Algebra 2 Polynomials Unit INB Pages

Yesterday I was tagged in the following tweet, asking for resources for Algebra 2’s Polynomials unit.  I’ve been meaning to get around to posting some of my Algebra 2 inb pages from last year, but never have.  This is finally the kick in the pants I needed, so…without further ado, here’s the pictures.  If you want to know more about what I did in conjunction with the notes, let me know!



Algebra 1 Unit 3 Interactive Notebook Pages | Solving Equations

Unit 3 of Algebra 1 is all about solving equations and their applications.  We start off with multi-step equations, because 1-step and 2-step equations were covered in Unit 1: Foundations of Algebrapic_Page_01

Day 1: Multi-Step Equationspic_Page_02pic_Page_03

In addition to the notes that went into our composition books, students were each given a full-sized flowchart over solving one-variable equations.  We did an example as a class, and then I also keep a class set laminated so students can use them with dry-erase markers whenever they like. Students referenced their notes and the laminated flowcharts while working on homework in class. Picture2

Day 2: Solving Multi-Step Equations with Special Case Solutions
To start off the lesson, we did a recap warm-up over the prior day’s lesson. pic_Page_04

We then went into a foldable that covers what special solutions are and when they arise. pic_Page_05pic_Page_06

To get even more practice, students did the following Types of Solutions Sort, which emphasized common student errors and misconceptions I’ve noticed in the past. pic_Page_07

Day 3: Writing Equations to Solve Multi-Step Equations
We started off the lesson with a recap warm-up that contained special solution types.  pic_Page_08

From there, we moved into our main set of notes for the day, with an emphasis on marking the text (NOTE: this is the same color-coding we used in Unit 1). pic_Page_09pic_Page_10

Day 4: Absolute Value Equations
Like usual, we started off the lesson with a recap warm-up of the previous day’s information. pic_Page_11

We started off the topic of absolute value equations by really thinking about what an absolute value means/does.  pic_Page_12pic_Page_13

From there, we used the information we’ve gathered to solve absolute value equations a bit more efficiently (without using the modified cover-up question mark method). Students had the even numbered problems as homework that night.  pic_Page_14pic_Page_15

In addition to the notes that went into the composition books, students were given a flowchart for solving absolute value equations to reference whenever they got stuck. Here’s an example of how they could use it!  Just like the others, I keep a class set of these laminated so students can use them with dry erase markers whenever they get stuck.  I like to color-code each type of flowchart to make it easy to grab the exact one that they need from that unit. IMG_1710

Day 5: Absolute Value Equations Word Problems
To begin the class, we started off by working backwards: writing the absolute value equation that could’ve produced the given solutions. pic_Page_16

From there, we went into story problems involving absolute value equations. pic_Page_17

Day 6: Ratios and Proportions
We started the day off with a recap warm-up covering the last two days of information (all absolute value equation related).

The first thing that we talked about is what a ratio is and what it means to be proportional. pic_Page_19

We then used the definition of proportional to solve equations requiring cross-multiplication. pic_Page_20

After these examples, students filled out the other side of the flowchart that they were given on Day 1 with a more difficult example of solving for a variable in a proportion. Picture1

Day 7: Percent of Change
Percent of change is a funny topic to cover in Oregon…most of our textbook’s examples are about sales tax, and we have none.  If we go to Washington, we just flash our Oregon ID and presto, bingo, bango, no more sales tax (for the little stuff).  Anyway, we find other examples to try to make it more meaningful. pic_Page_21pic_Page_22pic_Page_23

After taking notes, we did this Percent of Change Scavenger Hunt. Students worked really hard on it and had a lot of fun.  For some of them, it was difficult to remember to put a negative sign on their r-value when it was a percent decrease!

