You will learn
- Say what percent means.
- Write a percent as a fraction.
- Write a percent as a decimal.
- Shade percentages on a grid.
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
- Percent means per hundred.
- A percent is a fraction with denominator 100.
- Divide by 100 to get a decimal.
- 100% means the whole.
Words to know
Per hundred.
One of a hundred.
100 squares.
The full amount, 100%.
1. Discover: out of a hundred
45 of 100 squares are shaded. How can we describe the shaded part?
2. Understand: percent
- 45 out of 100 is 45%, the fraction 45/100 and the decimal 0.45.
- 7% = 7/100 = 0.07.
- The whole is 100%.
- 50% = 50/100 = 1/2.
Idea 1: Per hundred
30 out of 100 is 30%. 9% = 9/100.
Idea 2: Decimal
25% = 25 ÷ 100 = 0.25. 7% = 0.07.
Idea 3: Grid
20% of a 100-square grid is 20 squares. 100% means all of it.
Why 100? A common whole makes comparing easy.
3. Worked examples
Example 1 (I show you): Percent
30 out of 100
- Per hundred.
Answer: 30%
Example 2 (We do it together): Decimal
25%
- 25 ÷ 100.
Answer: 0.25
Example 3 (You try): Grid
20% of 100 squares
Show the steps and answer
- 20 per hundred.
Answer: 20 squares
Did you know?
The word percent comes from “per centum”, meaning per hundred.
Why this matters
Percentages describe discounts, scores and statistics.
4. Explore: shade
You need a grid.
- Count shaded squares.
- Write over 100.
- Write the percent.
- Write the decimal.
Think about it: what did you notice?
45%.
5. Practise
Say it in a sentence
Use these starters when you talk about the lesson. Say them out loud.
- ___ out of 100 is ___%.
- ___% as a fraction is ___/100.
- ___% as a decimal is ___.
- 100% means ___.
Guided practice
Question 1. 45 of 100 as a percent?
45%.
Question 2. 7% as a decimal?
0.07.
Question 3. 50% as a fraction?
1/2.
Independent practice
Level 1: Start
- 30 of 100 as a percent
- 9% as a fraction
- 25% as a decimal
- 100% means
- Shade 20% of the grid: how many squares?
Level 2: Grow
- 62 out of 100
- 8% as a fraction
- 40% as a decimal
Level 3: Stretch
- 75% as a fraction in lowest terms
- 3% as a decimal
- Ben says 20% of a 100-grid is 2 squares. What is wrong?
Answers are in the answer key below. Try first, then check.
6. Apply: everyday mathematics
A phone is 80% charged. How many parts out of 100?
Show a sample answer
80.
Another one. 35 squares of a 100-grid are shaded. What percent is not shaded?
Show a sample answer
65%
7. Common mistakes
Fix: 7% is 0.07.
Fix: 7% = 7/100 = 0.07.
Fix: 100% is the whole.
8. Lesson summary and revision card
- I can say what percent means.
- I can write a percent as a fraction.
- I can write a percent as a decimal.
- I can shade percentages on a grid.
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
- Percent means per hundred.
- Percent = fraction over 100.
- 100% is the whole.
11. Next lesson
Next lesson: Fractions, 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 30 out of 100 as a percent. [1 mark]
- Write 9% as a fraction. [1 mark]
- Write 25% as a decimal. [2 marks]
- What does 100% mean? [1 mark]
- Ali says 20% of a 100-square grid is 2 squares. Is he right? Explain. [3 marks]
Total: 8 marks.
Marking guide and model answers
- 30% [1]
- 9/100 [1]
- 25 ÷ 100 [1]; 0.25 [1]
- All of it, the whole [1]
- No [1]. Percent means out of 100 [1]. 20% is 20 squares [1].
Score guide: 7 to 8 = secure. 5 to 6 = nearly there, revise the parts you missed. Under 5 = work through the lesson again with a grown-up.
Printable worksheet
- 30 of 100
- 9% as a fraction
- 25% as a decimal
- 100% means
- 20% of the grid
- 30 out of 100
- 9% as a fraction
- 25% as a decimal
- 100% means
- 20% of a 100-grid
Homework
Shade 35% of a hundred-square grid.
Answer key and marking scheme
| Question | Expected response | Marks |
|---|---|---|
| 30 of 100 | 30% | 2 |
| 9% as a fraction | 9/100 | 2 |
| 25% as a decimal | 0.25 | 2 |
| 100% means | the whole | 2 |
| 20% of the grid | 20 | 2 |
| Total | 10 |
Practice answers: Worksheet: 1 30%; 2 9/100; 3 0.25; 4 the whole; 5 20.
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 9/100; 8 0.25; 9 all of it; 10 20 squares.
Independent practice answers. Level 1: 1 30%; 2 9/100; 3 0.25; 4 all of it, the whole; 5 20 squares. Level 2: 1 62%; 2 8/100; 3 0.4. Level 3: 1 3/4; 2 0.03; 3 20% is 20 per hundred: 20 squares..
Mastery and remediation
| Objective | Bronze (Developing) | Silver (Proficient) | Gold (Advanced) |
|---|---|---|---|
| O1 Say what percent means | 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 Write a percent as a fraction | 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 Write a percent as a decimal | 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 Shade percentages on a grid | 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: Writing 7% as 0.7. 7% is 0.07.
- Explain another way: use real objects first, then pictures.
- Show a simpler example: Hundredths.
- 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 learns that percent means per hundred. You do not need to be good at mathematics to help.
- Use a 10 × 10 grid on paper.
- Ask: out of 100?
- Link percent to prices.
- 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: say what percent means; write a percent as a fraction; write a percent as a decimal; shade percentages on a grid.
Prerequisite knowledge. Fractions and decimals.
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 a grid. 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. Out of 100? What is it as a decimal?
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% as 0.7. 7% is 0.07.
13–15. Assessment questions, answer keys, marking scheme
Use the quiz and worksheet on this page. The 8-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. Hundredths. 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 6 » Ratios & Proportional Relationships; Grade 6 » The Number System. These pages list the standards that cover this topic area; read them alongside the lesson.
Research used to shape this lesson. Common Core 6.RP.A.3c; Cambridge Primary Mathematics Stage 6 (percentages). These sources informed the lesson.