Tag Archives: solving equations

Hold Onto Your Hats: Algebra II Unit One

At the end of last year, my fellow Algebra II teachers agreed with me to try a modified version of Jonathan’s Pivot Algebra II. Basically turning a class I’ve taught some version of about 10 different years into an entirely new prep. Just like a new prep, I’ve had a lot of grand ideas that have resulted in some successes and A LOT of notes of what to modify for next year.

Side note: Because of some weird geometry class issues, my students are much more all over the board than previous years. I normally have about 90% juniors with 10% sophomores (who should be in PreAP). This year I have about 70% juniors, 20% sophomores and 10% seniors. And compared to previous years when 27 or 28 was a big class, these are 29-30. Also, we have 47 minute classes three times a week and 52 minutes two times a week.

Ok, let’s get started. The first real day of teaching, I thought I’d hit on all the mistakes students make, “Hey, if we learn this now we won’t make them later!”  Um, yeah, what that turned into was “Hey, these are all the things you struggle with and are hard to understand and remember, so let’s talk about them all on the first day!”

Starting with this card sort. Determine if these are true or false.

Alg II Unit One files from megcraig.org(file here)

Oh holy cow. This went horribly. They had no idea how to determine if they were true or not. I suggested using a calculator to check, but imagine them trying to put some of these in a calculator. Frustration mounted. Then we checked and I was trying to use this as a big “ta-da” moment to introduce the GERMDAS house that Kent Haines suggested (more about this below).  “See, we don’t have to memorize all these different rules!  We can just use this one big rule!”

Alg II Unit One files from megcraig.org(file here)

The worst part was, after a few example problems, I never really went back and used those rules again with the types of problems they saw on the cards. I don’t know if I’d just scrap the entire idea next year or spend a day just focusing on those types of problems, or what. I’m also getting really frustrated with the fact that it’s like we’re starting from scratch every year in math. Should I really have to be covering order of operations again?

But do take a moment to embrace the beauty and simplicity of the GERMDAS house. I’ll let Kent explain it:

I showed it to the other teachers at school and one of them who works with lower level kids said the kids really liked it and understood it. Another teacher is planning to show it to her Calculus students (and she showed it to her 5th grade son as well with a really good explanation–when you clean a floor of a house, you don’t just jump from room to room to room, you go in an order. So don’t jump around to addition and then subtraction, but just clean up in order!).  Thanks again, Kent!

And because throwing all that at them wasn’t enough, let’s practice plugging in values into the un-simplified and simplified version and see if we get the same thing!  Or next year, I’m thinking probably not because it was just too much going on in one problem. Instead we’re going to spend a day on the difference between 3 – (x + 7); -3(x + 7), 2(x + 4) – 3(x +7) and 2(x + 4) – (x + 7). BECAUSE SERIOUSLY WHY IS THIS SO HARD. DID I MENTION THIS IS ALGEBRA II? Then I would spend a day on the last third of the notetakermaker: with a caveat that after today, if anyone tells me *I’m* wrong because my answer doesn’t match theirs because you didn’t put parentheses around a negative when squaring, then you have to do ten pushups. Because I’m over it.

Ok, so now we’re onto day three in what actually happened. It’s like when I was planning this unit, I got caught up in all excitement and forgot everything I’ve learned about teaching math. Because I thought what would make things really exciting would be to introduce a new, somewhat confusing (it turns out) method to solve equations, as well as adding writing out tedious steps! It’s going to come as a shock, but it did not go over well. (Note: this NTM ended up taking two days)

Alg II Unit One files from megcraig.org(No file available and I don’t really want to talk about why.)

After the entire chapter, I am IN LOVE with the flowchart method. But a lot of kids struggled with it to begin with (I think it was “so easy” for me to see that I didn’t take into account that (a) they don’t know the order of operations (see day one) and (b) it is something completely new that needs some soak time).

Learn from my mistakes! Here’s how I’m going to go about it next year:

  1. Save the variables on two sides for a different day.
  2. Save writing the justification for another day.
  3. Work on just the flowchart for a few problems.
  4. THEN say, well, we’d like to make this a bit more “mathy” and “formalized” so here’s what we’re going to do: draw the top half (the building part) of the flow chart in short hand, with just the arrows and operations above them, and not each intermediate step. Now work with the actual equation algebraically, check off each arrow as you go. That epiphany came to me at the end of the week, and it seemed to make all the difference. They were a bit frustrated (rightly so) that I was making them solve the equations twice (oh, and write out each step). But they didn’t mind drawing a little flowchart to help them. And again, the flowchat is MAGICAL. Just wait until the next post when we use it for 5+3|x – 2| = 14. (Or read more about it here)

If you’re still not sold on the flowchart’s worth, just check out these literal equations:

Alg II Unit One files from megcraig.org(file here)

I *almost* want to make them solve these with just the flowchart. I would say the students got them right 90% of the time with the flowchart. It was beautiful. One type of problem I need to add is something like x/b – a = c, where they can see the need for parentheses for the answer: c + ab was a common answer on the test instead of (c + a)b.

Speaking of test, I decided to stop here, review and quiz:

Alg II Unit One files from megcraig.org(file here)

Also, I’ve been trying mixed and lagging homework to mixed results. The biggest problems are (a) at the start of the year there was only so much to mix in (b) making homework for the entire week, but getting behind so it’s not lagging anymore and (c) students really lagging their homework, i.e. only doing it the day before the quiz. But I guess it makes a good review that way! Here is the homework for the week:

Alg II Unit One files from megcraig.org(file here)

Ok, so that was just the first half of Unit One but I think I’m all reflected out. As always, any comments, questions, or suggestions for improvement are welcome in the comments or on twitter!