Day 8: Literal Equations, Part 1
We recap percent of change problems and then move into basic solving literal equations problems. pic_Page_24

We discuss what a literal equation is, compare and contrast the difference between literal equations and regular equations, and also introduce the flowchart method of solving. pic_Page_25pic_Page_26

Day 9: Literal Equations, Day 2
We move into more complicated literal equations that require more than one step to solve.  After doing a few, students are able to choose which method they wish to solve with (I’m partial to the algebraic method, but some students love the flowchart way). pic_Page_27pic_Page_28

After notes, we play my favorite Connect 4 game for solving literal equations.  We only played until 6 people won, which allowed us to get through about 70% of the problems.  From there, students spent the remainder of class working on a festive Carving Pumpkins coloring activity for solving literal equations.  This activity was awesome because students were super engaged in the coloring (every last one of them–even the boys! PS: I have 22 boys in this one class…ay, yai, yai), and it was super easy for me to find common trends that I might need to readdress (the eyes for Pumpkin #2 were the most common error).  Also, for students, this activity is fairly self-checking, which is a great confidence boost for many of them.

Here’s an example that one student colored!  She even named the pumpkins. carving_pumpkins_in_action

Day 10: Stations Review Activity Day
We did a recap warm-up over solving literal equations and then spend the rest of class doing a stations activity with my solving equations unit task cards. pic_Page_29

Day 11: Review Day
Day 12: TEST!

Algebra 1 Unit 2 Interactive Notebook Pages | Relations & Functions

Here are the notes I used this year for the 2nd unit of Algebra 1:


Day 1:
We started off the unit with a classifying variables sort. This was a good way to jog students’ memories about their prior knowledge, and it also served as a jumping point into domain and range!

From there, we went into what a relation, domain, and range is, and how it relates to independent and dependent variables. pictures_Page_03pictures_page_04.jpg

We then made the distinction that there are two types of relations, discrete and continuous, and we must pay attention to context to determine what type of relation we have. pictures_Page_05

From there, we started to talk about all of the different ways we could represent a discrete relation, and how we find the domain and range from each representation.  We used this foldable, which went over great with the students.  They caught on super quickly, and they mentioned that they liked having one example to do together, and one to do on their own for each representation. pictures_Page_06pictures_page_07.jpg

Day 2:
We started off with a word problem to review domain and range in a (discrete) relation. pictures_Page_08
From there, we filled out a Frayer vocabulary model for functions, to make sure that students really understood what they are and aren’t. pictures_Page_09

Then, using the definition for function we just wrote down on the Frayer model, we made a cheat sheet to refer back to that tells us all of the different ways a relation (discrete or continuous) would NOT be a function.  pictures_Page_10

We practiced classifying functions using a card sort from Amazing Mathematics.  Instead of cutting and pasting, we decided to color-code instead! Love it! (In the words of one of my students, this is the page that has “fourteen thousand graphs.”)pictures_Page_11

We then filled out another cheat sheet, this time for domain and range of continuous functions.  Students reasoned together through the inequalities and we talked about what a bound actually means (we used a lot of basketball references). pictures_Page_12
We practiced finding the domain and range for continuous relations (as well as determining whether or not they were a function), using the following set of notes.  PS: It took me a LONG time to figure out how to make a parabola or a trigonometric wave using Microsoft’s shape tools.  I feel overly proud of this set of notes!pictures_Page_13pictures_page_14.jpg

Day 3:

We began with a recap warm-up on domain and range for continuous relations. pictures_Page_15
To make sure that students didn’t forget about discrete relations, we went back and did more practice with determining their domain and range, and also stating whether or not the relations were functions.  pictures_Page_16pictures_page_17.jpg

Day 4:
We started off with a reference sheet on function notation and how to read/say it. pictures_Page_18
From there, we did a lot of practice with function notation.  pictures_Page_19

Inside this set of notes, we really emphasized interpreting what we were being given in a problem (input or output value) and what the problem was actually asking us to find (input or output value), before starting the problem.  This helped students from making a lot of careless mistakes.  After we practiced function notation in both directions (evaluating a function, and solving for an input given the function’s output), we mixed up the problems and even threw a few variables and function compositions in there!pictures_page_20.jpg

Day 5:
Recap warm-up on function notation.  Problems 5 and 6 both spurred amazing conversations about order of operations. pictures_Page_21

After doing this recap warm-up, we did my function notation mystery sum activity, which was a blast.  It encourages students to collaborate together and it’s really high engagement each time.


