3rd Grade Multiplication Properties Worksheet: Zero, Identity, Commutative

We worked out every equation of page one again, and each answer of the key is right. One name was wrong, though: the key said “identify property”, so we changed it to identity property, the word your child will meet in class. We also fixed a misspelled choice, which now reads “commutative property”. The times sign is now a small x in every equation.

In part two, item ii takes away (11 x 2) from (12 x 2) and gets 2 x (12 – 11). This shows the distributive property with a subtraction, which may surprise your child at first.

Ask the same question before each tick: what does this equation do? If one factor is 0, the answer is 0, and that is the zero property. When you multiply by 1, the number stays the same, so that is the identity property. If only the order of the factors changes, as in 6 x 7 = 7 x 6, it is the commutative property. Finally, a factor shared with each number inside the parentheses shows the distributive property.

Part one gives three choices, so your child can rule out the wrong ones first. Part two has no choices, which makes it a real check that the names are known.

An array of objects makes each property easy to see. Lay out 3 rows of 4 coins, then turn the tray a quarter turn: there are now 4 rows of 3, and the total stays 12. Next, ask how many coins are in 5 rows of 0, and laugh together at the empty table. Afterwards, let your child invent one equation for each property, such as 9 x 1 = 9. However, keep the game short and stop while it is still fun.