You will learn
- Share a unit fraction equally.
- Write the quotient as a unit fraction.
- Check by multiplying.
- Solve simple problems.
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 numerator 1.
- Dividing it by n multiplies the denominator by n.
- The quotient is a smaller unit fraction.
- Check by multiplying back.
Words to know
Numerator 1.
Share equally.
Answer.
Opposite operation.
1. Discover: sharing a piece
Half a pizza is shared equally among 3 children. What fraction of the pizza does each get?
2. Understand: unit fraction ÷ whole
- 1/2 ÷ 3 = 1/6 (1/6 × 3 = 1/2).
- 1/4 ÷ 2 = 1/8.
- 1/3 ÷ 4 = 1/12.
- 1/5 ÷ 5 = 1/25.
Multiply the denominator by the whole number.
Idea 1: Share
1/2 ÷ 4 = 1/8: half a bar shared among 4 gives each 1/8. 1/3 ÷ 2 = 1/6.
Idea 2: Same
1/5 ÷ 5 = 1/25. 1/4 ÷ 3 = 1/12.
Idea 3: Check
1/6 ÷ 2 = 1/12. Check: 2 × 1/12 = 1/6.
Why a smaller answer? Sharing splits the piece into smaller pieces.
3. Worked examples
Example 1 (I show you): Divide
1/2 ÷ 4
- 2 × 4 = 8.
Answer: 1/8
Example 2 (We do it together): Divide
1/4 ÷ 3
- 4 × 3 = 12.
Answer: 1/12
Example 3 (You try): Check
1/6 ÷ 2
Show the steps and answer
- Check 2 × 1/12.
Answer: 1/12
Did you know?
Dividing by 2 halves the piece; dividing by 3 cuts it into thirds.
Why this matters
This idea explains how we share portions fairly.
4. Explore: share
You need paper.
- Draw a half.
- Cut it into 3 equal parts.
- Name each part.
- Check by multiplying.
Think about it: what did you notice?
1/6.
5. Practise
Say it in a sentence
Use these starters when you talk about the lesson. Say them out loud.
- I share ___ into ___ parts.
- The new denominator is ___.
- Each part is ___.
- Check: ___ × ___ = ___.
Guided practice
Question 1. 1/2 ÷ 3?
1/6.
Question 2. 1/4 ÷ 2?
1/8.
Question 3. 1/3 ÷ 4?
1/12.
Independent practice
Level 1: Start
- 1/2 ÷ 4
- 1/3 ÷ 2
- 1/5 ÷ 5
- 1/4 ÷ 3
- 1/6 ÷ 2
Level 2: Grow
- 1/2 ÷ 3
- 1/4 ÷ 2
- 1/10 ÷ 2
Level 3: Stretch
- 1/3 ÷ 5
- 1/8 ÷ 4
- Ben says 1/4 ÷ 2 = 1/2. What is wrong?
Answers are in the answer key below. Try first, then check.
6. Apply: everyday mathematics
1/2 of a cake is shared among 3 children. What does each get?
Show a sample answer
1/6.
Another one. Ana has 1/2 of a chocolate bar and shares it equally among 3 friends. What fraction does each get?
Show a sample answer
1/2 ÷ 3 = 1/6
7. Common mistakes
Fix: Multiply the denominator.
Fix: Multiply the denominator.
Fix: Sharing gives smaller pieces.
8. Lesson summary and revision card
- I can share a unit fraction equally.
- I can write the quotient as a unit fraction.
- I can check by multiplying.
- I can solve simple problems.
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
- Multiply the denominator.
- Check by multiplying.
- Sharing picture.
11. Next lesson
Next lesson: Dividing whole numbers by unit 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.
- Find 1/2 ÷ 4. [3 marks]
- Find 1/3 ÷ 2. [2 marks]
- Find 1/5 ÷ 5. [2 marks]
- Find 1/4 ÷ 3. [2 marks]
- Ali says 1/6 ÷ 2 = 1/3. Is he right? Explain. [3 marks]
Total: 12 marks.
Marking guide and model answers
- 1/(2 × 4) [1]; 1/8 [1]; check 4 × 1/8 = 1/2 [1]
- 3 × 2 = 6 [1]; 1/6 [1]
- 5 × 5 = 25 [1]; 1/25 [1]
- 4 × 3 = 12 [1]; 1/12 [1]
- No [1]. Sharing 1/6 gives smaller pieces [1]. The answer is 1/12 [1].
Score guide: 11 to 12 = secure. 8 to 10 = nearly there, revise the parts you missed. Under 8 = work through the lesson again with a grown-up.
Printable worksheet
- 1/2 ÷ 4
- 1/3 ÷ 2
- 1/5 ÷ 5
- 1/4 ÷ 3
- 1/6 ÷ 2
- 1/2 ÷ 3 =
- 1/4 ÷ 2 =
- 1/3 ÷ 4 =
- 1/5 ÷ 5 =
- 1/2 ÷ 4 =
Homework
Share a unit fraction among different numbers of friends.
Answer key and marking scheme
| Question | Expected response | Marks |
|---|---|---|
| 1/2 ÷ 4 | 1/8 | 2 |
| 1/3 ÷ 2 | 1/6 | 2 |
| 1/5 ÷ 5 | 1/25 | 2 |
| 1/4 ÷ 3 | 1/12 | 2 |
| 1/6 ÷ 2 | 1/12 | 2 |
| Total | 10 |
Practice answers: Worksheet: 1 1/8; 2 1/6; 3 1/25; 4 1/12; 5 1/12.
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 1/6; 7 1/8; 8 1/12; 9 1/25; 10 1/8.
Independent practice answers. Level 1: 1 1/8; 2 1/6; 3 1/25; 4 1/12; 5 1/12. Level 2: 1 1/6; 2 1/8; 3 1/20. Level 3: 1 1/15; 2 1/32; 3 Sharing makes pieces smaller: 1/8..
Mastery and remediation
| Objective | Bronze (Developing) | Silver (Proficient) | Gold (Advanced) |
|---|---|---|---|
| O1 Share a unit fraction equally | 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 Write the quotient as a unit fraction | 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 Check by multiplying | 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 Solve simple problems | 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: Dividing the denominator. Multiply the denominator.
- Explain another way: use real objects first, then pictures.
- Show a simpler example: Share objects equally.
- 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 divides unit fractions by whole numbers. You do not need to be good at mathematics to help.
- Share half a snack among family.
- Ask: is the piece bigger or smaller?
- Use paper folding.
- 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: share a unit fraction equally; write the quotient as a unit fraction; check by multiplying; solve simple problems.
Prerequisite knowledge. Lessons 6 and 7.
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. How many parts? What is the new 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. Dividing the denominator. Multiply the denominator.
13–15. Assessment questions, answer keys, marking scheme
Use the quiz and worksheet on this page. The 12-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. Share objects equally. 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 5 » Number & Operations—Fractions; Grade 5 » 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 5.NF.B.7a; Cambridge Primary Mathematics Stage 6 (dividing fractions). These sources informed the lesson.