Additional Materials

Content Standard Strand

MATH: Algebra/Expressions & Equations

Materials Required

Estimated Time Needed

(Times are approximate and will depend on the needs of the students.)

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Optimization Problems: Boomerangs
  • Introduction: Mathematical Goals
    • This lesson unit is intended to help you assess how well students are able to:

      1. Interpret a situation, and represent the constraints and variables mathematically.
      2. Select appropriate mathematical methods to use.
      3. Explore the effects of systematically varying the constraints.
      4. Interpret and evaluate the data generated, and identify the optimum case, checking it for confirmation.
      5. Communicate their reasoning clearly.
  • Formative Assessment Task
    • A proposition is given to students in which Phil and Cath are going to make and sell boomerangs for a school event. The money they raise will go to charity. The premise is posed that they want to make as much money for charity as possible. Given the cost and time associated with making each style of boomerang, along with the selling price for each, students are asked to decide how many small and large boomerangs Phil and Cath should make. Then students are asked to calculate how much money will be made by selling the boomerangs?

  • 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.
      2. Reason abstractly and quantitatively.
      3. Construct viable arguments and critique the reasoning of others.
      4. Model with mathematics.

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

      • A-CED: Create equations that describe numbers or relationships.
      • A-REI: Solve equations and inequalities in one variable.
      • A-REI: Solve systems of equations.
  • Lesson Structure
    • This lesson is designed to help students develop strategies for solving optimization problems. Such problems typically involve scenarios where limited resources must be used to greatest effect, as in, for example, the location of time and materials to maximize profit.

      • Before the formative assessment lesson, students attempt the assessment task individually. The teacher then reviews their work and formulates questions for students to answer in order to improve their solutions.
      • During the lesson,
        • Students work alone answering the teacher’s questions about the Boomerang assessment task.
        • Students are then grouped and engage in a collaborative discussion of the same task.
        • In the same small groups, students are given sample solutions to comment on and evaluate.
        • In a whole-class discussion, students explain and compare the alternative solution strategies they have seen and used.
      • After the lesson, students revise their individual solutions and comment on what they have learned.
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