You will learn
- Say what a composite number is.
- Tell prime from composite.
- Write a composite as a product.
- Find the smallest factor greater than 1.
Version 0.2 · expanded edition · expert review pending Standards alignment: pending verification. Written in the style of common primary school assessments. No exam result is promised.
Student lesson
- A composite number has more than two factors.
- A prime has exactly two factors.
- 1 is neither prime nor composite.
- Write composites as products.
Words to know
Has more than two factors.
Has exactly two factors.
Result of multiplying.
A number that divides exactly.
1. Discover: sorting numbers
Sort 9, 11, 12 and 15 into those that make more rectangles and those that only make 1 by n.
2. Understand: composite numbers
A composite number has more than two factors.
- 12: factors 1, 2, 3, 4, 6, 12, so composite.
- 15 = 3 × 5, composite. 9 = 3 × 3, composite.
- 11 has only 1 and 11, so it is prime.
1 is neither prime nor composite. Every even number greater than 2 is composite.
Idea 1: Composite
21 = 3 × 7, so it has factors 1, 3, 7 and 21. 21 is composite.
Idea 2: Prime
23 has only the factors 1 and 23. 23 is prime.
Idea 3: Product
30 = 2 × 15, so 30 is composite. 18 = 2 × 9 or 3 × 6.
Why neither for 1? It has only one factor.
3. Worked examples
Example 1 (I show you): Composite
21
- 21 = 3 × 7.
Answer: Composite
Example 2 (We do it together): Prime
23
- Only 1 and 23.
Answer: Prime
Example 3 (You try): Smallest factor
Smallest factor greater than 1 of 25
Show the steps and answer
- 25 ÷ 5 = 5.
Answer: 5
Did you know?
Every composite number can be written as a product of primes.
Why this matters
Knowing prime and composite helps us find factors quickly.
4. Explore: sort
You need paper.
- List factors of 9, 11, 12, 15.
- Count the factors.
- Label each prime or composite.
- Explain 1.
Think about it: what did you notice?
11 is prime; others composite.
5. Practise
Say it in a sentence
Use these starters when you talk about the lesson. Say them out loud.
- ___ has the factors ___.
- So it is prime / composite.
- I can write ___ as ___ × ___.
- The smallest factor greater than 1 is ___.
Guided practice
Question 1. Is 12 prime or composite?
Composite.
Question 2. Is 11 prime or composite?
Prime.
Question 3. 1 is…?
Neither.
Independent practice
Level 1: Start
- Prime or composite: 21
- Prime or composite: 23
- Prime or composite: 30
- Write 18 as a product of two factors
- Smallest factor greater than 1 of 25
Level 2: Grow
- Prime or composite: 39
- Prime or composite: 41
- Write 28 as a product of two factors
Level 3: Stretch
- Is 91 prime or composite?
- List the composite numbers between 10 and 20
- Ben says 51 is prime. What is wrong?
Answers are in the answer key below. Try first, then check.
6. Apply: everyday mathematics
A teacher has 21 pupils. Can she make equal groups of other sizes than 1 and 21?
Show a sample answer
Yes, groups of 3 or 7.
Another one. Explain why every even number greater than 2 is composite.
Show a sample answer
It is divisible by 1, 2 and itself, so it has at least three factors.
7. Common mistakes
Fix: 1 is neither.
Fix: 1 is neither prime nor composite.
Fix: 9 is odd and composite.
8. Lesson summary and revision card
- I can say what a composite number is.
- I can tell prime from composite.
- I can write a composite as a product.
- I can find the smallest factor greater than 1.
9. Check and master
Answer all 14 questions. You will see feedback after each one.
Your result appears here after you answer every question.
10. Key takeaways
- Composite: more than two factors.
- Prime: exactly two.
- 1 is neither.
11. Next lesson
Next lesson: Number patterns. Keep going with the next idea in this course.
Exam practice
These questions are written in the style of common school and international primary assessments. Try them on your own, without looking back. Then check your answers in the marking guide. The marks are shown in brackets.
