Multiplicative vs. Additive Comparison

Lesson 2 of 2: Same Numbers, Different Questions

In this lesson:

• Compare multiplicative and additive comparison side by side
• Identify which type of comparison a problem uses
• Understand why the same pair of numbers can be described two ways

Learning Objective: Distinguish Comparison Types

By the end of this lesson, you should be able to:

5. Distinguish a multiplicative comparison ("5 times as many as") from an additive comparison ("5 more than") for the same pair of quantities

Direct preparation for 4.OA.A.2, which requires identifying comparison type in word problems.

Same Scenario — Two Questions

Alex has 3 trading cards. Beth has 15 trading cards.

• Question A: "How many more cards does Beth have than Alex?"
• Question B: "How many times as many cards does Beth have as Alex?"

These are two different questions about the same numbers

Same Numbers — Two Completely Different Answers

The Comparison at a Glance

The Decision Rule for Choosing Operations

One rule covers every problem you'll see:

• "How many more / how many fewer?" → additive → subtract
• "How many times as many / times as much?" → multiplicative → multiply

Read the question first — it tells you the operation before you touch a number.

From One Equation to Both Comparisons

Equation:

• Multiplicative: "18 is 6 times as many as 3"
• Additive: since , "18 is 15 more than 3"

One equation, two true comparison statements about the same numbers

Practice: Write Both Comparison Statements

For each equation, write both the multiplicative and the additive comparison statement:

Hint: subtract for the additive statement, then check your work against the equation.

Practice: Classify Comparisons, Set One

1. "Sara has 7 more markers than Jess."
2. "The elephant weighs 6 times as much as the horse."
3. "There are 4 fewer boys than girls."

Mark each A (additive) or M (multiplicative).

Practice: Classify Comparisons, Set Two

4. "A whale is 5 times as long as a dolphin."
5. "Our jar has 3 times as many marbles as theirs."
6. "I walked 8 more steps than you."

Mark each A (additive) or M (multiplicative).

Practice: Write a Multiplicative Equation

"A dolphin is 8 meters long. A whale is 5 times as long as the dolphin."

• Which comparison type is this?
• Write the equation for the whale's length.

Practice: Write an Additive Equation

"Alex has 3 trading cards. Beth has 12 more cards than Alex."

• Which comparison type is this?
• Write the equation or expression for Beth's total.

Quick Check: Train and Car Comparison

"The train is 6 times as long as the car."

• Is this additive or multiplicative?
• What operation would you use to find the train's length if the car is 8 m long?
• Write the equation.

Coming Up Next: Introducing 4.OA.A.2

In the next lesson, one quantity will be unknown:

• "Maria has 5 times as many stamps as Jake. Maria has 35. How many does Jake have?"

Your job: decide the comparison type, then set up the equation.

Key Takeaways From Today's Lesson

✓ Same numbers, two comparisons: one pair can be both additive and multiplicative

✓ Additive: "more/fewer" → subtract → a difference

✓ Multiplicative: "times as many" → multiply → a factor

"Times as many" means multiply — 5 groups of 3 is 15, not 3 + 5

What's Next: Multiplicative Comparison Word Problems

Multiplicative Comparison Word Problems

• Multiply or divide to solve word problems involving multiplicative comparison
• Distinguish multiplicative from additive comparison
• One quantity in the comparison will be unknown

Everything from Lessons 1 and 2 comes together in the next lesson