Leo the Rabbit

Our next challenges was to try to solve one of two rich task problems.  I chose the somewhat well-known Leo the Rabbit problem.  On first look I knew it had to do with patterns and sequences and that I could probably use a table to solve it.  I drew a few pictures.  My anxiety rose as I realized how many different ways Leo could get up the stairs and I didn't feel I was getting my head around the right approach.  I wished I had someone here to talk to about it.  I had Google so off I went after working on the problem alone for 10 minutes and my anxiety about my skills in math getting the better of me.  As a teacher, I find my anxiety about my math abilities is worse because I feel pressure from myself and other teachers to be able to find the answers skillfully and quickly.  I hate that feeling.  Anyway, Google gave me the helping hand I needed.  Here is one teacher's solution.  The question we were asked for our course is "How would you convince a skeptic that you are right?" To be honest, I would have to sit with the solution a while longer to be able to convince anyone else that it is right.  I totally get the solutions up to step four but when you add a fifth step and rely on Fibonacci's sequence (adding the two previous to get the next) and why that works with the steps, I would need to rattle it around a bit to be able to explain it to someone else.  I know it work and I know the answer 89 is right but I needed someone else to tell me that.  I also get that adding the previous steps options makes sense each time because each three and two step sequence will only have a certain number of options.  But coming up with that on my own? Uh-unh.