You will learn
- Say what equivalent fractions are.
- Make equivalent fractions by multiplying.
- Check with fraction bars.
- Test two fractions.
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
- Equivalent fractions have the same value.
- Multiply top and bottom by the same number.
- Fraction bars show they cover the same amount.
- Test two fractions by simplifying.
Words to know
Equal in value.
Same factor top and bottom.
A rectangle showing parts.
Parts in the whole.
1. Discover: half a pizza
Half a pizza is the same amount as 2 out of 4 slices. Is 1/2 the same as 2/4?
2. Understand: equivalent fractions
Equivalent fractions name the same amount.
- 1/2 = 2/4 = 3/6 = 4/8 (multiply top and bottom by 2, 3, 4).
- 2/3 = 4/6 = 6/9.
- Test: 3/4 and 6/8: 3 × 2 = 6 and 4 × 2 = 8, so equal.
Always multiply the numerator and denominator by the same number.
Idea 1: Multiply
1/2 = ?/6: 2 × 3 = 6, so multiply the top by 3 too: 1/2 = 3/6.
Idea 2: Another
2/3 = ?/9: multiply by 3: 6/9. 3/5 = ?/10: multiply by 2: 6/10.
Idea 3: Test
Is 2/4 = 3/6? 2/4 = 1/2 and 3/6 = 1/2, so yes.
Why the same number? Multiplying by 3/3 is multiplying by 1.
3. Worked examples
Example 1 (I show you): Multiply
1/2 = ?/6
- × 3 on top and bottom.
Answer: 3
Example 2 (We do it together): Multiply
3/5 = ?/10
- × 2 on top and bottom.
Answer: 6
Example 3 (You try): Test
Is 2/4 = 3/6?
Show the steps and answer
- Both equal 1/2.
Answer: Yes
Did you know?
Every fraction has endless equivalent fractions.
Why this matters
Equivalent fractions let us add, compare and simplify.
4. Explore: matching bars
You need paper strips.
- Fold a strip into 2 and colour 1.
- Fold another into 4 and colour 2.
- Compare.
- Write 1/2 = 2/4.
Think about it: what did you notice?
They match.
5. Practise
Say it in a sentence
Use these starters when you talk about the lesson. Say them out loud.
- I multiply the denominator by ___.
- So I multiply the numerator by ___.
- The equivalent fraction is ___.
- Both equal ___.
Guided practice
Question 1. 1/2 = ?/4
2.
Question 2. 2/3 = ?/6
4.
Question 3. 3/4 = ?/8
6.
Independent practice
Level 1: Start
- 1/2 = ?/6
- 2/3 = ?/9
- 3/5 = ?/10
- Is 2/4 = 3/6? (yes/no)
- 4/8 = ?/2
Level 2: Grow
- 1/4 = ?/8
- 3/4 = ?/12
- 2/5 = ?/20
Level 3: Stretch
- 7/8 = ?/32
- 6/9 = ?/3
- Ben says 2/3 = 5/6 because he added 3 to both numbers. What is wrong?
Answers are in the answer key below. Try first, then check.
6. Apply: everyday mathematics
Ada ate 2/4 of a pizza, Bayo ate 1/2. Who ate more?
Show a sample answer
Same amount.
Another one. A pizza has 8 slices. Ana eats 1/4 of it. How many slices is that? Write an equivalent fraction.
Show a sample answer
1/4 = 2/8, so 2 slices.
7. Common mistakes
Fix: Multiply by the same number.
Fix: Multiply or divide both by the same number.
Fix: Change the numerator in the same way.
8. Lesson summary and revision card
- I can say what equivalent fractions are.
- I can make equivalent fractions by multiplying.
- I can check with fraction bars.
- I can test two fractions.
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
- Same factor top and bottom.
- Equivalent means equal value.
- Check with bars.
11. Next lesson
Next lesson: Simplifying 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.
- Find the missing number: 1/2 = ?/6 [2 marks]
- Find the missing number: 2/3 = ?/9 [2 marks]
- Find the missing number: 3/5 = ?/10 [2 marks]
- Is 2/4 = 3/6? Explain. [2 marks]
- Ali says 1/2 = 2/3 because he added 1 to both numbers. Is he right? Explain. [3 marks]
Total: 11 marks.
Marking guide and model answers
- × 3 top and bottom [1]; 3 [1]
- × 3 top and bottom [1]; 6 [1]
- × 2 top and bottom [1]; 6 [1]
- Both simplify to 1/2 [1]; yes [1]
- No [1]. Adding does not keep the value; multiply both by the same number [1]. 1/2 = 2/4 [1].
Score guide: 10 to 11 = secure. 7 to 9 = nearly there, revise the parts you missed. Under 7 = work through the lesson again with a grown-up.
Printable worksheet
- 1/2 = ?/6
- 2/3 = ?/9
- 3/5 = ?/10
- Is 2/4 = 3/6? (yes/no)
- 4/8 = ?/2
- 1/2 = ?/6
- 2/3 = ?/9
- 3/5 = ?/10
- 2/4 is equivalent to
- 3/4 = ?/8
Homework
Write three fractions equivalent to 1/3.
Answer key and marking scheme
| Question | Expected response | Marks |
|---|---|---|
| 1/2 = ?/6 | 3 | 2 |
| 2/3 = ?/9 | 6 | 2 |
| 3/5 = ?/10 | 6 | 2 |
| Is 2/4 = 3/6? (yes/no) | yes | 2 |
| 4/8 = ?/2 | 1 | 2 |
| Total | 10 |
Practice answers: Worksheet: 1 3; 2 6; 3 6; 4 yes; 5 1.
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 3; 7 6; 8 6; 9 1/2; 10 6.
Independent practice answers. Level 1: 1 3; 2 6; 3 6; 4 yes, both equal 1/2; 5 1. Level 2: 1 2; 2 9; 3 8. Level 3: 1 28; 2 2; 3 Adding changes the value. Multiply both by 2: 2/3 = 4/6..
Mastery and remediation
| Objective | Bronze (Developing) | Silver (Proficient) | Gold (Advanced) |
|---|---|---|---|
| O1 Say what equivalent fractions are | 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 Make equivalent fractions by multiplying | 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 Check with fraction bars | 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 Test two 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 |
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: Adding the same number top and bottom. Multiply by the same number.
- Explain another way: use real objects first, then pictures.
- Show a simpler example: Compare fraction strips side by side.
- 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 finds equivalent fractions by multiplying top and bottom. You do not need to be good at mathematics to help.
- Fold paper to show equal parts.
- Ask: what did you multiply by?
- Use fraction bars side by side.
- 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 equivalent fractions are; make equivalent fractions by multiplying; check with fraction bars; test two fractions.
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 strips. 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 the bottom by? Do I do the same to the top?
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. Adding the same number top and bottom. Multiply by the same number.
13–15. Assessment questions, answer keys, marking scheme
Use the quiz and worksheet on this page. The 11-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. Compare fraction strips side by side. 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 4.NF.A.1 (equivalent fractions); Cambridge Primary Mathematics Stage 4 (equivalent fractions). These sources informed the lesson; no official alignment is claimed.