Algebra 2 Unit 2 Interactive Notebooks: Solving Quadratics

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.

Other Algebra 2 INB Posts:

Unit 1

Algebra 1 INB Posts:

Unit 1


Unit 2 in Algebra 2 covers N.CN.C.7:

Solve quadratic equations with real coefficients that have complex solutions.

On our index page you can see the skills I broke this down into. Skills 1-4 review methods they (should have) learned in Algebra 1 to solve quadratics with REAL solutions, then we get into the complex solutions idea.

I’ve already decided that I don’t really care about my students recording their assessment scores in their INBs (mostly because I constantly forget to remind them to do this) so starting with our next standard I’m taking those boxes at the bottom off.


In this unit I found myself creating most of my INB pages from scratch (or inspired by those of other teachers), so all of these were created by me!

Skill 1: I can solve quadratic equations using inverse operations.

I wanted to emphasize WHEN you can use this method, because my Algebra 1 students continuously try to use inverse operations always when solving quadratics and force it to work even when it shouldn’t.

The poof booklet underneath the instructions has 6 example problems that we solved together, including one that cannot be solved using inverse operations to reinforce that. I think this emphasis worked really well because I did  not have a lot of students trying to use this when they shouldn’t. We’ll see if it works as well with my Algebra 1 students when they get to quadratics at the end of the year!


Skill 2: I can factor a quadratic expression and use factored form to solve solutions or graph.

So this (and inverse operations, and completing the square, and quadratic formula) is supposed to be just a review from Algebra 1. First of all, I have a lot of students who definitely never mastered this in Algebra 1. Second, they were probably taught to factor using one of the many factoring strategies that involves, at some point, guessing and checking a bit. I prefer to teach factoring using the box method, as shown in these notes. My students prefer to have something concrete that doesn’t require them to guess and check. It’s a win-win. As we practice this, I encourage them to use other factoring methods if they learned them well and prefer them, or to skip writing down steps in this method (for example, not listing out every single factor if they can mentally find the right pair immediately). They see a lot of patterns when factoring this way, I find.

I made a dry erase template for them to use when practicing this, and we discussed what parts were the most critical parts to put on paper to show their work. The template is a new iteration formed by a few years of teaching factoring this way and inspired by versions of it from a few other teachers on twitter that I’ve seen! I really like this iteration and don’t think any major changes need to be made at this point.

I gave my students the factor chart you see in the pictures, and originally did not have them put it in their notebooks. When they asked “can we just put this in our notebooks too?” I thought, “duh, why did I not do that originally?”. So next year, I’ll probably print a slightly smaller or somehow more notebook-friendly version of that chart and include it.

We began by just factoring expressions, and then in a poof book moved to solving equations by factoring. I wish I had included some quadratics that cannot be factored here, because my students later got frustrated when they ran into quadratics that I told them they could choose a method to solve, and they wanted to choose factoring…and you couldn’t factor that particular quadratic.

The graph sketching was mostly to remind them that the solutions to the quadratics were the x-intercept of the graph, but I realize now that since this isn’t really the focus of this particular standard, I could have left that whole bit out and moved it to when we talk about polynomials later this year. The poof book itself was good, but it just isn’t necessary in this standard and we could  have had more practice time! (which we were short on at the end of this quarter)


Skill 3: I can solve quadratics by completing the square.

This is also supposed to be covered in Algebra 1, but it is the skill that most often gets cut at the end of the year due to time. If they can solve quadratics other ways, and you need to fit in that last unit…completing the square goes. So this was new to most of them.

We started by going back to algebra tiles, because I think this really reinforces two things about completing the square: first, the SQUARE that we are actually completing and second, the splitting the x term in half to form said square. We didn’t actually solve these all the way through, just got them to a point where they looked like inverse operations problems to see the setup. We did a few other examples as a class that they didn’t write down and talked about patterns like the splitting the x term and the fact that you always end up adding positive ones tiles.

I made another template to help us complete the square using algebra, but this one is at a not-so-final iteration stage. My students ended up struggling most with two things. 1. factoring out A – they always forgot to actually factor it OUT of the B term. I would like to somehow emphasize this more by giving them room to show the division on the template or something. 2. multiplying what they added by A before adding it back on to the other side. I put this in small print, so maybe just making it bigger would help. Otherwise, this is the best completing the square has gone for my students in my teaching history. I’m looking forward to making some small changes here and seeing how my Algebra 1 students get on with it later this year.


Skill 4: I can use the Quadratic Formula to find solutions to quadratics.

I am realizing as I type this post that I was really inconsistent with the wording of all these skills…I like this wording better than “solve quadratics using…” so NOTE TO SELF to change all of those to be the same for next year.

