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!
I took a poll on twitter and many of you said you would like me to still include pages that I didn’t change, so that’s what I’m doing, but I’m not going to write extensively about those pages.
You can find my Algebra 1 (year long class) INB posts here:
And my Algebra 2 INB posts here:
The first standard we prioritize in Algebra 1 is A.REI.B.3: Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.
You can read more about my INB index pages in other posts. I have added to the back side of them a proficiency tracking log that I am not sure how I feel about yet, so I will save discussing that for my next unit’s post!
Skill 1: I can evaluate expressions and check possible solutions to equations.
To quote myself from the first time I taught this unit this year…
Next year when I teach this, I want to add another skill to the beginning that is just evaluating equations/expressions for given values of a variable. I meant to do this, and then I just forgot, but one of the things my students have been struggling with most is actually inputting their solutions correctly into a calculator to check them! Then they end up thinking their solution is incorrect, when really it’s their evaluation that’s incorrect…
So, here that skill is! I do think it made my students more comfortable with what their goal was in solving equations and what their solutions meant. I stole the parenthetical promise from Sarah Carter, and we immediately looked at why it matters. We don’t deal with exponents much in our first three units, so I guess I won’t really see the effect this has until next quarter, but I think it was worth talking about right at the beginning. We also discussed that calculators don’t understand that negatives and subtracting are the same idea.
Skill 2: I can solve one and two step equations
The only changes I made from my original pages here were to include the actual property names in the “legal math moves” section, to make the definition boxes bigger on the front (the picture here is the original and you can see how cramped it was), and to show students both the traditional solving algorithm AND a do/undo list/chart for solving. I think all of these changes were good, but especially the do/undo solution method. This REALLY helped when we got to literal equations, but I’ll talk about that later.
All of these students came from the Foundations of Algebra class I mentioned, and that course ENDS with an introduction to simplifying expressions and solving equations. So all of these students had seen equations like this quite recently and we were able to go quickly through these skills. Nothing was brand new to them until literal equations, but repeating this gave a lot of students the chance to master this that were still confused before.
Skill 3: I can solve equations with like terms and distribution.
I didn’t change the pages for this skill at all! You can read a more thorough description in this post.
Skill 4: I can solve equations with variables on both sides.
I added a page here on possible results of solving an equation. The first time I taught this this year, we addressed these possibilities within the examples but I felt like students did not get a strong understanding that they were NOT solving the equations wrong when they ended up with 2=4. I think adding this page helped to combat that. I also adjusted the organizer for the examples to have less steps than before – I included moving the variables to one side in the “solve” step instead of separating it. Looking back, I think I might need to put that back in as a separate step because this was a stuck point for a lot of students, but I really don’t want to lock them in to ALWAYS moving variables first. I will have to think about this one more.
Skill 5: I can solve literal equations (equations with >1 variable).
I honestly feel like the do/undo chart was a mini miracle for my students. They were SO MUCH MORE SUCCESSFUL in solving literal equations than I have ever had students be the first time around. The only time it doesn’t work is if you have two instances of the variable, and then you have to simplify first before you can make the chart.
We did the same literal equations scavenger hunt that I’ve been doing for a few years now, where you have to get all of the equations into slope intercept form (except the students don’t know that’s what it’s called yet), and I had zero panic. ZERO PANIC. It was amazing. Obviously, I’ll have to teach it this way a few more times, but I think this was a breakthrough for me as a teacher.
I’ll need to address the multiple instances of the variable you’re solving for in my next version of these notes.
Skill 6: I can solve one and two step inequalities.
Another set of pages I did not alter – I like these and I think they’re effective. My students did continuously forget when to flip the inequality symbol even when we talked about it extensively. We had a discussion about how when you read your solution you should be talking ABOUT THE VARIABLE, for example “x is greater than 1” instead of “1 is less than x”, which is talking about 1 and not x. That helped with that understanding, so I may include that in my notes next time. I don’t know how else to get them to look out for multiplying and dividing by a negative number – we illustrated why it needs to happen, we listed it before we started every practice, and still the majority of them forgot to reverse the inequality symbol. Suggestions?
Skill 6: I can solve inequalities with multiple steps.
All of the Unit 1 A.REI.3 pages pictured in this post can be found here. Most of them can be downloaded in PDF or Publisher (editable) form. Within that link is a folder to the pages I used the first time around this year that I didn’t use this time around, if you are interested in those.