07_Hierarchical_Terms

Home > Key Terms & Concepts

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Key Terms & Concepts

• Lesson Unit
  • Evaluating Statements about Rational and Irrational Numbers
  • Formative Assessment Lesson
  • Mathematical Goals
    • Assess student reasoning
    • Identify student difficulties
    • Assist students in reasoning
    • Finding examples (rational and irrational)
    • Reasoning with properties of numbers
• Common Core State Standards
  • Standards for Mathematical Content
    • N-RN: Use properties of rational and irrational numbers
  • Standards for Mathematical Practice
    • 1. Make sense of problems and persevere
    • 2. Reason abstractly and quantitatively
    • 3. Construct viable arguments and critique reasoning
    • 5. Use appropriate tools strategically
    • 6. Attend to precision
    • 7. Look for and make use of structure
    • 8. Look for and express regularity in repeated reasoning
• Lesson Structure
  • Before the lesson (Individual Assessment)
    • Assessment task: Rational or Irrational?
    • Reviewing student work (Teacher)
    • Formulate questions for improvement (Teacher)
  • During the lesson (Collaborative Work & Discussion)
    • Collaborative small-group work: Always, Sometimes or Never True?
    • Whole-class discussion
  • Follow-up lesson (Individual Improvement)
    • Improve individual solutions to initial task
    • Second, similar task
• Key Concepts and Tasks
  • Rational Numbers
    • Definition
    • Examples
    • Decimal representations (terminating/repeating)
    • Fraction of integers
  • Irrational Numbers
    • Definition
    • Examples
    • Decimal representations (non-repeating non-terminating)
    • Cannot be written as fraction of integers
  • Evaluating Statements
    • Always True
    • Sometimes True
    • Never True
  • Reasoning and Justification
    • Finding examples
    • Constructing arguments
    • Critiquing reasoning
    • Conjectures
    • Proof (concept of)
    • Range of examples (integers, fractions, decimals, negative, radicals, pi)
  • Common Issues for Students
    • Distinguishing rational/irrational
    • Not attempting questions
    • Not providing examples
    • Limited range of examples
    • Empirical reasoning (false generalizations)
  • Application Contexts
    • Rectangle perimeter and area
    • Hypotenuse of a right triangle
• Materials Required
  • Mini-whiteboard, pen, eraser
  • Rational or Irrational? task sheet
  • Rational or Irrational? (revisited) task sheet
  • Always, Sometimes or Never True task sheet
  • Poster Headings
  • Large sheet of paper
  • Scissors
  • Glue stick
  • Rational and Irrational Numbers hint sheet
  • Extension Task
  • Calculators
  • Projectable resource
• Time Needed
  • 15 minutes (Before Lesson)
  • 60 minutes (Main Lesson)
  • 20 minutes (Follow-up Lesson)

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See also: 03_Study_Guide