As I said in my blog post on my Algebra 1 Unit 1 INBs, I feel like I’ve been taking advantage of other math teachers’ amazing resources and not contributing my own for a long time, so now it’s my turn! 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.

To see the intro pages we put into our notebooks to start off the year, you can read my post on my first unit from Algebra 1 here, where I go into more detail on those.

The first standard we prioritize in Algebra 2 is part b of **F.IF.7 (b): Graph piecewise-defined functions, including step functions and absolute value functions.**

This year, I bought some fancy composition notebooks at Walmart for myself, so that I can keep a teacher copy of all our notes in my classroom. The fancy notebooks make it easy for me to know when a student has my copy, and to make sure it doesn’t wander out of my classroom! Here’s what my Algebra 2 one looks like this year:

The first standard we prioritize in Algebra 2 is part b of **F.IF.7 (b): Graph piecewise-defined functions, including step functions and absolute value functions.**

After the intro pages, we put in their first divider page, which lets students easily find a unit of notes since the tab part of it sticks out on the outside of the notebook. I adapted mine from Sarah Carter’s (as with most math teachers, I use a lot of her resources). You can find her files in this post, and I’ll also include mine in the resources at the end. The students get to see the formal text of the standard they’re working on, and each of the individual skills we will learn on our way to meeting that standard.

At the start of each skill, I have my students record the page numbers we are putting the pages on so that they can find them more easily later. I’m not super strict on this, so some students don’t fill this out. Some students insist on also putting other work in their notebooks during class even if I ask them to write it elsewhere, so their page numbers aren’t the same as mine, which is also fine with me. At the bottom I have a place for them to record assessment scores (we use a standards based grading 1-4 scale) that fit this standard, so they can get a quick picture of how well they’re understanding this material. I’ve already decided I don’t love this feature because I’m really bad at reminding them to put their scores there, so it will probably disappear in future dividers.

On to the skills!

**Skill 1: I can determine if an equation is linear using its equation, table, or graph**

This skill is mostly a review for these students – they just need a little review on what they’re looking for. Then, we practice graphing by making x/y tables, which is also mostly a review. The students found it helpful to go over some hints of how to make graphing with fractional slopes easier. I should probably find something to put on the top of the inside of that foldable, but I haven’t figured out what that should be yet!

**Skill 2: I can determine the slope, x-intercept, and y-intercept of a linear function**

Slope should also be a review for them, but I sort of steer them away from the x2 – x1 formula they may have heard and emphasize that slope is the change in y values divided by the change in x values. This helps them translate the idea more easily to different contexts.

Graphing using slope intercept form was familiar to them, but a good review. Graphing with intercepts is covered by some Algebra 1 teachers but not all, so it was new to a lot of them. I didn’t give them enough room in this poof book to actually show how they found the intercepts, so I’ll probably rework this one when I do this skill with my Algebra 1 students in our graphing unit. The poof book was originally from Sarah Carter, and I think it worked well for her purposes (finding the intercepts after graphing), but my students needed more practice finding the intercepts using the equations to *make* a graph, so I need to give them more room to show that process in their notes.

**Skill 3: I can write equations using point-slope form and create parallel and perpendicular lines.**

I really dislike this foldable and it was not very effective. It has all the information, but it wasn’t clear to my students looking back on it which part they needed or what exactly they were looking at. I had them write the actual point-slope formula on the paper and it needs to be on the actual foldable. Anyways – don’t like this one, the end.

**Skill 4: I can identify key features of a quadratic graph and change a quadratic function to standard form**

Probably needed to put some dividing lines on the cover of the key features one, all of the definitions blended into each other a bit, especially on the students. After we did this, we played a few rounds of Polygraph: Parabola to practice the terms.

Getting quadratics into standard form isn’t technically part of this overall standard, but it fits nicely into this little intro to quadratics section, and their next standard is solving quadratics, so it will be nice to have seen this before when they get there. The right hand page of that foldable I used to have my students practice this on their own. The empty box is where I put a sticker once I had checked their work.

**Skill 5: I can graph piecewise, step, and absolute value functions.**

For our introduction to piecewise functions, I have students graph each of the functions separately on its own small graph, and then we literally cut them apart into *pieces* and put them back together to form the piecewise graph. I think this enforces the idea that different sections of the graph have different function rules. The students used highlighters where I used different color pens to color code the graph as well.

For step functions, we discussed that the key was to use decimal input values because integer values aren’t going to help you figure out what your steps should look like as much. I have a vertical number line hanging in my room that really helps with these functions and going up or down to the next integer. I often catch the students making up and down hand motions in the direction of that number line while they’re graphing these later, and I think it’s hilarious. I think it would be nice to put a short vertical number line on this notebook page as well next year, so they don’t have to look all the way across the room to do this.

The absolute value page I just got tired of making foldables…it happens! The main thing I would change about how I structured these notes is that we did an example that only have the absolute value of x, and students got confused about how to get the “v” shape when it was |x+3| or something similar.

**Skill 6: I can write an equation from the graph of piecewise functions**

Sometimes you need more practice than a poof book or a half-foldable can fit, so you make a pocket!

The steps I put on the pocket are okay. This was a skill that I really didn’t emphasize at all last year, but now that it’s part of our priority standard, I knew I needed to. This is definitely better than no formal practice with this skill! I need to be more explicit about the domain part, because students struggled with that a lot when we were practicing.

**Skill 7: I can describe the domain and range of a relationship using its graph.**

You’ll notice that this skill is not on their divider…because I forgot we had to cover this. Oops. Kind of a big concept to forget, but I’ll blame it on me making the divider during the craziness of our back to school inservice days.

Anyways, once I realized we needed to cover this, the students did really well with highlighting the “borders”. This really helps them find the x or y values they’re looking at because their line goes right through the axis. I should have included one graph that I didn’t make two copies of, because it threw them a bit when they were practicing and didn’t have a separate copy to do domain and range on! This ended up being one of the most used parts of their notes.

You can find all the links to intro files in the Algebra 1 Unit 1 post I made, and all the Unit 1 files for this Algebra 2 unit here.