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Evaluating Statements about Length and Area
  • Introduction: Mathematical Goals
    • This lesson unit is intended to help you assess how well students can:

      1. Understand the concepts of length and area.
      2. Use the concept of area in proving why two areas are or are not equal.
      3. Construct their own examples and counterexamples to help justify or refute conjectures.
  • Formative Assessment Task: Shape Statements
    • Students are presented three statements about area and shapes and are asked to decide if the statements are always, sometimes, or never 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. Reason abstractly and quantitatively.
      2. Construct viable arguments and critique the reasoning of others.

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

      • G-CO: Prove geometric theorems.
  • Lesson Structure
    • Students will need to be familiar with the concepts of area and perimeter. This activity will help consolidate understanding, and overcome common misconceptions such as the notion that perimeter and area are in some way related.

      The unit is structured in the following way:

      • Before the lesson, students work individually on an assessment task designed to reveal their current understandings and difficulties. You then review their work, and create questions for the students to answer in order to improve their solutions.
      • During the lesson,
        • The whole-class introduction models the level of reasoning that is required in the main part of the lesson. During this introduction, students critique examples of other students' work.
        • Students are grouped into pairs and given some mathematical statements.
        • Each pair chooses one of the statements, and using their own examples, counterexamples, and arguments decides if the statement is true or false.
        • They create posters showing their collaborative reasoning.
        • In a whole-class discussion, students explain and compare the various solution strategies they have used.
      • After the lesson, students return to their original assessment tasks, and try to improve their own responses.
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