*During this years MTBoS blogging initiative, I used the share the love prompt to capture some of the things I wanted to use and remember for teaching the quadratics unit. I am going to try to continue doing something similar to keep links and ideas for other units as well. I am really terrible about keeping all the activities I have used in the past or new things I want to try so this way I have an electronic record and I can share idea with other math people:*

We are knee deep into a systems of equations unit in one of my Algebra classes. So far we’ve done the Systems of Equations Launch which I wrote about here. Which led into graphing systems. At the bottom of that post I wrote how I would adapt it next year by adding in some lines that never cross or end up being the same. Since I hadn’t done that with the launch, I used that idea for the warm-up the next day.

I projected a Desmos graph with a few different lines and told them that the battleship path was the red line. They were tasked with estimating mine placement for the other 4 lines.

This quickly brought up the “missing” orange line and the inability to lay a mine on the green path. We discussed possible numbers of solutions to a linear system then I had them sketch ideas for a system that could have two solutions. Afterwards they did some more practice with graphing to find solutions. And ended by having the students create scenarios were you’d care about the intersection and then write up a problem which would fit that story. I collected them. Some will turn into warm ups or lagged review and some will end up on quizzes or the end of unit assessment. I’ve been working over the last few years to incorporate student generated problems. They seem to get excited about the possibility and its improved their problem writing because they want me to use theirs.

- Next we started the pictorial puzzles which lead into substitution. I enjoy this as an introduction because most students find success with it and it works well to move from the puzzle to the algebraic representation. I might also try something like Alex Overwijk’s Systems with Manipulatives. Then, I’m excited to try out the moving sticky note thing I’ve seen on twitter when we continue with the more formal version of the substitution method.

- For the elimination method, I think I’m going to launch with a magical Ms. Micaela warm up. I can’t remember where I saw this, but I’ll try to update with credit as soon as I can find it. Basically, each student is asked to think of two numbers. Then I ask them to add the two numbers together and tell me the sum. And subtract the two numbers and tell me the difference. I will then “magically” tell them the two numbers they started with. I’ve done this before, and I’m always amazed how easy it is to impress high school students with my prediction abilities. After correctly predicting a few of the students numbers, one of two things happens. A student figures out what is happening or I ask the students to try and figure out what is happening. We write out x+y= # and x-y = * and this leads into elimination method. I might actually use the sticky notes like I did in the substitution method to show why we can combine the two equations. I’m still looking for other good elimination type activities, so feel free to share some below!

- The
**meat of the unit**is after they’ve seen the three methods. Why do we learn three? Which one is better? This is**prime time for a math debate.**I love having math debates. They’ll pick teams and go for it. The first debate is usually informal. They debate with ideas they have already. The next debate is primed with examples. I pick out some systems for them, making sure I have a mix of problems that are suited for each method. In groups they have to solve each equation with all three methods. I provide some structure so that each person tries each method at least once. Then the small groups can discuss the pros and cons of each method. Then we go back to the whole class debate. Some team switching might occur here and all students usually are able to say “it depends” for the best method. But… I still have each team present their best case for why the method they are defending is awesome. The other teams then rebut by bringing up the draw backs. When all teams have had their say, we capture the strengths and weaknesses of each model into a visual for each student to keep. All future work, I don’t require them to solve any certain way, but leave a space for them to write why they chose their method. Come assessment time, I usually ask that each method be used at least once, but they are free to pick and chose when that happens.

Other things I want to remember to use this unit:

The MARs Formative Assessment Lesson on classifying solutions.

Trashketball. I used to launch with this, but it will be a fun problem to use with the graphing method later in the unit too!

Drive or Fly? Lab. Another way I’ve launched systems before. I’m thinking this one might be a wrap up project or something we do in smaller pieces over the course of the unit for those days when we have a bit of time, short days, snow delay days, or sub days. I’m thinking I’ll introduce the first bit about go through the guess and talking about what is important and then have students finish the project when it works for them. (More so than many schools, our attendance patterns often leaves days when a few students are in vastly different places so have a challenge for those ahead will allow me to spend time catching others up).

Also, some other fun labs that I might try to fit in, either during this unit or as a lagged review later: Oreos by Christopher Danielson (would adapt slightly to have students figure out what they’d need to prove or disprove whether double stuff is real) and Stacking Ups by Andrew Stadel. If I do stacking cups, I’ll bring some in to do a “live” 3 Act if possible. My students tend to get more engaged that way.

- Hopefully, as I actually teach, I’ll be able to update the blog with links to what we do in class. (Specifically, I use math debates a lot, so I really want to do a post focused on that, but I also get too wrapped up in them to get pictures/notes to share). If you have any other awesome systems work I’m all ears!
- Also, we will do systems of inequalities and non-linear systems as well. (Hinted at that in the Desmos warm up above) but this post is too long already so I’ll be capturing that in a future post!