Problem Statement
This problem was based on a specific staircase that had 21 stairs/steps. Our job was to find the amounts of steps that it would take a person to go up and down the stairs in two distinct patterns. One being the usual way to go up and down stairs, while the other a more intensive way; that would make a person repeat their process of stepping up and down with each step onto a new stair/step.
Process
For the process I first calculated the steps of the first pattern which was easy. I just added up the steps once going up and once going down. Then I, by hand, drew out a bit of stairs and connected lines to show the pattern in which we had to follow. I then got an idea of what was going on and drew a t-chart and tried to find a pattern. I found a pattern along with my group and we then came up with a formula to get the answer. In order to figure out if I got the correct answer I decided to go ahead and find the answer through my drawing as well, meaning I drew the rest of the stairs and counted one by one. I got the same answer.
Other's Process
Others process were basically the same mostly because we all started off doing the basic adding and then got to work in groups after we already had a plan. So we got to work together on getting our formula which was the part in which most of us needed help.
Solution
I dont think we ever got the actual solution from Kirby, but my group and I decided on an answer and found that a lot of other groups, if not all, got the same answer. The final formula was indeed x(x+1).
Self-Assessment
I think I did very well with this problem because even though we got a lot of group work time I was proud that I had my answer by the time we got to talk to each other. But I was also glad that I got to work in a group because that way I got a more solid formula and was able to widen my thinking because I don't think I would've gotten the same formula if it werent for my group. I think that the habit I demonstrated most during this problem was Patterns/Generalizing because all you really had to do was find the patterns in order to move forward with finding a formula and being able to find the final answer.
Edits
- Added habit used to self assessment
- Added pictures
- Corrected grammar
- Made sure to include final solution/formula