Today's lesson · 1 September 2026
Rational numbers, exponents and roots
Classifying rational and irrational numbers, the laws of exponents, and square and cube roots
Today's lesson is Rational numbers, exponents and roots, a Grade 8 (ages 13 to 14) Math unit. Rotates every day, so check back tomorrow for a different unit.
Not every number can be written as a fraction, and that is a big deal
Every whole number, fraction and repeating decimal you have ever used can be written as one whole number divided by another: a rational number. But some numbers, like the exact diagonal of a 1-by-1 square, can never be written that way, no matter how hard you try. Ancient mathematicians found this so unsettling that (according to legend) the discovery was kept secret. Today it just has a name: irrational.
What students will be able to do
Students will classify numbers as rational or irrational, convert a repeating decimal to an exact fraction, apply the properties of integer exponents to simplify numerical expressions, and evaluate square roots and cube roots of small perfect squares and cubes.
Curriculum anchor
Teach the whole lesson
This is a short preview. Open the full teaching unit for the step-by-step teaching sequence, worked examples, misconceptions to watch for, guided practice, differentiation and an exit ticket, ready to deliver in class today.
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