Eighth graders learn to tell rational numbers (which can be written as fractions or repeating/terminating decimals) from irrational numbers (like π and √2, whose decimals go on forever without repeating).
Students will be able to…
Some numbers, like ½, are neat fractions. Others, like π, have decimals that never end and never repeat. How do we sort numbers into rational and irrational?
Project this and sort each number into rational (a fraction or repeating/ending decimal) or irrational (never-ending, non-repeating).
Tap any phase to open the teacher moves and student actions.
½ is a neat fraction; π goes on forever. How are they different?
Teacher models.
Class uses Rational or Irrational?
Students classify.
One number.
Aligned to the Common Core State Standards for Mathematics.
Know that numbers that are not rational are called irrational.
Use rational approximations of irrational numbers.
Know that √2 is irrational.
Reason about number types.
Preview the three formative checks. Tap “Sample answer” to see what mastery looks like — hide them before you print for students.
Have students approximate √20 to the nearest tenth and place it on a number line between two whole numbers. A printable number-sets sheet is in the Math library.
Tap a card to flip it, then rate whether you knew it. Built from this lesson’s vocabulary.
A quick self-check with instant feedback, drawn from this lesson’s key terms.
A print-and-go review sheet with a built-in answer key. Tap “Show answer key” to reveal answers, or print the clean version for students.