Courseversity

Lesson

Comparing fractions

Primary EducationGrade 4MathematicsCV-PRI-G04-MATH-FRA-U01-L0445–60 min

You will learn

  • Compare fractions with the same denominator.
  • Compare fractions with the same numerator.
  • Use equivalent fractions for unlike denominators.
  • Use >, < and =.

Version 0.2 · expanded edition · expert review pending Standards alignment: pending verification. Written in the style of common primary school assessments. No exam result is promised.

Student lesson

The lesson in 60 seconds

  1. Same denominator: compare numerators.
  2. Same numerator: the smaller denominator is greater.
  3. Different denominators: make them the same first.
  4. Use >, < and =.

Words to know

compare
Say which is greater.
common denominator
A shared denominator.
greater than
>
less than
<

1. Discover: bigger piece

Which is bigger: 2/3 of a cake or 3/4 of the same cake?

2. Understand: comparing fractions

  • Same denominator: 3/5 > 2/5.
  • Same numerator: 1/3 > 1/4 (thirds are bigger than quarters).
  • Unlike: 2/3 = 8/12 and 3/4 = 9/12, so 3/4 > 2/3.
2/3
3/4

Idea 1: Like denominators

4/7 > 3/7 because 4 sevenths is more than 3 sevenths.

Idea 2: Like numerators

1/2 > 1/5 because halves are bigger pieces than fifths.

Idea 3: Unlike

3/4 vs 5/8: 3/4 = 6/8, and 6/8 > 5/8, so 3/4 > 5/8. Also 1/2 = 3/6, so 1/2 = 3/6.

Why a common denominator? Same-size pieces can be compared by counting.

Remember: Use a common denominator, then compare numerators.

3. Worked examples

Example 1 (I show you): Like

4/7 __ 3/7

  1. Compare 4 and 3.

Answer: >

Example 2 (We do it together): Unlike

3/4 __ 5/8

  1. 3/4 = 6/8.

Answer: >

Example 3 (You try): Equal

1/2 __ 3/6

Show the steps and answer
  1. 3/6 = 1/2.

Answer: =

Did you know?

The bigger the denominator, the smaller each piece.

Why this matters

Comparing fractions helps us choose the bigger share.

4. Explore: compare

You need paper strips.

  1. Make bars for 2/3 and 3/4.
  2. Convert to twelfths.
  3. Compare 8/12 and 9/12.
  4. Write > or <.
Think about it: what did you notice?

3/4 > 2/3.

5. Practise

Say it in a sentence

Use these starters when you talk about the lesson. Say them out loud.

  • I rewrite as ___ and ___.
  • The numerators are ___ and ___.
  • So ___ is greater / less than ___.
  • The sign is ___.

Guided practice

Question 1. 3/5 ? 2/5

>

Question 2. 1/3 ? 1/4

>

Question 3. 2/3 ? 3/4

<

Independent practice

Level 1: Start

  1. 4/7 ? 3/7
  2. 1/2 ? 1/5
  3. 1/2 ? 3/6
  4. 3/4 ? 5/8
  5. 2/5 ? 1/2

Level 2: Grow

  1. 2/5 __ 4/5
  2. 1/3 __ 1/6
  3. 3/4 __ 7/8

Level 3: Stretch

  1. 5/6 __ 3/4
  2. 2/3 __ 5/8
  3. Ben says 3/8 > 1/2 because 8 > 2. What is wrong?

Answers are in the answer key below. Try first, then check.

6. Apply: everyday mathematics

Ada ate 2/3 of a pie, Bayo ate 3/4. Who ate more?

Show a sample answer

Bayo.

Another one. Ana ate 3/8 of a pizza and Ben ate 1/2. Who ate more?

Show a sample answer

1/2 = 4/8, which is more than 3/8, so Ben ate more.

7. Common mistakes

Mistake: Thinking bigger denominator means bigger fraction.
Fix: Compare numerators with same denominators.
Another mistake: Thinking a bigger denominator means a bigger fraction.
Fix: Bigger denominator means smaller pieces.
Another mistake: Comparing only the numerators when denominators differ.
Fix: Make the denominators the same first.

