Grade five students should explore and apply the properties of addition and multiplication as strategies for solving addition, subtraction, multiplication, and division problems using a variety of representations (e.g., manipulatives, diagrams, and symbols).
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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: 8 x 7 = 8 (5 + 2), (8 x 5) + (8 x 2), 40 + 16 all equal 56; 5 x 23 = 5 (20 + 3), (5 x 20) + (5 x 3), 100 + 15 all equal 115.
Investigate and describe the associative property for multiplication as (3 x 2) x 4 = 3 x (2 x 4).
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 x (3 x 5) = (6 x 3) x 5).
The identity property of addition states that if zero is added to a given number, the sum is the same as the given number. The identity property of multiplication states that if a given number is multiplied by one, the product is the same as the given number.