You will learn
- Find equivalent ratios.
- Simplify a ratio.
- Test equivalence.
- Solve missing-value problems.
Version 0.1 · published for early use · expert review pending Standards alignment: pending verification. Not yet reviewed against the Courseversity scorecard.
Student lesson
Words to know
Same relationship.
Lowest terms.
Multiply both terms.
Divide both terms.
1. Discover: mixing drinks
A drink uses 2 cups of juice to 3 cups of water. How much water for 6 cups of juice?
2. Understand: equivalent ratios
- 2 : 3 = 4 : 6 = 6 : 9, so 6 cups of juice need 9 cups of water.
- Simplify 12 : 18 by dividing by 6 to get 2 : 3.
- 15 : 20 simplifies to 3 : 4.
- Test: 2 : 3 and 8 : 12 are equivalent because both terms × 4.
3. Explore: scale
You need paper.
- Find the multiplier.
- Multiply both terms.
- Write the ratio.
- Check by simplifying.
Think about it: what did you notice?
6 : 9.
4. Practise
Guided practice
Question 1. 2 : 3 = 6 : ?
9.
Question 2. 12 : 18 simplified?
2 : 3.
Question 3. 15 : 20 simplified?
3 : 4.
Independent practice
- 2 : 3 = 8 : ?
- Simplify 10 : 25
- Simplify 15 : 20
- Is 3 : 4 equivalent to 9 : 12?
- Is 2 : 5 equivalent to 6 : 12?
Answers are in the answer key below. Try first, then check.
5. Apply: everyday mathematics
Juice to water is 2 : 3. How much water for 6 cups of juice?
Show a sample answer
9 cups.
6. Common mistake
Fix: Multiply, do not add.
7. Check and master
Answer all questions. You will see feedback after each one.
Your result appears here after you answer every question.
8. Key takeaways
- Multiply both terms.
- Divide both terms.
- Do not add.
9. Next lesson
Next lesson: Ratio tables. Keep going with the next idea in this course.
Printable worksheet
- 2 : 3 = 8 : ?
- Simplify 10 : 25
- Simplify 15 : 20
- 3:4 = 9:12? (yes/no)
- 2:5 = 6:12? (yes/no)
Homework
Write four ratios equivalent to 3 : 5.
Answer key and marking scheme
| Question | Expected response | Marks |
|---|---|---|
| 2 : 3 = 8 : ? | 12 | 2 |
| Simplify 10 : 25 | 2 : 5 | 2 |
| Simplify 15 : 20 | 3 : 4 | 2 |
| 3:4 = 9:12? (yes/no) | yes | 2 |
| 2:5 = 6:12? (yes/no) | no | 2 |
| Total | 10 |
Practice answers: Worksheet: 1 12; 2 2 : 5; 3 3 : 4; 4 yes; 5 no.
Quiz answers: 1 A, 2 B, 3 C, 4 A, 5 B, challenge C.
Mastery and remediation
| Objective | Bronze (Developing) | Silver (Proficient) | Gold (Advanced) |
|---|---|---|---|
| O1 Find equivalent ratios | 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 Simplify a ratio | 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 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 |
| O4 Solve missing-value problems | 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 3 of 5 core questions correct; Silver = all 5; Gold = all 5 plus the challenge. A badge is never a full record of progress.
If a learner struggles
- Find the misconception: Adding the same number to both terms. Multiply, do not add.
- Explain another way: use real objects first, then pictures.
- Show a simpler example: Equivalent fractions.
- 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.
Teacher package
1–5. Objectives, prerequisites, materials, preparation, duration
Lesson objectives. Learners will: find equivalent ratios; simplify a ratio; test equivalence; solve missing-value problems.
Prerequisite knowledge. Lesson 2.
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. 35–45 minutes.
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.
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 both terms. Multiply, do not add.
13–15. Assessment questions, answer keys, marking scheme
Use the quiz and worksheet on this page. The 10-mark scheme and all answers are in the answer key above. Re-check every answer and the marking scheme before publication.
16–19. Remediation, enrichment, homework, teacher reflection
Remediation. Equivalent fractions. 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.