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Mathematics · Grade 8

Rational and Irrational Numbers

Learners use long division to see why every fraction becomes a decimal that stops or repeats, and then run the process backwards to turn repeating decimals into fractions. They solve x^2^ = p and x^3^ = p with square and cube roots, meet numbers such as √2 and π that are not fractions at all, and squeeze those irrational numbers between rational ones to place and compare them on the number line.

  • 4 lessons
  • About 90 minutes
  • Rational and irrational numbers check: 10 questions
  • Ways to answer: fill in the blanks, choose an answer, type a fraction, match pairs, type a number and place on a number line
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What learners will discover

  • Use long division to write fractions as decimals and explain why the decimal form of every rational number terminates or eventually repeats.
  • Rewrite a repeating decimal as a fraction by multiplying by a power of ten and subtracting (for example 100x − x).
  • Evaluate square roots of perfect squares and cube roots of perfect cubes, and solve equations of the form x^2^ = p and x^3^ = p.
  • Classify numbers as rational or irrational and approximate irrational numbers such as √2, √10 and π to locate and compare them on a number line.

Lessons

  1. Fractions as decimals: stop or repeat 8 steps4 practiceabout 22 min
  2. Repeating decimals as fractions 9 steps5 practiceabout 22 min
  3. Square roots and cube roots 9 steps5 practiceabout 22 min
  4. Irrational numbers: approximate, locate, compare 9 steps5 practiceabout 24 min
  5. Rational and irrational numbers check 10 questions at the end

Keep exploring

Games to practice with

  • Number-Line HopHelp the frog hop to the right number — from counting to negative fractions.
  • Algebra BalanceKeep the scale level and the equation true, step by step.
  • Function FactoryFeed the machine, crack its rule and predict what comes out.

More 8th grade math

Guide for grown-ups