You will learn
- Draw a factor tree.
- Write a prime factorisation.
- Use index notation.
- Check by multiplying.
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
A factor that is prime.
Splitting a number into factors.
The small raised number.
Result of multiplying.
1. Discover: number building blocks
Every number can be built from primes. What primes build 36?
2. Understand: prime factorisation
- 36 = 6 × 6 = (2 × 3) × (2 × 3).
- So 36 = 2 × 2 × 3 × 3 = 2² × 3².
- 60 = 2 × 2 × 3 × 5 = 2² × 3 × 5.
- Check: 4 × 3 × 5 = 60.
3. Explore: tree
You need paper.
- Split into two factors.
- Split composites again.
- Circle primes.
- Multiply to check.
Think about it: what did you notice?
2² × 3 × 5.
4. Practise
Guided practice
Question 1. Prime factors of 36?
2 and 3.
Question 2. 2² × 3² =?
36.
Question 3. 2² × 3 × 5 =?
60.
Independent practice
- Prime factorisation of 12
- Prime factorisation of 20
- Prime factorisation of 30
- What number is 2³ × 3?
- Is 2 × 9 a prime factorisation?
Answers are in the answer key below. Try first, then check.
5. Apply: everyday mathematics
A number is 2 × 3 × 5. What is it?
Show a sample answer
30.
6. Common mistake
Fix: Keep splitting until primes.
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
- Split to primes.
- Use indices for repeats.
- Check by multiplying.
9. Next lesson
Next lesson: Greatest common factor. Keep going with the next idea in this course.
Printable worksheet
- Prime factors of 12
- Prime factors of 20
- Prime factors of 30
- 2³ × 3
- Prime factors of 72
Homework
Make factor trees for 48 and 100.
Answer key and marking scheme
| Question | Expected response | Marks |
|---|---|---|
| Prime factors of 12 | 2² × 3 | 2 |
| Prime factors of 20 | 2² × 5 | 2 |
| Prime factors of 30 | 2 × 3 × 5 | 2 |
| 2³ × 3 | 24 | 2 |
| Prime factors of 72 | 2³ × 3² | 2 |
| Total | 10 |
Practice answers: Worksheet: 1 2² × 3; 2 2² × 5; 3 2 × 3 × 5; 4 24; 5 2³ × 3².
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 Draw a factor tree | 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 a prime factorisation | 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 index notation | 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 Check by multiplying | 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: Stopping at 4 × 9. Keep splitting until primes.
- Explain another way: use real objects first, then pictures.
- Show a simpler example: Factor pairs.
- 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: draw a factor tree; write a prime factorisation; use index notation; check by multiplying.
Prerequisite knowledge. Lesson 3.
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. Stopping at 4 × 9. Keep splitting until primes.
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. Factor pairs. 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.