You will learn
- Order fractions with like denominators.
- Order fractions with unlike denominators.
- Use benchmarks 0, 1/2 and 1.
- Explain an order.
Version 0.2 · expanded edition · built from cited public sources Content is based on the official frameworks and sources listed under Sources and standards. No official endorsement is claimed. Written in the style of common primary school assessments. No exam result is promised.
Student lesson
- Like denominators: order the numerators.
- Unlike denominators: rewrite with a common denominator.
- Use benchmarks 0, 1/2 and 1.
- Say how you know the order.
Words to know
Arrange in sequence.
A friendly reference number.
Smallest.
Largest.
1. Discover: order the portions
Put 1/2, 1/4 and 3/4 of a loaf in order from smallest to biggest.
2. Understand: ordering fractions
- 1/4 < 1/2 < 3/4. (1/2 = 2/4, so 1/4 < 2/4 < 3/4.)
- 2/3, 1/6, 1/2: change to sixths: 4/6, 1/6, 3/6. Order: 1/6, 1/2, 2/3.
- Benchmarks: smaller than 1/2, near 1/2, more than 1/2.
Idea 1: Like denominators
3/8, 1/8, 5/8: compare numerators. Order: 1/8, 3/8, 5/8. Greatest of 2/5, 4/5, 1/5 is 4/5.
Idea 2: Unlike
1/3, 1/2, 1/6 become 2/6, 3/6, 1/6. Order: 1/6, 1/3, 1/2.
Idea 3: Benchmark
3/7 vs 1/2: 1/2 is 3.5 sevenths, so 3/7 is less than 1/2. Order 1/2, 3/4, 3/8: 3/8, 1/2, 3/4.
Why a benchmark? 1/2 is a quick check for size.
3. Worked examples
Example 1 (I show you): Like
Order 3/8, 1/8, 5/8
- Compare numerators.
Answer: 1/8, 3/8, 5/8
Example 2 (We do it together): Unlike
Order 1/3, 1/2, 1/6
- Use sixths.
Answer: 1/6, 1/3, 1/2
Example 3 (You try): Benchmark
3/7 compared with 1/2
Show the steps and answer
- 3.5 sevenths is a half.
Answer: less
Did you know?
1/2 is a handy benchmark for deciding which fractions are big or small.
Why this matters
Ordering fractions helps us rank shares and measurements.
4. Explore: line them up
You need paper.
- Write each as sixths.
- Order the numerators.
- Write the original fractions.
- Check with a number line.
Think about it: what did you notice?
1/6, 1/2, 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 ___.
- From least to greatest: ___.
- I compare with 1/2 because ___.
- The greatest is ___.
Guided practice
Question 1. Least of 1/2, 1/4, 3/4?
1/4.
Question 2. Order 2/3, 1/6, 1/2.
1/6, 1/2, 2/3.
Question 3. Greatest of 1/2, 1/4, 3/4?
3/4.
Independent practice
Level 1: Start
- Order 3/8, 1/8, 5/8
- Order 1/3, 1/2, 1/6
- Greatest of 2/5, 4/5, 1/5
- Order 1/2, 3/4, 3/8
- Is 3/7 more or less than 1/2?
Level 2: Grow
- Greatest of 3/10, 7/10, 1/10
- Order 1/2, 1/8, 1/4 from least
- Is 5/9 more or less than 1/2?
Level 3: Stretch
- Order 3/4, 5/8, 1/2 from least
- Order 2/3, 3/4, 5/6 from least
- Ben says 1/3 is less than 1/4 because 3 is less than 4. What is wrong?
Answers are in the answer key below. Try first, then check.
6. Apply: everyday mathematics
Three pupils have 1/2, 3/4 and 1/4 of a ribbon. Who has the longest piece?
Show a sample answer
The one with 3/4.
Another one. Three friends ate 1/2, 1/4 and 3/8 of a cake. Who ate the least? Explain.
Show a sample answer
In eighths: 4/8, 2/8 and 3/8. The least is 2/8 = 1/4.
7. Common mistakes
Fix: Use equivalent fractions.
Fix: Bigger denominator means smaller pieces.
Fix: Use a common denominator or a benchmark.
8. Lesson summary and revision card
- I can order fractions with like denominators.
- I can order fractions with unlike denominators.
- I can use the benchmarks 0, 1/2 and 1.
- I can explain an order.
9. Check and master
Answer all 14 questions. You will see feedback after each one.
Your result appears here after you answer every question.
10. Key takeaways
- Common denominators.
- Benchmarks.
- Check with bars.
11. Next lesson
Next lesson: Adding fractions with like 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.
