## 2.4 **Relationships Between Multiplication and Division**

**Represent and solve problems involving multiplication and division.**

**Operations and Algebraic Thinking 3.OA**

3.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, or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each.

*For example, describe a context in which a number of shares or a number of groups can be expressed as 56 ÷ 8.*

3.OA.4 Determine the unknown whole number in a multiplication or division equation relating three whole numbers.

*For example, determine the unknown number that makes the equation true in each of the equations 8 × ? = 48, 5 =*

*÷ 3, 6 × 6 = ?.*

**Understand properties of multiplication and the relationship between multiplication and division.**

3.OA.5 Apply properties of operations as strategies to multiply and divide.2

*Examples: If 6 × 4 = 24 is known, then 4 × 6 = 24 is also known. (Commutative property of multiplication.) 3 × 5 × 2 can be found by 3 × 5 = 15, then 15 × 2 = 30, or by 5 × 2 = 10, then 3 × 10 = 30. (Associative property of multiplication.) Knowing that 8 × 5 = 40 and 8 × 2 = 16, one can find 8 × 7 as 8 × (5 + 2) = (8 × 5) + (8 × 2) = 40 + 16 = 56. (Distributive property.)*

2 Students need not use formal terms for these properties.

3.OA.6 Understand division as an unknown-factor problem

*. For example, find 32 ÷ 8 by finding the number that makes 32 when multiplied by 8.*

• How do you solve a division problem using whole numbers without remainders?

• When given two numbers, how do you show a fact family using multiplication and division?

• How does a fact family help you solve a division problem?

**Essential questions**• How do you solve a division problem using whole numbers without remainders?

• When given two numbers, how do you show a fact family using multiplication and division?

• How does a fact family help you solve a division problem?

*• How can you solve a multiplication problem with an unknown number?*

• How can you solve a division problem with an unknown factor?

• How can you solve a division problem with an unknown factor?