Standard

Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 × 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.

Student language:

• "I can multiply and divide within 100 easily and quickly because I know how multiplication and division are related."

Explanation

About the Math, Learning Targets, and Rigor

This standard uses the word fluently, which means accuracy, efficiency (using a reasonable amount of steps and time), and flexibility (using strategies such as the distributive property).

“Know from memory” does not mean focusing only on timed tests and repetitive practice, but ample experiences working with manipulatives, pictures, arrays, word problems, and numbers to internalize the basic facts (up to 9 x 9).

Strategies students may use to attain fluency include:

• Multiplication by zeroes and ones
• Doubles (2s facts), Doubling twice (4s), Doubling three times (8s)
• Tens facts (relating to place value, 5 x 10 is 5 tens or 50)
• Five facts (half of tens)
• Skip counting (counting groups of __ and knowing how many groups have been counted)
• Square numbers (ex: 3 x 3)
• Nines (10 groups less one group, e.g., 9 x 3 is 10 groups of 3 minus one group of 3)
• Decomposing into known facts (6 x 7 is 6 x 6 plus one more group of 6)
• Turn-around facts (Commutative Property)
• Fact families (Ex: 6 x 4 = 24; 24 ÷ 6 = 4; 24 ÷ 4 = 6; 4 x 6 = 24)
• Missing factors
• See Multiplication and Division Strategy Sheets.

Note: Students should have exposure to multiplication and division problems presented in both vertical and horizontal forms. (Problems presented horizontally encourage solving mentally.)

Associative Property of Multiplication

• The product stays the same when the grouping of addends or factors is changed.
• For example, when a student multiplies 7 x 5 x 2, a student could rearrange the numbers to first multiply 5 x 2 = 10 and then multiply 10 x 7 = 70.

Distributive Property of Multiplication

• Decomposing numbers to find products
• For example, to solve 6 x 12, a student could decompose 12 into 10 and 2. Then multiply 6 by each 10 and 2 (6 x 12 = 6 x 10 + 6 x 2 = 60 + 12 = 72).
• Multiple ways exist to decompose numbers using the distributive property to solve equations.

Resources

Videos

• Instructional Video (13:51 - 18:19)
• Khan Academy
  • scroll to 3.OA.7, 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.7
• Common Core Sheets

Released Assessment Questions

PARCC

3.OA.7-1

Fluently multiply and divide within 25. By end of grade 3, know from memory all products of two one-digit numbers.

• Tasks do not have a context.
• Only the answer is required.
• Tasks require finding products and related quotients accurately. For example, each 1-point task might require four or more computations, two or more multiplication and two or more division.
• Tasks are not timed.

3.OA.7-2

Fluently multiply and divide within 100. By the end of Grade 3, know from memory all products of two one-digit numbers.

• Tasks do not have a context.
• Only the answer is required.
• Tasks require finding of products and related quotients accurately. For example, each 1- point task might require four or more computations, two or more multiplication and two or more division.
• 75% of tasks are from the harder three quadrants of the times table (a × b where a > 5 and/or b > 5).
• Tasks are not timed.

Performance Indicators: 3.OA.7-1, 3.OA.7-2

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.