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Calculating Volumes of Compound Objects
  • Introduction: Mathematical Goals
    • This lesson unit is intended to help you assess how well students solve problems involving measurement, and in particular, to identify and help students who have the following difficulties:

      1. Computing measurements using formulas.
      2. Decomposing compound shapes into simpler ones.
      3. Using right triangles and their properties to solve real-world problems.
  • Formative Assessment Task: Glasses
    • Students solve problems in which they calculate the volume of liquid that would fill the bowls of glasses. They find the volumes of compound shapes by decomposing them into simpler ones and applying formulas.

  • 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. 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-SRT: Define trigonometric ratios and solve problems involving right triangles.
      • G-GMD: Explain volume formulas, and use them to solve problems.
  • Lesson Structure
    • The unit is structured in the following way:

      • Before the lesson, students attempt the task individually. You then review their work and formulate questions for students to answer in order for them to improve their work.
      • During the lesson,
        • At the start of the lesson, students work individually to answer the questions.
        • Next, students work in small groups on the same task to produce a better collective solution than those they produced individually. Throughout their work, they justify and explain their decisions to each other.
        • In the same small groups, students critique some student responses to the assessment task, Glasses, provided in the resource, Sample Responses to Discuss. They correct errors in those responses.
        • In a whole-class discussion, students discuss their own solutions and explain how to correct the common misconceptions seen in the Sample Responses to Discuss.
      • After the lesson, students work together on their own again to improve their individual solutions.
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