Exponential Problem

It has been a couple of weeks since I taught exponents and logarithms. We do all the normal things we do with them in Algebra 2. We changed from one to the other, we graphed, we looked at their properties, we did half-life and doubling problems. When my students took the test I was happy to see good scores this late in the school year when motivation can run low.

Today I found a great problem on a site called FiveThirtyEight it has a weekly puzzle people can submit to and it was relevant because Avengers EndGame had just come out. The problem looks like this:

I was going to use this as a bell ringer. I thought it would take them about 2-3 minutes to do. I gave them no further instruction than answer the question. They could use their notes from the last chapter, anything that could help them. After 5 minutes, some students had started to give up. Some students were having rich-mathematical conversations with each other. Talking about halving, did the number of Thanoses also halve, does the original Thanos die when he snaps his fingers. This bell ringer that was supposed to be taking 5 minutes at the maximum is now going on 10 minutes. I felt like there were some misconceptions that students about this problem and that more time would help solidify exponential equations.

I let students struggle for the next 25 minutes, working with partners or in groups, using their notes. Some of the students and groups persevered through the problem, other groups were harder to get moving through the question. Here are some examples of the work my students did.

 

I taught this class three times, after the first time I went to some of the teachers that teach the same thing and asked them if this was beyond their thinking, after a while they decided that the students should be able to answer the problems from what we went over in class, but they added that the student’s wouldn’t be able to get an answer. After two days of sitting on this I went back to them, I wanted to know why they thought the students couldn’t answer the problem and what we could do next year to remedy this.

Here were some of the teachers responses to why the students weren’t able to answer the problem:

• One teacher said we did exponentials and logarithms too long ago for students to remember. Also students only remember or do what we teach them.
• Another teacher said students don’t know how an exponential equation works.
• Another teacher said students can’t persevere or formulate questions.

Here were some of the teachers responses to what can we do differently for next year so we can solve this problem:

• One teacher said we need to be more connected across Algebra 2, we should start with a question and answer it over the course of the unit or chapter, it needs to be an expectation that students can problem solve, students need to get use to out of the box problems from the start of the year.
• Another teacher said we need more modeling and that students need more practice at it because the capability is there.
• Another teacher said we should start off the chapter and year with questions like these, we need to change the way vocabulary is taught especially when it comes to a problem like this, we need to teach students how to use a simpler problem to solve.

I agreed with all of the responses that we should be doing next year. When you value problem solving over speed and simplicity you help your students become better mathematicians. This was a good problem for my students to work on for a day, this will help me become a better teacher for them in the future.