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Applying Angle Theorems
  • Introduction: Mathematical Goals
    • This lesson unit is intended to help you assess how well students are able to use geometric properties to solve problems. In particular, it will support you in identifying and helping students who have the following difficulties:

      1. Solving problems relating to using the measures of the interior angles of polygons.
      2. Solving problems relating to using the measures of the exterior angles of polygons.
  • Formative Assessment Task : Four Pentagons
    • Students solve a problem related to the interior and exterior angles of four pentagons.

  • 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, 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 from across the grades, with emphasis on the following Domain.Cluster:

      • 7-G: Solve real-life and mathematical problems involving angle measure, area, surface area, and volume.
  • Lesson Structure
    • The lesson unit is structured in the following way:

      • Before the lesson, students work individually to complete an assessment task designed to reveal their current understandings and difficulties.
      • During the lesson,
        • Students work in pairs or threes on a collaborative discussion task.
        • They are shown four methods for solving an angle problem and work together to complete the problem using each of the methods in turn.
        • As they do, they justify their work to each other.
        • Working in the same small groups, students analyze sample solutions to the same angle problem produced by students from another class.
        • They identify errors and follow reasoning in the sample solutions and compare methods.
        • There is then a whole-class discussion in which students explain the reasoning in the sample solutions and compare the methods.
      • After the lesson, students return to their original task, and try to improve their own responses.
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