Rational and Irrational Numbers

Standard: 8.NS.1 Know that real numbers are either rational or irrational. Understand informally that every number has a decimal expansion which is repeating, terminating, or is non-repeating and non-terminating.

Vocabulary for this standard: rational, irrational, repeating, terminating, non-repeating, non-terminating
EngageNY module link – This unit requires familiarity with right triangles and the Pythagorean Theorem – it is in Math 8 Module 7


Quick thoughts: My strategy here is to use mini-lessons and games reinforce vocabulary upfront, do some standalone exercises so that Module 7 is more about the cognition of the Pythagorean Theorem and Right Triangles than introducing rationality concurrently.


An integer is a whole number that is not a fraction.
A rational number is a number that can be written as a ratio where the numerator and denominator are integers.
An irrational number is a number that cannot be written as a ratio of two integers.
A repeating number is a number whose digits are repeated indefinitely.
A nonrepeating number is a number whose digits no not repeat. It can be terminating or non-terminating.
A terminating number is a number with a finite number of digits.
A non-terminating number is a number with an infinite number of digits, but that does not always repeat a sequence.
Vocabulary practice:
Standalone lessons:
  • Formative