You will learn
- Name the numerator and denominator.
- Read and write fractions.
- Find a fraction of a set.
- Show fractions on bars and lines.
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
- The numerator is the top number: parts we have.
- The denominator is the bottom number: equal parts in the whole.
- Find a fraction of a set by dividing, then multiplying.
- Show fractions on bars and number lines.
Words to know
The top number: parts we have.
The bottom number: equal parts in the whole.
Part of a whole.
The complete thing.
1. Discover: sharing a cake
A cake is cut into 4 equal slices and you eat 3. What fraction did you eat?
2. Understand: fractions
A fraction names equal parts of a whole. In 3/4, the denominator 4 says the whole has 4 equal parts; the numerator 3 says we take 3 of them.
- 3/4 of 8 = (8 ÷ 4) × 3 = 2 × 3 = 6.
- The parts must be equal.
Idea 1: Parts
In 5/8 the denominator 8 tells us the whole is split into 8 equal parts. The numerator 5 tells us we have 5 of them.
Idea 2: Fraction of a set
1/4 of 12: 12 ÷ 4 = 3. 2/3 of 9: 9 ÷ 3 = 3, then 3 × 2 = 6.
Idea 3: Bigger sets
3/5 of 20: 20 ÷ 5 = 4, then 4 × 3 = 12. 1/2 of 10 = 5.
Why divide first? The denominator tells us how many equal groups.
3. Worked examples
Example 1 (I show you): Parts
Denominator of 5/8
- The bottom number.
Answer: 8
Example 2 (We do it together): Set
2/3 of 9
- 9 ÷ 3 = 3, then × 2.
Answer: 6
Example 3 (You try): Set
3/5 of 20
Show the steps and answer
- 20 ÷ 5 = 4, then × 3.
Answer: 12
Did you know?
The fraction bar means divided by.
Why this matters
Fractions describe parts of things, like a share of money or time.
4. Explore: fraction strips
You need paper strips.
- Fold a strip into 4 equal parts.
- Colour 3 parts.
- Write 3/4.
- Find 3/4 of 8 counters.
Think about it: what did you notice?
6 counters.
5. Practise
Say it in a sentence
Use these starters when you talk about the lesson. Say them out loud.
- The denominator is ___.
- The numerator is ___.
- I divide ___ by ___ to get ___.
- Then I multiply by ___ to get ___.
Guided practice
Question 1. Numerator of 3/4?
3.
Question 2. Denominator of 3/4?
4.
Question 3. 3/4 of 8?
6.
Independent practice
Level 1: Start
- 1/2 of 10
- 1/4 of 12
- 2/3 of 9
- 3/5 of 20
- Denominator of 5/8
Level 2: Grow
- 1/3 of 12
- 3/4 of 20
- 2/5 of 10
Level 3: Stretch
- 5/8 of 24
- 7/10 of 50
- Ben says 3/4 of 8 is 3 because the numerator is 3. What is wrong?
Answers are in the answer key below. Try first, then check.
6. Apply: everyday mathematics
A rope is 12 m. You use 1/4. How long is the piece used?
Show a sample answer
3 m.
Another one. A class has 30 pupils. 2/5 of them are girls. How many girls? How many boys?
Show a sample answer
30 ÷ 5 = 6 and 6 × 2 = 12 girls, so 18 boys.
7. Common mistakes
Fix: Parts must be equal.
Fix: The denominator is the number of equal parts in the whole.
Fix: Divide by the denominator first.
8. Lesson summary and revision card
- I can name the numerator and denominator.
- I can read and write fractions.
- I can find a fraction of a set.
- I can show fractions on bars and lines.
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
- Parts must be equal.
- Top: parts taken. Bottom: parts in all.
- Fraction of a set: divide then multiply.
11. Next lesson
Next lesson: Equivalent 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 of 10. [1 mark]
- Find 3/5 of 20. [2 marks]
- Find 2/3 of 9. [2 marks]
- What does the denominator of 5/8 tell us? [2 marks]
- Kofi says 1/4 of 12 is 4. Is he right? Explain. [3 marks]
Total: 10 marks.
Marking guide and model answers
- 5 [1]
- 20 ÷ 5 = 4 [1]; 4 × 3 = 12 [1]
- 9 ÷ 3 = 3 [1]; 3 × 2 = 6 [1]
- The number of equal parts in the whole [1]; 8 [1]
- No [1]. 12 ÷ 4 [1]. It is 3 [1].
Score guide: 9 to 10 = secure. 6 to 8 = nearly there, revise the parts you missed. Under 6 = work through the lesson again with a grown-up.
Printable worksheet
- 1/2 of 10
- 1/4 of 12
- 2/3 of 9
- 3/5 of 20
- Denominator of 5/8
- In 3/4 the denominator is
- 3/4 of 8 =
- 1/4 of 12 =
- 2/3 of 9 =
- 3/5 of 20 =
Homework
Find 3/4 of 16 and 2/5 of 20.
Answer key and marking scheme
| Question | Expected response | Marks |
|---|---|---|
| 1/2 of 10 | 5 | 2 |
| 1/4 of 12 | 3 | 2 |
| 2/3 of 9 | 6 | 2 |
| 3/5 of 20 | 12 | 2 |
| Denominator of 5/8 | 8 | 2 |
| Total | 10 |
Practice answers: Worksheet: 1 5; 2 3; 3 6; 4 12; 5 8.
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 4; 7 6; 8 3; 9 6; 10 12.
Independent practice answers. Level 1: 1 5; 2 3; 3 6; 4 12; 5 8. Level 2: 1 4; 2 15; 3 4. Level 3: 1 15; 2 35; 3 8 ÷ 4 = 2, then 2 × 3 = 6..
Mastery and remediation
| Objective | Bronze (Developing) | Silver (Proficient) | Gold (Advanced) |
|---|---|---|---|
| O1 Name the numerator and denominator | 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 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 Find a fraction of a set | 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 Show fractions on bars and lines | 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 unequal parts. Parts must be equal.
- Explain another way: use real objects first, then pictures.
- Show a simpler example: Fold paper into halves, quarters and eighths.
- 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 reviews numerators, denominators and fractions of a set. You do not need to be good at mathematics to help.
- Share sweets using fractions.
- Ask: how many equal parts?
- Fold paper to show halves and quarters.
- 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: name the numerator and denominator; read and write fractions; find a fraction of a set; show fractions on bars and lines.
Prerequisite knowledge. Grade 3 fractions.
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 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. How many equal parts? How many do we have?
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 unequal parts. Parts must be equal.
13–15. Assessment questions, answer keys, marking scheme
Use the quiz and worksheet on this page. The 10-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. Fold paper into halves, quarters and eighths. 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.1 and 4.NF.B.4; Cambridge Primary Mathematics Stage 4 (fractions). These sources informed the lesson; no official alignment is claimed.