You will learn
- Say what a ratio compares.
- Tell part-to-part from part-to-whole.
- Describe a ratio in words.
- Find totals from a ratio.
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
Comparison of two quantities.
One part with another.
A part with the total.
An amount.
1. Discover: beads in a bag
A bag has 3 red beads and 5 blue beads. How can we compare them?
2. Understand: what a ratio is
- The ratio of red to blue beads is 3 to 5.
- Part-to-part: red to blue is 3 : 5.
- Part-to-whole: red to all beads is 3 : 8, because 3 + 5 = 8.
- The order matters: blue to red is 5 : 3.
3. Explore: describe
You need paper.
- Count each kind.
- Choose the order.
- Write the ratio.
- Check the total.
Think about it: what did you notice?
3 to 5.
4. Practise
Guided practice
Question 1. Red to blue?
3 to 5.
Question 2. Total beads?
8.
Question 3. Blue to red?
5 to 3.
Independent practice
- Red to all beads
- Blue to all beads
- Ratio of 4 boys to 6 girls
- Total of 4 boys and 6 girls
- Is 3 : 5 the same as 5 : 3?
Answers are in the answer key below. Try first, then check.
5. Apply: everyday mathematics
A class has 4 boys and 6 girls. Write the ratio of boys to girls.
Show a sample answer
4 to 6.
6. Common mistake
Fix: Read the order of the words.
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
- A ratio compares.
- Order matters.
- Part-to-whole uses the total.
9. Next lesson
Next lesson: Ratio notation. Keep going with the next idea in this course.
Printable worksheet
- Red to all beads
- Blue to all beads
- 4 boys to 6 girls
- Total 4 boys and 6 girls
- Is 3:5 the same as 5:3? (yes/no)
Homework
Make a ratio from two things in your home.
Answer key and marking scheme
| Question | Expected response | Marks |
|---|---|---|
| Red to all beads | 3 to 8 | 2 |
| Blue to all beads | 5 to 8 | 2 |
| 4 boys to 6 girls | 4 to 6 | 2 |
| Total 4 boys and 6 girls | 10 | 2 |
| Is 3:5 the same as 5:3? (yes/no) | no | 2 |
| Total | 10 |
Practice answers: Worksheet: 1 3 to 8; 2 5 to 8; 3 4 to 6; 4 10; 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 Say what a ratio compares | 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 Tell part-to-part from part-to-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 Describe a ratio in words | 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 Find totals from 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 |
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: Reversing the order. Read the order of the words.
- Explain another way: use real objects first, then pictures.
- Show a simpler example: Counting groups.
- 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: say what a ratio compares; tell part-to-part from part-to-whole; describe a ratio in words; find totals from a ratio.
Prerequisite knowledge. 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. 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. Reversing the order. Read the order of the words.
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. Counting groups. 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.