers under the stairs are

[N + 20]
[N + 10] [N + 11]
[N] [N + 1] [N + 2]

and these add up to 6N + 44 (in the example, 6*25 + 44 = 194).

Pretend now that we don't know N. Suppose though that we know the coordinates (x, y) of the bottom-left square in the stairs. In the example, the bottom-left square is 5 along and 3 up, so (x, y) = (5, 3). Then N = x + 10y - 10. This is because

(1) N increases by 1 each time we increase x by 1,
(2) N increases by 10 each time we increase y by 1,
(3) N = 1 when x and y are 1 (the bottom-left square in the grid).

(The facts (1) and (2) tell us that N = x + 10y + a number. The fact (3) then tells us that the number is -10.)

Using the last red formula, the score is 6(x + 10y - 10) + 44 = 6x + 60y - 16 (in the example, 6*5 + 60*3 - 16 = 194).