You will learn
- Write a part as out of 100.
- Change out-of-n to percent.
- Use equivalent fractions with denominator 100.
- Compare 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
- Write a part as out of 100.
- Scale the fraction so the denominator is 100.
- The numerator is the percent.
- Compare percents easily.
Words to know
Out of 100.
Equal in value.
Multiply to make 100.
Per hundred.
1. Discover: test scores
You get 7 out of 20 on a quiz. What percent is that?
2. Understand: parts per hundred
- 45 of 100 squares = 45%.
- 7 out of 20: multiply by 5 → 35/100 = 35%.
- 12 out of 50: ×2 → 24/100 = 24%.
- 3 out of 4: ×25 → 75/100 = 75%.
Idea 1: Scale up
9/20: multiply by 5 to get 45/100, so 45%. 17/50: × 2 gives 34/100, so 34%.
Idea 2: Halves and fifths
1/2 = 50/100 = 50%. 4/5 = 80/100 = 80%.
Idea 3: More
3/25: × 4 gives 12/100 = 12%.
Why scale? A denominator of 100 shows the percent directly.
3. Worked examples
Example 1 (I show you): Convert
9/20
- × 5 top and bottom.
Answer: 45%
Example 2 (We do it together): Convert
17/50
- × 2 top and bottom.
Answer: 34%
Example 3 (You try): Convert
3/25
Show the steps and answer
- × 4 top and bottom.
Answer: 12%
Did you know?
Denominators that divide 100 (2, 4, 5, 10, 20, 25, 50) are easy to scale.
Why this matters
Percents make scores and shares easy to compare.
4. Explore: scale
You need paper.
- Write 7/20.
- Multiply by 5.
- Write 35/100.
- Write 35%.
Think about it: what did you notice?
35%.
5. Practise
Say it in a sentence
Use these starters when you talk about the lesson. Say them out loud.
- I multiply by ___ to get 100.
- The numerator becomes ___.
- So it is ___ out of 100.
- As a percent it is ___.
Guided practice
Question 1. 7/20 as a percent?
35%.
Question 2. 12/50?
24%.
Question 3. 3/4?
75%.
Independent practice
Level 1: Start
- 9/20
- 17/50
- 1/2
- 4/5
- 3/25
Level 2: Grow
- 1/5
- 7/10
- 9/25
Level 3: Stretch
- 33/50
- 15 out of 60
- Ben says 3/20 = 3%. What is wrong?
Answers are in the answer key below. Try first, then check.
6. Apply: everyday mathematics
You score 7 out of 20. What percent?
Show a sample answer
35%.
Another one. 18 of 20 pupils passed a test. What percent passed?
Show a sample answer
18/20 = 90/100 = 90%
7. Common mistakes
Fix: Scale to 100.
Fix: Make the denominator 100 first.
Fix: Multiply top and bottom by the same number.
8. Lesson summary and revision card
- I can write a part as out of 100.
- I can change out-of-n to percent.
- I can use equivalent fractions with denominator 100.
- I can compare 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
- Scale to 100.
- Numerator = percent.
- Check on a grid.
11. Next lesson
Next lesson: Fractions 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 9/20 as a percent. [3 marks]
- Write 17/50 as a percent. [3 marks]
- Write 1/2 as a percent. [3 marks]
- Write 3/25 as a percent. [3 marks]
- Ali says 4/5 = 45%. Is he right? Explain. [3 marks]
Total: 15 marks.
Marking guide and model answers
- × 5 on top and bottom [1]; 45/100 [1]; 45% [1]
- × 2 on top and bottom [1]; 34/100 [1]; 34% [1]
- × 50 on top and bottom [1]; 50/100 [1]; 50% [1]
- × 4 on top and bottom [1]; 12/100 [1]; 12% [1]
- No [1]. 4/5 = 80/100 [1]. It is 80% [1].
Score guide: 13 to 15 = secure. 9 to 12 = nearly there, revise the parts you missed. Under 9 = work through the lesson again with a grown-up.
Printable worksheet
- 9/20
- 17/50
- 1/2
- 4/5
- 3/25
- 7/20 =
- 12/50 =
- 3/4 =
- 9/20 =
- 4/5 =
Homework
Turn your last five test scores into percents.
Answer key and marking scheme
| Question | Expected response | Marks |
|---|---|---|
| 9/20 | 45% | 2 |
| 17/50 | 34% | 2 |
| 1/2 | 50% | 2 |
| 4/5 | 80% | 2 |
| 3/25 | 12% | 2 |
| Total | 10 |
Practice answers: Worksheet: 1 45%; 2 34%; 3 50%; 4 80%; 5 12%.
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 35%; 7 24%; 8 75%; 9 45%; 10 80%.
Independent practice answers. Level 1: 1 45%; 2 34%; 3 50%; 4 80%; 5 12%. Level 2: 1 20%; 2 70%; 3 36%. Level 3: 1 66%; 2 25%; 3 Multiply by 5: 15/100 = 15%..
Mastery and remediation
| Objective | Bronze (Developing) | Silver (Proficient) | Gold (Advanced) |
|---|---|---|---|
| O1 Write a part as out of 100 | 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 Change out-of-n to percent | 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 equivalent fractions with denominator 100 | 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 Compare 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 7 out of 20 as 7%. Scale to 100.
- Explain another way: use real objects first, then pictures.
- Show a simpler example: Equivalent fractions.
- 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 writes parts as percents. You do not need to be good at mathematics to help.
- Turn test scores into percents.
- Ask: what makes the bottom 100?
- Use a hundred grid.
- 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: write a part as out of 100; change out-of-n to percent; use equivalent fractions with denominator 100; compare percents.
Prerequisite knowledge. Lesson 1.
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 do I multiply by to get 100?
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 7 out of 20 as 7%. Scale to 100.
13–15. Assessment questions, answer keys, marking scheme
Use the quiz and worksheet on this page. The 15-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. Equivalent fractions. 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 (percentages). These sources informed the lesson; no official alignment is claimed.