## Algebra 1 – Unit 1 Interactive Notebook Pages | The Foundations of Algebra

Starting the year off right is SO important for any class, but especially in Algebra in particular, since everything that is done in the first unit is used throughout the entire year. Students NEED to have a strong foundation, or else they’ll be fighting an uphill battle all year, which is no good. I’ve spent a lot of time thinking about what topics are most important for students to know (from vocabulary to skills), so that each following unit has a strong foundation.

Here are all of the notes I used with my students during the 1st unit of Algebra 1.

Day 1 – Real Number System
To start the unit off, we began by talking about the real number system and how we classify numbers. Instilling this vocabulary is very important in helping students be able to hold fluent conversations about math. I can’t tell you how many students I’ve had in Algebra 2 (or Pre-Calc!) over the years that have asked “what’s an integer?” and they are unable to complete a problem that they otherwise know how to do solely because they lack the basic vocabulary and don’t understand what the question is asking. This is silly, and I want to prevent these things from happening as much as possible. Math really is its own language, and helping students learn it will allow them to be more confident and much more successful in the long run.

Next, I introduced my first flowchart of the year. I want to instill in students that their notebook is really a great reference, and that there are tools in there that are really meant to help them. We quickly filled out 3 flowchart examples, to show students how they can use this if they get stuck on their homework. (Note: flowcharts are included in a separate bundle and are not part of the Unit 1 interactive notebook kit, which contains notes and warm-ups).

To finish off the class, I used the warm-up on Closure from my set of Unit 1 Warm-Ups as an exit slip. I don’t always have a special, topic-specific, pre-printed exit slip for my lessons because I often use these exit slip templates that I print off in mass quantities at the beginning of the year. That said, it’s really nice to have a formal exit slip for the first few experiences of the year.

Day 2 – Properties of Real Numbers
I like to begin each day with a recap warm-up over the prior day’s lesson. Students work on the warm-up during the first 3-5 minutes of class and then students present solutions.

The second topic we covered was properties of real numbers. This used to be a really boring topic to cover, until I started asking students to generate examples based off of the rules I’ve given them. Students can participate at any level, from volunteering their favorite numbers for an example to generating an entire example to demonstrate a property. The more you involve students, the more fun it is. Also, coming up with corny ways to help students remember one property from the next is pretty fun, too.

Day 3 – Order of Operations
Recap warm-up over the prior day’s lesson. We’re really working on establishing a routine where students know that they will be presenting solutions/answers. For this warm-up, in particular, I let students know that they would have to justify their choice of property and convince the class.

Next, we moved on to reviewing the order of operations. I use PEMDAS, but I’ve included 3 other options (GEMDAS, GEMS, and BEDMAS) to fit whatever your needs are. I like to pick problems that I know will trigger common mistakes or misconceptions with students that way we can have great discussions about it during the lesson before they create any bad habits (or to, hopefully, fix any prior misconceptions such as you HAVE to multiply before dividing and add before subtracting).

Next, we did a review activity on Order of Operations and finished the class with an exit slip (again, this is a warm-up from my set of Unit 1 Warm-Ups that I’m using as an exit slip, instead).

Day 4 – Evaluating Algebraic Expressions
No warm-up, today! Straight into notes. Evaluating algebraic expressions is just an application of the order of operations and the substitution property. Like normal, examples have been chosen that I know typically trip students up so that way we can have much deeper conversations about the underlying math.

Day 5 – Quiz
We started off class with a quick recap warm-up on evaluating algebraic expressions and I had 4 students present solutions. From there, students had a few minutes to review their notes and ask questions if they still had any, and then we moved into a quiz. When students are done quizzing, I like to have them work on some sort of coordinate graphing connect the dot worksheet. They love coloring and it reinforces the skill of plotting points, which will be crucial throughout the year.

Day 6 – Combining Like Terms
We’ve made it to one of my favorite topics–combining like terms! From past experiences, I’ve noticed that students realllly want to combine x’s and x^2’s, so adding the conceptual understanding of why that doesn’t make sense is super important to me. Other common misconceptions are included, and students are asked to explain what’s going on.

Day 7 – Distributive Property
To start off the class, we did a recap warm-up on combining like terms. At this point in the year, I’m not worried about my students writing their answers in standard form. I do, however, typically try to write my answers that way most of the time, and then I ask my students if it matters that our order is different, which helps to reinforce the idea that the sign in front (no matter where it is in the final expression) always goes with the term.

We moved onto the distributive property. First, we did examples of just distributing, and I made sure to include lots of examples I know could make students uncomfortable. Just about every combination of distributing is covered. From there, we distribute and combine like terms. I particularly like the 3rd example in that section of the foldable because I know how tempted students are to subtract before distributing.

