The theme for week 3 of the #DCSDblogs challenge is Oops! The goal is to talk about a mistake you made in your classroom recently and how you addressed it.
This year is the first year I’ve taught Algebra 2. Starting last summer and throughout the year, I’ve made sure to start my planning for this class a bit earlier than normal so I can process the content I need to teach and get my mind around the best way to present it. This is also the first class I’ve used Interactive Notebooks in, which has actually overall helped me with finding the core ideas of the content and finding the pieces that are going to resonate most with students.
The unit we just finished covered rational functions. I took a bit to re-acquaint myself with the process of finding asymptotes, adding/subtracting/multiplying/dividing and solving these functions. However, this unit came right in the spring break / Iowa Assessments time of year, and so my planning all got a bit wonky.
I definitely didn’t leave myself enough time to do the planning of these lessons justice, and it showed. Here are my notes to myself for teaching this unit in the future:
We started with sketching graphs of rational functions. The very first thing I realized is that my students, while proficient at factoring quadratics, have not gotten very efficient at it. This meant that every single problem seemed more complex, because pretty much regardless of what you’re doing with a rational function, the first thing you need to do is factor the numerator and denominator.
*note to self: more practice factoring quadratics to enhance efficiency
I also realized that in my process of sketching a graph – finding x and y intercepts, vertical and horizontal asymptotes, holes, etc., I had them finding the intercepts first. This ended up not making sense, because if there’s a hole at one of the intercepts, that point isn’t actually an intercept, so the holes need to be the first thing you find. This one was a fairly easy fix because I just had them write on the inside of the foldable “move step 2 to after step 4” and explained why we needed to do it in a different order. Everyone was fine, and we moved on.
*note to self: use a few examples to make sure the order of your process makes sense
Then, we hit the exit slip problem I had included on their foldable. They were feeling okay about finding the characteristics of the graphs, not so great about actually sketching the final curves amongst the asymptotes, intercepts, and holes, but I figured we could give the exit slip a shot and then come back and discuss it the next day. Rookie mistake: I had taken the functions I used for the foldable from one of their textbook’s worksheets for the section, and I hadn’t graphed the exit slip one myself because I wanted to leave it blank in my teacher INB since the students were supposed to complete this one on their own.
Turns out, this particular rational function has no asymptotes, which we had not seen any examples of and so every student completely panicked. They correctly found that there were no vertical and no horizontal asymptotes, but then they all just stopped working because they were convinced that wasn’t possible for a rational function and they had done something wrong.
*note to self: check the exit slip problem. Also, don’t assign a unique case example for an exit slip!
Next, we covered simplifying, multiplying, and dividing rationals, along with complex fractions. This section actually went really well, and my students felt really good about themselves after having a freakout when they saw the complex fractions and then realizing that they had all the skills to deal with them already! The only thing I want to change here is…again…the order of the steps. It makes more sense to rearrange the problem into a multiplication problem before factoring. My students were the ones who figured this out, because they’re awesome.
*note to self: seriously, check to make sure the order of your process make sense.
Adding and subtracting rational expressions is probably the most complex process in our district’s Algebra 2 curriculum. Either that or factoring polynomials above degree 2. Regardless, I did not do a good job of presenting this, or practicing it, or anything. I kind of botched this one big time.
First, the foldable didn’t leave enough room for anything to happen.
*note to self: give students enough room to do math on the paper!
Then there’s the fact that I just…didn’t explain this well. There’s really no way around it. I did not teach this well. My students didn’t know when they were finished with a problem, what to do next, they kept getting lost in calculations.
*note to self: spend some time doing more problems with adding and subtracting rationals yourself, so you can break down the structure better
*note to self: search the #mtbos and other online resources to see how other people break this skill down
*note to self: really, just scrap this section and start over from scratch for next year
I can end this post on a good note, though, because I made sure to set aside extra time to plan for the last skill in this unit, solving rational equations, and I think that turned out pretty well. My students loved making the pockets for their INBs and getting to stick the practice problems in them, which we also did for simplifying rational expressions, and it was a good way to fit more practice problems into their INBs without taking up more pages.
They also showed me that they really had mastered solving quadratics earlier this year, because that’s what you end up having to solve when you’re solving a rational equation. I was really proud to see them pulling out the Quadratic Formula or factoring again and just going at it!
*note to self: good job on this one 🙂
I learned from this section that I need to be more intentional about planning, especially with content I haven’t worked with myself in a while. I have stellar students in my Algebra 2 class, so we were able to overcome my shortcomings in planning without too much trauma, but they did get lower quiz scores over this content than I’m used to from them.
I’m hoping to have a bit of time left at the end of the year to come back to this content before their final, but I don’t think it would be productive to keep pushing forward with it right now. They need a break from it after the train wreck I put them through.
Please let me know if you have any great lessons over rational expressions and functions – I would love the help in improving this unit for next year!
*note to self: word processing systems don’t think asymptote is a word and it’s incredibly frustrating.