Mathematics Investigation

# Mathematics Investigation - Mathematics Investigation...

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Mathematics Investigation Mathematics Investigation Staircase Numbers Staircase Numbers A staircase number is the number of cubes needed A staircase number is the number of cubes needed to make a staircase which has at least two steps to make a staircase which has at least two steps with each step (other than the first) being one cube with each step (other than the first) being one cube high. high.

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Pictures of Staircase Numbers Pictures of Staircase Numbers 1 3 2 3 1 5 4 2 5 3 1 7 6 4 2 7 5 3 1 9 8 6 4 2 2 Steps 1 3 2 3 Steps 6 5 4 2 1 5 4 3 9 8 7 6 3 2 1 7 6 6 4 12 11 10 9 8 3 5 7 9 6 9 12
First Breakthrough First Breakthrough I could see that there was a predictable pattern I could see that there was a predictable pattern to follow when you increased the number of to follow when you increased the number of steps. steps. The pattern for 2 steps was to plus 2. The pattern for 2 steps was to plus 2. The pattern for 3 steps was to plus 3. The pattern for 3 steps was to plus 3. The pattern for 4 steps was to plus 4 etc. The pattern for 4 steps was to plus 4 etc. I decided to test my theory and completed a I decided to test my theory and completed a table in excel. table in excel.

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Table for Staircase Number Table for Staircase Number Steps Column 1 Column 2 Column 3 Column 4 Column 5 Column 6 Column 7 Column 8 Column 9 Formula added up down the rows. 2 Steps 3 5 7 9 11 13 15 17 19 21 23 25 27 3 Steps 6 9 12 15 18 21 24 27 30 33 36 39 42 4 Steps 10 14 18 22 26 30 34 38 42 46 50 54 58 5 Steps 15 20 25 30 35 40 45 50 55 60 65 70 75 6 Steps 21 27 33 39 45 51 57 63 69 75 81 87 93 7 Steps 28 35 42 49 56 63 70 77 84 91 98 105 112 8 Steps 36 44 52 60 68 76 84 92 100 108 116 124 132 9 Steps 45 54 63 72 81 90 99 108 117 126 135 144 153 10 Steps 55 65 75 85 95 105 115 125 135 145 155 165 175 I then decided to investigate if there was any pattern to the numbers going down the columns and I discovered that there was.
Second Breakthrough Second Breakthrough Steps Column 1 Column 2

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Mathematics Investigation - Mathematics Investigation...

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