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

Greater or Less Than One-Half

Third graders learn to judge a fraction at a glance by comparing it to one-half, a handy benchmark, and sort common fractions into greater-than-half and less-than-half.

Grade 3Greater or Less Than One-Half30 minutes1 class periodPlay-BasedExplicit 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…

  • ✓Use one-half as a benchmark.
  • ✓Compare a fraction to half.
  • ✓Explain how you know.
  • ✓Sort each fraction.
Essential Question

You ate 3 of 8 pizza slices. More or less than half? Comparing a fraction to one-half answers it fast. How does that comparison work?

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Lesson Phases
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Vocabulary Terms
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Standards Aligned
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Interactive Task
Sort the Fractions · Interactive

Sort the Fractions

Project this and sort each fraction into greater than or less than one-half — tap a fraction, then tap where it belongs.

⚖️ Sort each fraction: greater or less than one-half?Try it
⬆️ Greater than 1/2
⬇️ Less than 1/2
Tap a fraction, then tap whether it is greater than or less than one-half.
The Lesson · Play-Based Learning (Gather · Explore · Play · Reflect)

30 minutes, five moves

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

1

Hook — Is It More Than Half?

5 min

You ate 3 of the 8 slices of a pizza. Did you eat more or less than half? A quick comparison to one-half answers it. How?

👩‍🏫 Teacher Moves

  • Show a fraction of a shape.
  • Ask: more or less than half?
  • Set the goal.

🎒 Student Actions

  • Think.
  • Share.
  • Get ready.
2

Use — Sort the Fractions

12 min

Students sort fractions by the half benchmark.

👩‍🏫 Teacher Moves

  • Send students to Sort the Fractions.
  • Drop each fraction.
  • Explain each choice.

🎒 Student Actions

  • Sort.
  • Say.
  • Explain.
3

Modify — Check the Half

13 min

Students compare numerator to half the denominator.

👩‍🏫 Teacher Moves

  • Pick a fraction.
  • Find half of the denominator.
  • Compare it to the numerator.

🎒 Student Actions

  • Pick.
  • Find.
  • Compare.
4

Create — My Fraction Sort

15 min

Students build a sorting card set.

👩‍🏫 Teacher Moves

  • Write six fractions.
  • Mark each more or less than half.
  • Draw one to prove it.

🎒 Student Actions

  • Write.
  • Mark.
  • Draw.
5

Reflect — Comparing to Half

5 min

Students reflect on the benchmark.

👩‍🏫 Teacher Moves

  • Is 3/8 more or less than half? How do you know?
  • When is a fraction exactly one-half?
  • 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 (Grade 3).

CCSS
3.NF.A.3.D

Compare two fractions by reasoning about their size and justify the conclusions.

CCSS
3.NF.A.1

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

CCSS
4.NF.A.2

Compare two fractions with different numerators and denominators using a benchmark like 1/2.

CCSS
MP.3

Construct viable arguments and critique the reasoning of others.

Differentiation

One lesson, every learner

Multilingual Learners

ELL / EMERGING READERS
  • Fraction cards with shaded pictures.
  • Sentence frame: “___ is greater / less than half.”
  • Sort two fractions at a time.

Support & Access

IEP / 504
  • Start with 3/4 and 1/4.
  • Shade each fraction on a bar to check.
  • Sort all greater-than-half first.

Stretch & Extend

GIFTED / EARLY FINISHERS
  • Add fractions very close to half (5/8, 4/9).
  • Explain the half-the-denominator rule.
  • Order a set from least to greatest.
Materials

What to gather

  • 📽️Projector / board
  • 📐Fraction bars
  • 💻Sort the Fractions
  • 🖼️Shaded fraction cards
  • ✏️Pencils
  • 🎫Exit-ticket slips
Vocabulary

Key terms — hover for a quick definition

fractiona number that shows parts of a whole, like 3/4one-halfthe fraction 1/2, one of two equal partsbenchmarka known value, like 1/2, used to compare othersnumeratorthe top number; how many parts you havedenominatorthe bottom number; how many equal parts in a wholegreater thanmore than another amount, shown with >less thansmaller than another amount, shown with <compareto decide which of two amounts is larger
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
Is 3/8 greater or less than one-half, and how do you know?
Less than half; half of 8 is 4, and 3 is less than 4, so 3/8 is less than 1/2.
QUESTION 2
When is a fraction exactly one-half?
When the numerator is exactly half of the denominator, like 4/8 or 5/10.
QUESTION 3
Is 5/8 more or less than half?
More than half, because 5 is greater than half of 8 (which is 4).

Create: my fraction sort.

Have students write six fractions, mark each as more or less than half, and draw one to prove it, so the benchmark becomes a quick mental check. A printable benchmark-fractions 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.

🃏 Greater or Less Than One-HalfFlip
Card 1
Term
Tap to flip →
Meaning
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Practice · Quiz

Check your understanding

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

📝 Greater or Less Than One-HalfQuiz
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.

🖨️ Greater or Less Than One-HalfPrint
Name: ________________________
Date: ____________

Part A · Write the word that matches each meaning

Word bank: benchmark, compare, denominator, fraction, greater than, less than, numerator, one-half
  1. the top number; how many parts you have
  2. the bottom number; how many equal parts in a whole
  3. smaller than another amount, shown with <
  4. to decide which of two amounts is larger
  5. a known value, like 1/2, used to compare others
  6. more than another amount, shown with >
  7. a number that shows parts of a whole, like 3/4
  8. the fraction 1/2, one of two equal parts

Part B · Show what you learned

  1. Is 3/8 greater or less than one-half, and how do you know?
  2. When is a fraction exactly one-half?
  3. Is 5/8 more or less than half?
Answer key — Part A: 1) numerator · 2) denominator · 3) less than · 4) compare · 5) benchmark · 6) greater than · 7) fraction · 8) one-half
Part B: 1) Less than half; half of 8 is 4, and 3 is less than 4, so 3/8 is less than 1/2. 2) When the numerator is exactly half of the denominator, like 4/8 or 5/10. 3) More than half, because 5 is greater than half of 8 (which is 4).