Math by the Mountain

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!