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Sorting Equations and Identities
  • Introduction: Mathematical Goals
    • This lesson unit is intended to help you assess how well students are able to:

      1. Recognize the difference between equations and identities.
      2. Substitute numbers into algebraic statements in order to test their validity in special cases.
      3. Resist common errors when manipulating expressions such as 2(x – 3) = 2x – 3; (x + 3)2 = x2 + 32
      4. Carry out correct algebraic manipulations.

      It also aims to encourage discussion on some common misconceptions about algebra.

  • Formative Assessment Task: Equations and Identities
    • Students distinguish equations and identities; provide examples of equations that have one solution, two solutions, an infinite number of solutions, and no solutions, and determine if mathematical statements are always true, never true, or sometimes true.

  • 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. Construct viable arguments, and critique the reasoning of others.
      1. Look for and make use of structure.

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

      • A-SSE: Interpret the structure of expressions.
      • A-SSE: Write expressions in equivalent forms to solve problems.
      • A-REI: Solve equations and inequalities in one variable.
  • Lesson Structure
    • The unit is structured in the following way:

      • Before the lesson, students work individually on an assessment task that is designed to reveal their current understandings and difficulties. You then review their work and create questions for students to answer that will help them improve their solutions.
      • During the lesson,
        • Whole Class Introduction
        • Then, students work in small groups on a collaborative discussion task.
      • After the lesson, students return to their original task and try to improve their own responses.
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