Reflection: Standards Alignment What's In an Intersection? - Section 1: Opener: Create These Tables on Desmos


Today, I'm thinking about Mathematical Practice #5: making strategic use of appropriate tools.  I'm thinking about it in two ways.  First, as it pertains helping students learn to use technology as a tool in their education, and second as we think about algebraic tools for representing a problem.

Technology matters for two reasons.  In the big picture, our world is full of new, shiny, high-tech tools that can do a lot more than most of my students realize.  I want kids to know the old-school-geeked-out-mathematical-power of a computer.  More immediately, as the roll-out of the PARCC exams continue, it's likely that kids are going to have to feel comfortable doing math on a computer screen in order to win their exit exams.  So today when students use Desmos, they get to practice using a computer-based mathematical tool in context, which prepares them for both broad and immediate goals.

Ok, so given that we're moving toward mastery on the strategic use of appropriate technological tools, what are the algebraic objectives of this lesson?  The dynamic nature of a digital graph is helpful for helping students notice the relationships between - and relative strengths of - different algebraic representations.  As students type the coordinates of each point into the table on Desmos, the points appear on the graph.  As they think about the equation of the line that connects those points, they get immediate feedback about whether or not they got the equation right.  When it's time to solve a problem, what feels most useful?  Is the table best?  Well, it's easy to make, but rather inefficient.  Are the graphs best?  Sure, if you've got technology for graphing them, but what if you didn't?  How about the equations?  Well, hey, do you recognize what a useful tool an equation is yet?

  Using Tools
  Standards Alignment: Using Tools
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What's In an Intersection?

Unit 9: Systems of Equations
Lesson 3 of 20

Objective: SWBAT to interpret the intersection of two graphs as the solution to a problem in two unknowns.

Big Idea: The "closeness" of one graph to another matches the accuracy of a guess and a check.

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