Standard

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 = ?

Student language:

• "I can find the missing number in a multiplication or division equation."

Explanation

About the Math, Learning Targets, and Rigor

This standard refers to Table 2 and equations for the different types of multiplication and division problem structures. The easiest problem structure includes Unknown Product (3 x 6 = ? or 18 ÷ 3 = 6). The more difficult problem structures include Group Size Unknown (3 x ? = 18 or 18 ÷ 3 = 6) or Number of Groups Unknown (? x 6 = 18, 18 ÷ 6 = 3).

The focus of 3.OA.4 goes beyond the traditional notion of fact families, by having students explore the inverse relationship of multiplication and division.

Students apply their understanding of the meaning of the equal sign as ”the same value as” to interpret an equation with an unknown. When given 4 x ? = 40, they might think:

• 4 groups of some number is the same as 40
• 4 times some number is the same as 40
• I know that 4 groups of 10 is 40 so the unknown number is 10
• The missing factor is 10 because 4 times 10 equals 40.

NOTE: Equations in the form of a x b = c and c = a x b should be used interchangeably, with the unknown in different positions.

Resources

Videos

• Instructional Video (4:45 - 13:50)
• Khan Academy
  • scroll to 3.OA.4, 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.4
• Common Core Sheets

Released Assessment Questions

PARCC

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 = ?.

• Tasks do not have a context.
• Only the answer is required.
• All products and related quotients are from the harder three quadrants of the times table (a × b where a > 5 and/or b > 5).

Performance Indicators: 3.OA.4

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.