8. Lesson summary and revision card

I can…

  • I can compare fractions with the same denominator.
  • I can compare fractions with the same numerator.
  • I can use equivalent fractions.
  • I can use >, < and =.

9. Check and master

Answer all 14 questions. You will see feedback after each one.

1. 3/5 ? 2/5

2. 1/3 ? 1/4

3. 2/3 ? 3/4

4. 1/2 ? 3/6

5. 3/4 ? 5/8

6. 5/9 __ 2/9

7. 1/6 __ 1/8

8. 3/5 __ 7/10

9. 2/3 __ 4/6

10. 5/8 __ 3/4

11. 4/5 __ 3/4

12. 3/7 __ 1/2

Challenge 1. 2/5 ? 1/2

Challenge 2. 5/6 __ 7/9

Your result appears here after you answer every question.

10. Key takeaways

  • Same denominator: compare tops.
  • Unlike: find equivalent fractions.
  • Draw bars.

11. Next lesson

Next lesson: Ordering fractions. Keep going with the next idea in this course.

Exam practice

These questions are written in the style of common school and international primary assessments. Try them on your own, without looking back. Then check your answers in the marking guide. The marks are shown in brackets.

  1. Compare 4/7 and 3/7 with >, < or =. [1 mark]
  2. Compare 1/2 and 1/5 with >, < or =. Explain. [2 marks]
  3. Compare 1/2 and 3/6 with >, < or =. Explain. [2 marks]
  4. Compare 3/4 and 5/8 with >, < or =. Explain. [3 marks]
  5. Kofi says 1/5 > 1/2 because 5 > 2. Is he right? Explain. [3 marks]

Total: 11 marks.

Marking guide and model answers
  1. > [1]
  2. Same numerator, smaller denominator is greater [1]; > [1]
  3. 3/6 = 1/2 [1]; = [1]
  4. 3/4 = 6/8 [1]; 6/8 > 5/8 [1]; 3/4 > 5/8 [1]
  5. No [1]. Fifths are smaller pieces than halves [1]. 1/5 < 1/2 [1].

Score guide: 10 to 11 = secure. 7 to 9 = nearly there, revise the parts you missed. Under 7 = work through the lesson again with a grown-up.

Printable worksheet

  1. 4/7 ? 3/7
  2. 1/2 ? 1/5
  3. 1/2 ? 3/6
  4. 3/4 ? 5/8
  5. 2/5 ? 1/2
  6. 3/5 __ 2/5
  7. 1/3 __ 1/4
  8. 2/3 __ 3/4
  9. 1/2 __ 3/6
  10. 3/4 __ 5/8

Homework

Compare five pairs of fractions.

Answer key and marking scheme

Question Expected response Marks
4/7 ? 3/7 > 2
1/2 ? 1/5 > 2
1/2 ? 3/6 = 2
3/4 ? 5/8 > 2
2/5 ? 1/2 < 2
Total 10

Practice answers: Worksheet: 1 >; 2 >; 3 =; 4 >; 5 <.

Quiz answers: 1 A, 2 B, 3 C, 4 A, 5 B, 6 A, 7 B, 8 C, 9 A, 10 B, 11 C, 12 A, Challenge 1 C, Challenge 2 C.

Extra worksheet answers (items 6 onward): 6 >; 7 >; 8 <; 9 =; 10 >.

Independent practice answers. Level 1: 1 >; 2 >; 3 =; 4 >; 5 <. Level 2: 1 <; 2 >; 3 <. Level 3: 1 >; 2 >; 3 1/2 = 4/8, so 3/8 < 1/2. A bigger denominator means smaller pieces..