Day 8 – Translating Expressions, Equations, and Inequalities
Like normal, the day started off with a recap warm-up over the distributive property.

We moved on to filling out a KEYWORDS foldable for translating words into math symbols. I asked students to generate as many words/phrases as possible, and then I filled in the rest. This doesn’t cover every possible keyword, but it gets the vast majority and is a killer resource for your students to refer back to.

After filling out the keyword foldable, we moved onto the main notes for the day. Color coding is SO important in making this a successful experience for your students. Color-coding helps them slow down enough to process, and it helps them know exactly what they should be looking for so it’s not overwhelming trying to do it all at once.

Here’s how I do it…for quite a few years now, I’ve kept with the same color-coding scheme, so in my mind “turn around words” are pink, “parentheses words” are green, and “equals” words are blue (along with words that turn into inequality symbols). Feel free to use whatever colors you like, but these color-associations are permanently ingrained in my brain.

Pass 1. Students read through the problem and look for any turn around words they need to highlight in pink.

Pass 2. Students read through the problem and look for any parentheses phrases they need to highlight in green.

Pass 3. Students read through the problem and look for any words that denote an equals sign (or inequality sign) that they need to highlight blue.

Pass 4. Students translate the expression.

Day 9 – Solving 1-Step & 2-Step Equations
Surprise, surprise! The day started off with a recap warm-up over translating expressions, equations, and inequalities from the day prior.

Before moving onto the main event for the day, solving 1-step and 2-step equations, I like to take a bit of class to pause and discuss exactly what a solution to an equation even is. So many students in Algebra 1 (or even Algebra 2 for that matter) can solve equations but have no idea what their answer really means. This one page is a great mental reference point for the entire year and should not be skipped over.

Then, with the knowledge of what a solution is in mind, we moved onto solving 1-step and 2-step equations. Checking answers is something that is really important to instill in your students, and it also helps to reinforce the idea of what a solution is. I ask my students to check their answers on every problem that they solve, during the first unit of Algebra 1.

Day 10 – Solving 1-Step & 2-Step Equations Activity Day
Solving equations can be hard, and we’ve been doing a lot of new things, so today, after the warm-up, we did various activities to review solving. My favorite was the 2-Step Equations Mystery Sum Activity (which is an exclusive freebie if you join my email list!) because it’s so collaborative and requires students to work together to spot-check and correct their work.

Day 11 – Solving 2-Step Inequalities
Last note day of the unit! Prior to solving inequalities, I like to do an investigation to help students internalize when a sign flips, and to see why it’s necessary. Due to the extremely similar nature between solving equations and solving inequalities, I skip over solving 1-step inequalities and just focus on 2-step inequalities. I find this works great for my students and allows us to focus on problems that have components that could trip them up.

Day 12 – Review
To start off class, we did a recap warm-up over solving 2-Step inequalities and then spent the remainder of the period reviewing for their test.

Day 13 – Test

I hope this post gives you a ton of ideas of how you can start your year in Algebra 1. If you like these notes, you can find them all here

## 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.

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.

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.

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

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.

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.”)

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).
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! You can download them here

Day 3:

We began with a recap warm-up on domain and range for continuous relations.
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.

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

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!

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

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.

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.

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

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:

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.

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.

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!

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.

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

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

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

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!

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

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.

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.

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

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

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

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

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.

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.

Day 8: Review

Day 9: Test!

Want the full unit? Get it here!

## My No. 1 “Teacher Hack” For Interactive Notebooks

Making things for interactive notebooks can be tedious, at times.  If you’re like me, you use a composition notebook so students will (hopefully) resist the urge to tear out pages for scratch paper.  The issue with composition notebooks, however, is their sizing.  A full sheet of paper is much too large to fit, but a half sheet makes the page feel a bit empty.

Also, unless you want to make everything from scratch to perfectly fit in your interactive notebook, you’re a bit stuck on what to do to get full-sized materials you may have used in the past to fit.

My hack: print any normal sized paper at 80-85% the size and, after cutting out the paper, it will fit PERFECTLY into a composition interactive notebook.  Use this hack to make the world your oyster.

Here’s how to do it:
1.  Make sure your document has been saved as a PDF.
2.  When you go to print, select the following setting:

Rule of Thumb:
If the margins on the original paper are 1″, print at 85%.
If the original margins on the paper are .5″, print at 80%.
If the original margins on the paper are at .25″, print at 75% (not common).

Here’s the difference it makes:

This has saved me a TON of time making interactive notebook pages, and also allows the writing space to be much larger for students.  Sometimes a half-sheet can be cramped.  Hopefully this teaching hack can help save you a ton of time, like it does for me!

