You will learn
- Say that a unit fraction has 1 as the numerator.
- Read and write unit fractions.
- Explain that more parts means smaller parts.
- Order unit fractions.
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
- A unit fraction has 1 on top.
- The denominator says how many equal parts.
- More parts means smaller parts.
- Order unit fractions by part size.
Words to know
A fraction with 1 on top.
The top number.
The bottom number.
Say which is bigger.
1. Discover: bigger piece
Would you rather have 1/3 or 1/6 of the same cake? Why?
2. Understand: unit fractions
A unit fraction is one equal part of a whole. It has 1 as the numerator: 1/2, 1/3, 1/4, 1/5, 1/6, 1/8.
The denominator tells how many equal parts make the whole. The more parts, the smaller each part. So 1/2 > 1/3 > 1/4 > 1/6 > 1/8.
1/3 is bigger than 1/6 because thirds are bigger pieces than sixths.
Idea 1: Unit fraction
A unit fraction has 1 as the numerator. One fifth is 1/5. One sixth is 1/6.
Idea 2: Bigger or smaller
1/4 is bigger than 1/8, because fourths are bigger parts than eighths. More parts means smaller parts.
Idea 3: Order
Smallest of 1/3, 1/5 and 1/2 is 1/5.
Why? Cutting into 5 gives the smallest piece.
3. Worked examples
Example 1 (I show you): Write
Write one fifth.
- 1 part of 5.
Answer: 1/5
Example 2 (We do it together): Compare
Bigger: 1/4 or 1/8?
- Fewer parts are bigger.
Answer: 1/4
Example 3 (You try): Order
Smallest of 1/3, 1/5, 1/2?
Show the steps and answer
- Largest denominator is smallest.
Answer: 1/5
Did you know?
The bottom number of a unit fraction tells how many equal parts make the whole.
Why this matters
Unit fractions are the building blocks of all fractions.
4. Explore: compare strips
You need 4 equal paper strips.
- Fold strips into halves, thirds, fourths and sixths.
- Shade one part of each.
- Compare the shaded parts.
- Order from biggest to smallest.
Think about it: what did you notice?
1/2 > 1/3 > 1/4 > 1/6.
5. Practise
Say it in a sentence
Use these starters when you talk about the lesson. Say them out loud.
- The numerator is ___.
- The denominator is ___.
- ___ is bigger than ___ because ___.
- In order: ___.
Guided practice
Question 1. Which is a unit fraction: 2/5 or 1/5?
1/5.
Question 2. Bigger: 1/3 or 1/6?
1/3.
Question 3. Smallest of 1/2, 1/4, 1/8?
1/8.
Independent practice
Level 1: Start
- Write one fifth.
- Bigger: 1/4 or 1/8?
- Smallest: 1/3, 1/5, 1/2
- Numerator of 1/6
- Denominator of 1/6
Level 2: Grow
- Write one sixth
- Bigger: 1/3 or 1/7?
- Denominator of 1/12
Level 3: Stretch
- Smallest of 1/4, 1/9, 1/2
- Order from biggest: 1/5, 1/3, 1/8
- Ben says 1/8 is bigger than 1/4 because 8 is bigger than 4. What is wrong?
Answers are in the answer key below. Try first, then check.
6. Apply: everyday mathematics
Ada gets 1/3 of a cake and Kofi gets 1/6 of an equal cake. Who gets more?
Show a sample answer
Ada.
Another one. Explain why 1/2 of a chapati is more than 1/4 of it.
Show a sample answer
Halves are cut into 2 parts so each part is bigger than a quarter.
7. Common mistakes
Fix: More parts means smaller parts.
Fix: More parts means smaller parts.
Fix: The numerator is 1, the denominator is 5: 1/5.
8. Lesson summary and revision card
- I know a unit fraction has 1 on top.
- I can read and write unit fractions.
- I know more parts means smaller parts.
