How can word problems be solved using multiplication and division?

In this unit, students will learn how to use multiplication and division strategies to solve problems. Students will work to become more fluent with multiplication and division facts through 10. Students will also learn to relate multiplication and division.

Students will build conceptual understanding of the properties of multiplication. They will learn to apply multiplication to real-world situations. Students will develop problem-solving skills and algebraic thinking.

Students will build conceptual understanding of the inverse relationship of multiplication and division. Students will apply division to real-world situations.

Print Version3.OA.1 Interpret products of whole numbers, e.g., interpret 5 x 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.

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.

3.0A.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.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 X ? = 48, 5 = ÷ 3, 6 X 6 = ?.

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.)

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.

3.OA.7 Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 x 5 = 40, one knows 40 ÷ 5 = 8) or properties of operations. By the end of Grade 3, know from memory all products of two one-digit numbers.

3.OA.8 Solve two-step word problems using the four operations. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. 3 3 This standard is limited to problems posed with whole numbers and having whole-number answers; student should know how to perform operations in the conventional order when there are no parentheses to specify a particular order (Order of Operations).

3.OA.9 Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations. For example, observe that 4 times a number is always even, and explain why 4 times a number can be decomposed into two equal addends.

3.NBT.3 Multiply one-digit whole numbers by multiples of 10 in the range 10-90 (e.g., 9 x 80, 5 x 60) using strategies based on place value and properties of operations.

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**Priority Learning Targets:**

**3.OA.1 I can interpret products of whole numbers. This means I can model multiplication facts by forming groups to represent the factors.**

**3.OA.2 I can interpret quotients of whole numbers. This means I can model division facts by separating objects into equal shares.**

**3.OA. 3 I can represent and solve multiplication/division word problems by using equations and drawings. (within 100)**

**3.OA. 3 & 3.OA. 4 I can determine the unknown whole number in a multiplication/division problem. (missing value)**

**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.**

**3.OA.7 I can fluently recall multiplication and division facts. This means I know from memory all products and quotients of two one-digit numbers.**

**3.OA.9 I can identify/explain arithmetic patterns in multiplication tables.**

*Supporting Learning Targets:*

*3.OA.5 I can apply commutative property to solve multiplication problems. This means I can apply turn-around facts.*

*3.OA.5 I can apply associative property to solve multiplication problems. This means when multiplying three numbers, I can choose two numbers to easily multiply then multiply that product by the remaining number.*

*3.OA. 5 I can apply distributive property to solve multiplication problems. This means I can change my problem to make it easier to multiply.*

*3.OA.8 I can solve two-step word problems using multiplication / division.*

*3.OA.8 I can use mental estimation strategies to see if my answer is reasonable.*

*3.NBT.3 I can use strategies to multiply one-digit whole numbers by multiples of 10. (10 - 90)*

**Thinking Strategy Highlights:**

Determining Importance

Visualizing Math

Mathmatical Practice #2 - I can think about numbers in many ways.

Print Versionarray, equal groups, partitions, factor, multiply, product, equation, repeated addition, divide, dividend, divisor, quotient, fact family, groups of, properties (associative, distributive, commutative, zero, identity), area models, patterns, sets, missing value, unknown, interpret, multiplication, division, row & column

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