Mrs.D Math · 8th Grade

REAL
DEAL

The Number System
📊 Rational Numbers
🌀 Irrational Numbers
🔢 Integers
🍿 π = 3.14159...
🌀 √2 = irrational
🎯 √25 = 5
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📚 Classifying Real Numbers

The Real Number Family — Sets Inside Sets

Every set fits inside the next one, like nesting dolls. A number belongs to its own set and every set around it.

1
Natural — the counting numbers
1, 2, 3, 4, ...
2
Whole — Natural numbers + zero
0, 1, 2, 3, ...
3
Integers — Whole numbers + negatives
..., −2, −1, 0, 1, 2, ...
4
Rational — ANY number that can be written as a fraction of two integers. Includes terminating decimals and repeating decimals.
1/2, −3, 0.75, 0.333..., √25
5
Irrational — decimals that go on forever with NO repeating pattern. They can NEVER be a fraction.
π, √2, √10, 0.121221222...
🌟
Real Numbers — Rational + Irrational together. Every number in this game is Real!

Square Root Secret 🔑

Your calculator is your friend here — type the square root in and look at the answer!

✓
Perfect square inside? → Rational!
√25 = 5    √81 = 9    √144 = 12
✗
NOT a perfect square? → Irrational! The decimal never ends and never repeats.
√2 = 1.41421356...    √10 = 3.16227766...
⚠
Watch the traps: 22/7 is close to π but it’s a fraction — Rational! And 3.14 stops — Rational! Only the real π is Irrational.

How to Play

📂
Classify It — See a number, pick the MOST specific set it belongs to.
🔎
Find It — Given a set, hunt down the number that belongs to it.
🌀
Mixed — Both types together for the ultimate challenge!
🖩
Calculator allowed! Use it to check square roots and decimals.
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