Standard

Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 × 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5. Represent verbal statements of multiplicative comparisons as multiplication equations.

Student language:

• "I can understand that multiplication fact problems can be seen as comparisons of groups (e.g., 24 = 4 x 6 can be thought of as 4 groups of 6 or 6 groups of 4)."

Explanation

About the Math, Learning Targets, and Rigor

A multiplicative comparison is a situation in which one quantity is multiplied by a specified number to get another quantity (e.g., “a is n times as much as b”). Students should be able to identify and verbalize which quantity is being multiplied and which number tells how many times.

Multiplicative Comparison

• 5 x 8 = 40.
  • Sally is five years old. Her mom is eight times older. How old is Sally’s Mom?
• Sally has five times as many pencils as Mary. If Sally has 5 pencils, how many does Mary have?
  • 5 x 5 = 25

Students need to solve word problems involving multiplicative comparison (product unknown, partition unknown) using multiplication or division as shown in Appendix, Table 2. They should use drawings or equations with a symbol for the unknown number to represent the problem.

Students need to be able to distinguish whether a word problem involves multiplicative comparison or additive comparison.

2 times as much (multiplicative) vs. 2 more than (additive)

Resources

Videos

• Khan Academy
  • scroll to find 4.OA.1, click on a skill, find videos on left side in each skill
• Learn Zillion
  • Videos
• Virtual Nerd

EngageNY Lessons

• Module 1, Topic A, Lesson 1: Interpret a multiplication equation as a comparison.

Extra Practice

• North Carolina Tasks
• Illustrative Math Tasks
• Howard County Tasks
  • Click on 4th grade at bottom, then 4.OA.1
• Common Core Sheets
• Teachers Cafe 1
• Teachers Cafe 2

Released Assessment Questions

PARCC

4.OA.1-1

Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 x 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5.

• Tasks have “thin context” or no context.

4.OA.1-2

Represent verbal statements of multiplicative comparisons as multiplication equations.

• Tasks have “thin context” or no context.

Performance Indicators: 4.OA.1-1, 4.OA.1-2

Level 5: Exceeds Expectations

Interprets multiplication equations as comparisons and represents statements of multiplicative comparisons as multiplicative equations. Distinguishes multiplicative comparisons. Uses multiplication or division to solve multi-step word problems involving multiplicative comparisons. Uses a symbol for the unknown number.

Level 4: Meets Expectations

Interprets multiplication equations as comparisons or represents statements of multiplicative comparisons as multiplicative equations. Uses multiplication or division to solve one- or two-step word problems involving multiplicative comparisons.

Integrated, Critiquing, & Modeling Standards

Students will need to use the phrase "times as many" to solve multi-step word problems.

Examples:

• There are 4,328 people at a baseball game. There were 6 times as many at a football game. How many people were at the football game?
• On Thursday, Michal rode 8 miles. On Friday, he rode 4 times as many miles as he did on Thursday. On Saturday, Michal rode 18 miles. How many total miles did he ride?
• Hamad painted 2 rooms.
  • He painted room A with 8 gallons of paint.
  • He used 4 times as many paint on room A than he did on room B.
  • Each bucket of paint contains 1/2 gallon paint.
  • How many gallons of paint did Hamad use to paint the 2 rooms?

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