You will learn
- Ask how many unit fractions fit in a whole.
- Write the quotient as a whole.
- Check by multiplying.
- Solve simple problems.
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
- Ask how many unit fractions fit in a whole.
- There are n pieces of 1/n in 1 whole.
- Multiply the whole number by n.
- Check by multiplying back.
Words to know
Numerator 1.
Count parts.
Answer.
0, 1, 2 …
1. Discover: cutting rope
How many half-metre pieces can be cut from a 3 m rope?
2. Understand: whole ÷ unit fraction
- 3 ÷ 1/2 = 6 (each whole has 2 halves).
- 4 ÷ 1/3 = 12.
- 5 ÷ 1/4 = 20.
- 2 ÷ 1/5 = 10.
Multiply the whole by the denominator.
Idea 1: Count
How many fifths in 2? 5 in each whole, so 2 × 5 = 10. 6 ÷ 1/2 = 6 × 2 = 12.
Idea 2: More
3 ÷ 1/4 = 3 × 4 = 12. 4 ÷ 1/8 = 4 × 8 = 32.
Idea 3: Tenths
10 ÷ 1/10 = 10 × 10 = 100.
Why bigger? Many small pieces fit in a whole.
3. Worked examples
Example 1 (I show you): Divide
2 ÷ 1/5
- 5 fifths in each whole.
Answer: 10
Example 2 (We do it together): Divide
3 ÷ 1/4
- 3 × 4.
Answer: 12
Example 3 (You try): Divide
4 ÷ 1/8
Show the steps and answer
- 4 × 8.
Answer: 32
Did you know?
Dividing by 1/2 is the same as doubling.
Why this matters
This tells us how many small portions we can make.
4. Explore: cut
You need paper.
- Draw 3 wholes.
- Cut each in halves.
- Count the halves.
- Write 3 ÷ 1/2 = 6.
Think about it: what did you notice?
6.
5. Practise
Say it in a sentence
Use these starters when you talk about the lesson. Say them out loud.
- In 1 whole there are ___ pieces.
- In ___ wholes there are ___ × ___.
- The answer is ___.
- Check: ___ × ___ = ___.
Guided practice
Question 1. 3 ÷ 1/2?
6.
Question 2. 4 ÷ 1/3?
12.
Question 3. 5 ÷ 1/4?
20.
Independent practice
Level 1: Start
- 2 ÷ 1/5
- 6 ÷ 1/2
- 3 ÷ 1/4
- 10 ÷ 1/10
- 4 ÷ 1/8
Level 2: Grow
- 3 ÷ 1/2
- 5 ÷ 1/3
- 2 ÷ 1/8
Level 3: Stretch
- 7 ÷ 1/4
- 12 ÷ 1/6
- Ben says 4 ÷ 1/2 = 2. What is wrong?
Answers are in the answer key below. Try first, then check.
6. Apply: everyday mathematics
A 3 m rope is cut into 1/2 m pieces. How many pieces?
Show a sample answer
6.
Another one. A ribbon is 5 m long and is cut into pieces of 1/4 m. How many pieces?
Show a sample answer
5 × 4 = 20 pieces
7. Common mistakes
Fix: Multiply by the denominator.
Fix: Multiply the whole by the denominator.
Fix: The answer should be bigger.
8. Lesson summary and revision card
- I can ask how many unit fractions fit.
- I can write the quotient as a whole.
- 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
- Count unit fractions.
- Multiply by denominator.
- Check by multiplying.
11. Next lesson
Next lesson: Fraction word problems. 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 2 ÷ 1/5. [2 marks]
- Find 6 ÷ 1/2. [2 marks]
- Find 3 ÷ 1/4. [2 marks]
- Find 4 ÷ 1/8. [2 marks]
- Ali says 10 ÷ 1/10 = 1. Is he right? Explain. [3 marks]
Total: 11 marks.
Marking guide and model answers
- 5 fifths in each whole [1]; 2 × 5 = 10 [1]
- 2 halves in each whole [1]; 12 [1]
- 4 quarters in each whole [1]; 12 [1]
- 8 eighths in each whole [1]; 32 [1]
- No [1]. Each whole has 10 tenths [1]. 10 × 10 = 100 [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
- 2 ÷ 1/5
- 6 ÷ 1/2
- 3 ÷ 1/4
- 10 ÷ 1/10
- 4 ÷ 1/8
- 3 ÷ 1/2 =
- 4 ÷ 1/3 =
- 5 ÷ 1/4 =
- 2 ÷ 1/5 =
- 6 ÷ 1/2 =
Homework
Cut paper strips into unit fractions and count them.
Answer key and marking scheme
| Question | Expected response | Marks |
|---|---|---|
| 2 ÷ 1/5 | 10 | 2 |
| 6 ÷ 1/2 | 12 | 2 |
| 3 ÷ 1/4 | 12 | 2 |
| 10 ÷ 1/10 | 100 | 2 |
| 4 ÷ 1/8 | 32 | 2 |
| Total | 10 |
Practice answers: Worksheet: 1 10; 2 12; 3 12; 4 100; 5 32.
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 6; 7 12; 8 20; 9 10; 10 12.
Independent practice answers. Level 1: 1 10; 2 12; 3 12; 4 100; 5 32. Level 2: 1 6; 2 15; 3 16. Level 3: 1 28; 2 72; 3 There are 2 halves in each whole, so 4 × 2 = 8..
Mastery and remediation
| Objective | Bronze (Developing) | Silver (Proficient) | Gold (Advanced) |
|---|---|---|---|
| O1 Ask how many unit fractions fit in a whole | 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 whole | 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 |
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
- Find the misconception: Dividing instead of multiplying. Multiply by the denominator.
- Explain another way: use real objects first, then pictures.
- Show a simpler example: Count halves in wholes.
- 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 whole numbers by unit fractions. You do not need to be good at mathematics to help.
- Count how many half-glasses fill a jug.
- Ask: how many pieces in one whole?
- Use pizza slices.
- 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: ask how many unit fractions fit in a whole; write the quotient as a whole; check by multiplying; solve simple problems.
Prerequisite knowledge. Lesson 8.
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 pieces in one whole? How many wholes?
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 instead of multiplying. Multiply by the denominator.
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. Count halves in wholes. 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 5.NF.B.7b and 5.NF.B.7c; Cambridge Primary Mathematics Stage 6 (dividing by fractions). These sources informed the lesson; no official alignment is claimed.