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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Algebra 1 Interactive Notebook Pages | Unit 4 – Linear Functions

If you follow me on Twitter, you might have seen the following tweet about a month ago.

gluing shame

You could say I got a bit behind on my semester 1 INB gluing and, as a result, my INB posts have fallen by the wayside.  Semester 1 ended the first week of February and I’m just now getting around to catching up on getting it organized, since I’ve had a few snow days in a row (I really thought this would be a snow-day free year, but nope!).

Without any further ado, here are my INB pages for Unit 4 of Algebra 1: Linear Functions. Note:  There were activity/quiz/review days built into this unit–the days listed out are for days that note-taking occurred.

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Day 1

We started the unit off with what it means to be linear in form:838839

From there, we moved onto a foldable that covered finding intercepts of linear functions using various representations:840841

Then, we used our skills of finding intercepts to graph linear functions in standard form:842843

We finished up our class with a foldable, focusing deeper on horizontal and vertical lines and continuing to build off the last two examples in the chunk of notes before.  844845

Day 2:

We continued to expand our abilities with finding and now interpreting intercepts. 846847

We finished off the class by solving linear functions by graphing and introducing the idea of a “zero” and how it relates to an intercept. My students found it REALLY hard to not just algebraically solve these equations.  We talked a lot about why we are practicing solving by graphing for linear functions when the algebraic method is quicker.  We discussed that, because later on in the year, the algebraic method may become much more time consuming, and graphing can be a quicker method for many functions. We also mentioned that the graph allows us to see more of the story. 848849

Day 3:

We started off with a recap warm up from the previous two days.  The boys in my class really loved problem 4. 850

We then talked about slope and connected it back to the graphs we’ve made in the previous two days and how they either had a constant incline or constant decline…slope!851

We looked closer at the different types of slope using this foldable from Lisa Davenport. 852853

Now that we had a bit of practice with calculating slope, we moved onto interpreting it and finding it from different representations. 854855

Day 4:

We started off with a recap warm-up of slope, and then learned about what proportionality means.

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We extended our ability to determine whether or not a relationship is proportion to create equations. 859860

Day 5:

We started with a recap warm-up on writing equations for proportional & non-proportional linear relationships. 861

We then did graphing absolute value equations by making tables.  This was mean to motivate students to use transformations instead of tables (we introduced transformations the next day), as well as help students remember the properties of absolute values and domain & range. 862

I started drawing the absolute values in with marker because |3-4| started looking like 13-41 for many students.  863

Lastly, we glued in a tips for success reference sheet that students can use if they ever get stuck. 864

Day 6:

We started class with a recap warm-up on graphing absolute value equations by tables.  To further motivate transformations (we started to learn about them RIGHT after doing this warm-up), I made sure to make the second example REALLY annoying. Either you’d have to go up by 3’s or deal with the decimals.  At this point, I think we established that making the tables takes SOOOOOOO much work, but it does get the job done. 865

Next, we were on the hunt for patterns.  What the heck do these a, h, and k things do, anyway?866

Now that students had some observations, we applied it to make graphing SO much quicker!  It only takes 3 points, you know! Once you have the vertex and the slope, you’re golden!867

Day 7:

We did a recap warm-up over graphing absolute value equations by transformations. 868

Lastly, we glued in a flowchart reference page, just in case students ever needed an easy refresher of how to graph absolute value functions by the quicker transformation method. 869

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).
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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:

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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!
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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! You can download them herepictures_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.

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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

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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