Standard

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.

Student language:

• "I can understand division by thinking about how one group can be split into smaller equal groups."

Explanation

About the Math, Learning Targets, and Rigor

This standard focuses on two types of division:

• Partitive Division
  • The number of groups is known, and you are trying to find the number in each group.
  • “How many in each group?”
  • Example: There are 12 cookies on the counter. If you are sharing the cookies equally among three bags, how many cookies will go in each bag?
• Quotative Division (known as repeated subtraction or measurement)
  • The number in each group is known, and you are trying to find the number of groups.
  • “How many groups can you make?”
  • Example: There are 12 cookies on the counter. If you put 3 cookies in each bag, how many bags will you fill?

To develop this understanding, students interpret a problem situation requiring division using pictures, objects, words, numbers, and equations. Given a division expression (e.g., 24 ÷ 6) students interpret the expression in contexts that require both interpretations of division.

Sets of counters, number lines to skip count and relate to division, and arrays/area models will aid students in solving problems involving division. Students should write an equation to represent their model.

Resources

Videos

• Instructional Video (1:05 - 4:44)
• Khan Academy
  • scroll to 3.OA.2, click on a skill, watch videos on left side in each skill
• Learn Zillion
  • Videos
• Virtual Nerd

EngageNY Lessons

Extra Practice

• North Carolina Tasks
• Illustrative Math Tasks
• Howard County Tasks
  • Click on 3rd grade at bottom, then 3.OA.2
• Common Core Sheets

Released Assessment Questions

PARCC

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.

• Tasks involve interpreting rather than calculating quotients in terms of equal groups, arrays, area, and/or measurement quantities. (See CCSSM, Table 2, Common multiplication and division situations, p. 89.). For example, “35 books are placed equally on 7 shelves” can be represented by the expression 35 ÷ 7 rather than “Marcie has 35 books. She placed the same number on each of 7 shelves. How many books did she place on each shelf?”
• Tasks do not require students to interpret quotients in terms of repeated subtraction, skipcounting, or jumps on the number line.
• The italicized example refers to describing a real-world context, but describing a context is not the only way to meet the standard. For example, another way to meet the standard would be to identify contexts in which a number of objects can be expressed as a specified quotient.
• Half the tasks require interpreting quotients as a number of objects in each share and half require interpreting quotients as a number of equal shares.

Performance Indicators: 3.OA.2

Level 5: Exceeds Expectations

• Understands and interprets products and quotients of whole numbers.
• Determines the unknown whole number in a multiplication or division problem by relating multiplication and division.
• Both factors are greater than 5 and less than or equal 10.
• Represents a multiplication or division situation as an equation.
• Accurately multiplies and divides within 100, using strategies relating multiplication and division or properties of operations

Level 4: Meets Expectations

• Interprets products and quotients of whole numbers.
• Determines the unknown whole number in a multiplication or division problem by relating multiplication and division. One factor is greater than or equal to 5.
• Accurately multiplies and divides within 100, using strategies relating multiplication and division or properties of operations.