# Teaching Systems of Linear Equations: Tips, Strategies & a Freebie

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This post originally appeared on the blog Free to Discover.

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.

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
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.

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!

A 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.

Be sure to scoop up
this free card sort that facilitates recognition of special solutions by
analyzing the equations!

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!

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

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Amanda Nix of Free to Discover lives in New Hampshire with her husband, two children, and English chocolate lab. She loves working with secondary math students! After five years as an 8th grade math teacher, she moved into a part-time role as a math interventionist for grades 5-8. Today she is a work-at-home mom who enjoys staying immersed in education by tutoring middle and high school students in math and science. She has a true passion for teaching math using fun, interactive methods. She holds a Master’s Degree in Mathematics Education from Lesley University, and considers herself a lifelong learner. She loves sharing her ideas and strategies for teaching mathematics on the Free to Discover Blog.  You can also connect with her on PinterestFacebook, and Instagram!