Multiplicative Comparison

Lesson 1 of 2: A New Kind of "More"

In this lesson:

• Learn what "times as many" means
• Read multiplication equations as comparisons — in both directions
• Translate between equations and comparison statements

Learning Objectives

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

1. Explain what a multiplicative comparison is and what "times as many" means
2. Interpret a multiplication equation as a comparison statement
3. Read a multiplication equation in both comparison directions
4. Represent a verbal comparison statement as a multiplication equation

Two Quantities — No Label Yet

I have 3 grapes.
You have 12 grapes.

How would you describe the relationship between our amounts?

Think for a moment before we continue...

"Times as Many": A New Way to Compare

Another Example: Octopus vs. Cat

A cat has 4 legs. An octopus has 8 legs.

"8 is 2 times as many as 4"

Three Key Terms

• Large quantity — the total, the product
• Comparison factor — how many copies; the multiplier
• Reference quantity — the unit being copied; the smaller factor

Your Turn: Dogs vs. Spiders

A dog has 4 legs. A spider has 8 legs.

1. Draw a tape diagram (reference bar first, then copies)
2. Write the multiplication equation
3. Write the comparison statement using "times as many"

Pause and try before advancing

Quick Check

In the equation :

• Which number is the large quantity?
• Which number is the comparison factor?
• Which number is the reference quantity?

Name all three before the next slide

Reading an Equation as a Comparison

What comparison statement can you write from this equation?

Write your answer before advancing...

Two Readings of One Equation

The Two-Direction Pattern

For any equation :

• Reading 1: is times as many as
• Reading 2: is times as many as

Both readings are always correct — because multiplication is commutative.

This means every equation gives you TWO comparison statements

Practice: Write Both Statements

Write both comparison statements for each equation:

Write all four statements before advancing

Reversing Direction: Statement → Equation

"A bin holds 5 times as many apples as a basket. The basket holds 7 apples. Write the equation."

Step 1: Identify the reference quantity: basket = 7 (the "as many as" quantity)

Step 2: Identify the comparison factor: 5 times

Step 3: Write the equation:

Practice: Statement to Equation

Write a multiplication equation for each comparison statement:

1. "24 is 6 times as many as 4"
2. "Maria has 3 times as many stickers as Tom. Tom has 8 stickers."

Write the equations before advancing

Quick Check: Put It Together

Sam has 5 times as many books as Leo. Leo has 6 books. Write the multiplication equation.

Think about the three parts: which is large quantity, factor, reference?

Key Takeaways

✓ "Times as many" means the large quantity is a certain number of copies of the reference quantity

✓ For any equation , you can write two comparison statements

✓ To go from statement to equation: identify the reference (after "as many as"), the factor, and the product

Watch out: Always say "times as many as," never "times more"

Watch out: Every equation gives two comparison statements — writing only one is incomplete

Watch out: Draw the tape diagram first — it shows you which number is the reference

What's Next: Lesson 2

Multiplicative vs. Additive Comparison

In Lesson 2, we'll compare the two types of comparison side by side:

• Additive: "How many more/fewer?" → subtraction
• Multiplicative: "How many times as many?" → multiplication

Same two numbers — two completely different questions — two different operations.

This is direct preparation for 4.OA.A.2, where one quantity will be unknown