You will learn
- List common factors.
- Find the GCF.
- Use prime factors.
- Solve sharing problems.
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 of both.
Greatest common factor.
Make smaller.
Share equally.
1. Discover: biggest equal groups
12 pens and 18 pencils are shared into identical packs with nothing left. Most packs?
2. Understand: greatest common factor
- Factors of 12: 1, 2, 3, 4, 6, 12. Factors of 18: 1, 2, 3, 6, 9, 18.
- Common: 1, 2, 3, 6. The GCF is 6.
- So 6 packs, each with 2 pens and 3 pencils.
- GCF of 24 and 36 is 12.
3. Explore: gcf
You need paper.
- List factors of each.
- Circle the common ones.
- Pick the greatest.
- Check each divides.
Think about it: what did you notice?
6.
4. Practise
Guided practice
Question 1. GCF of 12 and 18?
6.
Question 2. GCF of 24 and 36?
12.
Question 3. GCF of 16 and 40?
8.
Independent practice
- GCF of 8 and 12
- GCF of 15 and 25
- GCF of 14 and 21
- GCF of 9 and 10
- Packs from 12 pens and 18 pencils
Answers are in the answer key below. Try first, then check.
5. Apply: everyday mathematics
12 pens and 18 pencils make identical packs. How many pens in each pack?
Show a sample answer
2 pens.
6. Common mistake
Fix: Choose the greatest.
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
- List factors.
- Choose the greatest shared.
- GCF solves sharing.
9. Next lesson
Next lesson: Least common multiple. Keep going with the next idea in this course.
Printable worksheet
- GCF of 8 and 12
- GCF of 15 and 25
- GCF of 14 and 21
- GCF of 9 and 10
- Packs from 12 and 18
Homework
Find the GCF of 30 and 45.
Answer key and marking scheme
| Question | Expected response | Marks |
|---|---|---|
| GCF of 8 and 12 | 4 | 2 |
| GCF of 15 and 25 | 5 | 2 |
| GCF of 14 and 21 | 7 | 2 |
| GCF of 9 and 10 | 1 | 2 |
| Packs from 12 and 18 | 6 | 2 |
| Total | 10 |
Practice answers: Worksheet: 1 4; 2 5; 3 7; 4 1; 5 6.
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 List common factors | 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 GCF | 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 prime factors | 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 Solve sharing problems | 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: Giving the least common factor 1. Choose the greatest.
- Explain another way: use real objects first, then pictures.
- Show a simpler example: Factors of 12 and 18.
- 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: list common factors; find the GCF; use prime factors; solve sharing problems.
Prerequisite knowledge. Lessons 3 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. 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. Giving the least common factor 1. Choose the greatest.
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. Factors of 12 and 18. 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.