Courseversity

Lesson

Comparing simple fractions

Primary EducationGrade 3MathematicsCV-PRI-G03-MATH-FRA-U01-L0645–60 min

You will learn

  • Compare fractions with the same denominator.
  • Compare fractions with the same numerator.
  • Use and =.
  • Compare a fraction with one half.

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: more parts means smaller.
  3. Use >, < and =.
  4. Compare with one half.

Words to know

compare
Say which is bigger.
same denominator
The same number of equal parts in the whole.
same numerator
The same number of parts taken.
one half
Two quarters, 1/2.

1. Discover: who ate more?

Ada ate 3/8 of a pizza and Kofi ate 5/8 of an equal pizza. Who ate more? How can you tell without drawing?

2. Understand: comparing fractions

Same denominator: compare the numerators. 3/8 < 5/8 because 3 parts is less than 5 parts of the same size.

Same numerator: compare the denominators. The bigger the denominator, the smaller the part. 1/3 > 1/5 and 2/5 > 2/8.

Compare with 1/2: 3/4 > 1/2 because 3/4 is more than 2/4. 1/4 < 1/2.

Idea 1: Same denominator

2/6 < 5/6 because 2 sixths is fewer than 5 sixths.

Idea 2: Same numerator

2/5 > 2/8, because fifths are bigger than eighths.

Idea 3: With a half

3/4 > 1/2 because 3 fourths is more than 2 fourths.

Why? Comparing needs the same whole.

Remember: Same denominator: bigger numerator is bigger. Same numerator: smaller denominator is bigger.

3. Worked examples

Example 1 (I show you): Numerators

2/6 __ 5/6

  1. 2 is less than 5.

Answer: <

Example 2 (We do it together): Denominators

2/5 __ 2/8

  1. Fifths are bigger.

Answer: >

Example 3 (You try): Half

3/4 __ 1/2

Show the steps and answer
  1. 1/2 = 2/4.

Answer: >

Did you know?

We can only compare fractions of the same whole.

Why this matters

Comparing fractions helps us share fairly.

4. Explore: compare strips

You need paper strips.

  1. Make 3/8 and 5/8 strips.
  2. Compare.
  3. Make 1/3 and 1/5 strips.
  4. Compare.
Think about it: what did you notice?

3/8 < 5/8; 1/3 > 1/5.

5. Practise

Say it in a sentence

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

  • The denominators are the same so ___.
  • The numerators are the same so ___.
  • ___ is bigger than ___.
  • I compare with 1/2 because ___.

Guided practice

Question 1. 3/8 __ 5/8

<

Question 2. 1/3 __ 1/5

>

Question 3. 3/4 __ 1/2

>

Independent practice

Level 1: Start

  1. 2/6 __ 5/6
  2. 1/4 __ 1/8
  3. 2/5 __ 2/8
  4. 3/4 __ 1/2
  5. Order 1/2, 1/4, 1/8 from biggest

Level 2: Grow

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

Level 3: Stretch

  1. Biggest of 2/3, 2/5, 2/9
  2. Order from biggest: 1/2, 3/4, 1/4
  3. Ama says 1/8 > 1/4 because 8 > 4. What is wrong?

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

6. Apply: everyday mathematics

Ada ate 3/8 and Kofi ate 5/8 of equal pizzas. Who ate more?

Show a sample answer

Kofi.

Another one. Which is bigger, 3/5 or 3/8? Explain.

Show a sample answer

3/5. Fifths are bigger than eighths and both have 3 parts.

7. Common mistakes

Mistake: Thinking 1/8 is bigger than 1/3 because 8 is bigger than 3.
Fix: Same numerator: the bigger denominator gives the smaller part.
Another mistake: Thinking a bigger denominator means a bigger fraction.
Fix: More parts means smaller parts.
Another mistake: Comparing fractions of different wholes.
Fix: Use the same whole.

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 >, < and =.
  • I can compare with one half.

