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. 
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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). 67

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. 5

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.
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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. 101112

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. 
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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). 14151617

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).18

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. 
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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. 
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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. 
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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. 
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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. 272829

Day 8 – Translating Expressions, Equations, and Inequalities
Like normal, the day started off with a recap warm-up over the distributive property. 
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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. 313233

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. 3435

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. 
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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. 3839

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. 4041

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. 
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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. 
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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. 4748

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

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Mystery Sum Activities – The Perfect Practice Structure + FREE DOWNLOAD

This winter, I’ve been working with my first ever student teacher. One of the first things that we did was make a list of different practice structures and the benefits of each one. He had definitely heard of some of them from his MAT program, but several of them were brand new. One of the newbies, was a “Mystery Sum” activity, which happens to be one of my all-time favorites. I got to talking with the other math teachers in my department, and none of them had heard of it either!

Since Mystery Sum Group Challenge Activities are one of my favorite practice structures, I figured I’d share all of the details with you! Be forewarned, I will say it’s the most time-consuming of the practice structures if you’re making it from scratch.

To give you an example of how it works, I’ll walk you through my Solving 2-Step Equations Mystery Sum Activity (you can download it for free here, if you join my mailing list!).

Students work in teams of 4 to complete the mystery sum group challenge. The way this activity works is that there are six suits of cards (I make them with a flower, crown, star, peace sign, lightbulb, and phone but you can really use whatever). Each suit has four cards (one for each student). The cards are actually numbered. I always have it set up where the cards within each suit are differentiated as follows:

Card 1 – Basic
Cards 2 & 3 – Basic/Moderate mix
Card 4 – Moderate/Advanced mix

I do let my students know that each card is leveled so they can pick an appropriately challenging problem to work on. They’re pretty good at self-reflecting and choosing the right card.

Once students are in groups of 4, each student gets a work recording sheet, and each group gets an answer recording sheet. Finally, we’re ready to go. Also, teachers, this part is really important, this is an activity that you absolutely MUST have an answer key pre-made. Students will be checking in with you rapid-fire, so you need to be ready. I always include an answer key with my activities, so you don’t have to do any extra prep!

Now that students are in groups and they have all of their supplies, you’re ready to begin! Each group gets a suit of cards (each suit contains 4 cards). Students will take their designated number, and begin solving their problem on their personal work recording sheet. Once students get their answer, they will write it on the group answer recording sheet. After the whole group has finished their problems, they need to find the sum of all of their answers to the problems within that suit. Once the group has found the sum, they can check in with the teacher.

Now, we’re getting to the part that I LOVE so, SO much about this activity! At this point, the group should check in with you about their sum. If they’re correct, then exchange the suit of cards they’re working on for one they haven’t done yet.

If they’re incorrect, that’s where the magic happens! Don’t tell them anything other than the fact that their group has not found the correct sum. It is up to them to work collaboratively to find the error(s). This activity promotes so many things that are the best parts of math class:

  • Collaboration
  • Error analysis
  • Persistence
  • Precision
  • Effective team communication

Plus, it’s differentiated! Seriously, what else could you ask for in an activity?

Once a group has made it through all six levels, I like to have them go become helpers around the room.

It’s fantastic to see students progress over the course of the activity. They may struggle a bit initially (which is a big reason why this is a group activity so they have built-in support), but as they progress, suit through suit, they pick up speed and accuracy.

Hopefully, I’ve given you an idea of why Mystery Sum activities are one of my absolute favorite practice structures around.

If you’d like to try out an activity without having to make one yourself, you can download my Solving 2-Step Equations Mystery Sum activity, here by joining my mailing list! I promise to never spam you, and will only send updates about sales, new resources, giveaways, and the occasional tip or trick that I’ve learned.

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

updateHere’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.

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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!

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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.

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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?!).

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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.
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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!

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

Day 8: Review

Day 9: Test!

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