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Finding Equations of Parallel and Perpendicular Lines
  • Introduction: Mathematical Goals
    • This lesson unit is intended to help you assess how well students are able to understand the relationship between the slopes of parallel and perpendicular lines and, in particular, to help identify students who find it difficult to:

      1. Find, from their equations, lines that are parallel and perpendicular.
      2. Identify and use intercepts.
      3. It also aims to encourage discussion on some common misconceptions about equations of lines.
  • Formative Assessment Task : Parallel and Perpendicular Lines
    • In the assessment task, students use equations of straight lines to determine which lines intersect to form the sides of a rectangle.

  • 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.
      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:

      • G-GPE: Use coordinates to prove simple geometric theorems algebraically.
      • F-IF: Analyze functions using different representations.
  • Lesson Structure
    • The lesson unit is structured in the following way:

      • Before the lesson, students work individually on a task designed to reveal their current levels of understanding and their difficulties. You then review their work, and create questions for students to answer in order to improve their solutions.
      • During the lesson,
        • Students work in small groups on a task related to the assessment task.
        • Next, they regroup to critique each other's work.
        • Throughout this work they justify and explain their decisions to each other.
        • In a whole-class discussion, students explain and extend their methods and solutions.
      • After the lesson, students again work individually to improve their solutions to the assessment task.
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