8th Grade Math Lesson

Rational or Irrational? Classifying Numbers and Solving Root Equations

Shared by A STEM Educator

Grade 8 honorsBTC Style / Thinking Classrooms50 min

Learning Objective

Students will classify real numbers as rational or irrational using precise definitions, convert repeating decimals to fractions, and solve equations of the form $x^{2} = k$ and $x^{3} = k$ .

Lesson Overview

Students progress from classifying familiar numbers as rational or irrational, to converting repeating decimals to fractions, to solving square and cube root equations — changing only one variable of complexity at a time.

Materials

Vertical whiteboards or chart paper
Dry-erase markers (multiple colors)
Pencils and paper
Basic calculator (phone)

Scaffolded Task Progression

1Task 1

Sort these numbers into two groups — Rational and Irrational — on your whiteboard. Be ready to defend every placement.

\frac{3}{4}, 0.75, 9, 2, - 5, π

For each number you call rational, write it in the form

\frac{a}{b}

2Task 2

Same task — one variable changed. Now sort these numbers:

4, 5, 0. \overline{6}, 0.6060060006 \dots, \frac{- 7}{3}, 1.25

For each rational number, write it as

\frac{a}{b}

. For each irrational, explain in one sentence why it cannot be a fraction.

Look at the number line below. Place

5

as precisely as you can.

[ Interactive graph / diagram, available in the full lesson ]

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