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Unit 2: Operations and Algebraic Thinking: The Relationship Between Multiplication and Division

In this unit, students will:
• begin to understand the concepts of multiplication and division
• learn the basic facts of multiplication and their related division facts
• apply properties of operations (commutative, associative, and distributive) as strategies to multiply and divide
• understand division as an unknown-factor problem. For example, find 32 ÷ 8 by finding the number that makes 32 when multiplied by 8.
• fluently multiply and divide within 100, using strategies such as the patterns and relationships between multiplication and division
• understand multiplication and division as inverse operations
• solve problems and explain their processes of solving division problems that can also be represented as unknown factor multiplication problems.
• represent and interpret data

Standards:

Represent and solve problems involving multiplication and division.

MGSE3.OA.1 Interpret products of whole numbers, e.g., interpret 5 × 7 as the total number of objects in 5 groups of 7 objects each. For example, describe a context in which a total number of objects can be expressed as 5 x 7.

MGSE3.OA.2 Interpret whole number quotients of whole numbers, e.g., interpret 56 ÷ 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares (How many in each group?), or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each (How many groups can you make?). For example, describe a context in which a number of shares or a number of groups can be expressed as 56 ÷ 8.

MGSE3.OA.3 Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem.3

MGSE3.OA.4 Determine the unknown whole number in a multiplication or division equation relating three whole numbers using the inverse relationship of multiplication and division. For example, determine the unknown number

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