Courseversity

Fraction equivalence

Primary EducationGrade 6MathematicsCV-PRI-G06-MATH-FRA-U01-L0145–60 min

You will learn

  • Make equivalent fractions.
  • Test equivalence.
  • Use a fraction wall.
  • Write a missing numerator.

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

The lesson in 60 seconds

  1. Equivalent fractions have the same value.
  2. Multiply or divide top and bottom by the same number.
  3. A fraction wall shows equal parts.
  4. Cross-check by finding the missing number.

Words to know

equivalent
Equal in value.
numerator
Top number.
denominator
Bottom number.
factor
Number you multiply by.

1. Discover: same amount, new name

Two-thirds of a cake is the same as how many sixths?

2. Understand: equivalent fractions

  • Multiply top and bottom by 2: 2/3 = 4/6.
  • Multiply by 3: 2/3 = 6/9; by 4: 2/3 = 8/12.
  • Divide top and bottom by 4: 8/12 = 2/3.
  • Test: 3/4 and 9/12 are equal because 3 × 3 = 9 and 4 × 3 = 12.
2/3
4/6 is equal to 2/3

Idea 1: Multiply

1/2 = ?/8: 2 × 4 = 8, so 1 × 4 = 4. 1/2 = 4/8. 3/5 = 6/10.

Idea 2: Divide

4/6 = ?/3: 6 ÷ 2 = 3, so 4 ÷ 2 = 2. 4/6 = 2/3.

Idea 3: Test

2/5 and 4/10: 2 × 2 = 4 and 5 × 2 = 10, so they are equal. 3/4 and 6/9: 3 × 2 = 6 but 4 × 2 = 8, not 9, so not equal.

Why same factor? Doing the same to top and bottom keeps the value.

Remember: Do the same to top and bottom.

3. Worked examples

Example 1 (I show you): Missing numerator

1/2 = ?/8

  1. 8 ÷ 2 = 4.
  2. Top: 1 × 4 = 4.

Answer: 4/8

Example 2 (We do it together): Simplify down

4/6 = ?/3

  1. 6 ÷ 2 = 3.
  2. Top: 4 ÷ 2 = 2.

Answer: 2/3

Example 3 (You try): Test

Are 3/4 and 6/9 equal?

Show the steps and answer
  1. 3 × 2 = 6.
  2. 4 × 2 = 8, not 9.

Answer: not equal

Did you know?

Every fraction has endless equivalent fractions.

Why this matters

Equivalent fractions let us add, compare and simplify.

4. Explore: make

You need paper.

  1. Pick a multiplier.
  2. Multiply the top.
  3. Multiply the bottom.
  4. Check by dividing back.
Think about it: what did you notice?

2/3 = 4/6.

5. Practise

Say it in a sentence

Use these starters when you talk about the lesson. Say them out loud.

  • I multiply top and bottom by ___.
  • I divide top and bottom by ___.
  • So ___ = ___.
  • They are / are not equal because ___.

Guided practice

Question 1. 2/3 = ?/6

4.

Question 2. 2/3 = ?/12

8.

Question 3. 3/4 = 9/?

12.

Independent practice

Level 1: Start

  1. 1/2 = ?/8
  2. 3/5 = ?/10
  3. 4/6 = ?/3
  4. Are 2/5 and 4/10 equal?
  5. Are 3/4 and 6/9 equal?

Level 2: Grow

  1. 1/3 = ?/9
  2. 2/4 = ?/2
  3. Are 1/2 and 5/10 equal?

Level 3: Stretch

  1. 3/8 = ?/24
  2. Write a fraction equal to 2/3 with denominator 12
  3. Ben says 1/4 = 2/5 because both add 1. What is wrong?

Answers are in the answer key below. Try first, then check.

6. Apply: everyday mathematics

Half a pizza is eaten. A pizza has 8 slices. How many slices?

Show a sample answer

4 slices.

Another one. A pizza is cut into 6 slices and 3 are eaten. Write this as a fraction with denominator 12.

Show a sample answer

3/6 = 6/12

7. Common mistakes

Mistake: Adding the same number to top and bottom.
Fix: Multiply, do not add.
Another mistake: Adding the same number to top and bottom.
Fix: Multiply or divide both by the same number.
Another mistake: Changing only the top.
Fix: Change top and bottom together.

