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Defining Regions Using Inequalities
  • Introduction: Mathematical Goals
    • This lesson unit is intended to help you assess how well students are able to use linear inequalities to create a set of solutions. In particular, the lesson will help you identify and assist students who have difficulties in:

      1. Representing a constraint by shading the correct side of the inequality line.
      2. Understanding how combining inequalities affects a solution space.
  • Formative Assessment Task : Combining Inequalities
    • Students are presented a scenario in which they must use a series of mathematical clues to help them find the location of treasure on a graph.

  • 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.

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

      • A-REI: Represent and solve equations and inequalities graphically.
  • Lesson Structure
    • This lesson unit is structured in the following way:

      • Before the lesson, students work individually on an assessment task that is designed to reveal their current levels of understanding and difficulties. You then review their work and create questions for students to answer in order to improve their solutions.
      • During the lesson,
        • Whole-class introduction
        • Then students work collaboratively, in pairs, on a game.
          • One student decides on the position of a "target point" on a coordinate grid and gives clues in the form of algebraic inequalities (e.g. 3y + 2x ≤ 12).
          • The other student uses these clues to find the location of the target point.
          • There is a strategic element to the game: what are the best clues to give so that the target may be found quickly?
        • In a whole-class discussion, students review the main math concepts of the lesson.
      • After the lesson, students return to their original assessment tasks, and try to improve their own responses.
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