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

Unlike Fractions: Finding a Common Bottom Number

Students add fractions with different denominators and discover the key move — rewriting both fractions with a common denominator so the parts are the same size and can be combined.

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…

  • ✓Explain why fractions need a common denominator to add.
  • ✓Find a common denominator for two fractions.
  • ✓Rewrite fractions with a common denominator.
  • ✓Add and subtract fractions with unlike denominators.
Essential Question

You can’t add 1/2 and 1/3 by adding the tops — the pieces are different sizes. So how do you add fractions that don’t match?

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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

Make the Bottoms Match

Project this and set two fractions with different bottoms. Watch them get re-cut into the same-size pieces (a common denominator) so they can be added.

➕ Add unlike fractions — find a common denominatorTry it
Fraction 1: top1
Fraction 1: bottom2
Fraction 2: top1
Fraction 2: bottom3

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 — Different-Size Pieces

5 min

1/2 + 1/3 — why can’t you just add the tops?

👩‍🏫 Teacher Moves

  • Show 1/2 and 1/3 as bars.
  • Note the pieces are different sizes.
  • Set the goal: common denominators.

🎒 Student Actions

  • Compare the two pieces.
  • See they don’t match.
  • Predict the fix.
2

I Do — Find a Common Bottom

10 min

Teacher models.

👩‍🏫 Teacher Moves

  • Find a common denominator (like 6).
  • Rewrite 1/2 = 3/6 and 1/3 = 2/6.
  • Add the tops: 3/6 + 2/6 = 5/6.

🎒 Student Actions

  • Find the common denominator.
  • Rewrite both fractions.
  • Add the tops.
3

We Do — Match Together

12 min

Class drives the tool.

👩‍🏫 Teacher Moves

  • Use Make the Bottoms Match.
  • Try several unlike fractions.
  • Do a subtraction example.

🎒 Student Actions

  • Set unlike fractions.
  • Read the common denominator.
  • Add or subtract.
4

You Do — On Your Own

13 min

Students add/subtract unlike fractions.

👩‍🏫 Teacher Moves

  • Assign unlike-denominator problems.
  • Include a word problem.
  • Watch for adding bottoms.

🎒 Student Actions

  • Find common denominators.
  • Add and subtract.
  • Solve a word problem.
5

Close — Close

5 min

Solve the opener.

👩‍🏫 Teacher Moves

  • Return to 1/2 + 1/3.
  • Have students solve it fully.
  • Hand out the exit ticket.

🎒 Student Actions

  • Solve 1/2 + 1/3 = 5/6.
  • Explain the common bottom.
  • 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.1

Add and subtract fractions with unlike denominators by replacing them with equivalent fractions with a common denominator.

CCSS
5.NF.2

Solve word problems involving addition and subtraction of fractions.

CCSS
4.NF.3

Understand addition and subtraction of fractions referring to the same whole.

SMP
MP.7

Look for and make use of structure to find common denominators.

Differentiation

One lesson, every learner

Multilingual Learners

ELL / EMERGING READERS
  • Fraction strips to line up and re-cut.
  • Sentence frame: “The common denominator is ___.”
  • Say “make the pieces the same size.”

Support & Access

IEP / 504
  • Provide the common denominator.
  • Use fraction bars to convert.
  • Start with one denominator that is a multiple of the other (1/2 + 1/4).

Stretch & Extend

GIFTED / EARLY FINISHERS
  • Add three unlike fractions.
  • Add a fraction and a mixed number.
  • Find the least common denominator quickly.
Materials

What to gather

  • 📽️Projector / board
  • 📓Math notebooks
  • 💻Make the Bottoms Match
  • 📏Fraction strips
  • ✏️Colored pencils
  • 🎫Exit-ticket slips
Vocabulary

Key terms — hover for a quick definition

numeratorthe top number — parts you havedenominatorthe bottom number — total partscommon denominatora shared bottom numberunlike denominatorsdifferent bottom numbersequivalentequal in valuemultiplea number in a times tableleast common denominatorthe smallest common bottomsumthe answer to addition
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
Why do you need a common denominator to add 1/2 and 1/3?
Because the pieces are different sizes — you must rewrite them as the same-size pieces (like sixths) before you can add.
QUESTION 2
Solve: 1/4 + 1/2.
1/4 + 2/4 = 3/4.
QUESTION 3
Rewrite 2/3 and 1/6 with a common denominator, then add.
2/3 = 4/6, so 4/6 + 1/6 = 5/6.

Going deeper? Add on a number line.

Have students add unlike fractions by marking a common-denominator number line and hopping to the sum. A printable fraction number line 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.

🃏 Adding & Subtracting Unlike 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.

📝 Adding & Subtracting Unlike 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.

🖨️ Adding & Subtracting Unlike FractionsPrint
Name: ________________________
Date: ____________

Part A · Write the word that matches each meaning

Word bank: common denominator, denominator, equivalent, least common denominator, multiple, numerator, sum, unlike denominators
  1. the bottom number — total parts
  2. different bottom numbers
  3. equal in value
  4. a shared bottom number
  5. the answer to addition
  6. the top number — parts you have
  7. a number in a times table
  8. the smallest common bottom

Part B · Show what you learned

  1. Why do you need a common denominator to add 1/2 and 1/3?
  2. Solve: 1/4 + 1/2.
  3. Rewrite 2/3 and 1/6 with a common denominator, then add.
Answer key — Part A: 1) denominator · 2) unlike denominators · 3) equivalent · 4) common denominator · 5) sum · 6) numerator · 7) multiple · 8) least common denominator
Part B: 1) Because the pieces are different sizes — you must rewrite them as the same-size pieces (like sixths) before you can add. 2) 1/4 + 2/4 = 3/4. 3) 2/3 = 4/6, so 4/6 + 1/6 = 5/6.