Algebra 2 Unit 1 Interactive Notebooks

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.

Algebra 1 Unit 1 Interactive Notebooks

I’ve been feeling like I take advantage of resources other teachers share without really sharing my own for far too long. Last year, I wrote a few blog posts sharing resources, and decided that this year I wanted to share all the files I use for my interactive notebooks. I’m hoping these posts will also serve as helpful notes when I teach these classes next year, so I can remember which pages didn’t quite work as well as I wanted them to or when students said they didn’t have enough room or wanted something different, etc.

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.

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.

We started off our INBs with a page called Me, In August, where I had each student answer a few math-y and personality questions – last year was my first year using INBs and I had so many students who didn’t have their name anywhere on them even though I asked them to write it on the front, so I am hoping that having this page will help me identify the notebooks that get left out in my classroom!

The other intro-type page I had students put in was a growth mindset quiz. I didn’t make this one myself, it’s from Sarah Carter and you can find her post about it as well as the file here.

I bought composition notebooks with pretty covers for myself to use this year – this lets students easily identify my notebook when they go to grab it to make up notes they missed, etc.

We then put in our 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. Not sure how much I love this feature yet – it’s new this year!

To the actual pages!

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…

Skill 1: I can solve one and two step equations.

Both of these equation types are ones they should have been solving in eighth grade, but I go in assuming that they either don’t remember or didn’t understand any of it – it usually goes better. Either the students feel confident starting off with something they know, or they get instruction that they didn’t master last year (or a few years ago, since I have several students who are retaking Algebra 1 for the nth time). We started off with four important definitions – and I should have made the boxes for students to write in bigger here because they all ran out of room!

I called some of the properties we use “legal math moves” – trying to promote that there are things it’s okay to do to solve an equation and that what we’re trying to do is make it look different but still be equivalent. Next year, I would like to add the technical terms in parentheses after the definition I gave (addition property of equality, etc)

Then we did example problems for both one and two step equations, on separate days.

Skill 2: I can solve equations with like terms or distribution.

First we did a review of how like terms work, getting out our highlighters, and how the distributive property works. Emphasizing these things on their own has been really helpful to my students, as evidenced in my post about a specific inequality we solved together here!

Then, we did a poof book of 6 practice problems involving these skills, with a little guide for what steps to consider while solving above the practice book. I’d like to make this into more of a checklist style guide for next year. There’s a good step by step guide on how to fold the poof books here – students will think this is really hard the first time you use one!

Skill 3: I can solve equations with variables on both sides

Each table on this foldable is like a checklist for the students to follow. In the first table, we filled in what to look for at each step, then we did practice problems with the other 5. I realized as we were doing the examples in class that I didn’t include a single one that required them to combine like terms, so I’ll end up changing one of the examples to include that for next year.

Skill 4: I can solve literal equations (equations with >1 variable)

I took the inside of this foldable from mathdyal, and put instructions on the front to guide students. I don’t love the instructions. I’m just putting that out there, I’m not sure how I would edit them. Maybe I’d just delete them and use mathdyal’s notes page full sized. We solved all of the problems together and then I had them solve the “try it” ones below where we glued the foldable in their notebook. That was the most beneficial part of this one because I went around and checked on each student to figure out how they were processing this topic!

Skill 5: I can solve one and two step inequalities

I combined resources from a few other teachers for the front of this one, but I had saved them all last year so at this point I can’t remember where I originally found them – let me know if it was you or you know where they were! I love the flip flops for them to remember two situations in which they need to flip/reverse the inequality symbol. I need to include a space for them to write down in words which symbol is which because my students never know how to read the problems!

Skill 6: I can solve inequalities with multiple steps

Since I emphasized in skill 5 that the only way inequalities are different from equations when solving them is the symbol in between, we just had a few reminders here and then got right to some examples. I made sure to include some special cases so students would know what to do when they encountered them. We graphed the number lines separately so students wouldn’t have to squash their work.

If you’re wondering what the “my speed math problem(s) go here” means, go read my post about speed dating inequality style!

Intro page links can be found here, and 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.

Speed Dating: Solving Inequalities

Have you heard of speed dating?

That’s a question to get a room full of high schoolers to stare at you like you’ve grown a second head…

Whenever we do this activity for the first time, I ask that, and there’s usually one student willing to explain what it is. Speed dating – you sit across from someone for a few short minutes and try to get to know them, and then you switch.

This is math speed dating!

The previous day in class I had them each solve a different inequality in their INBs – I also used this as a concept check to see how they were doing on this. I checked each solution to make sure it was accurate and helped walk students through where they were stuck. By the end of class yesterday, EVERY student had an accurate solution to a different inequality in their INB.

Today, after we all learned how speed dating works, I explained MATH speed dating: They would sit across from each other for approximately 5 minutes. In that time, the goal was to trade inequalities, solve the other person’s, and then correct each other’s work.