From there, we continued talking about function notation, but now in terms of a graph.  Interpreting what the function notation was telling us was such a huge part of the previous day’s lesson, that I wanted to see how they could do when we attached a context to the problem. pictures_Page_22

Inside, we worked on graphing functions, and using the graph to find an x-value.  Some students preferred solving for x, but others were impressed by my tracing over on the graph method.  To each their own–that’s the beauty of math, in my opinion. pictures_Page_23

Day 6:
Recap warm-up over function notation with graphs, and then we reviewed for the test. pictures_Page_24

Day 7: Test!

Algebra 1 – Unit 1 INB Pages | The Foundations of Algebra

Here’s what went into our INBs for the 1st unit of Algebra 1:pic_Page_01

Day 1:
We glued in a reference sheet for the real number system. Our textbook uses I for the set of irrational numbers.  I went with the same notation this year, but I think I’m going to go with R-Q for next year, since I is used for imaginary numbers, later on.  pic_Page_02

To practice working with these definitions, we did a real number system sort, which I found from Amazing Mathematics! My students enjoyed doing it, and it spawned many great conversations about the difference (however subtle they may be), between the sets of real numbers.

Real Number System Sort from Amazing Mathematics 

For homework, students did this Always/Sometimes/Never sort, which is also from Amazing Mathematics. They were given about 20 minutes in class to begin their assignment, and then had whatever was left as their take-home assignment for the night.  This one was even better than the last card sort, in terms of spurring student conversations.  Students were justifying with counterexamples and providing fully flushed out reasons for where each card should get placed.  It was awesome!

Always/Sometimes/Never Sort for Real Numbers from Amazing Mathematics

As a note, we also keep a binder for the class which holds extra handouts, like additional reference sheets and homework assignments that don’t go in the INB. My favorite reference sheet that didn’t go into the INB was this real numbers flowchart that I made.  The day of teaching my lesson on real numbers, I noticed that using the “Venn diagram” approach wasn’t meshing well with some of my students.  That afternoon, I went home and made a flowchart handout that they could refer to, in addition to their INB pages.  Next year, I think I’ll just use this flowcharts in a mini-book format for notes, instead!  I found that students started making more connections about the sets each number belongs to (i.e. not only is a number natural, but it’s a whole number, and an integer, and a rational number), and students were able to remember the questions they need to ask themselves when determining the best classification for a real number.

Classifying Real Numbers Flowchart from Math by the Mountain

Day 2:
We started off with a recap warm-up on the real number system, which we covered the day before. pic_Page_05

From there, we did a translating expressions sort, also from Amazing Mathematics.  (Can you tell I love her sorts?!).

Words into Math Sort from Amazing Mathematics

From there, we used our key words and started defining what a variable is, and what an expression is. pic_Page_07pic_Page_08

For homework, students did the following problems.  They had about 15 minutes of class time to get started.  We color-coded “turn-around words” in pink, “parentheses-words” in green, and “equals words” in blue.  Students marked the page in highlighter before beginning to translate the expressions.  They mentioned that this made the process much easier for them! pic_page_09.jpg

Day 3:
We began with a recap warm-up over translating expressions.pic_Page_10

From there, we talked about evaluating expressions and also reviewed the order of operations.

From there, we discussed the properties of real numbers and students made up their own examples for each property.  pic_Page_12

For in-class practice, students did the a properties of real numbers puzzle from Lisa Davenport.  A student volunteered to glue it into my notebook.  Notice the lack of glue?  Notice the crooked edges?  It was a very sweet offer, but I’m I don’t think it’s one I’ll be taking again any time soon. IMG_1668

Day 4:
We started with a recap warm-up over evaluating expressions and identifying properties of real numbers. pic_Page_14

Next we took notes on combining like terms and the distributive property, cutesy of Sarah at Math Equals Love.pic_Page_15pic_Page_16pic_page_17.jpg

Day 5:
Recap warm-up over distributing and combining like terms. pic_Page_18

What is a solution?  What does it mean to be a solution?  What does it look like? pic_Page_19

Up next, we focused on solving and verifying solutions to 1-step and 2-step equations.  I’ve found that verifying a solution is a skill that students struggle with more than solving (at least in Algebra 1), so I wanted to make sure it got emphasized. pic_Page_20pic_page_21.jpg

Day 6:
We filled out a foldable for solving 2-step equations.  Those pesky fractions are going to be our friends by the end of today!