## Class Info Stations Activity for Day 1 of Class and Algebra 1 Syllabus

I read a lot of blog posts last week about people’s first day plans, since that was a prompt for one of the #SundayFunday challenges.  I can’t remember who I got the idea from, but someone posted about doing a class syllabus stations activity and my gears started turning.

This year I updated my syllabus a bit. It’s twice the length that is has been in the past (I love nothing more than 1-page documents), but I felt the need to add more information to communicate to parents.  I’m hoping that this syllabus will give parents a better understanding about what their student is doing each day in my class.

Students will work in groups of 3-ish moving station to station to answer the questions from each station’s card.  I am going to have students record their answers on a scratch paper and, once everyone is done, we will compare answers as a class and see how they did.

How do you go over expectations, policies, and procedures with your students?  Please share in the comment section below!

Recently, I reached out to the MTBoS looking for fun ideas for practicing solving literal equations.  I had searched pretty thoroughly to find any pre-existing activities on the internet, but there wasn’t a lot available.  On top of that, what was there, required way more pre-existing skills (SO MUCH FACTORING!) than my Algebra 1 students currently had a month and a half into the school year.   Unfortunately, the MTBoS and I were pretty stuck.

Farther down in this Twitter conversation, however, it was mentioned that someone recently used BetterLesson’s lesson for teaching literal equations.  At that point I had already taught the lesson and most of my students caught onto solving them quite quickly, but I still was looking for a fun way to get a bit more practice in.  While exploring what BetterLesson had, I found this worksheet  that gave me inspiration for a game I could play with my students.  After a little bit of brain-storming, I created what I’m calling a Connect 4 Activity.  Essentially, it’s BINGO, but 4×4 instead of 5×5.

How to play:

• Before game: print enough game cards so each student has one, and cut apart the 16 problems.  I fold the problems in half (the problem number to the inside) and put them into a plastic bin.  (When printing from your computer, make sure it says “print double sided, flip on long-edge.”)
• To start off the game, each student gets a game board, on which they randomly place the numbers 1-16.  Students then pull out a piece of scratch paper, where they will be doing their work.
• The teacher brings the plastic bin containing the 16 equations around the classroom, letting a student volunteer pick a problem at random. (They LOVE getting to pick!)
• The teacher then places the problem under the document camera (or writes it on the chalk/white-board if you’re at a low-tech school) for students to solve.
• After all students have solved the problem, discuss the solution as a class.
• Once all students are silent, the problem number is revealed for students to cross off on their game card. (The excitement levels usually explode at this point, hence the moments of silence in between.)
• Repeat for as much class time as you have available, or until all 16 problems have been solved.
• Each time a student gets 4 in a row, they bring up their card and their work for inspection (they showed their work and corrected any mistakes for each problem), and are allowed to choose a small piece of candy (Jolly Rancher, a Starburst, etc.).

Reasons why I LOVE this game:

1. It is super easy to set up and is so adaptable for other topics.  This has probably been the lowest prep activity I have made for my students, yet it has been one of the most successful.
2. Students felt much more confident about their skills and were able to get nearly-instant feedback about how they’re doing.
3. Students LOVED it. The class begged me to continue letting them play the game through passing time.

(Updated September 2017)
This year I wanted to find more ways to practice literal equations with my Algebra 1 students.  We teach literal equations the week before Halloween, so I wanted to make something really fun and “Halloween-y.”  I made a Carving Pumpkins activity that’s self-checking and SUPER fun!  I couldn’t wait to try it out, so I gave it to my Algebra 2 students mid-September (patience never was my virtue) since they review literal equations in their first unit.  Students though it was fun, and they also found it really comforting that it’s self-checking.  To quote a group of boys, “this is super dope, we should do this for all of the holidays!”

Students are given 12 literal equations to solve for a specific variable.  Depending on what their answer was, they “carve” color the corresponding pumpkin in a particular way. In the end, each of the pictures should end up looking the same, as far as the color and carvings go.

I’ll be making more activities, and will update the post!

## Systems of Linear Equations and Inequalities Unit Interactive Notebook Pages (Algebra 1)

Here are the notebook pages my students completed on Systems of Linear Equations and Inequalities during the last school year.  Let me know if you would like me to post any of the documents I used.  Thoughts or suggestions on how I can improve interactive notebooking?  I started this as my work sample for my MAT degree so I am still very new to the world of INBs/ISNs.  I’m not entirely sold on the Left/Right hand page for in’s and out’s.  I understand the concept behind it, but I also don’t believe in forcing notes to be in a specific format for the sake of being in this format.  Anyway, this was my first take on my “INB” inspired notebook…not fully an Interactive Notebook, but on its way.

## Sequences and Series Unit Interactive Notebook Pages (Algebra 1)

How do you teach sequences and series?  Do you have a way of making it a bit more engaging and interactive?  Activities?  I’d love to hear from you.