Reflection: Developing a Conceptual Understanding From Guess and Check to Graphing Systems - Section 3: Two Routes, Based on Friday's Results


Today I was reminded once again why I chose to explicitly incorporate guess and check into the systems unit.  Particularly in one of my algebra sections, where all students needed a little more time on SLT 5.1 (rendering any differentiated plans unnecessary), we had an incredible day of making sense.

By really slowing down to look at how guess and check works, students were able to see how each successive guess can lead them closer to the correct solution.  As that happened, they were developing number sense and the conceptual background necessary to be amazed by what a system of equations is capable of revealing.

I showed all students how to solve the first problem by guess and check, this time as a whole-class discussion.  When I showed everyone that a "way too high" guess and a "way too low" would provide bounds that we'd quickly narrow, students really bought in.  When we got close to a solution, we saw that, if we were 70 cents away from our goal, then adding two each of dimes and quarters would make up for that difference.  This was a big moment for kids, where "the math" and "reality" really seemed like one and the same -- which isn't always what kids expect to see!

Then, when everyone got to work, both the conversations I heard and the errors I saw made the necessity of this lesson so clear, and kids felt it too.  It was one of those days where I could watch students learn from moment to moment.  Sometimes, we teach a lesson, hope that something stuck, and may have to wait weeks to know for sure if everything worked out.  That was not today - learning was happening in each moment.  For example, as students recapped to each other what they saw in the opener, they were trying on new language and critiquing the approaches of their colleagues.  I think the accessibility of the problems fosters that.  One example of an error I saw was that students were calculating the value of, say, 12 nickels by using 0.5(12).  Do I wish that all students recognized that 5 cents is expressed as $0.05?  Of course!  But how much worse would it be to get through 9th grade without addressing that.  That's how employing a guess and check strategy can blossom into a skill drill without even naming it as such.  Students have to run these calculations, because that's how the strategy works.  They're motivated to run the calculations because each time they do, they receive feedback about whether or not they're close to a solution.  Watching the anticipation as students do the arithmetic is pretty fun to watch.

And that's the biggest takeaway today: this strategy is engaging, and kids have fun with it.  The problems I used were pretty traditional, but no student was disengaged.  As we move forward, the familiarity with the situation, and yes, the fun kids had today, will make it easier for everyone to access new content as we study tried-and-true algebraic methods for solving systems.

  Never Underestimate the Power of Guess and Check!
  Developing a Conceptual Understanding: Never Underestimate the Power of Guess and Check!
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From Guess and Check to Graphing Systems

Unit 9: Systems of Equations
Lesson 6 of 20

Objective: SWBAT to solve a system of linear equations by graphing, and to solve problems by creating and graphing linear equations.

Big Idea: Student work from the previous lesson informs my approach with each student.

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