You will learn
- Use fractions of a whole in a story.
- Use fractions of a collection in a story.
- Compare fractions in a story.
- Explain the answer.
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
- Use fractions of a whole or a collection.
- Read the story and decide which.
- Compare fractions in a story.
- Explain the answer.
Words to know
A part of a whole.
The complete thing.
Give out equally.
Say which is more.
1. Discover: a pizza shared
A pizza has 8 equal slices. Ada eats 2 and Kofi eats 3. What fraction did each eat, and what fraction is left?
2. Understand: fraction problems
Read the story, find the whole and the equal parts, then use fractions.
Pizza: Ada ate 2/8, Kofi 3/8. Kofi ate more (3/8 > 2/8). Together they ate 5/8, so 3/8 is left.
A tank holds 20 L and is 3/4 full: 3/4 of 20 = 15 L. 1/3 of 24 pupils = 8 pupils. Half of 18 mangoes = 9.
Idea 1: Fraction of a collection
3/4 of 40: 40 ÷ 4 = 10, then 3 × 10 = 30. 1/3 of 24 pupils: 24 ÷ 3 = 8.
Idea 2: Fraction of a whole
A pizza of 8 slices, 3 eaten: 3/8 eaten and 5/8 left.
Idea 3: Compare
Ada ate 2/8 and Kofi ate 3/8. Same whole, so Kofi ate more.
Why the same whole? 1/2 of a small pizza may be less than 1/4 of a big one.
3. Worked examples
Example 1 (I show you): Collection
3/4 of 40 = ?
- 40 ÷ 4 = 10.
- 3 × 10.
Answer: 30
Example 2 (We do it together): Pizza
8 slices, 3 eaten. What fraction is eaten?
- 3 out of 8.
Answer: 3/8
Example 3 (You try): Compare
Ada 2/8, Kofi 3/8. Who ate more?
Show the steps and answer
- 3 is more than 2.
Answer: Kofi
Did you know?
Bakers, builders and farmers use fractions every day.
Why this matters
Fractions help us share fairly in real life.
4. Explore: story time
You need paper and a pencil.
- Draw the pizza in 8 slices.
- Shade 2 for Ada and 3 for Kofi.
- Write the fractions.
- Find the fraction left.
Think about it: what did you notice?
2/8, 3/8, 5/8 eaten, 3/8 left.
5. Practise
Say it in a sentence
Use these starters when you talk about the lesson. Say them out loud.
- The whole is ___.
- The fraction is ___.
- ___ of ___ is ___.
- ___ ate more because ___.
Guided practice
Question 1. Ada ate 2/8 and Kofi 3/8. Who ate more?
Kofi.
Question 2. How much is left?
3/8.
Question 3. 3/4 of 40?
30.
Independent practice
Level 1: Start
- 3/4 of 40
- 1/3 of 24
- Half of 18
- Pizza of 8 slices, 3 eaten: fraction left?
- A tank is 3/4 full of 20 L. How many litres?
Level 2: Grow
- 1/2 of 30
- 1/5 of 45
- 2/3 of 12
Level 3: Stretch
- 3/5 of 40
- A pizza has 12 slices and 5 are eaten. What fraction is left?
- Kofi says 1/3 of 24 is 72. What is wrong?
Answers are in the answer key below. Try first, then check.
6. Apply: everyday mathematics
A tank holds 20 L and is 3/4 full. How many litres are in it?
Show a sample answer
15 L.
Another one. A farmer has 36 goats. 2/9 are sick. How many are sick?
Show a sample answer
8 goats
7. Common mistakes
Fix: Find the whole first.
Fix: Divide by the denominator.
Fix: Use the same whole.
8. Lesson summary and revision card
- I can use fractions of a whole in a story.
- I can use fractions of a collection.
- I can compare fractions in a story.
- I can explain my answer.
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
- Find the whole.
- Fraction of a collection.
- Compare and explain.
11. Next lesson
Next lesson: Fractions mastery assessment. 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 3/4 of 40. [3 marks]
- Find 1/3 of 24 pupils. [2 marks]
- A pizza of 8 slices; 3 are eaten. What fraction is eaten? [1 mark]
- Ada ate 2/8 and Kofi ate 3/8. Who ate more? [2 marks]
- A tank holds 20 L and is 3/4 full. How many litres? [3 marks]
Total: 11 marks.
Marking guide and model answers
- 40 ÷ 4 = 10 [1]; 3 × 10 [1] = 30 [1]
- 24 ÷ 3 [1] = 8 [1]
- 3/8 [1]
- 3 is more than 2 [1]; Kofi [1]
- 20 ÷ 4 = 5 [1]; 3 × 5 [1] = 15 L [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
- 3/4 of 40
- 1/3 of 24
- Half of 18
- 8 slices, 3 eaten: fraction left
- 3/4 of 20 L
- 3/4 of 40 =
- 1/3 of 24 pupils =
- Pizza of 8 slices; 3 eaten. Fraction eaten?
- Half of 18 mangoes =
- A tank holds 20 L and is 3/4 full. Litres?
Homework
Write a fraction story from home life and solve it.
Answer key and marking scheme
| Question | Expected response | Marks |
|---|---|---|
| 3/4 of 40 | 30 | 2 |
| 1/3 of 24 | 8 | 2 |
| Half of 18 | 9 | 2 |
| 8 slices, 3 eaten: fraction left | 5/8 | 2 |
| 3/4 of 20 L | 15 | 2 |
| Total | 10 |
Practice answers: Worksheet: 1 30; 2 8; 3 9; 4 5/8; 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 30; 7 8; 8 3/8; 9 9; 10 15 L.
Independent practice answers. Level 1: 1 30; 2 8; 3 9; 4 5/8; 5 15 litres. Level 2: 1 15; 2 9; 3 8. Level 3: 1 24; 2 7/12; 3 He multiplied. Divide by 3: 8..
Mastery and remediation
| Objective | Bronze (Developing) | Silver (Proficient) | Gold (Advanced) |
|---|---|---|---|
| O1 Use fractions of a whole in a story | 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 Use fractions of a collection in a story | 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 Compare fractions in a story | 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 the answer | 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: Using the wrong whole. Find the whole first.
- Explain another way: use real objects first, then pictures.
- Show a simpler example: Draw the whole and the parts.
- 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 uses fractions in real situations. You do not need to be good at mathematics to help.
- Ask your child to share your snack using fractions.
- Ask: what is the whole?
- Use recipes.
- 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: use fractions of a whole in a story; use fractions of a collection in a story; compare fractions in a story; explain the answer.
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 and a pencil. 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 fraction? Is it a part of a shape or a group?
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. Using the wrong whole. Find the whole first.
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. Draw the whole and the parts. 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 3.NF.A.3 and 4.NF.B.4c; Cambridge Primary Mathematics Stage 3 (fractions in context). These sources informed the lesson; no official alignment is claimed.