Day 7:
Recap warm-up over solving equations. pic_Page_24

Day 8: Review

Day 9: Test!



{FREEBIE} Test or Quiz Retake Form

Last week each of my classes had their first test.  Most did quite well, but, like normal, a few did not.  In my school, the math department policy is that students are allowed to retake tests, but not quizzes.  Honestly, I wish it was the other way around, but that’s a topic for another post.  Since tests are worth 40% of a students grade at my school (we have a 10-40-40-10 grade distribution for homework, quizzes, tests, and final exam), it is important that students do a retake whenever they have performed poorly on an assessment.  Not only should they do a retake for the sake of their grade, but also so they are in a position to better understand the material going forward.  Math is constantly building on itself, so I’m glad that students have the opportunity to go back and revise their learning.

The past two years, I have used a retake form created by someone else in my department, but I never quite liked it.  Although it asked students honest reflection questions, I felt like it was a bit condescending to students and I questioned if it might prevent some students from pursuing a retake opportunity.  I used it anyway since everyone else in the department used the same form, but silently feeling like a bad teacher because of it.

This year, I wanted to create a new retake form.  Over the summer I had played with a few different versions, but it wasn’t until today (the day before my students actually need the retake form, lol!) that I came up with something that just felt right.  It asks students to reflect without pointing any fingers or making them feel guilty for not doing well the first time.  It’s straight to the point, and requires them to revisit the material in new ways so that they can improve their understanding.  Tomorrow I am going to walk through the retake form together as a class so my students know what my expectations are for it and have an idea about how to productively go about preparing for a retake opportunity.

test retake form

If you would like to use this retake form in your own classroom, you can download it for free from my Teachers Pay Teachers store.  While you’re there, make sure to follow my store so you don’t miss any other resources I post!

How I do Homework

Friday evening I was tagged in a tweet that was asking about my homework policies and I just had too much to say in to fit in 140 characters or less, so I figured I’d write a blog post as a response.  One thing I make sure to do in class is to always call “homework” a “practice assignment.”  You’ll never hear the word “homework” come out of my mouth at school because that seems to open up a very unproductive can of worms.  Practice Assignment is clear to students and it can be worked on both at school and at home, and also reminds students why they’re doing it.

A bit about me, I teach on a 7-period a day schedule.  On Mondays and Fridays each class is 51 minutes long, Tuesdays and Thursdays are 46 minutes long to account for a 30-minute advisory class that happens twice a week, and Wednesdays are 43 minutes long to account for our early release professional development sessions.  I definitely am not a teacher whose sole purpose is teaching to the state test and “exposing” students to 100% of the topics in the textbook.  I like a much more balanced approach.  I think it’s important enough to go slow enough that students actually have a chance to absorb the material, but it is also important to me that we get through the required material as to not disservice them for their next math class.

how i do homework

I also believe in homework.  This has become quite controversial over the years, especially in the online teacher communities.  However, I do believe in a balanced approach to homework.  Maybe 15 questions a night, and it’s rarely due the very next day.  I have homework due on quiz or test days, which allows students a bit of wiggle room to work around their schedules.  I think homework does so much for students.  It gives them a chance to play with the material more on their own so they can really figure out what questions they have.  It teaches them how to self-advocate for themselves when they need help.  It teaches them time-management skills to work around their busy schedules and how to prioritize tasks.  To completely get rid of homework at the high school level seems like it would be quite a disservice to students, in my opinion, and doesn’t seem like it’s setting them up for success in their next endeavors (whether that be entering the work force or higher education).  However, I do acknowledge that each teacher certainly knows what works best for their own class, so the no-homework approach may be just right for other groups of students.  It just doesn’t work for mine.

