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Mixed Numbers and Improper Fractions

Fourth graders learn two ways to write an amount bigger than one whole, as a mixed number and as an improper fraction, and how to change one form into the other, then check what they know.

Grade 4Mixed Numbers and Improper Fractions50 minutes1 class periodGradual ReleaseExplicit teaching4 StandardsCommon Core
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Lesson at a Glance

Everything you need before the bell rings

Learning Objectives

Students will be able to…

  • ✓Define a mixed number.
  • ✓Define an improper fraction.
  • ✓Convert between them.
  • ✓Check what you know.
Essential Question

One and a half pizzas is more than a whole, but less than two. How can you write an amount greater than one whole, and why are there two ways to do 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

Fractions Check

Project this and answer each question about mixed numbers and improper fractions — read the explanation after each one.

🍜 Check what you know about mixed numbers and improper fractionsTry it
Answer each question about mixed numbers and improper fractions.
The Lesson · Gradual Release (I Do · We Do · You Do)

50 minutes, five moves

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

1

Hook — More Than One Whole

5 min

Three friends share pizzas and end up with one whole pizza and a half left over. How can you write an amount that is more than one whole as a single number?

👩‍🏫 Teacher Moves

  • Show 1 and a half pizzas.
  • Ask how to write it.
  • Set the goal.

🎒 Student Actions

  • Think.
  • Share.
  • Get ready.
2

Use — Fractions Check

12 min

Students answer questions about mixed numbers and improper fractions.

👩‍🏫 Teacher Moves

  • Send students to the Fractions Check.
  • Answer each question.
  • Read the why.

🎒 Student Actions

  • Answer.
  • Check.
  • Read it.
3

Modify — Convert It

13 min

Students convert between the two forms.

👩‍🏫 Teacher Moves

  • Write an improper fraction.
  • Change it to a mixed number.
  • Then change it back.

🎒 Student Actions

  • Write.
  • Change.
  • Check.
4

Create — Fraction Pictures

15 min

Students draw both forms.

👩‍🏫 Teacher Moves

  • Draw 2 and 1/4 as shaded wholes.
  • Count all the quarter pieces.
  • Write it as an improper fraction.

🎒 Student Actions

  • Draw.
  • Count.
  • Write.
5

Reflect — Two Ways, One Amount

5 min

Students reflect on the two forms.

👩‍🏫 Teacher Moves

  • What is an improper fraction?
  • How do you change 7/4 to a mixed number?
  • Complete the exit ticket.

🎒 Student Actions

  • Say it.
  • Say it.
  • Complete the exit ticket.
Standards Alignment

Built to the standards you report on

Aligned to the Common Core State Standards for Mathematics.

CCSS
4.NF.B.3

Understand a fraction a/b with a greater than 1 as a sum of unit fractions 1/b, including writing mixed numbers.

CCSS
4.NF.B.3.C

Add and subtract mixed numbers with like denominators, including by converting to improper fractions.

CCSS
3.NF.A.1

Understand a fraction 1/b as one part when a whole is partitioned into b equal parts.

CCSS
MP.2

Reason abstractly and quantitatively.

Differentiation

One lesson, every learner

Multilingual Learners

ELL / EMERGING READERS
  • Fraction-circle picture cards.
  • Sentence frame: “___ wholes and ___ parts is ___ .”
  • Answer one question at a time.

Support & Access

IEP / 504
  • Start with pictures of shaded wholes.
  • Use fraction tiles to build each amount.
  • Convert one direction before the other.

Stretch & Extend

GIFTED / EARLY FINISHERS
  • Convert both directions fluently.
  • Compare a mixed number to an improper fraction.
  • Add two mixed numbers with like denominators.
Materials

What to gather

  • 📽️Projector / board
  • 🍜Fraction tiles or circles
  • 💻Fractions Check
  • 🖼️Shaded-whole picture cards
  • ✏️Pencils
  • 🎫Exit-ticket slips
Vocabulary

Key terms — hover for a quick definition

mixed numbera whole number and a fraction written together, like 2 and 1/3improper fractiona fraction whose numerator is greater than or equal to its denominatorproper fractiona fraction whose numerator is smaller than its denominatornumeratorthe top number of a fraction; how many parts you havedenominatorthe bottom number of a fraction; how many equal parts in a wholewholeone complete unit, made of all its equal partsconvertto rewrite a number in a different but equal formremainderthe amount left over after dividing
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
What is an improper fraction?
A fraction whose numerator is greater than or equal to its denominator, so it equals one whole or more.
QUESTION 2
How do you change 7/4 into a mixed number?
Divide 7 by 4 to get 1 with 3 left over, so 7/4 equals 1 and 3/4.
QUESTION 3
Change 2 1/3 into an improper fraction.
Multiply 2 by 3 and add 1 to get 7, over the same denominator: 7/3.

Create: fraction pictures.

Have students draw 2 and 1/4 as shaded wholes, count every quarter piece, and write the total as an improper fraction, so the two forms connect to one picture. A printable mixed-numbers worksheet is in the Mathematics 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.

🃏 Mixed Numbers and Improper 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.

📝 Mixed Numbers and Improper FractionsQuiz
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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.

🖨️ Mixed Numbers and Improper FractionsPrint
Name: ________________________
Date: ____________

Part A · Write the word that matches each meaning

Word bank: convert, denominator, improper fraction, mixed number, numerator, proper fraction, remainder, whole
  1. the top number of a fraction; how many parts you have
  2. the bottom number of a fraction; how many equal parts in a whole
  3. to rewrite a number in a different but equal form
  4. the amount left over after dividing
  5. a fraction whose numerator is smaller than its denominator
  6. one complete unit, made of all its equal parts
  7. a whole number and a fraction written together, like 2 and 1/3
  8. a fraction whose numerator is greater than or equal to its denominator

Part B · Show what you learned

  1. What is an improper fraction?
  2. How do you change 7/4 into a mixed number?
  3. Change 2 1/3 into an improper fraction.
Answer key — Part A: 1) numerator · 2) denominator · 3) convert · 4) remainder · 5) proper fraction · 6) whole · 7) mixed number · 8) improper fraction
Part B: 1) A fraction whose numerator is greater than or equal to its denominator, so it equals one whole or more. 2) Divide 7 by 4 to get 1 with 3 left over, so 7/4 equals 1 and 3/4. 3) Multiply 2 by 3 and add 1 to get 7, over the same denominator: 7/3.