solving multi-step 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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August 22, 2016November 12, 2017Math by the MountainLeave a comment

Over the last year or so, I’ve done a lot of work with very low-end students. Between teaching summer school for two years straight in the inner city, and teaching support classes in my regular semi-rural school, I’ve really been pushed to find other ways to convey information that work for my students.

One thing that I found is that no matter how small and bite-sized of steps I could break a process down to in our notes, many of my ELL students and students with IEPs for processing disabilities just couldn’t follow along and rework through the steps to get themselves “unstuck” on a problem. Working toward self-sufficiency is really big for me. I strongly believe that the purpose for high school is to prepare students to be productive once they enter the “real world,” whatever that means for them (school, workforce, military, etc.). Being self-sufficient and being able to problem-solve on their own is a big part of being able to reach this point. So, I kept searching and trying new things until I made my first flowchart graphic organizer. It was a game changer for my class!

Students were able to easily follow along. Using the graphic organizer, they were forced to read and do only one small chunk at a time and they had enough space to do their work right on the flowchart (it’s hard for some students to go back and forth between where the steps are written and where they’re doing a problem on a separate page of paper). Students were able to use the flowcharts as long as they wanted. As soon as they felt comfortable enough without it, they stopped using it. I have also laminated a class set that we used for practice early on.

I’ve also found that these have been very successful with my older students to jog their memories about a method they haven’t used in a while (such as solving systems by elimination). For a lot of my seniors, I’m not the only math class that they are taking–many of them are also taking a class called Math Skills that gives them opportunities to take more Work Samples, which are needed for graduation. Work Samples are an animal of their own and the topics on them can vary widely, so students find themselves needing review on topics that they may have not seen for a couple of years. I’ve had a lot of these students specifically ask if I had a flowchart for topic _______ that they could look over to remind themselves of the details of how to do ________.

With my younger classes, the first time we learn a method, I have a student working at the document camera as our class’ scribe, and the class (no help from me) discusses their way through the problem. They determine which path they need to go down (the “yes” path, or the “no” path), and then work in pairs to do that step. Then, they compare their work for that step as a class, and then move onto the next part of the flowchart and repeat the process. I love, love, LOVE how student and discussion centered this makes my lessons! Seriously! LOVE! It’s almost as if I’m not needed (shh! don’t tell anyone that, because I still want my job).

From there, we do a few examples that we glue into our INBs, and do some practice with dry-erase pens on the laminated copies of the flowcharts. I find that starting slow and having them work their way through a problem as a class, without me, helps them remember the ins and outs of the process a bit better, since they had to struggle together as a class.

Although I don’t have students referring to their notes quite as much as I would like, I have found that they go back to these flowchart examples in their INBs more than anything. When I ask my students why they like these so much, a lot of what they say comes back to the fact that they have the steps on the paper, and the space to do the work on the paper, and the flowchart really forces them to go one step at a time. A lot of them know that they have a tendency to rush through steps, and using the flowchart makes that very difficult to do. Students then self-wean off of the flowcharts at their own pace, which is great in my books! They are taking accountability for their knowledge. If they can do their work straight away, they do so. If they need a bit more help to get through a problem, they don’t just give up–rather, they walk to where I keep extra copies of the flowcharts, grab one, and work through the problem. This has really helped develop the no opt-out culture in my classroom. If students want to learn, there are tools to help them learn. For my classes, the flowchart has been an instrumental tool for their development, both in math skills as well as self-motivation and persistence.

If you like the flowcharts, you can find them at my TPT store! Today, they are 19% off when you couple your purchase with the 10% discount code OneDay.

Solving Systems of Linear Equations Flowchart BUNDLE

Solving Multi-Step Equations Flowchart

Thank you so much for reading!