- Is 21 prime or composite? Explain. [2 marks]
- Is 23 prime or composite? Explain. [2 marks]
- Write 18 as a product of two factors. [1 mark]
- Find the smallest factor greater than 1 of 25. [2 marks]
- Ali says 1 is composite. Is he right? Explain. [3 marks]
Total: 10 marks.
Marking guide and model answers
- 21 = 3 × 7 [1]; composite [1]
- Only factors 1 and 23 [1]; prime [1]
- 2 × 9 or 3 × 6 [1]
- 25 ÷ 5 [1]; 5 [1]
- No [1]. 1 has only one factor [1]. It is neither prime nor composite [1].
Score guide: 9 to 10 = secure. 6 to 8 = nearly there, revise the parts you missed. Under 6 = work through the lesson again with a grown-up.
Printable worksheet
- 21 prime or composite
- 23 prime or composite
- 30 prime or composite
- 18 as a product
- Smallest factor over 1 of 25
- A composite number has
- Which is composite? 19, 21 or 23
- Which is prime? 21, 23 or 25
- 30 is
- The smallest factor greater than 1 of 25 is
Homework
Sort the numbers 20 to 30 into prime and composite.
Answer key and marking scheme
| Question | Expected response | Marks |
|---|---|---|
| 21 prime or composite | composite | 2 |
| 23 prime or composite | prime | 2 |
| 30 prime or composite | composite | 2 |
| 18 as a product | 2 × 9 | 2 |
| Smallest factor over 1 of 25 | 5 | 2 |
| Total | 10 |
Practice answers: Worksheet: 1 composite; 2 prime; 3 composite; 4 2 × 9; 5 5.
Quiz answers: 1 A, 2 B, 3 C, 4 A, 5 B, 6 A, 7 B, 8 C, 9 A, 10 B, 11 C, 12 A, Challenge 1 C, Challenge 2 C.
Extra worksheet answers (items 6 onward): 6 more than two factors; 7 21; 8 23; 9 composite; 10 5.
Independent practice answers. Level 1: 1 composite; 2 prime; 3 composite; 4 for example 2 × 9; 5 5. Level 2: 1 composite, 3 × 13; 2 prime; 3 4 × 7. Level 3: 1 composite, 7 × 13; 2 12, 14, 15, 16, 18; 3 51 = 3 × 17, so it is composite..
Mastery and remediation
| Objective | Bronze (Developing) | Silver (Proficient) | Gold (Advanced) |
|---|---|---|---|
| O1 Say what a composite number is | 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 prime from composite | 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 a composite as a product | 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 the smallest factor greater than 1 | 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 8 of 12 core questions correct; Silver = all 12; Gold = all 12 plus both challenge questions. A badge is never a full record of progress.
If a learner struggles
- Find the misconception: Calling 1 composite. 1 is neither.
- Explain another way: use real objects first, then pictures.
- Show a simpler example: Make rectangles with counters.
- 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.
For parents and guardians
In this lesson your child tells composite numbers from prime numbers. You do not need to be good at mathematics to help.
- Quiz each other on primes up to 30.
- Ask: can you write it as a product?
- Use factor lists.
- Ask “how do you know?” after each answer, and listen.
- Praise effort, not only right answers. Mistakes are how we learn.
- Ten to fifteen minutes a day is better than one long session.
Teacher package
1–5. Objectives, prerequisites, materials, preparation, duration
Lesson objectives. Learners will: say what a composite number is; tell prime from composite; write a composite as a product; find the smallest factor greater than 1.
Prerequisite knowledge. Lessons 1, 2 and 4.
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. 45–60 minutes. It can be split into two shorter sessions.
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.
Key questions. How many factors does it have? Can I write it as a product?
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. Calling 1 composite. 1 is neither.
13–15. Assessment questions, answer keys, marking scheme
Use the quiz and worksheet on this page. The 10-mark exam practice scheme, the 10-mark scheme and all answers are in the answer sections above. Re-check every answer and the marking scheme before publication.
16–19. Remediation, enrichment, homework, teacher reflection
Remediation. Make rectangles with counters. 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.
Research used to shape this lesson. Common Core 4.OA.B.4; Cambridge Primary Mathematics Stage 5 (prime and composite numbers). These sources informed the lesson; no official alignment is claimed.