Courseversity

Lesson

Comparing fractions

Primary EducationGrade 5MathematicsCV-PRI-G05-MATH-FRA-U01-L0245–60 min

You will learn

  • Find a common denominator.
  • Compare using equivalent fractions.
  • Use benchmarks 0, 1/2 and 1.
  • Write > < =.

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. Use a common denominator to compare.
  2. Use benchmarks 0, 1/2 and 1.
  3. Write >, < or =.
  4. Check by drawing or estimating.

Words to know

common denominator
A shared bottom number.
benchmark
Reference number like 1/2.
compare
Say which is greater.
equivalent
Equal in value.

1. Discover: bigger share

Ada gets 3/4 of a cake and Bayo gets 5/6. Who gets more?

2. Understand: comparing

  • 3/4 = 9/12 and 5/6 = 10/12, so 5/6 > 3/4.
  • 2/5 = 16/40 and 3/8 = 15/40, so 2/5 > 3/8.
  • Benchmark: 3/7 < 1/2, 5/8 > 1/2.
3/4
5/6

Idea 1: Common denominator

2/3 and 3/5: 10/15 and 9/15, so 2/3 > 3/5. 5/8 and 3/4: 5/8 and 6/8, so 5/8 < 3/4.

Idea 2: Benchmark

4/9 and 1/2: 1/2 is 4.5/9, so 4/9 < 1/2.

Idea 3: More

7/10 and 3/4: 14/20 and 15/20, so <. 1/3 and 2/7: 7/21 and 6/21, so >.

Why not compare the bottoms? A bigger denominator means smaller pieces.

Remember: Same denominator, then compare numerators.

3. Worked examples

Example 1 (I show you): Compare

2/3 __ 3/5

  1. 10/15 and 9/15.

Answer: >

Example 2 (We do it together): Compare

5/8 __ 3/4

  1. 5/8 and 6/8.

Answer: <

Example 3 (You try): Compare

1/3 __ 2/7

Show the steps and answer
  1. 7/21 and 6/21.

Answer: >

Did you know?

With the same numerator, the smaller denominator makes the bigger fraction.

Why this matters

Comparing fractions helps us choose better deals and measure fairly.

4. Explore: compare

You need paper.

  1. Find the LCD of 4 and 6.
  2. Convert both.
  3. Compare.
  4. Check with a benchmark.
Think about it: what did you notice?

10/12 > 9/12.

5. Practise

Say it in a sentence

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

  • The common denominator is ___.
  • The fractions become ___ and ___.
  • So ___ is greater.
  • It is near the benchmark ___.

Guided practice

Question 1. 3/4 ? 5/6

<

Question 2. 2/5 ? 3/8

>

Question 3. 3/7 ? 1/2

<

Independent practice

Level 1: Start

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

Level 2: Grow

  1. 3/4 __ 5/8
  2. 2/5 __ 1/2
  3. 3/10 __ 1/3

Level 3: Stretch

  1. 5/12 __ 3/8
  2. Order 1/2, 1/3, 1/4 from least
  3. Ben says 3/5 > 3/4 because 5 > 4. What is wrong?

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

6. Apply: everyday mathematics

Ada ate 3/4 of a cake and Bayo 5/6. Who ate more?

Show a sample answer

Bayo.

Another one. Ana runs 3/4 km and Ben runs 4/5 km. Who runs farther?

Show a sample answer

15/20 and 16/20, so Ben runs farther.

7. Common mistakes

Mistake: Comparing denominators only.
Fix: Make common denominators.
Another mistake: Comparing only the denominators.
Fix: Use a common denominator.
Another mistake: Comparing only the numerators.
Fix: Make the denominators the same first.

8. Lesson summary and revision card

I can…

  • I can find a common denominator.
  • I can compare using equivalent fractions.
  • I can use benchmarks.
  • I can write >, < and =.

9. Check and master

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

1. 3/4 ? 5/6

2. 2/5 ? 3/8

3. 3/7 ? 1/2

4. 2/3 ? 3/5

5. 5/8 ? 3/4

6. 3/5 __ 2/3

7. 3/4 __ 2/3

8. 5/6 __ 4/5

9. 3/8 __ 1/3

10. 4/7 __ 1/2

11. 2/9 __ 1/4

12. The greatest of 1/2, 3/5 and 4/7 is…

Challenge 1. 4/9 ? 1/2

Challenge 2. 1/2, 2/3 and 3/5 in order from least are…

Your result appears here after you answer every question.

10. Key takeaways

  • Common denominators.
  • Benchmarks.
  • Compare tops.

11. Next lesson

Next lesson: Adding fractions with unlike denominators. 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 2/3 and 3/5. [3 marks]
  2. Compare 5/8 and 3/4. [3 marks]
  3. Compare 4/9 and 1/2 using the benchmark 1/2. [2 marks]
  4. Compare 7/10 and 3/4. [3 marks]
  5. Ali says 2/7 > 1/3 because 7 > 3. Is he right? Explain. [3 marks]

Total: 14 marks.

Marking guide and model answers
  1. Common denominator 15 [1]; 10/15 and 9/15 [1]; > [1]
  2. Common denominator 8 [1]; 5/8 and 6/8 [1]; < [1]
  3. 1/2 is 4.5/9 [1]; 4/9 < 1/2 [1]
  4. Common denominator 20 [1]; 14/20 and 15/20 [1]; < [1]
  5. No [1]. 7/21 and 6/21 [1]. 1/3 is greater [1].

Score guide: 12 to 14 = secure. 9 to 11 = nearly there, revise the parts you missed. Under 9 = work through the lesson again with a grown-up.

Printable worksheet

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

Homework

Compare five pairs of fractions.

Answer key and marking scheme

Question Expected response Marks
2/3 ? 3/5 > 2
5/8 ? 3/4 < 2
4/9 ? 1/2 < 2
7/10 ? 3/4 < 2
1/3 ? 2/7 > 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 1/4, 1/3, 1/2; 3 Fifths are smaller pieces than fourths, so 3/4 is greater..

Mastery and remediation

Objective Bronze (Developing) Silver (Proficient) Gold (Advanced)
O1 Find a common 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 using equivalent fractions 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 benchmarks 0, 1/2 and 1 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 Write > < = 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: Comparing denominators only. Make common 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 unlike denominators. You do not need to be good at mathematics to help.

  • Compare recipe amounts.
  • Ask: can we make the bottoms the same?
  • Use 1/2 as a benchmark.
  • 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: find a common denominator; compare using equivalent fractions; use benchmarks 0, 1/2 and 1; write > < =.

Prerequisite knowledge. Lesson 1.

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. 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. What is the common denominator? Which is greater?

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. Comparing denominators only. Make common denominators.

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

Use the quiz and worksheet on this page. The 14-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; Cambridge Primary Mathematics Stage 5 (comparing fractions). These sources informed the lesson; no official alignment is claimed.

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