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Increasing and Decreasing Quantities by a Percent
  • Introduction: Mathematical Goals
    • This lesson unit is intended to help you assess how well students are able to interpret percent increase and decrease, and in particular, to identify and help students who have the following difficulties:

      1. Translating between percents, decimals, and fractions.
      2. Representing percent increase and decrease as multiplication.
      3. Recognizing the relationship between increases and decreases.
  • Formative Assessment Task: Percent Changes
    • Students are presented a series of scenarios in which they determine the keys they would press on a calculator to determine percentage increase and decrease.

  • Common Core State Standards
    • Common Core State Standards for Mathematical Practice 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.
      1. Look and make use of structure.

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

      • 7.RP: Use proportional relationships to solve multistep ratio and percent problems.
      • 7.NS: Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers.
      • 7.NS: Solve real-world and mathematical problems involving the four operations with rational numbers.
  • 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 understandings and difficulties. You then review their work and create questions for students to answer in order to improve their solutions.
      • Students work in small groups on collaborative discussion tasks to organize percent, decimal, and fraction cards. As they do this, they interpret the cards' meanings and begin to link them together. They also try to find relationships between percent changes. Throughout their work, students justify and explain their decisions to their peers.
      • Students return to their original assessment tasks and try to improve their own responses.
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