Critical Thinking Systems Of Equations

Posted by: All Things Algebra

I love teaching systems of equations, like seriously LOVE it!  I always teach it right after the linear equations unit, and it’s the perfect transition from graphing one line, to graphing two.   Students catch on right away and think, “this unit is going to be easy!”

Then…. we hit Day 2:  Substitution.  Their little hearts sink.  I hear “Why does this seem so hard?”, and  “I remember solving equations in the fall, but not like this!”, and “Can’t we just solve it by graphing?”  This seemed to be a struggle every year.  That ended the year I introduced it as “the blob” method.  Sometimes students just need something fun to remember a certain method.  Something that always makes them giggle 🙂

These are the steps I have my students follow:

If they get an equation like x + y = 7, I tell them they can choose to solve for x or y, it won’t matter.    If they get two equations both solved for y (like y = x + 1 and y = 2x – 7), then they can just choose one to be “the blob”.  This way of teaching substitution works like a charm!  I noticed that after teaching elimination, students would stop using substitution, even when it was the most efficient method.  After switching over to “the blob”, it really resonated with them and they saw how easy and quick it can be.

After I’ve taught all three methods (graphing, substitution, and elimination), we do a slew of activities to review them all.  I always leave the following poster up on my board as a reminder of the different methods so students have a reference.  I also throw this up on the board at the end of the year when we are reviewing for the state test.  One look at it and I hear the “oh yeah!”‘s and they are off to work.   You can download this poster for free here!  It’s offered as both an image file (PNG) and Smart Notebook file.

Last but not least, here are some of my favorite activities for to do with my students on systems of equations.  Check them out if you’re looking to give your systems unit a boost!

All Things Algebra



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Product Description

In this inquiry based, discovery activity students graph two lines and then answer questions about solutions to equations and points on the lines of the equations. The goal of this activity is for students to observe that the solution to a system will occur where the graphs of the lines intersect and that systems can be solved by graphing. Students construct their own meaning and understanding, and will be making observations and answering critical thinking questions that will help them to make sense of the solutions to a system of equations.

Solve Systems of Equations Resource Packet
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Solve Systems by Elimination Race Game
Systems of Inequalities Exploration Activity and Notes

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