There was some great conversation about strategies and I think a lot of them had mistakes pointed out to them that they normally missed! Many students also realized that there were certain types of inequalities they still need practice on and were able to describe those on their paper at the end of class.

This was also the first time a lot of my students learned each other’s names.

For the inequalities I gave each of them, I printed out a worksheet from their textbook and cut the problems apart, then gave each student one problem to glue in their INBs. This is the worksheet I used in particular, but any one would work.

You can download the recording sheet I have students use here – it isn’t specific to inequalities, so you could use this activity with any content, just assign each student a different problem!

Little Victory

I’ve been trying really hard this year to steer my students away from “tricks” to memorizing math rules – you know, the ones where they don’t really understand the content but remember some weird rhyme but don’t necessarily exactly remember how it works.

“Two positives make a negative!” is a great example of one of these tricks. They all remember it, but few of them remember for sure when it applies (when you’re adding two negative numbers? Multiplying? Subtracting? Solving? Graphing?) which leads to mistakes all the time.

I really emphasized choosing careful prompts when we were learning the Distributive Property this year – continuously asking them what operation we were doing every time we distributed, making them always use the name of the property (instead of “those rainbows” or “that thing!” with accompanying hand gestures). I also tried to emphasize that if there were parentheses without any number directly in front of it, you could always treat it like multiplying by 1, since 1 is the multiplicative identity and doesn’t change the value of the number it’s multiplied by.

The other day in class, we began solving inequalities. I emphasize that these are the same as solving equations, except we have to make sure we don’t do anything tricky to make the inequality symbol false – in an equation it doesn’t matter because both sides are the same, but in an inequality you’re stating that one side is smaller, and you need to make sure you keep the symbol identifying the smaller side.

We started doing examples of simple inequalities – one or two solving steps – to get them used to using the inequality symbols and reading them out loud, etc.

Then we came to this example.

I put this one in their notes on purpose to test their understanding of the operations and what we’re really doing when solving an equation or inequality. I was expecting one of two things. One, that they would suggest adding negative four to both sides, which is not the prettiest thing but I would have let happen and been okay with because there’s nothing wrong with that.

Two, that they would spout the “two positives make a negative!” trick and remind me that we could “turn those two minuses into a big plus sign”, like so:

I was ready to give a talk and redirect them or maybe chat about why we could turn that into a “big plus sign”, but INSTEAD, in ALL THREE OF MY ALGEBRA 1 CLASSES, the first student to volunteer a suggestion said, “couldn’t we distribute?”

“Distribute what?” I asked, excited but trying not to show that.

“Well we can use that negative in front of the parentheses as a -1 and then distribute it to the negative 4 and if you multiply those it’s positive four, so we can write m + 4”

Thanks for teaching my lessons for me, students!

My students in Algebra 1 are just starting to solve inequalities and learn the small differences between solving an inequality and solving an equation. We finished up our notes in our interactive notebooks today, and then with the remaining 25 minutes or so of class, I had them complete this Question Stack activity to start practicing. I find that especially with needing to know when to flip the inequality symbol, they can’t really start understanding until they’re doing problems on their own and finding the questions they need to ask.

Question Stacks are an activity format I got from Sarah Carter (she has so many of them, I linked to one but search her blog for question stacks and you will find many!) and I love the self checking aspect of it.

The way it works is this: students flip all of the cards so that the SOLUTIONS (in this case, the number lines) are face up on their tables. Then, they choose any card they want and flip it over. This becomes their first QUESTION to solve (a one step inequality in this case).

My students love showing their work on my tables with dry erase markers!

Once they solve the inequality, they find the face up number line that matches their solution, and flip that card over, starting to form a stack on top of their first question. This process continues until the final question is solved, and MAGIC, the solution to that is on the very bottom of their stack, underneath their first question!

The best part of question stacks is that students know immediately when they’ve gotten a wrong answer and need to ask for help, instead of me not knowing until I’m grading their assignments later. There’s also usually a lot of them figuring out their own mistakes because they can see the answer they think it should match!

This question stack was pretty easy for my students because we’ve been solving much more complicated equations prior to this, but it was a perfect introduction to them practicing inequalities and what to do with the symbols and it let me really see where all of them are at – we’re going to do a more traditional written practice tomorrow and I already know exactly who I’m going to need to check in with first to get on the right track!

You can download this question stack here, and this is the template I use to create them (Publisher file).

Here are some more pictures of my students work on their question stacks!

Book Recommendations (Vol. 03)

We’re 3 weeks and a bit into a new school year, it’s September, my birthday is on Friday, and we’re ALMOST THREE QUARTERS OF THE WAY THROUGH 2017?????

I’m a little early on my 3rd quarter book recommendations, but I’ve certainly read enough books since the last post, so I think it’s ok to be a bit early.

I’ve now read 60 books this year (blowing past my 52 book goal for a book a week for the year in August…), which makes 26 books since my last recommendations post.

