This year I’ve committed to posting each unit of both my Algebra 1 and Algebra 2 INBs.
My district is moving to a standards based curriculum, and has identified priority standards for every course. These are the standards we are required to address and assess our students over, so they pretty much form our units.
I normally teach year-long courses (47 minute classes per day). However, due to a lot of district specific things involving SPED students, a new course introduction, and graduation requirements, this year I taught a block course (94 minute classes per day) of Foundations of Algebra first semester, which covered skill gaps students would need to find success in Algebra 1. This semester, I am teaching (most of) those same students Algebra 1 on a block schedule. This means I get to start Algebra 1 from the beginning in the same year and revise my activities and INB pages!
You can find my Algebra 1 (year long class) INB posts here:
And my Algebra 2 INB posts here:
And finally, my posts from this second round of Algebra 1 here:
The third standard we cover in Algebra 1 is A.REI.6:
Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables.
I finally wrote a post about my journey through the other side of this index page – the evolution of my student proficiency log! You’ll notice if you’re a regular reader of my INB posts that I have been avoiding talking about them for awhile and that I only show the index side in these posts, and I am finally ready to share, but they deserve their own post 🙂
In my first post about this unit earlier this year, I said:
I pretty much like the way I organized this, except for the way I presented the elimination method
This means many of the pages I used are unchanged – but there are a few besides just the elimination that I made some minor changes to. However, I probably won’t have as much to say about each skill and you can read my original post about this unit to get more insight into the other pages.
Skill 1: I can determine if a given point is a solution to a system of equations
Getting down those definitions and learning how to check possible solutions. None of my students use the “storing values in the calculator” method to check their solutions, but our curriculum coordinators in the district specifically told us that we need to show them this, so it’s there.
Skill 2: I can graph a system of equations to find the solution
First we talk about the possible outcomes when solving a system of equations. This was more fluid for these students than my first Algebra 1 group this year, because I added a page that is essentially just like this into their original solving equations unit. The only different thing about solving equations really is that you also have to know what the graphs look like, and that there is an x AND y value.
I changed the graphing pages to be cleaner and reduced the number of examples. Really, I have discovered that my students just need more practice graphing – by themselves, without me. So these notes have one example of each possible outcome, and then they practiced. I like these notes, but I really struggled to get the x and y axis to show up in Publisher the way I wanted to, so I ended up just drawing them in with a permanent marker before I made copies. I then tried to scan this copy so that I could just print it in the future, but the office copier hates me recently and it did not turn out well. It’s included in the files anyway, so you can see how poorly this ended up. Drawing in the axes each time you make copies is really not that bad, compared to a long and drawn out fight with the scanner!
Skill 3: I can solve a system of equations when given the value of one variable
The only thing I changed here from before is that we still did a notice/wonder with the systems included in these notes, but I did not have them attach that notice/wonder to their notes, we just did it on the board. I still really like this as an intermediary step, since it’s essentially a review of solving equations once they substitute in that known variable.
Skill 4: I can solve a system of equations using substitution
I kept this one exactly the same. Upon using it with this group of students, I think it may be beneficial to cut the number of examples here as well, like I did with the graphing. We hand wrote an example with no solutions in the center fold of this stapled notes section, since there ends up being two blank half pages in the middle, but I plan to just change it to be two one solution examples and one special case example.
Skill 5: I can solve a system of equations using elimination
I am moderately happy with how I set up the elimination method this time. We started with looking at what happens when you multiply entire equations by a constant and discussing what elimination means as a word. We looked at the equation x+2=4 and solved it, and then I asked what would happen if we multiplied the entire equation by a number of their choice. They chose 4. They were adamant during the entire process that the solution was now going to be x=8, even down to the moment where we were ready to divide 8 by 4. Their minds were blown. I think they’re still mad at me about it. But it stuck in their heads that multiplying these equations by some constant doesn’t affect their answers!
We then began with systems that are already set up for elimination – where either the x coefficients or y coefficients are already opposites. This was the step I missed last time. This was easy for my students.
Then we moved into how you can GENERATE this opposite effect if it isn’t there to begin with. I think one of the issues is that my students just aren’t fluent enough in multiples to think through this well. “What do 8 and 12 both go into?” is the hardest question in the world for them. I think I need to bring multiplication tables into this the next time I teach it. Anyways, we practiced just getting these opposites a few times, and then went into the last page of notes which is three examples of completing the elimination method all the way through to a solution.
I think part of my issue with teaching elimination is that it is my personal preference for a solution method when I solve systems myself, and so I do it so automatically that I think I have trouble thinking through all of the intricacies that my students are going to struggle with. Would love to accept suggestions from people on this one!
Skill 6: I can write and solve a system of equations to represent a situation
I didn’t change these last two pages at all from the last time I taught this. I did, however, struggle to get students to actually consider the most efficient method when they were solving systems. I tell them that they can choose whatever method they want to use, but I kind of screwed myself over with that statement when several of my students decided they were going to solve every single system by graphing it – and they were not quite proficient in graphing. I ended up encouraging them to look back at these notes and having them think about what they system was “set up for” and I won some of them over. The main issue was that they wanted to use graphing every time (or some of them were on team substitution or team elimination), but they really only knew how to use that method if the system was already set up for it. So they would go, “I want to graph this system but what is the y intercept” and I would respond “that equation is not in slope intercept form” and then they would give up. I’ll have to work on that.
You can find the files for these pages here, including a subfolder with the previous versions of the pages.