Tuesday, November 29, 2016

Staircase problem day two

Students were presented with another staircase problem. This time, their task was to determine how many sides are present based on the number of stairs. Students created an input/output table showing the function.

Students used craft sticks to build the staircase, counting the sides as they went.

As the students approached ten, they realized that it was pretty hard.A lot is going on here, but there are a few takeaways.
1. For the most part, students agreed on the outcomes for terms 1-5.
2. Students started to see a pattern emerge.
3. When students "jumped" from 5 to 10, the output for ten was varied. Some students thought that they could use what they knew about the fifth term to help them determine the tenth term.  Another student pointed out that if we look at the second and fourth term's outputs, they are not just "doubling" them.
4. A student noticed the terms were all factors of its corresponding output. This led to another pattern... 1X4=5, 2X5=10, 3X6=18, etc... 
5. Students recognized that if we could figure out an expression or a rule, we could easily compute the 100th term without having to build with the sticks or making a really elaborate table.

We will keep thinking on how we can create a rule, using an expression, to help us compute with greater values.