The past couple of years, the math department at my school has focused on paring back our pacing guide a bit to focus on the core concepts in a deeper way, and our state test scores shot up 13% each year in a row.   Focusing on 90% of the topics and pairing back the most peripheral 10% has done amazing things for our students.  Exposure to content means nothing if it’s at a pace students can’t absorb, but there is a tricky balance.  If you’re only getting through half of the pacing guide each year, that’s definitely not setting up your students for success either.

Anyway, to get back to the main topic, I treat each class a bit differently when it comes to how we do in-class work and homework, so I’ll break up what I do by subject:

Algebra 1 + Support:
Info: This class is 2-periods long each day.  I have them the first two periods of each day. Students are part of a cohort of 30 students that take math, English, and science together each day.  They have been identified by their 8th grade principals for being at extreme risk of not graduating and their parents have agreed for them to be in a special program at the high school to help them be more successful. 

Students pick up notes and homework as they walk in the door each morning.  We record homework assignments on our practice tracker after our daily warm-up problems have been completed.  As we are taking notes together in class, students are encouraged to switch back and fourth between notes and similar homework problems.   Most days there is 15-40 minutes of work time.  On our practice tracker, we write down the minimum required number of problems to enter the classroom the next day.  Let me explain how this works:

Let’s say that the homework sheet has 15 problems.  If they are given 30 minutes of homework time that day, as a class we come up with the minimum expected amount to be finished during that work time.  The class might decide that, given the time they have to work in class that day, they think everyone should be able to finish at least 6 of these 15 homework problems during our in-class homework time, so we write this on our practice trackers (min=6).  The next morning, I stop each student on their way into the classroom.  They must show me that they have completed at least any 6 of the 15 homework problems to get inside the classroom.  If they have failed to do so, they sit outside the classroom to work with our aide and finish up those problems with 1-on-1 help while the daily announcements are being played, and then come back to join the class who have already begun to work independently on the daily warm-up problems.  Students are given one grace period to be “stuck outside,” after that a call home is made to discuss ways we can help the student be successful at staying on top of homework, especially when class time is being given.  Now, since only 6 of the problems were required to be done the next day, students have until the next quiz or test (whichever comes first) to complete the remainder of the assignment.  All homeworks are graded on a 3-point completion scale.  Quizzes normally are given once or twice a week. NOTE: if a student emails me the previous night letting me know that they will not be able to complete their minimum required amount for whatever reason and what their plan is to make it up, then they are allowed in to class, no questions asked.  Again, I really want students to learn how to advocate for themselves, so this is part of that goal.

Practice trackers get turned in on the unit test date, and then a new one is handed out the next day to start off the new unit.  Students have mentioned how much they like using the practice trackers because it helps them remember their homework, and they have also commented that they like having the minimum required amount since it makes them stay on top of things and helps them focus better during work time.

I also offer a “double stamps” policy in all of my classes (except for Statistics because it’s college credit) where if a student finishes an assignment the day I give it to them and brings it back before I go home that day, not only does their practice tracker get stamped as 3 points “all done” for that assignment, but they get a bonus 3pt stamp for working so hard at completing it that day.

Lastly, I accept homework late up until the unit test.  I also allow students to “move up” points.  Let’s say they just got the minimum done and didn’t do more before the quiz where homework gets stamped off.  They’d probably get stamped for 1 point or “a bit” completed.  If they did more before the test, they could improve their score and I would re-stamp their practice tracker for 2 points.

Algebra 2 and Geometry:
Exactly the same as Algebra 1, except for the minimum required amount and having to show me the assignments at the door.  They also don’t usually get 15-40 minutes of homework time each class, since these are only 1-period long classes.  Most days, they get 5-10 minutes of work time.  Other days, they get a bit more.

