## 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

## Number Challenges – A Team-Building Perseverance Challenge

If you’re looking for a great way to get your students working together, talking about math (particularly the order of operations), and working on perseverance, then search no further! This set of Number Challenges is perfect for any secondary math class.

Originally, taken from Math Equals Love, I wanted to reformat her activity because I didn’t have as much wall-space as she did, and I also wanted to add an extra element of reflection to turn the lesson’s focus more to perseverance, than order of operations (the math is definitely a welcome addition, though!).

I used this activity on the first day of school with my Algebra 1 students, but I think it would be perfect for a “top-up” lesson right before a big break. What I mean by that is, throughout the year, some messages need to be revisited and “topped up.” Perseverance and working as a group are always great things to revisit and place an emphasis on so that skills don’t backslide. Sometimes we have to intentionally be explicit when we teach students how to do these skills, so activities like these are a great framework for a larger conversation about the many “soft skills” that come up in a math classroom (like perseverance and teamwork).

To find the original activity instructions, check out Math Equal’s Love’s original blog post! Here’s a link to the plastic pockets I used, which allowed students to write on the papers with a dry erase marker (this is not an affiliate link)!

Here’s the copy of the number challenges! Print them double sided and place them inside of the plastic pockets so students can work on them with dry erase markers! I make two for each level and had groups of 3 working on different number challenges. When they finished one challenge, there was always a different number challenge waiting to go.

Here’s the perseverance reflection form that I had students fill out as an exit slip. It made for fantastic conversations the next day!

If you give it a try, let me know how it goes!

## 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.

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.

## Day 1

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

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

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

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.

## Day 2:

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

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.

## Day 3:

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

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!

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

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

## Day 4:

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

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

## Day 5:

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

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.

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

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

## 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.

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

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!

## Day 7:

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

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.

## 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 Algebra

Day 1: Multi-Step Equations

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.

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.

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

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.

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

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).

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

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

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.

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.

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.

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

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.

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

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.

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.

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.

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.

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).

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.

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.

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.

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!

## How I Teach Factoring Trinomials

When I teach the unit on polynomials and factoring in Algebra 1, I start off my first lesson on factoring trinomials with a discussion on which has fewer options: multiplying to a number, or adding to the same number?  Students take a couple minutes to list out all pairs of numbers they can think of and then share out to the class.  After doing this twice, quite a few students start catching on to the fact that there’s an infinite amount of ways to add to any given number, but only a handful of ways to multiply to the same number.  Multiplication gives us fewer options, which will allow us to do less work.  This will be really important to what we do in just a moment. (NOTE #1: I provide students with a factor pair chart as an aid to help with identifying factors later on. NOTE #2: We originally began using only whole numbers as a starting point, but students then wanted to branch out further.  Could we extend this question to include integers?! Yes-and we did!)

From there, we go back to something students have just learned a few sections earlier: multiplying two linear binomials of the form (x+A)(x+B).  We do this a few times and then look at a bunch of already expanded examples and I ask students what they notice.  It doesn’t take long before students start realizing that the middle term, the coefficient of the x, always comes from adding the two numbers A+B, and the end term, the constant, always comes from multiplying the two numbers, AB.

Then, I switch the question around.  How can we figure out what someone expanded to create a quadratic expression?  Is there any easy way to figure this out?  Students start to volunteer info that they know: the middle term comes from the addition (A) of the two factors, and the constant term comes from the multiplication of these two numbers (M).

So, then the question is, which number do we look at?  The addition number, or the multiplication number? Technically, it doesn’t matter, BUT mathematicians love to be lazy efficient, so we’ll look at the multiplication number.  Students justify looking at the the multiplication number first because, just a few questions prior,  they determined that there’ll be fewer options with multiplication than for addition.

From there, I ask students to make further generalizations and predictions about the signs of the terms and the signs of the factors and use that information to work both forward (expanding) and backward (factoring) using some diamond puzzles.

The next day, we practice some more with basic factoring when a=1, using the patterns we found from the investigation the day before:

Then, we kick it up a notch.  How the heck do we do this factoring thing when there’s more than one x-squared?!  No problem! GCF to the rescue.

After that, we look at what do we do if a GCF alone isn’t enough to get rid of the a-value, or, even worse, there’s no GCF at all?

This brings us to my FAVORITE part of factoring quadratic trinomials: Slide, Divide, Bottoms Up!  If you are unfamiliar with this method, let me start off by telling you that it’s awesome.  It’s firmly rooted in the same concepts we’ve been using for the last three sections of factoring, and it just makes sense.  Another benefit to the Slide, Divide, Bottoms Up method is that it is efficient.  Doing guess and check (or the box method) can become very frustrating for students when the a-value is larger than, say, 4 or 5.  There’s just too many options and it ends up taking forever, even with a decent intuition about which numbers to test out as factors.  Also, this method even works for special factoring cases like difference of squares!  Students can certainly utilize the factoring shortcut for difference of squares, but, if they forget, Slide, Divide,  Bottoms Up still has their back.

