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Forming Quadratics
  • Introduction: Mathematical Goals
    • This lesson unit is intended to help you assess how well students are able to understand what the different algebraic forms of a quadratic function reveal about the properties of its graphical representation. In particular, the lesson will help you identify and help students who have the following difficulties:

      1. Understanding how the factored form of the function can identify a graph's roots.
      2. Understanding how the completed square form of the function can identify a graph's maximum or minimum point.
      3. Understanding how the standard form of the function can identify a graph's intercept.
  • Formative Assessment Task : Quadratic Functions
    • In the task, students examine the key features of a quadratic curve and match equations of quadratic functions with graphs of those functions.

  • Common Core State Standards
    • Common Core State Standards for Mathematical Practices Common Core State Standards for Content

      This lesson involves a range of mathematical practices from the standards with emphasis on:

      1. Make sense of problems, and persevere in solving them.
      2. Reason abstractly and quantitatively.
      3. Construct viable arguments, and critique the reasoning of others.

      This lesson involves mathematical content in the standards from across the grades, including with emphasis on the following Domain.Cluster:

      • A-SSE: Write expressions in equivalent forms to solve problems.
      • F-IF: Analyze functions using different representations.
  • Lesson Structure
    • The lesson is structured in the following way:

      • Before the lesson, students work individually on an assessment task that is designed to reveal their current understanding and difficulties. You then review their work and create questions for students to answer in order to improve their solutions.
      • During the lesson,
        • Whole-class interactive introduction, then
        • Students work in pairs on a collaborative discussion task in which they match quadratic graphs to their algebraic representation.
        • As they do this, they begin to link different algebraic forms of a quadratic function to particular properties of its graph.
        • Whole-class discussion.
      • After the lesson, students return to their original assessment task and try to improve their own responses.
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