GRADE 3 · ALBERTAOUTCOME AB-MAT3-N3
L3 · Multiplying by 0 and by 1; the commutative property
Learning goal
“I can multiply by 1 and by 0, and I can explain what each does. I know the factors can swap places without changing the product - and I can use that to make hard facts easy.”
Factor — a number being multiplied. The two factors in 3 x 7 are 3 and 7. (Pre-taught in L1; revisited because this lesson plays with them.)
Commutative property — swapping the order of the factors does not change the product: 3 x 7 and 7 x 3 are both 21.
Identity property (x1) — multiplying a number by 1 gives the number itself: one group of it, or it in one group.
Zero property (x0) — any number times 0 is 0: zero groups hold nothing, and groups of zero hold nothing.
Worked example
Find 7 x 1 and 7 x 0. 7 x 1: seven groups of 1 -> 1 + 1 + 1 + 1 + 1 + 1 + 1 = 7. Or one group of 7 -> 7. Either way, multiplying by 1 returns the number itself. 7 x 0: seven groups of 0 -> 0 + 0 + 0 + 0 + 0 + 0 + 0 = 0. Empty groups hold nothing. And 0 x 7: zero groups - there is nothing to count at all -> 0.
Check yourself — explain it
7 x 0 is 0 and not 7 because...
Paired problem — example still visible
9 x 1 = 9 and 9 x 0 = 0 (say why, in the group language)
Faded completion — last step is yours
"6 x 0 = ___ and 6 x 1 = ___" -> 0; 6
Ready to practise?
10 scored questions with a 3-rung hint ladder. Mastery needs 8/10 plus both gate questions.