solving literal equations – Math by the Mountain

Algebra 1 Unit 3 Interactive Notebook Pages | Solving Equations

October 17, 2017October 17, 2017Math by the Mountain5 Comments

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 Solving Equations Unit Review Stations/Task Cards Activity

October 17, 2016October 17, 2016Math by the MountainLeave a comment

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).

Click HERE to download the stations/task cards activity.

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!

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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. fullsizerender-16

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. fullsizerender-17

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. fullsizerender-18

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).

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Solving Literal Equations “Connect 4” Activity {Student Approved} FREE DOWNLOAD

October 14, 2016September 21, 2019Math by the Mountain6 Comments

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:

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.
Students felt much more confident about their skills and were able to get nearly-instant feedback about how they’re doing.
Students LOVED it. The class begged me to continue letting them play the game through passing time.

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

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