9. Check and master

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

1. 3/8 __ 5/8

2. 1/3 __ 1/5

3. 2/5 __ 2/8

4. 3/4 __ 1/2

5. Which is biggest?

6. 2/8 __ 6/8

7. 1/3 __ 1/4

8. 4/5 __ 4/9

9. 3/8 __ 1/2

10. Bigger: 5/8 or 3/8?

11. Which is the biggest: 1/10, 1/5, 1/3?

12. Which fraction is less than a half?

Challenge 1. Which is the biggest: 3/8, 3/4 or 3/6?

Challenge 2. Order from smallest: 3/4, 1/2, 1/4

Your result appears here after you answer every question.

10. Key takeaways

  • Same denominator: compare numerators.
  • Same numerator: compare denominators.
  • Compare with 1/2.

11. Next lesson

Next lesson: Recognising equivalent 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. Write >, < or =: 2/6 __ 5/6 [1 mark]
  2. Write >, < or =: 1/4 __ 1/8 [1 mark]
  3. Write >, < or =: 3/4 __ 1/2 [2 marks]
  4. Order from biggest: 1/2, 1/4, 1/8. [2 marks]
  5. Ali says 2/8 is bigger than 2/5 because 8 is bigger. Is he right? Explain. [3 marks]

Total: 9 marks.

Marking guide and model answers
  1. < [1]
  2. > [1]
  3. 1/2 = 2/4 [1]; > [1]
  4. 1/2 [1]; 1/4; 1/8 [1]
  5. No [1]. Same numerator: more parts means smaller parts [1]. 2/5 is bigger [1].

Score guide: 8 to 9 = secure. 6 to 7 = nearly there, revise the parts you missed. Under 6 = work through the lesson again with a grown-up.

Printable worksheet

  1. 2/6 __ 5/6
  2. 1/4 __ 1/8
  3. 2/5 __ 2/8
  4. 3/4 __ 1/2
  5. Biggest of 1/2, 1/4, 1/8
  6. 3/8 __ 5/8
  7. 1/3 __ 1/5
  8. 2/5 __ 2/8
  9. 3/4 __ 1/2
  10. Biggest: 3/8, 3/4 or 3/6?

Homework

Compare five pairs of fractions using paper strips.

Answer key and marking scheme

Question Expected response Marks
2/6 __ 5/6 < 2
1/4 __ 1/8 > 2
2/5 __ 2/8 > 2
3/4 __ 1/2 > 2
Biggest of 1/2, 1/4, 1/8 1/2 2
Total 10

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

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 3/4.

Independent practice answers. Level 1: 1 <; 2 >; 3 >; 4 >; 5 1/2, 1/4, 1/8. Level 2: 1 <; 2 <; 3 >. Level 3: 1 2/3; 2 3/4, 1/2, 1/4; 3 Same numerator: more parts means smaller parts. 1/8 < 1/4..

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 <, > 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
O4 Compare a fraction with one half 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 1/8 is bigger than 1/3 because 8 is bigger than 3. Same numerator: the bigger denominator gives the smaller part.
  2. Explain another way: use real objects first, then pictures.
  3. Show a simpler example: Compare using a number line.
  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 simple fractions. You do not need to be good at mathematics to help.

  • Compare slices of pizza or fruit.
  • Ask: same denominator or same numerator?
  • Use fraction strips.
  • 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 <, > and =; compare a fraction with one half.

Prerequisite knowledge. Lessons 2 and 5.

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. Same denominator or numerator? Which is bigger? Compare with one half.

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 1/8 is bigger than 1/3 because 8 is bigger than 3. Same numerator: the bigger denominator gives the smaller part.

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

Use the quiz and worksheet on this page. The 9-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 using a number line. 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 3.NF.A.3d (compare fractions); Cambridge Primary Mathematics Stage 3 (fractions). These sources informed the lesson; no official alignment is claimed.

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