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Logo Symmetry

Matt Winking
State of Georgia Recipient
2007 Presidential Award for Excellence in Mathematics and Science Teaching
Mathematics I: Algebra/Geometry/Statistics
Phoenix High School
Gwinnett County Schools

Contents

Task
Overview
The Logo Symmetry Learning Task explores graph symmetry and odd and even functions. Students are asked to solve simple radical equations. In working with symmetry of graphs, students will apply the concepts of similarity and transformations of geometric figures inherent in the Grade 7 standards for geometry. The task offers students an in-depth discussion of even and odd symmetry of graphs of functions and transformations of graphs by reflection in the coordinate axes. These topics and the discussion of solving rational equations and quadratic equations of the form x² – c = 0, c ≥ 0, reinforce topics from geometry, especially the topics of symmetry and transformation of geometric figures, similar triangles, and the Pythagorean Theorem.

GPS Addressed
MM1A1. Students will explore and interpret the characteristics of functions, using graphs, tables, and simple algebraic techniques.
    c. Graph transformations of basic functions including vertical shifts, stretches, and shrinks, as well     as reflections across the x- and y-axes.
    d. Investigate and explain the characteristics of a function: domain, range, zeros, intercepts, intervals     of increase and decrease, maximum and minimum values, and end behavior.
    h. Determine graphically and algebraically whether a function has symmetry and whether it is even,     odd, or neither.
MM1A3. Students will solve simple equations.
    a. Solve quadratic equations in the form ax² + bx + c = 0 where a = 1 by using factorization and     finding square roots where applicable.
    d. Solve simple rational equations that result in linear equations or quadratic equations with leading     coefficient of 1.

Video Information
Use these questions to guide your thinking about some of the important teacher ideas in the lesson featured in the video clip.
  1. What kinds of questions does the teacher ask to promote students’ problem solving?
  2. How is the teacher gauging students’ current understandings and building from those understandings?
  3. Consider the GPS standards listed with this video.
  4. What makes this lesson different from lessons you have taught on this topic?

Classroom Materials

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