Solving Systems of Equations Using Substitution Color by Solution
If systems of equations were a person, it would probably be my arch nemesis. I've struggled to find ways to get students to understand what systems of equations represents and then for them to solve using different methods. My first year teaching it I remember just trying to teach my math lab kids one way to do it so that they could "survive" the end of unit test. Man, do I wish I could have those students back and have a second chance to teach them systems of equations. Now, not only do I have more tricks up my sleeve for teaching students to solve systems of equations, I also have found so many fun systems of equations activities that help students really understand how to solve with different strategies. So check out these 15 systems of equations activities that will help students understand and practice finding the solution to two linear equations.
I feel like it is really important for students to really understand what they are doing when they solve a system of equations. They need to not just go through the motions, but be able to see a system of equations in different ways. In this post I've curated a list of activities that will help your students practice solving systems of equations with different methods. These activities focus on solving systems of equations by substitution or elimination. For activity ideas to solve systems of equations with graphing, check out this post.
The list
System of Equations Mazes
Whole Class Review Game
Put It Into Slope Intercept Form Freebie
Coloring Activity
Task Cards
Think, Pick, Flip, Check
Mystery Boxes
Oreo Activity
Quick Check
Alien Search and Shade
Picture Challenges
Worksheets
Manga High Online Practice-Elimination
Online Practice Game-Substitution
Three Act Math-In and Out Burger and Other 3 Act Problems
Let's dive in
In this post we'll take a look at some activities and how they might work in your classroom. Systems of equations have a lot of moving parts, so we have a lot of activities to look at. Some of them will work to introduce the topic and others are better suited for practice. Remember that you can use any of these activities to review systems of equations later in the year.
System of Equations Mazes
Mazes are a staple in my class and we do them almost every day. Whenever we take a break for a few days or a couple of weeks from mazes students seem so relieved when we start doing them again. They have confidence doing mazes because they aren't so intimidating.
This set of 3 mazes gets students solving a system of equations in a variety of ways. It has one maze for substitution, one for elimination, and one that is mixed. These mazes take a little longer to complete than some other mazes because the problems take longer to solve. So, when planning to use these mazes, keep in mind that they'll take a chunk of time.
In addition to these mazes, there's a maze 3-pack that focuses on just solving systems of equations by elimination, and another maze 3-pack that focuses on solving systems of equations by substitution.
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Whole Class Review Game
I like to review for unit tests by playing whole class review games. One of my go to games is Knockout. You play it on the projector and it works with a Smartboard or without one. Students choose a character from the board and it reveals a question. My favorite feature of this game has to be that all students answer all questions. Sometimes I feel like when you play a review game some students get off the hook, but that doesn't happen with this game. To learn more about knockout, check out this post.
This systems of equations knockout game has a variety of question types including asking students to change an equation into slope intercept form, and solve using substitution, elimination, and graphing. Students love this game and they really get into completing their work while playing it.
Put It Into Slope-Intercept Form Practice FREEBIE
My students seem to need a lot of practice putting equations into slope intercept form. I feel like we practice this skill all year long and every time we do it clicks more and more with them. This is a a freebie page for students to just practice changing an equation to slope intercept form. It's a good way to practice adjusting a linear equation to slope intercept form when solving with substitution. If it's in slope intercept form, then it becomes super easy to solve.
Coloring Activity
Coloring activities get students engaged and give them a brain break. In this systems of equations coloring activity the actual coloring students do is minimal. It's just enough to give them a break without taking the whole class period coloring in the picture. When completing this activity students practice solving using substitution or elimination. I find that with this topic students need a lot of practice and each problem takes a while to complete. When it comes to equations, it's important to give students a variety of problem types. It isn't enough for them to understand the concept, they also have to be able to solve in novel situations. This set of problems will give them a fair amount of repetitions. 
Task Cards and the Target Game
This set of systems of equations task cards has graphing, substitution, and how many solutions problems. The questions aren't complicated. It gives students some additional practice to hone their newfound skill. The cards are small and students can complete them with a partner or in a small group.
I like to use this set of task cards with the target game. You can read more about the target game here. Basically, it's a game where students solve problems and get to throw a ball at a target. It's the perfect combination of work and fun. Or, check out even more ideas on how to use task cards in the middle school classroom. 
Think, Pick, Flip, Check
This self-checking activity works great as a center or for fast finishers. Students are presented with a system of equations and a solution. They have to evaluate if the solution is true or not. If it's correct, they mark it with a paperclip. When they've finished the side of problems students can turn the page over to see if they were correct, giving them instant feedback on their learning.
These particular problems can be solved with substitution or elimination. If you give students graphs then they could also practice graphing. This is a good practice activity that helps students find multiple correct answer choices, rather than the traditional multiple choice format. Your students will like the challenge of this activity.
