You will learn
- Convert common fractions to percents.
- Convert percents to fractions.
- Simplify fractions.
- Recall benchmark percents.
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
- A percent is a fraction out of 100.
- Convert fractions by scaling to 100.
- Convert percents by simplifying.
- Remember benchmarks: 25%, 50%, 75%.
Words to know
Common reference value.
Lowest terms.
Per hundred.
Part of a whole.
1. Discover: half, quarter
Why is 1/4 the same as 25%?
2. Understand: fractions and percents
- 1/2 = 50%; 1/4 = 25%; 3/4 = 75%; 1/5 = 20%; 3/10 = 30%.
- 60% = 60/100 = 3/5.
- 35% = 35/100 = 7/20.
Idea 1: To percent
1/10 = 10/100 = 10%. 3/10 = 30%. 2/5 = 40/100 = 40%.
Idea 2: To fraction
80% = 80/100 = 4/5. 25% = 25/100 = 1/4.
Idea 3: Benchmarks
25% = 1/4, 50% = 1/2, 75% = 3/4.
Why simplify? It gives the neatest form.
3. Worked examples
Example 1 (I show you): To percent
1/10
- 10/100.
Answer: 10%
Example 2 (We do it together): To fraction
80%
- 80/100 ÷ 20.
Answer: 4/5
Example 3 (You try): To fraction
25%
Show the steps and answer
- 25/100 ÷ 25.
Answer: 1/4
Did you know?
Learn a few benchmark pairs and the rest become easy.
Why this matters
Fractions and percents are two ways to say the same share.
4. Explore: convert
You need paper.
- Write 60%.
- Write 60/100.
- Simplify by 20.
- Get 3/5.
Think about it: what did you notice?
3/5.
5. Practise
Say it in a sentence
Use these starters when you talk about the lesson. Say them out loud.
- As a fraction out of 100: ___.
- In lowest terms: ___.
- As a percent: ___.
- The benchmark is ___.
Guided practice
Question 1. 1/5 as a percent?
20%.
Question 2. 60% as a fraction?
3/5.
Question 3. 35% as a fraction?
7/20.
Independent practice
Level 1: Start
- 1/10
- 3/10
- 80%
- 25%
- 2/5
Level 2: Grow
- 1/5
- 50%
- 60%
Level 3: Stretch
- 35%
- 3/8 as a percent
- Ben says 1/4 = 14%. What is wrong?
Answers are in the answer key below. Try first, then check.
6. Apply: everyday mathematics
70% of a class is present. What fraction?
Show a sample answer
7/10.
Another one. 3/5 of the marbles in a bag are red. What percent are red?
Show a sample answer
3/5 = 60/100 = 60%
7. Common mistakes
Fix: 1/5 = 20/100.
Fix: Divide top and bottom by the common factor.
Fix: 1/4 = 25% and 1/5 = 20%.
8. Lesson summary and revision card
- I can convert common fractions to percents.
- I can convert percents to fractions.
- I can simplify fractions.
- I can recall benchmark percents.
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
- Know benchmarks.
- Simplify over 100.
- Scale to 100.
11. Next lesson
Next lesson: Decimals and percentages. 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.
- Write 1/10 as a percent. [2 marks]
- Write 3/10 as a percent. [2 marks]
- Write 80% as a fraction in lowest terms. [3 marks]
- Write 25% as a fraction in lowest terms. [3 marks]
- Ali says 2/5 = 25%. Is he right? Explain. [3 marks]
Total: 13 marks.
Marking guide and model answers
- 10/100 [1]; 10% [1]
- 30/100 [1]; 30% [1]
- 80/100 [1]; divide by 20 [1]; 4/5 [1]
- 25/100 [1]; divide by 25 [1]; 1/4 [1]
- No [1]. 2/5 = 40/100 [1]. It is 40% [1].
Score guide: 12 to 13 = secure. 8 to 11 = nearly there, revise the parts you missed. Under 8 = work through the lesson again with a grown-up.
Printable worksheet
- 1/10
- 3/10
- 80%
- 25%
- 2/5
- 1/5 =
- 60% =
- 35% =
- 3/10 =
- 25% =
Homework
Make a chart of ten fractions and percents.
Answer key and marking scheme
| Question | Expected response | Marks |
|---|---|---|
| 1/10 | 10% | 2 |
| 3/10 | 30% | 2 |
| 80% | 4/5 | 2 |
| 25% | 1/4 | 2 |
| 2/5 | 40% | 2 |
| Total | 10 |
Practice answers: Worksheet: 1 10%; 2 30%; 3 4/5; 4 1/4; 5 40%.
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 20%; 7 3/5; 8 7/20; 9 30%; 10 1/4.
Independent practice answers. Level 1: 1 10%; 2 30%; 3 4/5; 4 1/4; 5 40%. Level 2: 1 20%; 2 1/2; 3 3/5. Level 3: 1 7/20; 2 37.5%; 3 1/4 = 25/100 = 25%..
Mastery and remediation
| Objective | Bronze (Developing) | Silver (Proficient) | Gold (Advanced) |
|---|---|---|---|
| O1 Convert common fractions to percents | 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 Convert percents to 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 Simplify 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 |
| O4 Recall benchmark percents | 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: Writing 1/5 as 5%. 1/5 = 20/100.
- Explain another way: use real objects first, then pictures.
- Show a simpler example: Review 1/2, 1/4, 3/4.
- 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 links fractions and percents. You do not need to be good at mathematics to help.
- Talk about “half off” and “25% off”.
- Ask: which fraction is that?
- Learn the benchmarks.
- 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: convert common fractions to percents; convert percents to fractions; simplify fractions; recall benchmark percents.
Prerequisite knowledge. Lesson 2.
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. Can I scale to 100? Can I simplify?
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. Writing 1/5 as 5%. 1/5 = 20/100.
13–15. Assessment questions, answer keys, marking scheme
Use the quiz and worksheet on this page. The 13-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. Review 1/2, 1/4, 3/4. 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 6.RP.A.3c; Cambridge Primary Mathematics Stage 6 (fractions and percents). These sources informed the lesson; no official alignment is claimed.