Home›Lesson Plans›Mathematics›Number & Operations—Fractions · Grade 5

Multiplying Fractions: A Fraction of a Fraction

Students multiply two fractions using an area model and discover that multiplying tops and bottoms works because you’re finding a part of a part — which makes the answer smaller, not bigger.

Grade 5Fractions45 minutes1 class periodGradual ReleaseExplicit teaching4 StandardsCommon Core
Start the Lesson
Lesson at a Glance

Everything you need before the bell rings

Learning Objectives

Students will be able to…

  • ✓Multiply a fraction by a fraction.
  • ✓Use an area model to show the product.
  • ✓Explain why multiplying tops and bottoms works.
  • ✓Explain why the product is smaller.
Essential Question

Half of a half is a quarter — smaller than either. Why does multiplying two fractions make the answer SMALLER, and how do you find it?

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Lesson Phases
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Vocabulary Terms
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Standards Aligned
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Interactive Task
Model · Interactive Tool

The Fraction Grid

Project this and set two fractions. One shades columns, the other shades rows — the overlap is the product. Watch it get smaller as you multiply parts of parts.

✖️ Multiply fractions — find the overlapTry it
First fraction: a/b1/2
Second fraction: c/d1/3

The Lesson · Gradual Release (I Do · We Do · You Do)

45 minutes, five moves

Tap any phase to open the teacher moves and student actions.

1

Launch — Half of a Half

5 min

What is half of half a pizza?

👩‍🏫 Teacher Moves

  • Ask for half of a half.
  • Note the answer is smaller.
  • Set the goal: multiplying fractions.

🎒 Student Actions

  • Picture half of a half.
  • Notice it’s smaller.
  • Predict the rule.
2

I Do — The Area Model

10 min

Teacher models.

👩‍🏫 Teacher Moves

  • Shade 1/2 of a grid one way, 1/3 the other.
  • The overlap is the product (1/6).
  • Show: multiply tops, multiply bottoms.

🎒 Student Actions

  • Watch the overlap form.
  • Read the product.
  • Learn the top/bottom rule.
3

We Do — Grid Together

12 min

Class drives the Fraction Grid.

👩‍🏫 Teacher Moves

  • Use the Fraction Grid for several pairs.
  • Read the overlap each time.
  • Notice the product is smaller.

🎒 Student Actions

  • Set two fractions.
  • Read the product.
  • Explain why it shrinks.
4

You Do — On Your Own

13 min

Students multiply fractions.

👩‍🏫 Teacher Moves

  • Assign fraction × fraction problems.
  • Include a word problem (2/3 of a cup).
  • Simplify where possible.

🎒 Student Actions

  • Multiply fractions.
  • Solve a word problem.
  • Simplify answers.
5

Close — Close

5 min

Solve half of a half.

👩‍🏫 Teacher Moves

  • Return to half of a half.
  • Have students write 1/2 × 1/2 = 1/4.
  • Hand out the exit ticket.

🎒 Student Actions

  • Solve 1/2 × 1/2 = 1/4.
  • Explain the rule.
  • Complete the exit ticket.
Standards Alignment

Built to the standards you report on

Aligned to the Common Core State Standards for Mathematics, including the Standards for Mathematical Practice.

CCSS
5.NF.4

Apply and extend previous understandings of multiplication to multiply a fraction by a fraction.

CCSS
5.NF.4b

Find the area of a rectangle with fractional side lengths by tiling and multiplying.

CCSS
5.NF.6

Solve real-world problems involving multiplication of fractions.

SMP
MP.4

Model with mathematics using an area model.

Differentiation

One lesson, every learner

Multilingual Learners

ELL / EMERGING READERS
  • Fold paper to show a fraction of a fraction.
  • Sentence frame: “___ of ___ is ___.”
  • Say “multiply tops, multiply bottoms.”

Support & Access

IEP / 504
  • Start with unit fractions (1/2 × 1/3).
  • Use a pre-drawn grid to shade.
  • Focus on the overlap = product idea.

Stretch & Extend

GIFTED / EARLY FINISHERS
  • Multiply a fraction by a whole number.
  • Multiply a mixed number by a fraction.
  • Explain when a product is bigger vs. smaller.
Materials

What to gather

  • 📽️Projector / board
  • 📓Math notebooks
  • 💻The Fraction Grid
  • 📐Grid paper
  • ✏️Colored pencils
  • 🎫Exit-ticket slips
Vocabulary

Key terms — hover for a quick definition

fractiona number of equal partsnumeratorthe top numberdenominatorthe bottom numberproductthe answer to a multiplicationarea modela rectangle used to multiplyoverlapwhere two shadings meetofmeans multiply, with fractionssimplifywrite with smaller numbers
Evaluate

Exit Ticket

Preview the three formative checks. Tap “Sample answer” to see what mastery looks like — hide them before you print for students.

QUESTION 1
Solve: 1/2 × 1/3.
1/6 (multiply tops: 1×1=1; multiply bottoms: 2×3=6).
QUESTION 2
Why is 1/2 × 1/4 smaller than both fractions?
Because you are taking a part OF a part — half of a quarter is even smaller than a quarter.
QUESTION 3
Solve: 2/3 × 3/4.
6/12, which simplifies to 1/2.

Going deeper? Tile a rectangle.

Have students find the area of a rectangle with fractional side lengths (like 2/3 by 3/4) by tiling it and multiplying. A printable area-model grid is in the Math library.

Study · Flashcards

Study the key terms

Tap a card to flip it, then rate whether you knew it. Built from this lesson’s vocabulary.

🃏 Multiplying FractionsFlip
Card 1
Term
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Meaning
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Practice · Quiz

Check your understanding

A quick self-check with instant feedback, drawn from this lesson’s key terms.

📝 Multiplying FractionsQuiz
Score: 0
1 / 6
Question 1
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Practice · Worksheet

Printable worksheet

A print-and-go review sheet with a built-in answer key. Tap “Show answer key” to reveal answers, or print the clean version for students.

🖨️ Multiplying FractionsPrint
Name: ________________________
Date: ____________

Part A · Write the word that matches each meaning

Word bank: area model, denominator, fraction, numerator, of, overlap, product, simplify
  1. means multiply, with fractions
  2. the answer to a multiplication
  3. a rectangle used to multiply
  4. the bottom number
  5. write with smaller numbers
  6. the top number
  7. where two shadings meet
  8. a number of equal parts

Part B · Show what you learned

  1. Solve: 1/2 × 1/3.
  2. Why is 1/2 × 1/4 smaller than both fractions?
  3. Solve: 2/3 × 3/4.
Answer key — Part A: 1) of · 2) product · 3) area model · 4) denominator · 5) simplify · 6) numerator · 7) overlap · 8) fraction
Part B: 1) 1/6 (multiply tops: 1×1=1; multiply bottoms: 2×3=6). 2) Because you are taking a part OF a part — half of a quarter is even smaller than a quarter. 3) 6/12, which simplifies to 1/2.