Here’s the top 5 from this quarter:

Every Soul a Star – Wendy Mass

Ally has lived at her parent’s campsite on the path of the August 2017 solar eclipse most of her life. She is so excited for the eclipse, and she loves space and the outdoors. Bree is popular and very concerned about staying that way. Jack is awkward, not great at school, and used to kind of blending in and staying out of the way. What happens when just before the eclipse, Ally finds out her parents are selling the camp to Bree’s parents as soon as the eclipse ends, and Jack ends up at the campsite with his science teacher so that he can make up his failing science grade?

I was one of the many who kind of went eclipse crazy last month (pictures of our staff watch party here). I loved every minute of it. A friend who works at a library recommended this book to me and I am so glad I read it before the eclipse, even though it’s a juvenile fiction chapter book. The character depictions were all very real and pulled you in, and the eclipse and space information included was really well researched and detailed. Even though the eclipse is over, I still think this would be an enjoyable read that explores a pure dynamic of three very different kids being forced together by circumstance and letting themselves enjoy science.

Zenn Diagram  – Wendy Brandt

Eva Walker has a strange gift. She can read people’s emotions by touching their belongings. This comes in handy when she’s tutoring people in math and can touch their calculators and figure out exactly what they don’t understand, but the rest of it has basically led to her…not touching anyone or getting close to anyone or having friends. Then she meets Zenn – he’s cute, and the violent set of emotions she gets when she touches his jacket accidentally should make her steer clear, but instead…

I was recommended this book by Diann, who informed me: “it’s kind of about math only it’s not really about math, but that’s why I picked it up and then it was really good and you’ll like it”. And she was totally right. This book is enveloping – the emotions you feel and see along with Eva are intense and all you want is for her to figure out how to build a relationship with someone outside her family. When you also find out about what happened to her parents, your heart is twisted even more. The ending totally floored me and this was one that I stayed up (in the summer, not on a school night, although I won’t pretend that hasn’t happened before) until around 3 am reading to finish.

Eliza and Her Monsters – Francesca Zappia

Eliza is the weird girl at school who doesn’t really interact with anyone. That’s fine, because at home, she’s the secret and anonymous creator of the wildly popular webcomic, Monstrous Sea. Like, so popular that she has secret bank accounts hidden from her parents with the profits. Then Wallace transfers to her school. She discovers that he is one of Monstrous Sea’s biggest fanfiction writers, and decides to start sharing her secrets with him.

As someone who has partaken in the online worlds of fanfiction and fandom in general a lot over the years, I’m very partial to this type of plot. This caught my eye as being a similar thought to Rainbow Rowell’s Fangirl, and it kind of is at first glance, but it also ends up being a deeper exploration of mental health and privacy and a lot of other things that I really loved. The book also contains images from Eliza’s webcomic throughout which was really cool. Another thing I loved about this one is that Eliza started as a super fan of a series of books, and then created her webcomic not as a fan work of that, but as an original work inspired by something she loved a lot. Then she inspired her own fanworks! Way cool. But also, Zappia has written the fictional work that Eliza was originally interested in. That’s totally on my list to read now (it’s online available to read here). Sort of a reverse of what Rainbow Rowell did, since she wrote about Cath’s fanfic in Fangirl and then published said fanfic as a novel in Carry On. Very interesting exploration of fandom and really fun.

Brain on Fire: My Month of Madness – Susannah Cahalan

A nonfiction account of Susannah, a reporter at a major NY newspaper, at a promising moment in her career, who gets bit by bedbugs. Or did she get bit by bedbugs? She goes to the doctor, who suggests she’s drinking too much (she’s not). Soon after, she finds herself in the ICU, labeled a flight risk, unable to remember things or control her responses or do basic tasks. What happened? A rare disease – one that almost didn’t get diagnosed soon enough to save her life.

Wow, this book was riveting and terrifying. I now suddenly get scared that I’ve contracted the disease Susannah had and panic about how much time I have to find someone who actually knows how to diagnose it. She writes painfully honestly and so captivatingly about what happened to her. There is a lot that she cannot even tell, because she doesn’t remember it. She refers to her parents’ accounts, her boyfriend’s, the doctors, and video security footage from the ICU. She pulls together this story of this bizarre thing that happened to her and almost killed her because only a few doctors knew about it. It’s really remarkable.

Made You Up – Francesca Zappia

Alex can’t tell the difference between her real life and what her brain makes up. Well, she can, when she takes pictures. Or does that work? She meets Miles, and she thinks he’s the boy she freed the lobsters with in the grocery store when she was little. But her mom told her that wasn’t real. So is Miles real? What is real? How can she tell?

Oh look, another book by Francesca Zappia! I fell in love with this author’s writing during Eliza and her Monsters, so I figured I’d give this one a shot. Also incredible. This puts you right into Alex’s mind and leaves you just as frustrated as her about telling what is real. I even totally called the plot twist in this one and still found myself sobbing when it actually came, that’s how impactful the writing was. Wonderful and captivating read.