I’ve spent many years working exclusively with 8th graders who struggle with math in some way or another. Sometimes they struggle because they lack background knowledge. Other times they struggle because they aren’t ready to understand, and sometimes their own fixed mindset holds them back. Teaching solving multi-steps equations can bring out the worst for struggling students. There are a lot of steps students need to keep track of and even more details.
It comes as no surprise, then, that I’ve spent a lot of time trying to find a way to support these students and get them to be successful with this foundational set of skills. One of the things I’ve come up with is a method to organize your work when solving equations. We call it the box method. This approach has helped countless students become proficient in solving equations. I’d like to walk you through the whole process for teaching this topic using interactive notebooks.
Teaching Solving Linear Equations with Interactive Notes
If you don’t use interactive notebooks for instruction yet, let me encourage you to look into them. They help you bring best together teaching practices and put them into one place. I use 5 notebook components in every unit, and I’m going to show you what each piece looks like with solving multi-step linear equations. Of course, you could use any of these pieces that match your students’ needs, or use the whole unit.
I can statements
Students need to know what they’ll be learning and practicing. One way that I like to share objectives with students is through I Can Statements. We glue this sheet into our notebooks as the first page of the unit. We refer to it throughout the unit and interact with it. I find this helps students take more ownership of their learning.
You’ll notice the check boxes on the left of each statement. These serve as a way for students to reflect on their learning. When they have evidence that they have mastered an objective, they put a check in the box.
In this particular case you can see that we start with some pre-requisite skills like combining like terms and using the distributive property. Some of the students start with a high level of proficiency because they learned these things in 7th grade. They may be able to mark these statements off from the get go. Ultimately, by the end of the unit students will solve linear equations with or without fractions. This sheet shows students the natural progression of skills.
This topic has two sets of I Can Statements because part of solving these types of equations is knowing when there’s no solution or infinite solutions.
This same concept resurfaces when we get to solving systems of equations. At our school we teach these standards months apart, so I include these objectives in both units.
Activating Prior Knowledge
Since students have previously worked with combining like terms and distributive property, it’s helpful to activate their prior learning before diving into new concepts. The next activity in the interactive notebook is designed to help you see what they remember. Students have to find the error and then explain why it’s an error. This will give you a glimpse into their readiness for this topic and allow you to intervene early if students need a refresher, or move ahead with confidence.
Looking for more tips & tricks on implementing interactive notebooks and foldables in your classroom? You’ll want to check out this FREE mini-course on how to get the most out of interactive notebooks. It’s a 5 part series delivered right to your inbox. By the end, you’ll have your own customized plan for either starting, or ramping up, interactive notebooks in your class.
Using foldable notes and graphic organizers
The next part of the notebook is dedicated to notes. Students will put the information that they need related to steps or algorithims. I like to complete the foldable, then the practice problems and then let students practice with other activities. Then, on a different day we start the process over with a different set of notes. Let’s look at the notes that we use for this topic.
Combining like terms foldable notes
As a refresher, we complete this combining like terms foldable. It gets students thinking about how and why they have to combine like terms. Also, it gives me a chance to overwrite some common misconceptions that students bring to the table.
One of the questions students always ask is, “Is that a negative or subtraction?” This gives you a chance to teach them that negatives and subtraction mean the same thing. The foldable gives them a clear vision of how to combine like terms.
Solving for x using the box method
When you use the box method, students are basically collecting like terms across the equals sign. When they cross over the equals sign they have to change the sign of the term. It’s really that simple. For an old school math teacher this might make you cringe because they aren’t showing all of the steps, but it really cuts out places where kids make a lot of mistakes. You can see the steps more spelled out below.
After looking at the steps then we go through a practice example together. When you do this example with students, they should follow you exactly. This is your chance to model. In this example the boxes have been drawn for them. In the future, the students will have to draw the boxes. We took a lot of time and trial and error to create this method (I share more about the box method in this post). I’m confident that if you use it with your students, they’ll get much better at solving equations.
How many solutions does this equation have?
When students solve equations, we’re working with equations that have one solution. We also introduce the idea that an equation can have no solution or infinite solutions. That’s the purpose of this set of foldable notes. It walks students through a series of questions that leads them to how many solutions the equation has.
Here’s how the questions work:
Are the slope and y-intercept the same on both sides?
If yes, then it is infinite solutions.
If no, then go to the next question.
Are the slope the same with different y-intercept?
If yes, then it has no solution.
If no, then it has different slopes on both sides and it has one solution.
It’s that easy. Make sure you give students time to really think through what is happening. They have a tendency to think that different slopes means no solution. Something in their heads tells them that different signifies no. (for activities to practice finding how many solutions, check out this post)
Practice makes permanent
The next section of the notebook contains guided practice. This is the “We Do” part of the instruction. Doing this work in the notebook helps students see exactly what they’re going to be doing during independent practice. It also gives them a place to look back to worked problems as a reference.
Combining like terms practice
Now, let’s practice. The first game that we play in our notebooks is a connect the lines game for practicing combining like terms. This partner game works great for an anticipatory set to warm kids up. I model the game and show them how it works, and then they’re off.
How many solutions practice
The second practice activity has students sort equations into the categories of one solution, no solution, or infinite solutions. They’re given equations that are cut into strips. They evaluate them and put them into the correct category. Then, they write down their own hints and characteristics of each category to the side.
Solving multi-step linear equations practice
Lastly, we practice some solving for x in a linear equation. We complete these problems using the boxes method. I show them how to do one of them and let students move forward on their own or do more with me. It depends on how they feel with the process.
Cheat sheet
The final piece we put into our notebooks is the cheat sheet. The cheat sheet gives students some ideas and reminders during the unit. For this particular unit I’ve added some reminders to help them with common misconceptions.
Like I mentioned before, students often forget that different slopes means one solution. That’s why I have the little penguin holding the sign. When a students is making a lot of silly or careless mistakes I like to send them back to the cheat sheet. They might just need a quick refresh for this topic.
Let’s do this
Now, it’s your turn to take some of these ideas to your classroom. Remember that notes don’t have to be drudgery and an interactive notebook should be interactive. By implementing these ideas in students’ notebooks, or some new ones of your own, you’ll see the students engage more with the material they’re learning.
You can use the ideas above to bump up your interactive notes, or you can grab the entire set of notes I use in my classroom in the “Solving Linear Equations Interactive Notebook“. For ideas on how to get students the practice they need with solving multi-step equations, check out “Activities to Make Practicing Multi-Step Equations Awesome.”
Thanks so much for reading! Until next time.