Mystery Boxes
Kim Hughey over on Math Tales from the Spring uses mystery boxes to introduce systems of equations to her class. This consists of giving students a box with a challenge problem on it and coins inside. Students work in groups to try and figure out the "riddle". The problem is not impossible, but the students have to dig deep to use what they know to figure it out. I love these types of discovery activities because it gives kids a chance to show their growth mindset skills. While I haven't used this approach yet, it's an intriguing way to start off this unit of study.
Oreo Activity
The other day a student asked when systems of equations would be relevant in their lives. She asked in a rather flippant way as if nothing we ever learn in math will matter in her life. Well, I proceeded to tell her that systems of equations was one of the most relevant math concepts she'll ever learn about.
A few days later, I reminded her of this conversation as we used Oreos to explore solving systems of equations. This activity from Math Made Possible gets students to figure out the weight of one wafer from other information given. It's a great example the way people figure things out or solve a variety of problems with systems of equations. As a bonus, I brought actual, real life Oreos. Anytime you can connect the problems students are solving to edible treats, students suddenly consider the math very relevant!
Quick Check
As teachers we are always looking for quick ways to check and see if students get it. Well, this quick check from Scaffolded Math and Science works perfectly. It's a blank template that you can put any system of equations on. That makes it convenient because you can add the exact type of problem that you want. It comes with two problems to a page, and I print that two to a page, so I get 4 problems to a page. I have students complete two problems each. Of course that depends on how much time we have. Often I don't see to have enough time at the end of class for every kid to finish all the problems on the quick check.
Alien Search and Shade
This Alien Search and Shade activity from Hoppe Ninja Math works perfectly for homework. It has 9 problems and the students solve the problem and the shade all of the boxes with that answer the same way. In the end they'll reveal a picture from all of the shading. They'll also get a lot of practice in a fun way.
This activity doesn't have an answer key, so you'll have to complete it yourself if you want an answer key. When I do this I usually challenge my first period class and see if any of them can beat me and be accurate as well. It adds a little friendly competition.
Picture Challenges
Mash-up Math has a slew of these picture challenges that has a visual presentation of systems of equations. I love to use them as warm-up activities after our maze or as a fast finisher challenge problem. Some of them are easier than others and they give kids great practice with mental math, as well. The uses for them are endless. At first, some of my students wanted to give up pretty quickly, but after they'd done a few they really seem to enjoy and embrace the challenge. Plus, they love the pictures in these riddles.
Worksheets and Pick a Card Game
Sometimes I just want to have my students get a lot of practice. I find that when I give them a worksheet and say go, they can get overwhelmed. That's why I created the pick a card game. I snag a worksheet from a site like the one here and my kids get out their whiteboards. We then start to play the pick a card game. It's a Price is Right style game that I break down step by step here. Basically, after each question students pick a card from my over-sized deck of card and the one with the highest card gets the most points. Kids love it and it helps motivate them when they're working on practice problems.
This link will take you to a set of 12 free worksheets that include graphing, substitution, and elimination. Also, the problems go from simple to more complex. It even has systems where you have more than two equations for an extra challenge.
Manga High Online Practice-Elimination
When students play this game from Manga High they get practice solving systems of equations with elimination. When playing, students have free hints and a free solve. Also, the questions ask more that just to solve a problem. Students also have to answer questions about what's happening in the system of equations. This game is fun and challenging. It works perfectly for fast finishers. They love that they get to do something that the other students aren't doing. In the end you can have the students tell you their score to keep them accountable.
Online Practice Game-Substitution
This systems of equations game from Math Games gives students a lot of practice with substitutions. When playing, students get immediate feedback on how they're doing. These problems take some time to complete and everyone can go at their own pace. When students finish a question it tells them if they are right or wrong, however it doesn't tell them why their answer is wrong. The game says that it's for solving with substitution, but I find that many of the questions are better suited for elimination. This means students can look at each system of equations and decide which method would be better fitted to solve the problem.
Three Act Math-In and Out Burger and Other 3 Act Problems
Once students have gained the skills for solving systems of equations, then they can put it to use. You can find a plethora of real life problems for this topic. One that I really like is this 3 Act problem related to the restaurant In-N-Out. It's a very popular place to eat for the junior high students in our area.
You can find more 3 Act problems here to get students applying their new skills to solve real world problems, just in case burgers aren't your thing. You can choose one about Disneyland tickets, or another about flushing the toilet. I can see appeal for 8th graders with both of those topics. Watching students work with and struggle with these types of problems is awesome. They get a chance to not just find a quick and easy answer. It builds their perseverance muscles and they get to see real world math at the same time.
Try one thing
Systems of equations can feel like eating the 100 x 100 burger at In-N-Out because it has so many layers. Don't feel like you have to do everything. Just try one new thing and see how your students react to it. You can increase engagement one activity at a time, and in turn increase students' retention of the concept. Good luck out there and remember to have fun teaching math.
Thanks so much for reading! Until next time.
Solving Systems of Equations Using Substitution Color by Solution
Source: https://ideagalaxyteacher.com/systems-of-equations-activities/