Reflection: Developing a Conceptual Understanding Finishing Five Point Graphs - Section 2: Work Time: Finishing Up Five Point Graphs


Here's a beautiful thing about Five Point Graphs: they're actually overkill.  In order to make a reasonable sketch of a parabola, three points will do.  Heck, the vertex, a solid understanding of the axis of symmetry, and one other point are really enough. When kids begin to see that we don't need all five points, they're able to draw their own conclusions about which points are most useful in context, and to develop their strategies accordingly.

Once students start creating their own strategies and deciding for themselves what's really necessary, they are making strategic use of tools, growing in their ability to model with mathematics, and using what they know to solve new problems.  I make sure to express my admiration for students who come up with their own ideas, and I'll refer students to each other to share what they've noticed.

  More than we actually need!
  Developing a Conceptual Understanding: More than we actually need!
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Finishing Five Point Graphs

Unit 10: Quadratic Functions
Lesson 14 of 21

Objective: SWBAT sketch quick graphs of quadratic functions, identifying and labeling the key points on each: the roots, the vertex, and the y-intercept.

Big Idea: A focus on special cases can reveal a lot about the fascinating behavior of quadratic functions.

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2 teachers like this lesson
Math, quadratic formula, quadratic functions, Quadratic Equations, graphing functions, y-intercept, axis of symmetry, vertex form, Growth Mindset, Algebra 1
  43 minutes
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