Teaching Systems of Equations

Teaching systems of linear equations: ideas, strategies, & a freebie

Introduce with a Real Example
I love introducing systems of equations with a super basic example:
The cost of buying a treadmill is $450.  y=450
The cost of a gym membership is $150 per year.  y=150x
I explain to my students that I have a dilemma and I’m trying to decide which option to go with.  We graph the system.  Interpret different parts of the system – especially where one option might be more cost effective over the other and the meaning of the point of intersection.
Teaching systems of linear equations: ideas, strategies, & a freebie 
I always allow a few minutes to discuss other factors that need to be considered like other types of equipment at the gym, electricity costs, etc.  These little debates mean that my students are *really* thinking about the scenario.  They are connecting to it and developing a solid understanding of the topic.  This part is key because it really increases student engagement.  They LOVE to feel like they are helping me solve a dilemma, too!

Guided Notes
Developing lists of steps and rules lays the foundation for practicing the skill of solving systems of linear equations.  Always start with graphing because it provides students with a visual to associate with the concept.  When teaching substitution, be on the lookout for errors with distributing (especially a negative).  When teaching elimination, emphasize that students should watch their signs when adding or subtracting the two equations.  I offer a complete set of differentiated notes for sale in my store.  There are three versions of notes: skeletal, examples-only filled in, and teacher notes.  There are three versions of the homework: advanced (with tougher numbers), basic, and shortened.
Teaching systems of linear equations: ideas, strategies, & a freebie 

Practice, Practice, Practice
One way that I engage my students in this topic is to host a “jumbo day.”  We use poster-sized graph paper, yard sticks, and markers.  Students work together in groups to solve systems of equations using graphing.  This also results in awesome classroom décor!  Start with basic examples and end with a word problem or two.

Mini-whiteboards provide an awesome way to formatively assess student progress.  Write a system of equations on the front board.  Have each student solve the system using either substitution or elimination, showing their work on their whiteboard.  When it appears most students are done say “hold ‘em up!” and visually scan the boards.  If needed, do the problem out at the board in front of the class.  I walk around while they are trying the problem so I can correct errors along the way.  So fun!

Teaching systems of linear equations: ideas, strategies, & a freebieA variation of the mini-whiteboards is to have 4-5 students come to the front of the room at the main whiteboard.  I read aloud a system of equations for students to record.  The students at the front write and solve the system at the front board while the students at their seat write and solve the system on a piece of paper at their desks.  My focus is on the few students at the front so I can find and correct any misconceptions, but I walk around to check on students at their seats as well.  I make sure each student gets 1-2 turns at the front board.

And you know I love scavenger hunts!  I have a 16-problem scavenger hunt available here.  Hang the 16 pages around the room and give each student a workspace.  1-2 students start at each problem.  They solve it and they look for their answer on another sheet to find the next problem they should do.  You know they are correct if they solved the problems in the correct order.  Incorporates movement, collaboration, and self-checking!

I also have available a discovery worksheet that serves as a great summarizer.  Perfect for a sub plan or independent practice day.  Discovery-Based Worksheets have been specially designed to engage students in learning that moves beyond traditional skills practice. Students develop a deeper understanding of the big idea and make connections between concepts.
Teaching systems of linear equations: ideas, strategies, & a freebie

Be sure to scoop up this free card sort that facilitates recognition of special solutions by analyzing the equations!
Teaching systems of linear equations: ideas, strategies, & a freebie

Car Loan Project
To end the unit, my teaching partner and I developed a project involving car loans.  Students have to compare car loan options and summarize when one is a better option than another.  A quick Google search will help you find a car loan calculator.
First, students researched a car they would like to buy.
They partnered up and selected one car to move forward with.
Then they used the loan calculator to input the down payment and a set length of the loan.
We gave them a standard interest rate to use as well.
The loan calculator provided the monthly payment.
Then they selected a different down payment and recalculated the monthly payment.
Finally, they graphed the system, solved using a second method, and summarized their findings.
Students were fascinated by the effects of interest and learned some valuable lessons about buying a car, which for many of them would only be 2-3 years away!
Teaching systems of linear equations: ideas, strategies, & a freebie

Teaching systems of linear equations: ideas, strategies, & a freebie

I love this unit because they are so many real world connections!  Which activities would your students love?

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