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Grade 08 Mathematics - EC: M08.A-N.1.1.1

Grade 08 Mathematics - EC: M08.A-N.1.1.1

Continuum of Activities

Continuum of Activities

The list below represents a continuum of activities: resources categorized by Standard/Eligible Content that teachers may use to move students toward proficiency. Using LEA curriculum and available materials and resources, teachers can customize the activity statements/questions for classroom use.

This continuum of activities offers:

  • Instructional activities designed to be integrated into planned lessons
  • Questions/activities that grow in complexity
  • Opportunities for differentiation for each student’s level of performance

Grade Levels

8th Grade

Course, Subject

Mathematics

Activities

  1. Define rational numbers.

  2. Identify two examples of irrational numbers.
  1. Classify each of the numbers below as rational or irrational:

    1. -5.3232…
    2. 0.14527…
    3.       
    4. 4.252627


  2. Convert each of the following rational numbers into a decimal and organize them into the appropriate category: repeating or terminating decimals.

  1. Your friend, Brian, is having trouble classifying numbers as rational or irrational.  Write a letter to Brian explaining what they are and how he can identify each.  Use specific examples.

  2. Is it possible for a fraction to have a decimal equivalent that does not repeat and does not terminate?  Explain.

Answer Key/Rubric

  1. Rational numbers are real numbers that can be written in the form a/b, where .  In decimal form, rational numbers are either terminating or repeating.

  2. Examples include, but are not limited to:
  1. Answers are as follows:

    1. Rational – repeating decimal
    2. Rational – = 8
    3. Irrational – neither a terminating nor repeating decimal
    4. Rational – all fractions are rational       
    5. Rational – terminating decimal
    6. Irrational – 50 is not a perfect square
    7. Rational – repeating decimal
    8. Rational – all fractions are rational

  2. Answers are as follows:

    1. = 0.4; terminating
    2. = ; repeating
    3. = 0.125; terminating
    4. = ; repeating
    5. = ; repeating
    6. = 0.75; terminating
  1. Acceptable responses might include, but are not limited to:
  • Rational numbers are all numbers in the form a/b; where b does not equal 0
  • All fractions are rational
  • All repeating and terminating decimals are rational
  • The square root of any perfect square is rational
  • Irrational numbers, when written as a decimal, will not repeat or stop (terminate)
  • Specific examples must be included
  1. No, it is not possible.
    Acceptable explanations might include, but are not limited to:
  • All fractions are rational numbers
  • Rational numbers must be either terminating or repeating decimals
  • All decimals that do not terminate or repeat are irrational and cannot be written in the form a/b
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