- Order 3/8, 1/8, 5/8 from least. Explain. [2 marks]
- Order 1/3, 1/2, 1/6 from least. Explain. [3 marks]
- Find the greatest of 2/5, 4/5 and 1/5. [1 mark]
- Is 3/7 more or less than 1/2? Explain. [3 marks]
- Ana says 1/6 > 1/3. Is she right? Explain. [2 marks]
Total: 11 marks.
Marking guide and model answers
- Same denominator, compare numerators [1]; 1/8, 3/8, 5/8 [1]
- Sixths: 2/6, 3/6, 1/6 [1]; order the numerators [1]; 1/6, 1/3, 1/2 [1]
- 4/5 [1]
- 1/2 = 3.5/7 or 6/14 against 7/14 [1]; 6/14 < 7/14 [1]; less [1]
- No [1]. Sixths are smaller pieces so 1/6 < 1/3 [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
- Order 3/8, 1/8, 5/8
- Order 1/3, 1/2, 1/6
- Greatest of 2/5, 4/5, 1/5
- Order 1/2, 3/4, 3/8
- 3/7 ? 1/2
- Least of 1/2, 1/4, 3/4:
- Order 2/3, 1/6, 1/2:
- Order 3/8, 1/8, 5/8:
- Greatest of 2/5, 4/5, 1/5:
- Is 3/7 more or less than 1/2?
Homework
Order five fractions of your own.
Answer key and marking scheme
| Question | Expected response | Marks |
|---|---|---|
| Order 3/8, 1/8, 5/8 | 1/8, 3/8, 5/8 | 2 |
| Order 1/3, 1/2, 1/6 | 1/6, 1/3, 1/2 | 2 |
| Greatest of 2/5, 4/5, 1/5 | 4/5 | 2 |
| Order 1/2, 3/4, 3/8 | 3/8, 1/2, 3/4 | 2 |
| 3/7 ? 1/2 | less than | 2 |
| Total | 10 |
Practice answers: Worksheet: 1 1/8, 3/8, 5/8; 2 1/6, 1/3, 1/2; 3 4/5; 4 3/8, 1/2, 3/4; 5 less than.
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 1/4; 7 1/6, 1/2, 2/3; 8 1/8, 3/8, 5/8; 9 4/5; 10 less.
Independent practice answers. Level 1: 1 1/8, 3/8, 5/8; 2 1/6, 1/3, 1/2; 3 4/5; 4 3/8, 1/2, 3/4; 5 less than 1/2. Level 2: 1 7/10; 2 1/8, 1/4, 1/2; 3 more. Level 3: 1 1/2, 5/8, 3/4; 2 2/3, 3/4, 5/6; 3 Thirds are bigger pieces than quarters, so 1/3 > 1/4..
Mastery and remediation
| Objective | Bronze (Developing) | Silver (Proficient) | Gold (Advanced) |
|---|---|---|---|
| O1 Order fractions with like 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 |
| O2 Order fractions with 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 |
| 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 Explain an order | 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 |
Courseversity badge thresholds (overall quiz score): Gold = 90–100%; Silver = 80–89.9%; Bronze = 70–79.9%. A badge is never a full record of progress.
If a learner struggles
- Find the misconception: Ordering by denominator only. Use equivalent fractions.
- Explain another way: use real objects first, then pictures.
- Show a simpler example: Place fractions on a number line.
- Guided practice: work through one example together and let the learner try the next one.
- Reassess: use the quiz again or the worksheet.
- Move on when the learner shows Silver-level evidence independently.
For parents and guardians
In this lesson your child orders fractions using common denominators and benchmarks. You do not need to be good at mathematics to help.
- Order pieces of paper folded into fractions.
- Ask: is it more or less than a half?
- Use a number line from 0 to 1.
- 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: order fractions with like denominators; order fractions with unlike denominators; use benchmarks 0, 1/2 and 1; explain an order.
Prerequisite knowledge. Lesson 4.
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. Do the fractions have the same denominator? Is it more or less than 1/2?
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. Ordering by denominator only. Use equivalent fractions.
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. Place fractions on 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
This lesson is based on the sources below, and no official 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. Where a standard code is named, it points to the official framework.
Official standards for this topic area. Common Core State Standards for Mathematics (official site): Grade 4 » Number & Operations—Fractions; Grade 4 » Number & Operations in Base Ten. These pages list the standards that cover this topic area; read them alongside the lesson.
Research used to shape this lesson. Common Core 4.NF.A.2; Cambridge Primary Mathematics Stage 4 and 5 (ordering fractions). These sources informed the lesson.