You will learn
- Compare unit rates.
- Find the better buy.
- Compare ratios.
- Justify a choice.
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
Lower cost per unit.
Look at both.
Price for one.
Give a reason.
1. Discover: which is cheaper?
3 mangoes cost 12 and 5 mangoes cost 15. Which is the better buy?
2. Understand: comparing rates
- 3 for 12: 12 ÷ 3 = 4 each.
- 5 for 15: 15 ÷ 5 = 3 each.
- 3 each is less than 4 each, so 5 for 15 is cheaper.
- Compare speeds the same way: 150 km in 3 h (50 km/h) is slower than 240 km in 4 h (60 km/h).
3. Explore: compare
You need paper.
- Find each unit rate.
- Compare them.
- Pick the lower price.
- Write why.
Think about it: what did you notice?
5 for 15.
4. Practise
Guided practice
Question 1. 3 for 12 is how much each?
4.
Question 2. 5 for 15 is how much each?
3.
Question 3. Better buy?
5 for 15.
Independent practice
- 2 for 10: price each
- 4 for 24: price each
- Better buy: 2 for 10 or 4 for 24
- Speed of 150 km in 3 h
- Faster: 50 km/h or 60 km/h
Answers are in the answer key below. Try first, then check.
5. Apply: everyday mathematics
3 mangoes for 12 or 5 for 15. Which is cheaper per mango?
Show a sample answer
5 for 15.
6. Common mistake
Fix: Compare per item.
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
- Use unit rates.
- Lower price is the better buy.
- Say why.
9. Next lesson
Next lesson: Ratio word problems. Keep going with the next idea in this course.
Printable worksheet
- 2 for 10, each
- 4 for 24, each
- Better: 2 for 10 or 4 for 24
- 150 km in 3 h
- Faster: 50 or 60 km/h
Homework
Compare the price per unit of two products at home.
Answer key and marking scheme
| Question | Expected response | Marks |
|---|---|---|
| 2 for 10, each | 5 | 2 |
| 4 for 24, each | 6 | 2 |
| Better: 2 for 10 or 4 for 24 | 2 for 10 | 2 |
| 150 km in 3 h | 50 km/h | 2 |
| Faster: 50 or 60 km/h | 60 km/h | 2 |
| Total | 10 |
Practice answers: Worksheet: 1 5; 2 6; 3 2 for 10; 4 50 km/h; 5 60 km/h.
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 Compare unit rates | 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 Find the better buy | 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 Compare 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 |
| O4 Justify a choice | 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: Comparing total prices only. Compare per item.
- Explain another way: use real objects first, then pictures.
- Show a simpler example: Unit rates.
- 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: compare unit rates; find the better buy; compare ratios; justify a choice.
Prerequisite knowledge. Lesson 5.
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. Comparing total prices only. Compare per item.
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. Unit rates. 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.