Mastery and remediation

Objective Bronze (Developing) Silver (Proficient) Gold (Advanced)
O1 Compare fractions with the same denominator Shows this with help from an adult or a picture Does this independently and explains how they know Explains it clearly and uses it in a new situation
O2 Compare fractions with the same numerator Shows this with help from an adult or a picture Does this independently and explains how they know Explains it clearly and uses it in a new situation
O3 Use equivalent fractions for unlike denominators Shows this with help from an adult or a picture Does this independently and explains how they know Explains it clearly and uses it in a new situation
O4 Use >, < and = Shows this with help from an adult or a picture Does this independently and explains how they know Explains it clearly and uses it in a new situation

Proposed Courseversity thresholds for this page: Bronze = at least 8 of 12 core questions correct; Silver = all 12; Gold = all 12 plus both challenge questions. A badge is never a full record of progress.

If a learner struggles

  1. Find the misconception: Thinking bigger denominator means bigger fraction. Compare numerators with same denominators.
  2. Explain another way: use real objects first, then pictures.
  3. Show a simpler example: Compare fraction strips.
  4. Guided practice: work through one example together and let the learner try the next one.
  5. Reassess: use the quiz again or the worksheet.
  6. Move on when the learner shows Silver-level evidence independently.

For parents and guardians

In this lesson your child compares fractions with >, < and =. You do not need to be good at mathematics to help.

  • Cut a cake into different equal pieces and compare.
  • Ask: are the pieces the same size?
  • Use a number line.
  • Ask “how do you know?” after each answer, and listen.
  • Praise effort, not only right answers. Mistakes are how we learn.
  • Ten to fifteen minutes a day is better than one long session.

Teacher package

1–5. Objectives, prerequisites, materials, preparation, duration

Lesson objectives. Learners will: compare fractions with the same denominator; compare fractions with the same numerator; use equivalent fractions for unlike denominators; use >, < and =.

Prerequisite knowledge. Lessons 2 and 3.

Materials. Counters (stones, seeds or bottle tops), paper, pencils, board or chalkboard. Low-resource options: use stones, seeds, sticks, bottle tops or drawings in the sand or on the board instead of printed materials.

Preparation. Gather the counters and draw the example pictures on the board before the lesson.

Suggested duration. 45–60 minutes. It can be split into two shorter sessions.

6–9. Teaching procedure, explanation notes, guided and independent activities

Introduction (5 min). Start with the Discover situation and let learners suggest ideas before you teach.

Explanation (10 min). Teach the Understand section with real objects first, then pictures, then symbols and words.

Guided activity (10 min). You need paper strips. Learners follow the Explore steps in pairs.

Independent activity (10 min). Learners complete the independent practice and the worksheet.

Assessment and reflection (5 min). Ask each learner to say one thing they learned and how they know it.

Key questions. Are the pieces the same size? What is the common denominator?

Teacher explanation notes. Use the concrete, pictorial, abstract order: real objects first, then pictures, then symbols and words. Return to real objects whenever a learner needs support.

10–12. Differentiation, formative assessment, common misconceptions

Support. Use real objects and work with a partner; say each step aloud together. Extension. Ask learners to make up their own example and explain it to a partner.

Formative assessment. Listen to learner explanations, ask “how do you know?”, and check the independent work.

Misconceptions. Thinking bigger denominator means bigger fraction. Compare numerators with same denominators.

13–15. Assessment questions, answer keys, marking scheme

Use the quiz and worksheet on this page. The 11-mark exam practice scheme, the 10-mark scheme and all answers are in the answer sections above. Re-check every answer and the marking scheme before publication.

16–19. Remediation, enrichment, homework, teacher reflection

Remediation. Compare fraction strips. Enrichment. Invite learners to find or create three more examples at home or in the classroom and explain them. Homework. See above.

Teacher reflection. After teaching, record: which concepts learners understood; which misconceptions occurred; which activities worked; which learners need more practice; and what to improve next time.

Sources and standards

Alignment is pending verification and no external endorsement is claimed. Reference starting points named in the Courseversity standard: Common Core State Standards for Mathematics, Cambridge Primary and the IB Primary Years Programme. Specific standard codes will be added once checked against the official documents.

Research used to shape this lesson. Common Core 4.NF.A.2 (compare fractions); Cambridge Primary Mathematics Stage 4 and 5 (comparing fractions). These sources informed the lesson; no official alignment is claimed.

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