You will learn
- Tell equal from unequal parts.
- Name equal parts by how many make the whole.
- Say that equal parts make the whole again.
- Partition a shape into equal parts.
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
- Equal parts are the same size.
- Name parts by how many make the whole.
- Equal parts put together make the whole.
- Cut a shape into equal parts.
Words to know
The complete thing.
Parts of the same size.
Four equal parts.
Eight equal parts.
1. Discover: sharing the cassava cake
Six friends share one cassava cake fairly. How should the cake be cut? What would each piece be called?
2. Understand: equal parts of a whole
A whole can be cut into equal parts. We name the parts by how many make the whole:
- 2 equal parts: halves
- 3 equal parts: thirds
- 4 equal parts: fourths (quarters)
- 5: fifths; 6: sixths; 8: eighths
The parts must be the same size. If they are not, they cannot be named this way. Equal parts put together make the whole again.
Idea 1: Equal parts
A whole can be cut into equal parts. Parts are equal when they are exactly the same size.
Idea 2: Names
2 equal parts are halves, 3 are thirds, 4 are fourths (quarters), 5 are fifths, 6 are sixths and 8 are eighths.
Idea 3: Make the whole
4 quarters make one whole. Pieces of different sizes are not fourths.
Why equal? A fair share needs equal parts.
3. Worked examples
Example 1 (I show you): Name
A bar is cut into 3 equal parts. What are they?
- 3 equal parts.
Answer: thirds
Example 2 (We do it together): Name
A bar is cut into 5 equal parts. What are they?
- 5 equal parts.
Answer: fifths
Example 3 (You try): Unequal
4 pieces of different sizes. Are they fourths?
Show the steps and answer
- Fourths must be equal.
Answer: No
Did you know?
Fourths and quarters are two names for the same thing.
Why this matters
Equal parts are the beginning of fractions.
4. Explore: fold and name
You need paper strips and scissors.
- Fold a strip into 2 equal parts. Name them.
- Fold another into 4, then 8 equal parts.
- Check that the parts match.
- Try 3 and 6 equal parts.
Think about it: what did you notice?
Halves, fourths, eighths; thirds and sixths.
5. Practise
Say it in a sentence
Use these starters when you talk about the lesson. Say them out loud.
- The whole is cut into ___ equal parts.
- Each part is a ___.
- ___ parts make the whole.
- The parts are / are not equal because ___.
Guided practice
Question 1. A whole cut into 8 equal parts: each is an…
eighth.
Question 2. 6 equal parts are called…
sixths.
Question 3. 3 pieces of different sizes. Equal parts?
No.
Independent practice
Level 1: Start
- Name 3 equal parts.
- Name 5 equal parts.
- Are 4 pieces of different sizes fourths?
- How many fourths make a whole?
- Draw a rectangle in 6 equal parts.
Level 2: Grow
- Name 4 equal parts
- Name 8 equal parts
- How many halves make a whole?
Level 3: Stretch
- How many sixths make a whole?
- Cut a rectangle into 3 equal parts. What is each part?
- Ama cuts a circle into 4 pieces of different sizes and says each is a quarter. What is wrong?
Answers are in the answer key below. Try first, then check.
6. Apply: everyday mathematics
Six friends share a cake fairly. Into how many equal parts is it cut?
Show a sample answer
6 equal parts (sixths).
Another one. Draw a square and cut it into 4 equal parts in two different ways. Name each part.
Show a sample answer
fourths (quarters)
7. Common mistakes
Fix: The parts must be equal.
Fix: Equal parts must be the same size.
Fix: Count the parts.
8. Lesson summary and revision card
- I can tell equal from unequal parts.
- I can name equal parts.
- I know equal parts make the whole.
- I can cut a shape into equal parts.
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.
- Name by the number of parts.
- Equal parts make the whole.
11. Next lesson
Next lesson: Unit 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.
- What are 3 equal parts called? [1 mark]
- What are 5 equal parts called? [1 mark]
- Are 4 pieces of different sizes fourths? Explain. [2 marks]
- How many fourths make a whole? [1 mark]
- Ben says a rectangle cut into 2 unequal pieces is in halves. Is he right? Explain. [3 marks]
Total: 8 marks.
Marking guide and model answers
- Thirds [1]
- Fifths [1]
- No [1]. Fourths must be equal [1]
- 4 [1]
- No [1]. Halves must be equal [1]. The pieces must be the same size [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
- Name 3 equal parts
- Name 5 equal parts
- Are 4 pieces of different sizes fourths? (yes/no)
- How many fourths make a whole?
- Name 8 equal parts
- Equal parts are the ___ size.
- 8 equal parts are called ___.
- 6 equal parts are called ___.
- 3 equal parts are called ___.
- Four equal parts are also called ___.
Homework
Fold paper into halves, fourths and eighths. Name the parts.
Answer key and marking scheme
| Question | Expected response | Marks |
|---|---|---|
| Name 3 equal parts | thirds | 2 |
| Name 5 equal parts | fifths | 2 |
| Are 4 pieces of different sizes fourths? (yes/no) | no | 2 |
| How many fourths make a whole? | 4 | 2 |
| Name 8 equal parts | eighths | 2 |
| Total | 10 |
Practice answers: Worksheet: 1 thirds; 2 fifths; 3 no; 4 4; 5 eighths.
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 same; 7 eighths; 8 sixths; 9 thirds; 10 quarters.
Independent practice answers. Level 1: 1 thirds; 2 fifths; 3 No, fourths must be equal; 4 4; 5 a rectangle with 5 lines drawn so there are 6 equal parts (sixths). Level 2: 1 fourths (quarters); 2 eighths; 3 2. Level 3: 1 6; 2 a third; 3 Quarters must be equal parts..
Mastery and remediation
| Objective | Bronze (Developing) | Silver (Proficient) | Gold (Advanced) |
|---|---|---|---|
| O1 Tell equal from unequal parts | 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 equal parts by how many make the whole | 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 Say that equal parts make the whole again | 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 Partition a shape into equal parts | 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: Calling unequal parts thirds or fourths. The parts must be equal.
- Explain another way: use real objects first, then pictures.
- Show a simpler example: Fold a paper strip into halves, then fourths.
- 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 fractions start with equal parts of a whole. You do not need to be good at mathematics to help.
- Cut a chapati or paper into equal parts.
- Ask: are the parts equal? what are they called?
- Fold paper into 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: tell equal from unequal parts; name equal parts by how many make the whole; say that equal parts make the whole again; partition a shape into equal parts.
Prerequisite knowledge. Grade 2 halves, thirds and quarters.
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 and scissors. 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. Are the parts equal? How many make the whole? What are they called?
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. Calling unequal parts thirds or fourths. The parts must be equal.
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. Fold a paper strip into halves, then fourths. 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 (partition into equal parts); Cambridge Primary Mathematics Stage 3 (fractions). These sources informed the lesson; no official alignment is claimed.