The Number Family

~ every number has a home ~

Alberta Grade 8 Math
Organizing Idea Number — Number sense is developed through understanding the ways numbers describe the world.
Guiding Question How can the density of the number line contribute to a sense of number?
Learning Outcome Students interpret rational and irrational numbers.
This lesson covers: classifying real numbers into their sets (natural, integer, rational, irrational); understanding that natural ⊂ integer ⊂ rational ⊂ real, with irrational numbers filling the gaps between rationals.

The Number Family Tree

Real Numbers Irrational √2 π √5 √3 non-terminating, non-repeating cannot be written as a/b Rational ½ −¾ 0.7 0.3̅ a/b (b ≠ 0) Integers −10 −3 −1 0 whole numbers Natural 1 2 3 100 1 000 000 positive whole numbers Natural ⊂ Integer ⊂ Rational ⊂ Real

classified numbers will appear here as you play ↓

Round 1 of 3
Integers & Simple Fractions
Place each number in its most specific set.

Why these categories?

Natural numbers (1, 2, 3…) are the counting numbers — the ones humans used first. Integers extend them to include zero and negatives. Rational numbers add any number that can be written as a⁄b where b ≠ 0 — so every fraction and every terminating or repeating decimal is rational.

Irrational numbers cannot be written as a fraction. Their decimal expansions never terminate and never repeat — they fill in the “gaps” between rationals on the number line. Together, rationals and irrationals make up the Real numbers.

Watch out for traps: √9 = 3 (Natural!), 22⁄7 is Rational (it’s just a fraction), and 0.333… = ⅓ (Rational, because it repeats). Only numbers that cannot be written as a⁄b are irrational.
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