3rd Grade Distributive Property Missing Numbers Worksheet: 3 Puzzles

The answers are 20, 26 and 1. In a, 40 = 20 + 20, so 3 × 40 = (3 × 20) + (3 × 20). In b, both products share the factor 4, so 4 × 2 + 4 × 24 = 26 × 4, because 2 + 24 = 26. In c, the shared factor is 12. Since 2 − 1 = 1, the missing factor is 1.

The distributive property is a third grade idea, but it is often new. So check each answer by computing both sides. For example, 3 × 40 = 120, and 60 + 60 = 120 too. Item c also shows that the rule works with subtraction, not only with addition.

For item a, draw 3 rows of 40 dots, or just sketch 3 long bars. Then split each bar into two parts of 20, so that your child sees that the two parts are the same size and the blank is 20.

Page two has small slips. Item c says "the common digit", but 12 is a common factor, not a digit. Item a mixes a capital X with a small x for times, so tell your child that both mean ×. Because there are only three items, you can add one more, such as 5 × 12 = (5 × 10) + (5 × __).

Set out 3 plates with 12 grapes each. Count the grapes by tens first and then by twos: 3 × 10 and 3 × 2. Then add the two results, which gives 36. This is the same split as on the page. In the end, check the three blanks against the answer key on page two.