Properties of Operations
📋 What it is
Commutative (order), associative (grouping), distributive (sharing) — properties that make maths flexible.
🗣️ Coach says
These "properties" are permissions that make arithmetic easier. Commutative: order doesn't matter for + and × (3 + 5 = 5 + 3). Associative: grouping doesn't matter. Distributive: share a multiply across a sum. They let you rearrange for speed.
🧠 Memory hook
Commutative = order free (+ and ×). Associative = grouping free. Distributive = share the multiply.
😂 Giggle
What did the calculator say to the student?
"You can count on me!"
😲 Whoa!
Mental-maths champions win by USING these properties — rearranging a sum into an easier order in a split second.
✅ Quick check: Which property says 3 + 5 = 5 + 3?
Say your answer out loud first — then reveal.
The commutative property of addition — order doesn't change the sum.
Commutativity means you can swap the order of the numbers.
🪄 Trick question: Does the commutative property work for subtraction? Is 7 − 3 the same as 3 − 7?
Careful — think it through, then reveal.
No — 7 − 3 = 4 but 3 − 7 = −4; subtraction is not commutative.
Only addition and multiplication are commutative, not subtraction or division.
🧪 Try it! (2 minutes)
Compute 2 × 17 × 5 by reordering to (2 × 5) × 17 = 10 × 17 = 170. The order freedom made it easy.