I made a dry erase template for this as well, but after realizing that I would pretty much want my students to write all of it on paper to show me their work, I didn’t think there was much point to using them. So we used it as a structure to take notes on, but then didn’t use the templates when practicing. I would like to make an actual box to write about what the discriminant means next time instead of just writing it in the corner, but the students did really well with this. None of them struggled with finding B squared with a negative B value, either, so our note about using parentheses must have helped!

I wish I would have made sure there was an example here with a discriminant of 0. A negative discriminant might have been nice to see as well, although we address those after we learn about complex numbers, just to put in our notes “to be continued in a few days” or something, to get them curious about the square root of a negative number. However, some of them ran into this when they did their practice, because they calculated their discriminants incorrectly and then were trying to take square roots of negative numbers on their calculators.

Skill 5: I can do math with complex numbers and find complex solutions to quadratics.

We introduced this skill by sharing the experiences students had during the last practice when they got a negative discriminant, and then watched this video to introduce imaginary numbers.

We then did some basic math with i to see how its powers form a cycle. Students thought this was pretty wild, that it went from imaginary to real and back again! We used the square roots on the right side of the table to talk about what to actually do with i for our purposes of solving quadratics. There should have also been a lesson in here about simplifying radicals, but we ran out of time, so we left the radicals as is unless it came out to a whole number. I’m hoping we can get to that skill when we address solutions to polynomials 2nd semester – there’s a lot more time scheduled in for that standard than this one!

Then, we just did some examples. Most of them have no real solutions, but a few of them had real solutions just to show students that they need to be able to identify when to use i.

I wish that we had not solved all of these using the Quadratic Formula, because when my students were trying to solve using different methods and came upon the square root of a negative number, they somehow thought it was different than this! I could have used the same examples and just solved one by completing the square instead.

Skill 6: I can select an efficient and appropriate solution method for any quadratic.

Students were pretty easily able to fill in which method went where at the bottom of this flow chart. Again, we were running out of time in the quarter (my students this year really did not act like the solution methods to quadratics were review, so we needed to spend a lot of time on them) and if we had more time, I would have done a card sort and discussion with students sorting various quadratics by the method they would use to solve them WITHOUT actually solving them. It also would have been cool to have students race to solve the same quadratic using different methods and discuss that.

My students were mostly able to settle on one or two methods they felt most comfortable with, and realize that they needed to be able to feel comfortable with either the Quadratic Formula or completing the square to be able to solve ANY quadratic, but they definitely were not choosing the most efficient methods each time. However, this little discussion did help them to know when certain methods wouldn’t work and give them a bit of insight into how to save themselves time.


You can find all the resources shown in this post HERE, most of them in both PDF and Publisher (or Word) format.


Put Down the Pencil

Something one of my professors in college told me, and something I read again in someone’s tweet or blog post recently (cannot remember where…) is that the teacher should never be the one holding the pen(cil) when helping a student with independent work.

When helping a student, the STUDENT should be the one doing all the writing. It’s so tempting to grab their pencil, or unclip my own pen from my lanyard, or grab the dry erase marker at their table, and write for them as I walk them through the problem. But what do they get from this? They’ll be at the same point they probably were before: “It makes sense when you do it at the board, I just can’t do it myself!”

I’ve been trying so hard in the last week to put down the pencil. To instruct them what to write, point to where they should write it, but NOT WRITE IT MYSELF. It’s hard. Students move SO SLOWLY sometimes and you just want to finish up so you can go help the other 3 students raising their hands. Yes, it would be easier to write it myself, even upside down. NO, that is not what is best for my student’s learning.

I have not been 100% successful here. It’s especially hard for me when I literally point to the exact spot where a student should write a number and then they inexplicably DON’T PUT THE NUMBER IN THAT SPOT.

My strategy for when I absolutely cannot make myself leave the pencil down is to grab the dry erase marker and write them out a SIMILAR example, but still make them write the one we were working on themselves.

I can tell this is going to be a long process. But I think it’s worthwhile, and I’m going to work hard at it. I’ve found myself with my pen in hand this week, halfway through writing something on a student’s paper and thought “shoot! I’m holding the pen!”

Students holding pencils. Students writing math. That’s my goal. I’m working on it.

Eternal Newness

It’s my fifth year teaching this year, and I guess some part of me wildly thought that I would be starting to get “on top of things”. Instead I feel like Sisyphus, eternally pushing the boulder up the hill.

