You will learn
- Find a fraction of an amount.
- Add and subtract fractions in problems.
- Use bar models.
- Check answers.
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
- Divide by the denominator, then multiply by the numerator.
- Add or subtract fractions of the same whole.
- Draw a bar model.
- Check that the answer makes sense.
Words to know
Divide then multiply.
What is left.
A diagram of parts.
All together.
1. Discover: real fractions
A class has 24 pupils. 3/4 are present. How many are present? What fraction of a pizza is left if 2/8 and 3/8 were eaten?
2. Understand: fraction problems
- 3/4 of 24 = 24 ÷ 4 × 3 = 6 × 3 = 18.
- Pizza: 2/8 + 3/8 = 5/8 eaten, so 8/8 − 5/8 = 3/8 left.
- 2/5 of 30 = 6 × 2 = 12.
Idea 1: Fraction of an amount
1/3 of 27: 27 ÷ 3 = 9. 3/5 of 25: 25 ÷ 5 = 5, then 5 × 3 = 15.
Idea 2: More
4/9 of 36: 36 ÷ 9 = 4, then 4 × 4 = 16. 5/6 of 18: 18 ÷ 6 = 3, then 3 × 5 = 15.
Idea 3: Remaining
1/4 + 1/2 = 1/4 + 2/4 = 3/4 eaten. The remainder is 1 − 3/4 = 1/4.
Why a bar model? It shows the parts and what is left.
3. Worked examples
Example 1 (I show you): Amount
1/3 of 27
- 27 ÷ 3.
Answer: 9
Example 2 (We do it together): Amount
4/9 of 36
- 36 ÷ 9 = 4, then × 4.
Answer: 16
Example 3 (You try): Remaining
1 whole, 1/4 and 1/2 eaten
Show the steps and answer
- 3/4 eaten.
Answer: 1/4
Did you know?
The word “of” in fractions means multiply.
Why this matters
Fraction problems show up in sharing, cooking and money.
4. Explore: model it
You need paper.
- Draw a bar for 24 pupils.
- Divide into 4 parts.
- Shade 3 parts.
- Count.
Think about it: what did you notice?
18 pupils.
5. Practise
Say it in a sentence
Use these starters when you talk about the lesson. Say them out loud.
- The whole is ___.
- One part is ___.
- The fraction of the amount is ___.
- What is left is ___.
Guided practice
Question 1. 3/4 of 24?
18.
Question 2. Pizza left after 2/8 and 3/8?
3/8.
Question 3. 2/5 of 30?
12.
Independent practice
Level 1: Start
- 1/3 of 27
- 3/5 of 25
- 4/9 of 36
- Left after 1/4 and 1/2 eaten (of 1 whole)
- 5/6 of 18
Level 2: Grow
- 1/4 of 28
- 2/3 of 21
- 3/10 of 50
Level 3: Stretch
- 5/12 of 60
- A cake: 2/9 is eaten, then 4/9. How much is left?
- Ben says 2/5 of 30 = 6. What is wrong?
Answers are in the answer key below. Try first, then check.
6. Apply: everyday mathematics
A tank of 40 litres is 3/4 full. How many litres?
Show a sample answer
30 litres.
Another one. A farmer has 48 goats. 5/8 are female. How many are female? How many are male?
Show a sample answer
48 ÷ 8 = 6 and 6 × 5 = 30 female, so 18 male.
7. Common mistakes
Fix: Divide, then multiply.
Fix: Multiply by the numerator too.
Fix: Check they are fractions of the same whole.
8. Lesson summary and revision card
- I can find a fraction of an amount.
- I can add and subtract fractions in problems.
- I can use bar models.
- I can check my answers.
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
- Fraction of amount: divide, multiply.
- Whole = all parts.
- Bar models help.
11. Next lesson
Next lesson: Understanding tenths. 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 1/3 of 27. [2 marks]
- Find 3/5 of 25. [2 marks]
- Find 4/9 of 36. [2 marks]
- A cake is cut. 1/4 and 1/2 are eaten. What fraction is left? [3 marks]
- Ali says 5/6 of 18 is 3. Is he right? Explain. [3 marks]
Total: 12 marks.
Marking guide and model answers
- 27 ÷ 3 [1]; 9 [1]
- 25 ÷ 5 = 5 [1]; 15 [1]
- 36 ÷ 9 = 4 [1]; 16 [1]
- 1/4 + 2/4 = 3/4 [1]; 1 − 3/4 [1]; 1/4 [1]
- No [1]. 18 ÷ 6 = 3 is only 1/6 [1]. 3 × 5 = 15 [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
- 1/3 of 27
- 3/5 of 25
- 4/9 of 36
- 1 − 1/4 − 1/2
- 5/6 of 18
- 3/4 of 24 =
- After 2/8 and 3/8 are eaten, left:
- 2/5 of 30 =
- 3/5 of 25 =
- 4/9 of 36 =
Homework
Write a fraction word problem about your family.
Answer key and marking scheme
| Question | Expected response | Marks |
|---|---|---|
| 1/3 of 27 | 9 | 2 |
| 3/5 of 25 | 15 | 2 |
| 4/9 of 36 | 16 | 2 |
| 1 − 1/4 − 1/2 | 1/4 | 2 |
| 5/6 of 18 | 15 | 2 |
| Total | 10 |
Practice answers: Worksheet: 1 9; 2 15; 3 16; 4 1/4; 5 15.
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 18; 7 3/8; 8 12; 9 15; 10 16.
Independent practice answers. Level 1: 1 9; 2 15; 3 16; 4 1/4; 5 15. Level 2: 1 7; 2 14; 3 15. Level 3: 1 25; 2 3/9 = 1/3; 3 30 ÷ 5 = 6 is only 1/5. 6 × 2 = 12..
Mastery and remediation
| Objective | Bronze (Developing) | Silver (Proficient) | Gold (Advanced) |
|---|---|---|---|
| O1 Find a fraction of an amount | 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 Add and subtract fractions in 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 |
| O3 Use bar models | 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 Check answers | 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 but forgetting to multiply by the numerator. Divide, then multiply.
- Explain another way: use real objects first, then pictures.
- Show a simpler example: Use counters for fractions of a set.
- 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 solves word problems with fractions. You do not need to be good at mathematics to help.
- Share a bag of sweets in fractions.
- Ask: what is one part?
- Draw a bar model together.
- 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: find a fraction of an amount; add and subtract fractions in problems; use bar models; check answers.
Prerequisite knowledge. Lessons 1 to 9.
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. What is the whole? What is one part? What is left?
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 but forgetting to multiply by the numerator. Divide, then multiply.
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. Use counters for fractions of a set. 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.B.3d and 4.NF.B.4c; Cambridge Primary Mathematics Stage 4 and 5 (fraction problems). These sources informed the lesson.