8. Lesson summary and revision card

I can…

  • I can make equivalent fractions.
  • I can find a missing numerator.
  • I can test equivalence.
  • I can use a fraction wall.

9. Check and master

Answer all 14 questions. You will see feedback after each one.

1. 1/2 = ?/8

2. 3/5 = ?/10

3. 4/6 = ?/3

4. 2/5 and 4/10 are:

5. 3/4 and 6/9 are:

6. 1/3 = ?/12

7. 2/5 = ?/15

8. 3/4 = 9/?

9. Which fraction equals 1/2?

10. Are 3/9 and 1/3 equal?

11. Which fraction equals 4/5?

12. Are 5/6 and 10/11 equal?

Challenge 1. Which equals 2/3?

Challenge 2. Which fraction is not equal to 2/3?

Your result appears here after you answer every question.

10. Key takeaways

  • Same factor top and bottom.
  • Value is unchanged.
  • Test by cross-multiplying.

11. Next lesson

Next lesson: Fraction simplification. 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.

  1. Complete: 1/2 = ?/8 [2 marks]
  2. Complete: 3/5 = ?/10 [2 marks]
  3. Complete: 4/6 = ?/3 [2 marks]
  4. Are 2/5 and 4/10 equal? Explain. [2 marks]
  5. Ali says 3/4 = 6/9. Is he right? Explain. [3 marks]

Total: 11 marks.

Marking guide and model answers
  1. Multiply top and bottom by 4 [1]; 4/8 [1]
  2. Multiply top and bottom by 2 [1]; 6/10 [1]
  3. Divide top and bottom by 2 [1]; 2/3 [1]
  4. Multiplying 2/5 top and bottom by 2 gives 4/10 [1]; yes, equal [1]
  5. No [1]. 3 × 2 = 6 but 4 × 2 = 8, not 9 [1]. 3/4 = 6/8 [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. 1/2 = ?/8
  2. 3/5 = ?/10
  3. 4/6 = ?/3
  4. 2/5 = 4/10? (yes/no)
  5. 3/4 = 6/9? (yes/no)
  6. 1/2 = ?/8
  7. 3/5 = ?/10
  8. 4/6 = ?/3
  9. Are 2/5 and 4/10 equal?
  10. Are 3/4 and 6/9 equal?

Homework

Write four fractions equal to 3/4.

Answer key and marking scheme

Question Expected response Marks
1/2 = ?/8 4 2
3/5 = ?/10 6 2
4/6 = ?/3 2 2
2/5 = 4/10? (yes/no) yes 2
3/4 = 6/9? (yes/no) no 2
Total 10

Practice answers: Worksheet: 1 4; 2 6; 3 2; 4 yes; 5 no.

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 4; 7 6; 8 2; 9 equal; 10 not equal.

Independent practice answers. Level 1: 1 4; 2 6; 3 2; 4 equal; 5 not equal. Level 2: 1 3; 2 1; 3 yes. Level 3: 1 9; 2 8/12; 3 Multiply, not add: 1/4 = 2/8..

Mastery and remediation

Objective Bronze (Developing) Silver (Proficient) Gold (Advanced)
O1 Make equivalent 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
O2 Test equivalence 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 a fraction wall 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 Write a missing numerator 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

  1. Find the misconception: Adding the same number to top and bottom. Multiply, do not add.
  2. Explain another way: use real objects first, then pictures.
  3. Show a simpler example: Halves, quarters, eighths.
  4. Guided practice: work through one example together and let the learner try the next one.
  5. Reassess: use the quiz again or the worksheet.
  6. Move on when the learner shows Silver-level evidence independently.

For parents and guardians

In this lesson your child finds fractions that have the same value. You do not need to be good at mathematics to help.

  • Cut a chapati or paper into equal parts.
  • Ask: what did you multiply by?
  • Use a fraction wall picture.
  • 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: make equivalent fractions; test equivalence; use a fraction wall; write a missing numerator.

Prerequisite knowledge. Grade 5 fractions.

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 or divide by? Do top and bottom match?

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 to top and bottom. Multiply, do not add.

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. Halves, quarters, eighths. 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 4.NF.A.1; Cambridge Primary Mathematics Stage 6 (equivalent fractions). These sources informed the lesson.

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