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 for Multiplicative Comparison

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

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

12 = 4 × 3

Another Example: Octopus vs. Cat

8 = 2 × 4

Three Key Terms for Multiplicative Comparison

• 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: Name the Three Parts

In the equation 12 = 4 × 3:

• 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

35 = 5 × 7

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

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 Comparison Statements

Write both comparison statements for each equation:

1. 18 = 3 × 6
2. 40 = 8 × 5

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: Reference quantity: basket = 7

Step 2: Comparison factor: 5

Step 3: Equation: bin's apples = 5 × 7 = 35

35 = 5 × 7

Practice: Turn Statements into Equations

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 From Lesson One

✓ "Times as many": the large quantity is copies of the reference quantity

✓ Every equation gives two comparison statements

✓ Statement → equation: reference first, then factor, then product

Say "times as many," never "times more" — draw the tape diagram first

What's Next: Additive vs. Multiplicative Comparison

Multiplicative vs. Additive Comparison

Lesson 2 compares both types side by side:

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

Same numbers, two different questions, two different operations.

Direct preparation for 4.OA.A.2, where one quantity will be unknown.