Reflection: Checks for Understanding Emerging Pictures: Graphing Inequalities in Two Variables - Section 2: Investigation

This piece of student work show two typical responses that I see in my classes to this task. In the first graph, the student started out plotting five points in green that would satisfy the inequality and five points in red that would not.  In all of these cases, the student tried equal numbers of cats and dogs and ended up with what would look like a line from the origin.  I see students make this line quite a bit.  Presumably, what happened next is that the student realized the key to figuring out where the green and red points would be is finding the dividing points that are right on the boundary line.  I believe he added the purple points next, realized they were collinear and then shaded the red and green sections of the graph.

Students who struggle will generally not take this same approach. They usually have a lot more discrete red and green points and less purple points. In the second example, we can see that this student made a lot of green points first.  He also made them very systematically, starting with 1 dog and figuring out how many cats all the way up the y-axis and so son.  In general, this kind of student adds more points before s/he sees a pattern but usually reaches the same conclusion.

I think it's important not to show them a "math shortcut" here but let students develop their own understanding of where the dividing line is between points that satisfy the inequality and those that do not.  It can be tricky to keep students from overhearing what others who are further along might have figured out!

Checks for Understanding: Typical Student Graphs

Emerging Pictures: Graphing Inequalities in Two Variables

Unit 3: Systems of Equations and Inequalities
Lesson 2 of 17

Big Idea: Students plot points that satisfy and do not satisfy a linear inequality until they see a picture emerge in their graphs.

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60 minutes

Amanda Hathaway

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