Sometimes I feel like this because it is so stressful. We have what feels like 17 new initiatives in my building/district this year, from standards based grading pilots to PBIS implementation. I’m teaching a new course that has only been taught once before in district and is now co-taught when it wasn’t previously. I started grad school this summer and am trying to adapt my life to be able to work and be a student at the same time. (I’m currently procrastinating on my statistics homework by writing this post, so you judge for yourself how well that balance is going).

Yet, sometimes I feel like this because it is so delightfully new. Rebecka Peterson’s post this week really resonated with me.

I love that I have a job I’ll never master. I love that there will always be room to grow. I love that there’s never an excuse for boredom in this field.

I love that every year, I get a new group of students. It’s like a puzzle to figure them out – what motivates them? What are their prior successes in math (usually very few or none)? What do they dream for themselves? How can I break down their walls?

It’s at this point of the year that I’m finally starting to figure that part out. I’m building the relationships with my students that I so treasure, the ones that literally make me get up in the morning to go fight a war for these kids – a war that some people don’t recognize as a war because my battles come in the form of helping them understand math, helping them find academic success so they can achieve whatever they want to achieve.

The relationships are a double edged sword too, though. After the shooting in Las Vegas, my kids came to school and spoke with fear about how many guns the shooter legally had. They note that their uncle, their cousin, their dad also legally has n assault rifles, pistols, machine guns in their home. They wonder how we can be ready if it happens in our halls. They wonder how they can be safe.

As I get to know them, they open up to me. They tell me of the anxiety they feel, the intrusive thoughts, the terrible words spoken to them by parents, by bosses, by other teachers even (hopefully, hopefully never in our building). They describe their parents in jail, the drug use in their homes, the need for them to take care of siblings or their own children with little help. How they have to work from 4-11 after school to support themselves or their family and don’t get home until after midnight, just to wake up before 6 to catch the bus to school.

Rebecka goes on in her post to describe how incredibly hard teaching is, and I’ve had the realization this school year so far that it is never going to get easier. There’s never going to be a point in my teaching career where I don’t have to work incredibly hard. I will never be “on top of things”, which is super hard for my logical, organized, need-to-know-all-information-possible Ravenclaw personality to handle. I know I will always want to tailor my lessons from last year to fit this precious and incredible group of students that I have this year. I will always want to adjust my grading practices, to stay after school and have discussions with my office mate about the best ways to give them feedback, the best ways to give them second chances to show understanding.

I will always build relationships with my students that lead them to sharing the horrors of their young lives with me. I will continue to hear about experiences that I could never imagine dealing with at my own age of 27 (or older, as I continue to widen the age gap between myself and my students) but that they have had to deal with at 16, at 12, their whole lives. I will lie awake at night thinking helplessly about how I can find a way to provide the girl in my second period with some clothes, or food. About how I can make sure the girl in my Algebra class has the right support around her when her baby is born. About the boy who shared with me his suicidal thoughts, and the fear I feel every time he hears bad news, that he will react by giving in to those thoughts. I will continue to bear the burdens of my hundreds of students, how they fear going to a party, even just a bonfire at someone’s home, and never returning because someone showed up with a gun.

It is such a hard job. Those who think that teachers have it easy are delusional, and I am not afraid of using language that strong. They fail to understand that while our contracts are from 7:30 – 3:30, Monday-Friday, August-May, the job follows us everywhere. It’s with us at home when we’re grading or preparing lessons for next week (my students express concern when their gradebook app gives them notifications at 10 pm on a Friday). It’s with us when we check twitter and see news of another shooting in town, hearts beating and hoping against hope that when we open the article it’s not one of our kids. It’s there when we stay in a hotel and grab all the toiletries before we leave to bring to school for students who can’t afford them. It’s there in pride as well, when we run into former students at the grocery store or at the bar where they work, students who tell you how their college classes are going, the job they just got. When you listen to an entire album of  band you’ve never heard of because one of your students is so excited to go to their concert. When you think of the inside joke with your Algebra 2 class about you being a vampire who’s really 217 years old.

Teaching has all the highs and all the lows. It is always, always worth it, but sometimes it is so, so hard.

This week was one of the hard ones. Then, at the end of the week, our English department decided to participate in Alicia Keys’ #wearehere campaign. I found myself sobbing on my couch on a Friday night looking at all of the hopes and dreams of my students. Their courage, their relentless perseverance, their positivity through it all are what bring me back in every time I have a day where I think, “wow, think about how easy having an office job could be.”

Edit: You can view the students’ video here.


But how boring. How could you ever want anything else but the crazy, intense, 24/7 rollercoaster that we have. How could you not take Sisyphus’ boulder willingly on your shoulders and push it up the nearest incline for your students on a daily basis?

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!