In 8th grade math when we introduce the concept of how many solutions there can be to a system of equations, it pretty much blows students minds. They get so used to everything having one right answer and it being one number. But when we start talking about the different number of solutions, now they have to identify how many answers it may have, and some of them fight against that idea. In our scope and sequence we introduce this topic when we learn about solving multi-step equations that have a variable on both sides because you can have infinite solutions or no solutions in these cases. We teach it again later in the year when we get to solving systems of equations. Check out these nine activities sure to help students understand and find how many solutions exist in a system of equations.
To introduce this topic, I use a discovery lab that I wrote all about here. It helps students understand conceptually what’s going on. But in this post I want to focus on how to get students practicing with activities and games. When I first was looking for activities to practice identifying how many solutions are in a system of equations, I couldn’t find a lot. So, I made my own. I feel really strongly that students need to see this concept in action over and over until it clicks.
The list:
Watch Your Step…You May Collide
Let’s do this
In this article we’ll look a little deeper at each of the activities so that you can get an idea of where they’ll fit into your lessons. You’ll see that some of the activities are good at the beginning of unit and some are better fit after students have a background with the topic. Some activities work best as partner practice or even as homework. Let’s dive in.
How Many Solutions? Maze
Mazes are life in my class. We complete a maze every day. Whenever I don’t have a maze for them, for whatever reason, I get a lot of confused faces. They work perfectly as a non-threatening warm-up for students. These three how many solutions mazes get students practice finding how many solutions exist for two equations. I use them for 3 days in a row and it’s great practice. Then, I use them again later in the year for review.
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Spoons Game and Card Sort
This Spoons Game & Card Sort is designed after the classic card game Spoons. It’s a fun way for students to practice finding how many solutions a system of equations has. Here’s the directions to play the game:
1.Students play in groups of 3 to 5. Use the cards from both sorting sets of cards (30).
2.Arrange spoons in the middle of the group, with one fewer than there are players and deal three cards to each player.
3.Each player tries to make three of a kind (3 equations with one solution, infinite solutions, or zero solutions). One player is the dealer (rotate for each round). The dealer takes a card off the top of the deck to have four cards in his/her hand, then removes one from the hand and passes it face down to the left. Each player discards one card to the player to the left. The last player places the discard into a “trash pile”.
4.Cards are picked up and passed around the table until someone gets three of a kind and takes a spoon from the center. Allow 10-15 seconds between passing cards to allow students to analyze equations. Once the player with three of a kind takes a spoon, anyone can take a spoon. The player left without a spoon gets a letter. If at any time the draw cards run out, pause to reshuffle the trash pile and keep going.
5.The winner is the last player remaining. Players move closer to elimination each time they don’t get a spoon and take the next letter in the word S-P-O-O-N. Spell it and you’re out.
6.Variation: rather than collecting three of a kind, have students collect one of each of the three types of equations. The objective would be to hold an equation with no solutions, with infinite solutions, and one solution.
Coloring Activity
Sometimes students need a little brain break. I find that coloring activities can provide such a break. I love this coloring activity because students get to color the design and the identify how many solutions something has at the same time. It takes a while for them to complete this entire activity. I like to use it as an end of the year review activity or when I have a substitute teacher.
Sorting Activity FREEBIE
Sorting gives students a different way of practicing. They can process the information quickly, and for many kids they get the repetition they need to help them remember a new concept for the long term. This sorting activity for finding how many solutions gets kids to look at a set of equations and determine how many solutions it has. You can have the students create the pockets and then you can get this activity out at your convenience. It works great as an anticipatory set or something for fast finishers to do while they wait for everyone else. Also, they can complete it over and over.
You can get this sorting activity download free here.
Hand Signals
I use these hand signals to help students remember what the lines look like in a system of equations.
Students seem to have the misconception that if the slopes are different then there is no solution. However, when they use the hand signals over the course of a week or two then they start to remember that different slope means one solution. Additionally, I have them chant the saying, “different slopes one solution!” This serves as an ear worm that they can use.
Reference Sheet
This cheat sheet from Miss Math Dork really gives a clear picture of when you would use different methods to solve systems of equations and how to determine the number of solutions. It fits perfectly in an interactive notebook if you print it two to a page. You can have students explain how it works to their partner and they can use it as a reference throughout the unit.
Discovery Lab
If you want a detailed explanation of the discovery lab I use to get students looking at the possible number of solutions for a system of equations, you can read about it here. Basically, this discovery lab gives students a chance to make their own discoveries for how many solutions. It builds students’ background a little bit and then they dive into a discovery activity. They have to identify characteristics of the different systems of equations being shown. In the end, students draw conclusions and essentially write the rules related to slope and y-intercept for systems of equations.
Watch Your Step…You May Collide
Another way to build background for students is to try this activity. Students all start in different parts of the room and lay a trail of string in a straight line as they walk across the room. They they look for where they crossed other lines. This gives everyone a shared experience that can be referred to about what a system of equations looks like. The activity continues with some partner exercises as well.
Predicting Activity
You will find this predicting activity for finding the number of solutions on LearnZillion. It’s a video that takes kids through a prediction activity with equations. It could be viewed as a class or students could go through it on their own. In the additional resources section you’ll find another video that explains what how many solutions is. This works perfect as an anticipatory set to get kids focused on the day’s lesson.
Try one thing
So, there you have it. You have a variety of activities to choose from to help your students understand and determine how many solutions a system of equations has. These activities are great for the 8th grade math or Algebra I class and will really get your students engaged in your lesson. But please, don’t feel like you have to try all of the activities. Just try one and see how it works. If it’s a success, then you have a new tool in your math tool box.
Thanks so much for reading! Until next time.
