Explanation

About the Math, Learning Targets, and Rigor

The standard interprets products of whole numbers. Students need to recognize multiplication as a means of determining the total number of objects when there are a specific number of groups with the same number of objects in each group. Students learn that the multiplication symbol ‘x’ means “groups of” and problems such as 5 x 7 refer to 5 groups of 7.

In Grade 2, students found the total number of objects using rectangular arrays, such as a 5 x 5, and wrote equations to represent the sum. This strategy is a foundation for multiplication because students should make a connection between repeated addition and multiplication.

Sets of counters, number lines to skip count and relate to multiplication, and arrays/area models will aid students in solving problems involving multiplication. Students should represent the model or drawing with an equation. They should begin to use the terms factor and product as they describe multiplication.

Three types of multiplication

• Repeated addition of equal groups
  • 2 + 2 + 2 + 2 = 4 groups of 2 = 4 x 2
• Rate or price.
  • If a car travels four hours at 50 miles per hour, then it travels a total of 4 • 50, or 200 miles;
  • If DVDs cost eight dollars each, then three DVDs will cost 3 x $8, or $24.
• Multiplicative comparison (taught in 4th grade - 4.OA.1)
  • Sara has four blankets. Joanne has three times as many as Sara. Thus, Joanne has 3 x 4, or 12 blankets.

Resources

Videos

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

EngageNY Lessons

Extra Practice

• North Carolina Tasks
• Illustrative Math Tasks
• Howard County Tasks
  • Click on 3rd grade at bottom, then 3.OA.1
• Common Core Sheets

Released Assessment Questions

PARCC

3.OA.1

Interpret products of whole numbers, e.g., interpret 5 × 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 × 7.

• Tasks involve interpreting rather than calculating products in terms of equal groups, arrays, area, and/or measurement quantities. (See CCSSM, Table 2, Common multiplication and division situations, p. 89.) For example, “the total number of books if 5 shelves each have 7 books” can be represented by the expression 5x7 rather than “Marcie placed 7 books on each of 5 shelves. How many books does she have?”
• Tasks do not require students to interpret products in terms of repeated addition, 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 total can be expressed as a specified product.
• Tasks have “thin context” or no context.

Performance Indicators: 3.OA.1

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.