You will learn
- Shade a fraction of a shape.
- Name the fraction that is shaded.
- Name the unshaded part.
- See that the whole equals denominator over denominator.
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
- Shade parts of an equal-parts shape.
- Name the shaded fraction.
- Name the unshaded fraction.
- The whole is denominator over denominator.
Words to know
Coloured in.
Not coloured.
The complete thing.
A fraction with numerator more than 1.
1. Discover: colouring the bar
A bar is split into 5 equal parts. 2 are shaded. What fraction is shaded? What fraction is not shaded?
2. Understand: non-unit fractions
A non-unit fraction has a numerator more than 1, like 2/3, 3/4, 5/6.
2 of 5 equal parts shaded is 2/5. The unshaded part is 3/5, because 2/5 + 3/5 = 5/5 = 1 whole.
When the numerator equals the denominator, we have the whole: 4/4 = 1, 6/6 = 1, 8/8 = 1.
Idea 1: Shaded
3 of 8 equal parts shaded is 3/8. 5 of 6 shaded is 5/6.
Idea 2: Unshaded
If 2/5 is shaded, 3 parts are unshaded: 3/5.
Idea 3: The whole
6/6 is all the parts, which equals 1 whole.
Why? Shaded plus unshaded always make the whole.
3. Worked examples
Example 1 (I show you): Shaded
3 of 8 equal parts shaded.
- 3 out of 8.
Answer: 3/8
Example 2 (We do it together): Unshaded
2/5 shaded. What is unshaded?
- 5 − 2 = 3 parts.
Answer: 3/5
Example 3 (You try): Whole
6/6 = ?
Show the steps and answer
- All parts.
Answer: 1 whole
Did you know?
A non-unit fraction has a numerator bigger than 1.
Why this matters
Shading shows what a fraction means.
4. Explore: shade and name
You need paper and crayons.
- Draw a bar of 5 equal parts.
- Shade 2 parts: 2/5.
- Name the unshaded part: 3/5.
- Shade all 4 parts of a bar of 4 equal parts.
Think about it: what did you notice?
2/5 and 3/5; 4/4 is 1 whole.
5. Practise
Say it in a sentence
Use these starters when you talk about the lesson. Say them out loud.
- ___ of ___ parts are shaded.
- The unshaded part is ___.
- ___/___ equals one whole.
- I draw ___ equal parts and shade ___.
Guided practice
Question 1. 2 of 5 shaded?
2/5.
Question 2. The unshaded part?
3/5.
Question 3. 4/4 equals?
1 whole.
Independent practice
Level 1: Start
- 3 of 8 shaded
- 5 of 6 shaded
- Unshaded part when 2/5 is shaded
- 6/6 equals?
- Draw 3/4.
Level 2: Grow
- 2 of 7 equal parts shaded
- Unshaded part when 3/8 is shaded
- 5/5 equals
Level 3: Stretch
- Draw 2/3
- Unshaded part when 7/10 is shaded
- Ali says 3 of 8 shaded is 3/5. What is wrong?
Answers are in the answer key below. Try first, then check.
6. Apply: everyday mathematics
A farm has 8 plots. 5 are planted with maize. What fraction is maize? What fraction is not?
Show a sample answer
5/8 maize and 3/8 not.
Another one. A bar has 10 equal parts and 6 are shaded. Write the shaded and unshaded fractions.
Show a sample answer
6/10 shaded, 4/10 unshaded
7. Common mistakes
Fix: 5/5 is exactly 1 whole.
Fix: The denominator counts all the equal parts.
Fix: Shaded plus unshaded make the whole.
8. Lesson summary and revision card
- I can shade a fraction of a shape.
- I can name the shaded fraction.
- I can name the unshaded part.
- I know denominator over denominator is 1.
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
- Numerator: shaded parts.
- Unshaded = denominator minus numerator.
- Whole = n/n.
11. Next lesson
Next lesson: Fractions on number lines. 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.
- 3 of 8 equal parts are shaded. Write the fraction. [1 mark]
- 2/5 of a bar is shaded. What fraction is unshaded? [2 marks]
- What does 4/4 equal? [1 mark]
- A bar has 8 equal parts and 5 are shaded. What fraction is unshaded? [2 marks]
- Ana says 5 of 6 shaded is 5/5. Is she right? Explain. [3 marks]
Total: 9 marks.
Marking guide and model answers
- 3/8 [1]
- 5 − 2 = 3 [1]; 3/5 [1]
- 1 whole [1]
- 8 − 5 = 3 [1]; 3/8 [1]
- No [1]. The denominator is all the parts [1]. It is 5/6 [1].
Score guide: 8 to 9 = secure. 6 to 7 = nearly there, revise the parts you missed. Under 6 = work through the lesson again with a grown-up.
Printable worksheet
- 3 of 8 shaded
- 5 of 6 shaded
- Unshaded when 2/5 shaded
- 6/6 equals?
- Draw 3/4 (shaded parts)
- 2 of 5 equal parts shaded =
- Unshaded when 2/5 is shaded =
- 4/4 =
- 3 of 8 shaded =
- 5 of 6 shaded =
Homework
Make three bars with different shaded fractions. Write the unshaded fraction.
Answer key and marking scheme
| Question | Expected response | Marks |
|---|---|---|
| 3 of 8 shaded | 3/8 | 2 |
| 5 of 6 shaded | 5/6 | 2 |
| Unshaded when 2/5 shaded | 3/5 | 2 |
| 6/6 equals? | 1 | 2 |
| Draw 3/4 (shaded parts) | 3 | 2 |
| Total | 10 |
Practice answers: Worksheet: 1 3/8; 2 5/6; 3 3/5; 4 1; 5 3.
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 2/5; 7 3/5; 8 1 whole; 9 3/8; 10 5/6.
Independent practice answers. Level 1: 1 3/8; 2 5/6; 3 3/5; 4 1 whole; 5 draw a shape in 4 equal parts and shade 3 of them. Level 2: 1 2/7; 2 5/8; 3 1 whole. Level 3: 1 a shape in 3 equal parts with 2 shaded; 2 3/10; 3 The denominator is all 8 equal parts. It is 3/8..
Mastery and remediation
| Objective | Bronze (Developing) | Silver (Proficient) | Gold (Advanced) |
|---|---|---|---|
| O1 Shade a fraction of a shape | 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 Name the fraction that is shaded | 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 Name the unshaded part | 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 See that the whole equals denominator over 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 |
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: Thinking 5/5 is more than a whole. 5/5 is exactly 1 whole.
- Explain another way: use real objects first, then pictures.
- Show a simpler example: Colour parts of a bar one at a time and count.
- 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 shades and names fractions of shapes. You do not need to be good at mathematics to help.
- Draw and shade shapes together.
- Ask: what is shaded? what is not?
- Use paper strips.
- 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: shade a fraction of a shape; name the fraction that is shaded; name the unshaded part; see that the whole equals denominator over denominator.
Prerequisite knowledge. Lesson 3.
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 crayons. 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 shaded? What is unshaded?
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. Thinking 5/5 is more than a whole. 5/5 is exactly 1 whole.
13–15. Assessment questions, answer keys, marking scheme
Use the quiz and worksheet on this page. The 9-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. Colour parts of a bar one at a time and count. 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 3 » Number & Operations—Fractions. These pages list the standards that cover this topic area; read them alongside the lesson.
Research used to shape this lesson. Common Core 3.NF.A.1; Cambridge Primary Mathematics Stage 3 (fractions of shapes). These sources informed the lesson.