You will learn
- Write a ratio with a colon.
- Write with “to”.
- Write as a fraction.
- Link ratio and fraction of the total.
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
The mark : in a ratio.
Way of writing.
Part divided by total.
A number in a ratio.
1. Discover: three ways
In a class the ratio of boys to girls is 2 to 3. How else can we write it?
2. Understand: ratio notation
- 2 to 3, 2 : 3 and 2/3 all compare boys to girls.
- Total parts: 2 + 3 = 5, so boys are 2/5 of the class and girls 3/5.
- In a class of 30, each part is 6, so 12 boys and 18 girls.
- Check: 12 + 18 = 30.
3. Explore: convert
You need paper.
- Add the terms.
- Divide the total by that.
- Multiply for each part.
- Check the sum.
Think about it: what did you notice?
12 and 18.
4. Practise
Guided practice
Question 1. Boys fraction of the class?
2/5.
Question 2. Value of one part in 30?
6.
Question 3. Girls?
18.
Independent practice
- Write 2 to 3 with a colon
- Girls as a fraction of class
- Parts in 2 : 3
- One part when class is 30
- Boys in 30 (ratio 2:3)
Answers are in the answer key below. Try first, then check.
5. Apply: everyday mathematics
Ratio boys : girls is 2 : 3 in a class of 30. How many boys?
Show a sample answer
12.
6. Common mistake
Fix: Boys are 2/5 of the class.
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
- Same ratio, several notations.
- Add terms for the total.
- Divide to find a part.
9. Next lesson
Next lesson: Equivalent ratios. Keep going with the next idea in this course.
Printable worksheet
- 2 to 3 with a colon
- Girls fraction
- Parts in 2 : 3
- One part (30)
- Boys (30, 2:3)
Homework
Find the ratio of boys to girls in your class.
Answer key and marking scheme
| Question | Expected response | Marks |
|---|---|---|
| 2 to 3 with a colon | 2 : 3 | 2 |
| Girls fraction | 3/5 | 2 |
| Parts in 2 : 3 | 5 | 2 |
| One part (30) | 6 | 2 |
| Boys (30, 2:3) | 12 | 2 |
| Total | 10 |
Practice answers: Worksheet: 1 2 : 3; 2 3/5; 3 5; 4 6; 5 12.
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 Write a ratio with a colon | 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 Write with “to” | 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 Write as a fraction | 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 Link ratio and fraction of the total | 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: Treating 2 : 3 as 2/3 of the class. Boys are 2/5 of the class.
- Explain another way: use real objects first, then pictures.
- Show a simpler example: Fractions of a total.
- 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: write a ratio with a colon; write with “to”; write as a fraction; link ratio and fraction of the total.
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. 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. Treating 2 : 3 as 2/3 of the class. Boys are 2/5 of the class.
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. Fractions of a total. 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.