Here’s how Slide, Divide, Bottoms Up works:

Let’s talk through an example:

Like all factoring problems, we check if there is a GCF, first.  If we’re lucky, that will remove the a-value and we will be good to do what we normally do.  However, in this example, we weren’t that lucky.  No GCF, so what to do with the 6?  We certainly don’t want more than 1 n-squared, so we’re going to temporarily transfer it to the constant term by multiplication (we “SLIDE” it over).  At this point, we discuss what “temporarily” means.  It means, “only for a while,” so that tells us that, at some point, we’re going to have to undo it. This should be perfectly “legal” because if we do something but then undo it later, that just cancels out to what we started with.  It might also be worth noting that we transfer the a-value through multiplication because we are factoring, which literally means returning an expression back into a product (multiplication) of two factors.

Now that we’ve gotten rid of the a-value of 6 for a moment, we’re left with a standard trinomial that students know how to factor in their sleep with their eyes shut, at this point.  The only thing they have to remember after factoring it is that our factored form is for our temporary expression, not the one we started with.  So, how to undo what we did?

Well, if we multiplied the a-value into the coefficient, it stands to reason that we should do the inverse operation and just divide it back out (DIVIDE)!  Since we’re dividing, make sure to reduce the fractions!

Lastly, we didn’t start out with any fractions.  Actually, we started out with a number that was a coefficient (our a-value of 6).  To get rid of any fraction(s) that we introduced, we bring the denominator(s) back up in front of the variable to be a coefficient, once again (bring the “BOTTOMS UP“).

Here’s some more examples.  Note example 5 where there’s a GCF but we’re still left with an a-value of 4.

Here’s how it works with difference of squares problems.

After using Slide, Divide, Bottoms Up for the past 3 years, I can’t see myself doing factoring any different.  I’m pretty smitten with this method, and, hopefully, it’s easy to see why.

After doing all of the different factoring, I give students one last reference sheet to use in their notebooks, which can be used at any time to refresh their memory on how to solve ANY quadratic trinomial.

If you are interested in this flowchart, it is available in three different sizes here.

Let me know how you teach factoring quadratic trinomials in the comments below!

## 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!

## Algebra 1 *Solving Equations* Unit Review Stations/Task Cards Activity

My students are finishing up their 3rd unit which is all about solving equations.  The unit includes:

• Solving 1-step through multi-step equations.
• Writing equations from applications and then solving
• Special solution cases (no solution and infinite solutions)
• Solving Absolute Value Equations
• Writing absolute value equations from a graph
• Writing and solving absolute value equations from a scenario
• Ratios and proportions
• Solving proportions
• Percent of change problems (emphesis on working backwards to find original value or final value)
• Literal equations

To help them review, I’ve made the following set of task cards (to be done at 11 different stations around the room), using problems from a variety of different resources.  I have my students for 2 periods each day, so we should be able to finish in one class.  If you have only one period per day, this might take you 2 periods.  OR you could give students the choice of picking any 2 problems from each station to complete.

I will have students work in groups of 4 and will give them 8 minutes per station.  If they finish early, I have an additional review assignment for them to work on in the meantime. On the back of each card is the final solution, so students can quickly check if their work is on the right track, or not.  If they’re really off and can’t find where they’ve gone wrong, I’ve also provided the fully worked out solutions for each problem at the given station (but that is only to be used if truly needed).

The fonts Riffic and Arcon are used, throughout.  If you plan on editing the Word Document to fit the needs of your own class, you’ll want to download those two free fonts.  Otherwise, the PDF is good to go!

I have each station paper-clipped together.  Each station contains 4 problems that are placed inside a white half-sheet of paper that contains the fully worked out solutions.  The  white paper with full solutions are there only in case a full group of students truly get stuck.

The front of the cards have the question (and problem number).  The back side has just the answer–no hints as to how that answer was reached.  Students can collaborate together to get the right answer, if their answer didn’t initially match.  If they’re really stuck, they are allowed to use the white solutions paper for the station.

Here’s an example of the solution paper for Station 8.  It’s nothing fancy, but it does the job.  It’s meant to get a group “unstuck” if they couldn’t figure something out together.  After all, there’s only one of me and 36 of them, so extra help is sometimes good to provide.

Here’s a look at all of the questions, from each station (the problems are to be cut apart, and turn into 3″x5″ rectangles).

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.