Smart Starters · Ages 8 to 10
Commutative Property
Decide whether each reordered multiplication statement is true. Five levels of printable practice with answer keys.
The learning journey
Every activity is one step. Here is where this one fits.
- PlayLearn the idea in a game
- Practise(you are here)Lock it in on paper
- ReviewCome back and keep it sharp
- MasterTake on a harder challenge
- AchieveEarn a certificate
About Commutative Property
The commutative property is a statement about how multiplication behaves, not about particular numbers — and that distinction is the first genuinely algebraic idea most children meet. This worksheet is built to test the property rather than the arithmetic. The false statements are deliberately near misses: the reordered product stated one or two out, so a child cannot pass by spotting an obviously silly number and has to actually check. From the middle levels a second and harder family appears — the same reordering applied to subtraction and division, where it does not hold. That family is the point of the whole worksheet, because a child who believes reordering always works has learned a rule that will fail them badly later. The True and False answers are balanced by construction, never left to chance: exactly half of each on every page, shuffled, with no run longer than three, so neither ticking one column nor spotting an alternating pattern will get anyone through. Factor sizes grow across the levels. Eight statements per page with tick boxes. Each level prints cleanly in black and white and downloads with its own separate answer key. Its on-screen twin is Commutative Flip Twins.
Common questions
- Why are subtraction and division statements included?
- Because reordering does not work for them. A child who believes it always works has learned a rule that will fail them later.
- Is the True/False split balanced?
- Yes, by construction — exactly half of each on every page, shuffled, with no run longer than three.
- Are the false statements obviously wrong?
- No. They are near misses, stated one or two out, so the statement has to be genuinely checked.
- Which game goes with this worksheet?
- Commutative Flip Twins, which pairs facts like 3 × 8 and 8 × 3 on screen.
A hand for grown-ups
- Before you start
- Think of it as groups: "4 × 3" is four groups of three. Have something you can arrange into equal groups.
- While they work
- Skip-counting (3, 6, 9, 12…) is a solid way in before facts are memorised. Let them use it — speed comes later.
- Afterwards
- Spot arrays in real life together — eggs in a box, tiles on a floor. Rows-and-columns is multiplication you can see.
- Watch out for
- Treating it as harder addition and losing track. Grouping objects physically keeps the "equal groups" idea in view.
- Away from the screen
- Lay out objects in rows and columns and count them two ways. Cooking with doubled recipes is multiplication too.
Where to go next
Chosen by the skills this activity practises.