Home›Lesson Plans›Mathematics›Number & Operations—Fractions · Grade 3

Equivalent Fractions: Same Amount, Different Pieces

Students slice a fraction into more parts and watch the amount stay exactly the same — discovering why 1/2, 2/4, and 4/8 are all the same size.

Grade 3Fractions45 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…

  • ✓Explain that equivalent fractions name the same amount.
  • ✓Show equivalence by splitting parts into smaller pieces.
  • ✓Find an equivalent fraction by multiplying top and bottom.
  • ✓Compare fractions using equivalence.
Essential Question

Half a pizza is half a pizza whether you cut it into 2 big slices or 8 small ones. So how can 1/2 and 4/8 be the same number?

0
Lesson Phases
0
Vocabulary Terms
0
Standards Aligned
0
Interactive Task
Model · Interactive Tool

The Equivalent Fraction Bars

Project this and slice each part into more pieces. Watch the shaded amount stay the same while the fraction gets new numbers.

✂️ Slice the parts — keep the same amountTry it
Shaded parts1
Total parts2
Slice each part into1

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 — Same Pizza

5 min

2 big slices or 8 small — still half?

👩‍🏫 Teacher Moves

  • Show half a pizza cut two ways.
  • Ask if the amount changed.
  • Set the goal: equivalent fractions.

🎒 Student Actions

  • Compare the two cuts.
  • Decide if it’s still half.
  • Predict how 1/2 and 4/8 relate.
2

I Do — Slice and Compare

10 min

Teacher shows equivalence.

👩‍🏫 Teacher Moves

  • Draw 1/2, then slice each half in two.
  • Show it becomes 2/4 — same amount.
  • Multiply top and bottom by 2.

🎒 Student Actions

  • Copy both bars.
  • See the amounts match.
  • Write 1/2 = 2/4.
3

We Do — Slice Together

12 min

Class drives the Fraction Bars.

👩‍🏫 Teacher Moves

  • Use the bars to build equivalents.
  • Slice into 3, 4, more pieces.
  • Show the multiply-both rule.

🎒 Student Actions

  • Slice parts and read the new fraction.
  • Confirm the amount stays the same.
  • Multiply top and bottom to match.
4

You Do — On Your Own

13 min

Students find equivalents.

👩‍🏫 Teacher Moves

  • Assign equivalent-fraction problems.
  • Include comparing two fractions.
  • Check the multiply-both method.

🎒 Student Actions

  • Find equivalent fractions.
  • Compare two fractions using equivalence.
  • Show the multiplication used.
5

Close — Prove They’re Equal

5 min

Show 1/2 = 4/8 together.

👩‍🏫 Teacher Moves

  • Return to the pizza.
  • Have students prove 1/2 = 4/8.
  • Hand out the exit ticket.

🎒 Student Actions

  • Prove 1/2 = 4/8 with a bar.
  • Explain the multiply-both 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
3.NF.A.3

Explain equivalence of fractions in special cases and compare fractions by reasoning about their size.

CCSS
4.NF.A.1

Explain why a fraction a/b is equivalent to (a×n)/(b×n) using visual models.

CCSS
4.NF.A.2

Compare two fractions with different numerators and denominators.

SMP
MP.7

Look for and make use of structure — slicing parts to keep the amount equal.

Differentiation

One lesson, every learner

Multilingual Learners

ELL / EMERGING READERS
  • Fraction strips to fold and overlay.
  • Sentence frame: “___ / ___ is the same as ___ / ___.”
  • Match equivalent-fraction cards.

Support & Access

IEP / 504
  • Start with halves and fourths.
  • Provide pre-sliced bars to compare.
  • Use folded paper strips before the tool.

Stretch & Extend

GIFTED / EARLY FINISHERS
  • Simplify a fraction by dividing top and bottom.
  • Find three equivalents for one fraction.
  • Compare fractions by making common denominators.
Materials

What to gather

  • 📽️Projector / board
  • 📓Math notebooks
  • 💻The Equivalent Fraction Bars
  • 📏Paper fraction strips
  • ✏️Colored pencils
  • 🎫Exit-ticket slips
Vocabulary

Key terms — hover for a quick definition

equivalentequal in valuenumeratortop number — parts you havedenominatorbottom number — total partsfractiona number of equal partssimplifywrite a fraction with smaller numberscomparedecide which is greatermultiplythe rule to find equivalentswholethe complete amount
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
Write a fraction equivalent to 1/2 with a denominator of 8.
4/8 (multiply top and bottom by 4).
QUESTION 2
How can you tell if 2/3 and 4/6 are equivalent?
Multiply 2/3’s top and bottom by 2 to get 4/6 — same amount, so they are equivalent (a bar shows the shaded parts match).
QUESTION 3
Which is bigger, 1/2 or 3/8? Explain using equivalence.
1/2 = 4/8, and 4/8 is more than 3/8, so 1/2 is bigger.

Going deeper? Build an equivalence wall.

Have students line up fraction strips (halves, fourths, eighths) and record every equivalent fraction they can find. A printable fraction-strip set 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.

🃏 Equivalent FractionsFlip
Card 1
Term
Tap to flip →
Meaning
0

Nice work!

Practice · Quiz

Check your understanding

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

📝 Equivalent FractionsQuiz
Score: 0
1 / 6
Question 1
0%

Nice work!

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.

🖨️ Equivalent FractionsPrint
Name: ________________________
Date: ____________

Part A · Write the word that matches each meaning

Word bank: compare, denominator, equivalent, fraction, multiply, numerator, simplify, whole
  1. the rule to find equivalents
  2. write a fraction with smaller numbers
  3. top number — parts you have
  4. bottom number — total parts
  5. equal in value
  6. the complete amount
  7. a number of equal parts
  8. decide which is greater

Part B · Show what you learned

  1. Write a fraction equivalent to 1/2 with a denominator of 8.
  2. How can you tell if 2/3 and 4/6 are equivalent?
  3. Which is bigger, 1/2 or 3/8? Explain using equivalence.
Answer key — Part A: 1) multiply · 2) simplify · 3) numerator · 4) denominator · 5) equivalent · 6) whole · 7) fraction · 8) compare
Part B: 1) 4/8 (multiply top and bottom by 4). 2) Multiply 2/3’s top and bottom by 2 to get 4/6 — same amount, so they are equivalent (a bar shows the shaded parts match). 3) 1/2 = 4/8, and 4/8 is more than 3/8, so 1/2 is bigger.