College Credit Statistics (MTH 243 and MTH 244):
Since this class is dual credit, homework is inherently done differently.  Each Monday students are given a quiz over problems taken from the prior week’s assignments, and once they are done, they begin working on an Algebra and Geometry review to make sure that their other math skills are staying fresh.  After everyone has finished the quiz, students work together in groups to complete the weekly Algebra and Geometry review.  During the last 10 minutes of class, I allow them to ask me to go over any 2 of the 10 questions with them as a class.  At this point, the rest of their homework is assigned, corresponding to whichever sections of the textbook we will be covering that week.  Homework is always assigned on Monday and due the following Monday so students can manage their time as they see fit, in order to work around their schedules.  The general format of the statistics class is:

Monday: quiz and Algebra & Geometry review.  Tuesday, Wednesday, Thursday: new notes.  Friday: work day where students are able to work on their homework assignment together for the period.

Late work is not accepted in this class due to the dual credit aspect.
I could write a ton more about how homework works in each class, but I’ll leave it here so I don’t end up boring you all with a novel.  If you would like me to go over anything in more depth, or have a question about something I forgot to address, please let me know and I will make sure to answer it right away.  Thanks for reading!


3 Thoughts on Teachers Pay Teachers

Today, the question about what the #MTBoS thinks about Teachers Pay Teachers (TPT) was brought up.

Some love it, some hate it.  Here’s my take.

I LOVE Teachers Pay Teachers.

  1. My first  year teaching, I had 4 preps, one of which was Geometry.  I had a non-traditional high school path, and had never taken Geometry, myself, so I was extremely nervous (All of those proofs! Back then, they had me shaking in my boots.). There wasn’t enough time to create everything myself, maintain my sanity, and have my lessons be to the quality that I desired.  It just wasn’t possible.  So, I went to TPT and found a curriculum for Geometry–complete with notes, homework assignments, quizzes, and activities.  It was expensive, but cost the equivalent of 14 hours of work.  There is no way I could’ve created a twenty-fifth of the materials available in that product in the same amount of time, so it was well worth it for me.  And everything in it was AMAZING–truly, high quality materials.  There is no way I could’ve provided the same level of quality for my students that year without it, PLUS it saved my sanity.
  2. I should disclose that I am a TPT seller.  I have a small store, but it’s definitely a passion for me.  I find that TPT drives me to create better and better materials to provide to my students and makes me more creative.  What I would’ve provided to my students without TPT would be a 9/10, and what I’d provide with the intention of selling a product on TPT would be a 10/10.  I don’t think people realize the amount of hours it takes to put a quality product on TPT.  Maybe it takes 10 hours to create and perfect it, and another 5 hours to do the finishing touches.  Those extra 5 or so hours really take a resource to the next level, but the time commitment is not practical at all for a teacher that doesn’t have the monetary incentive attached.  5 extra hours of work for just one resource would be a crippling time constraint to do regularly, if there was no other benefit.  Even doing it for a resource that would be shared online for free wouldn’t make sense to commit that much extra time to a resource.  Sure there are some bad products on TPT and there are some amazing resources offered for free from the #MTBoS community.  Generally speaking, though, I find the distribution would be as follows:FullSizeRender (29)
    Like any online purchase, reading customer reviews on TPT can help you easily stay in the upper quartile of the TPT distribution.
  3. I really like the idea that teachers can get recognition for their talents through TPT.  Teaching has a pretty low ceiling as far as job recognition goes, and TPT definitely helps with that. Teaching can also be a financially difficult profession to choose.  It takes a lot of money to get the Master’s degree required to be a teacher (at least for my state), which leaves many with crippling debt. TPT can provide supplemental income that can help the financial strain that many teachers face, allowing them to actually stay teaching.  In addition to the monetary assistance that TPT can provide helping to keep teachers in the professions, I think it makes many of the sellers feel more valued, which definitely helps to avoid teacher burnout.  I find a overwhelming sense of pride in my TPT store and it makes me feel valued as a teacher.  I know how hard teaching is, and I know how little we get paid, so it makes me feel so valued as a teacher each time someone decides that my product is worth spending those hard-earned dollars on and bringing into their own classrooms.  It makes me feel like what I’m doing is good and I’m appreciated in the teaching world.  I also hope that I can be that life-saver for someone else out there like that Geometry curriculum was for me in my 1st year teaching.