As students work to solve multiplication and division problems, they naturally tend to utilize strategies that involve place value understanding and properties of the operations. Applying the commutative property of multiplication (e.g., 5 x 8 = 8 x 5) reduces in half the number of multiplication facts that students must learn. The distributive property of multiplication allows students to find the answer to a problem such as 6 x 7 by decomposing 7 into 3 and 4 (e.g., 6 x 7= 6 x (3 + 4)) allowing them to think about (6 x 3) + (6 x 4) = 18 + 24 = 42.

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### Related standards

- This standard is part of: 3.4

#### Similar standards in other grades

The associative property of addition states that the sum stays the same when the grouping of addends is changed (e.g., 15 + (35 + 16) = (15 + 35) + 16). The associative property of multiplication states that the product stays the same when the grouping of factors is changed [e.g., 16 × (40 × 5) = (16 × 40) × 5].

In order to develop and use strategies to learn the multiplication facts through the twelves table, students should use concrete materials, a hundreds chart, and mental mathematics. Strategies to learn the multiplication facts include an understanding of multiples, properties of zero and one as factors, commutative property, and related facts. Investigating arithmetic operations with whole numbers helps students learn about the different properties of arithmetic relationships. These relationships remain true regardless of the whole numbers.

The associative property of addition states that the sum stays the same when the grouping of addends is changed (e.g., 15 + (35 + 16) = (15 + 35) + 16).

The distributive property states that multiplying a sum by a number gives the same result as multiplying each addend by the number and then adding the products.

The associative property of multiplication states that the product stays the same when the grouping of factors is changed (e.g., 6 × (3 × 5) = (6 × 3) × 5).