# 3.OA.A.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.1

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TNCore Focus Standard

## Summary:

Once students have a more sophisticated understanding of multiplication and division, this skill asks them to apply that understanding when solving word problems. Students should feel comfortable modeling the components of such word problems through pictures and drawings. See table in the "understanding" section for all combinations required in this standard.

## Understanding the Standard:

• Like addition and subtraction, students need to be familiar with the vocabulary and clue words used in multiplication and division word problems in order to determine which operation is appropriate for use.
• In the table below, the measurement examples should be taught after the discrete examples.
 Unknown Product Group Size Unknown (“How many in each group?” Division) Number of Groups Unknown (“How many groups?” Division) 3 x 6 = ? 3 x ? = 18, and 18 ¸ 3 = ? ? x 6 = 18, and 18 ¸ 6 = ? Equal Groups There are 3 bags with 6 plums in each bag. How many plums are there in all? Measurement example: You need 3 lengths of string, each 6 inches long. How much string will you need altogether? If 18 plums are shared equally into 3 bags, then how many plums will be in each bag? Measurement example: you have 18 inches of string, which you will cut into 3 equal pieces. How long will each piece of string be? If 18 plums are to be packed 6 to a bag, then how many bags are needed? Measurement example: You have 18 inches of string, which you will cut into pieces that are 6 inches long. How many pieces of string will you have? Arrays, Area There are 3 rows of apples with 6 apples in each row. How many apples are there? Area example: What is the area of a 3 cm by 6 cm rectangle? If 18 apples are arranged into 3 equal rows, how many apples will be in each row? Area example: A rectangle has area 18 square centimeters. If one side is 3 cm long, how long is a side next to it? If 18 apples are arranged into equal rows of 6 apples, how many rows will there be? Area example: A rectangle has area 18 square centimeters. If one side is 6 cm long, how long is a side next to it? Compare A blue hat costs \$6. A red hat costs 3 times as much as the blue hat. How much does the red hat cost? Measurement example: A rubber band is 6 cm long. How long will the rubber band be when it is stretched to be 3 times as long? A red hat costs \$18 and that is three times as much as a blue hat costs. How much does a blue hat cost? Measurement example: A rubber band is stretched to be 18 cm long and that is 3 times as long as it was at first. How long was the rubber band at first? A red hat costs \$18 and a blue hat costs \$6. How many times as much does the red hat cost as the blue hat? Measurement example: A rubber band was 6 cm long at first. Now it is stretched to be 18 cm long. How many times as long is the rubber band now as it was at first? General a x b = ? a x ? = p, and p ¸ a = ? ? x b = p, and p ¸ b = ?

## Questions to Focus Instruction:

•  Are students able to determine when it is appropriate to multiply or divide in a word problem?
• Can students justify the reasonableness of their answer and use pictures or drawings?

## Skills:

Prior to: Students have had a variety of opportunities solving addition and subtraction word problems and are able to identify the terminology that is used to determine which operation to use. They are also able to fluently calculate multiplication and division problems. Go to 2.OA.A.1 to see previous skills in this progression.