- I can order unit fractions.
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
- Unit fractions have numerator 1.
- More parts, smaller part.
- Order by the denominator.
11. Next lesson
Next lesson: Numerators and 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.
- Write one fifth as a fraction. [1 mark]
- Which is bigger, 1/4 or 1/8? [1 mark]
- Find the smallest of 1/3, 1/5 and 1/2. [2 marks]
- What is the numerator of 1/6? [1 mark]
- Ana says 1/6 is bigger than 1/3 because 6 is bigger than 3. Is she right? Explain. [3 marks]
Total: 8 marks.
Marking guide and model answers
- 1/5 [1]
- 1/4 [1]
- 1/5 [1]; because it has the most parts [1]
- 1 [1]
- No [1]. More parts means smaller parts [1]. 1/3 is bigger [1].
Score guide: 7 to 8 = secure. 5 to 6 = nearly there, revise the parts you missed. Under 5 = work through the lesson again with a grown-up.
Printable worksheet
- One fifth in numbers
- Bigger: 1/4 or 1/8?
- Smallest: 1/3, 1/5, 1/2
- Numerator of 1/6
- Denominator of 1/6
- Which is a unit fraction: 1/5, 2/5 or 5/2?
- Bigger: 1/3 or 1/6?
- Smallest of 1/2, 1/4, 1/8
- The numerator of a unit fraction is ___.
- The denominator tells how many ___ make the whole.
Homework
Draw bars for 1/2, 1/3 and 1/6 and order them.
Answer key and marking scheme
| Question | Expected response | Marks |
|---|---|---|
| One fifth in numbers | 1/5 | 2 |
| Bigger: 1/4 or 1/8? | 1/4 | 2 |
| Smallest: 1/3, 1/5, 1/2 | 1/5 | 2 |
| Numerator of 1/6 | 1 | 2 |
| Denominator of 1/6 | 6 | 2 |
| Total | 10 |
Practice answers: Worksheet: 1 1/5; 2 1/4; 3 1/5; 4 1; 5 6.
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 1/5; 7 1/3; 8 1/8; 9 1; 10 equal parts.
Independent practice answers. Level 1: 1 1/5; 2 1/4; 3 1/5; 4 1; 5 6. Level 2: 1 1/6; 2 1/3; 3 12. Level 3: 1 1/9; 2 1/3, 1/5, 1/8; 3 More parts means each part is smaller. 1/4 is bigger..
Mastery and remediation
| Objective | Bronze (Developing) | Silver (Proficient) | Gold (Advanced) |
|---|---|---|---|
| O1 Say that a unit fraction has 1 as the 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 |
| O2 Read and write unit 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 Explain that more parts means smaller parts | 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 Order unit 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 |
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: Thinking 1/8 is bigger than 1/2 because 8 is bigger than 2. More parts means smaller parts.
- Explain another way: use real objects first, then pictures.
- Show a simpler example: Compare 1/2 and 1/4 with folded strips first.
- 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 learns unit fractions and how to compare them. You do not need to be good at mathematics to help.
- Fold paper into halves, thirds and quarters.
- Ask: which part is bigger?
- Cut a fruit into equal parts.
- 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: say that a unit fraction has 1 as the numerator; read and write unit fractions; explain that more parts means smaller parts; order unit fractions.
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 4 equal 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. What is the denominator? Is the numerator 1? Which has more parts?
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 1/2 because 8 is bigger than 2. More parts means smaller parts.
13–15. Assessment questions, answer keys, marking scheme
Use the quiz and worksheet on this page. The 8-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 1/2 and 1/4 with folded strips first. 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 3 » Number & Operations—Fractions. These pages list the standards that cover this topic area; read them alongside the lesson.
Research used to shape this lesson. Common Core 3.NF.A.1 and 3.NF.A.3d; Cambridge Primary Mathematics Stage 3 (fractions). These sources informed the lesson.