I always loved finding a variety of ways to introduce, teach and explore systems of equations. It can seem like a daunting, overwhelming concept when students first hear it, but I think it’s so fun and interesting! And solving systems certainly doesn’t have to be as difficult or scary as kids think it is. What I love about this systems of equations activity, is that students get to explore graphing and solving systems in a non-threatening way, as they allow their graphing calculator to do the hard work. This means students can focus on observing patterns, and making sense of the connection between the graph and the solution.
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Welcome back to the Math+Technology teaching series! This set of lessons includes a variety of ways to incorporate graphing calculators into your home or classroom, in a meaningful way.
Yesterday we talked about a better use of calculators: to explore, observe and discover.
Today’s lesson is no different.
Using Technology in Algebra:
One of the most important concepts in Algebra is not knowing how to graph a function. It’s understanding what the graph shows about that function, how it relates to the table and what it means in the context of a problem.
So while it is worthwhile to teach kids how to graph by hand, and understand the relationship between a linear equation, it’s table and it’s graph, graphing by hand can quickly become tiring and cumbersome.
It’s much faster to let a graphing calculator graph lots of equations at once and analyze and compare them. Students can then notice what happens when the only thing that changes is the y-intercept. Or what piece of the equation affects the width of a parabola. Or how the symmetry and vertex are evident in the table of a quadratic function.
These kinds of explorations will deepen students understanding and help them form connections, so that graphing by hand becomes much easier.
Systems of Equations Activity:
So today’s free lesson is an exploration of systems of linear equations.
Students begin by using their calculator to graph 9 linear systems. They then use these visual models to answer questions, go deeper and see the different possible solutions.
This exploration also allows kids to better understand parallel lines, and how they can determine parallel lines from the equation.
You can discuss slope, look at tables on the calculator, and compare it all to the graph.
Students will also see infinite solutions, and what the equations and graphs look like.
You can then use this to discuss systems further, or expand on questions that students had trouble with.
And if you’re not ready to teach systems yet, I hope this has still given you some ideas for how you can use your calculator to explore the relationships between an equation, a table and a graph!
And you may also like this fun set of puzzles to introduce substitution and solving a system of equations.
Or if you’re looking for practice, these silly Christmas riddles are a fun way to work on solving systems.
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