You will learn
- Recall division facts to 144 ÷ 12.
- Link division to multiplication.
- Use fact families.
- Solve quick division problems.
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
- Division is the reverse of multiplication.
- Use a multiplication fact to find the quotient.
- Every fact belongs to a family.
- Know the dividend, divisor and quotient.
Words to know
The number being divided.
The number we divide by.
The answer to division.
Related multiplication and division facts.
1. Discover: sharing equally
56 oranges are shared equally among 7 children. Which multiplication fact helps?
2. Understand: division facts
Division undoes multiplication.
- 7 × 8 = 56, so 56 ÷ 7 = 8 and 56 ÷ 8 = 7.
- 9 × 8 = 72, so 72 ÷ 9 = 8.
- 12 × 12 = 144, so 144 ÷ 12 = 12.
In 56 ÷ 7 = 8: 56 is the dividend, 7 the divisor, 8 the quotient.
Idea 1: Reverse
48 ÷ 6: 6 × 8 = 48, so 8. 81 ÷ 9: 9 × 9 = 81, so 9.
Idea 2: Bigger
108 ÷ 12: 12 × 9 = 108, so 9. 63 ÷ 7: 7 × 9 = 63, so 9.
Idea 3: Family
132 ÷ 11: 11 × 12 = 132, so 12.
Why a family? One fact gives two multiplications and two divisions.
3. Worked examples
Example 1 (I show you): Reverse
48 ÷ 6
- 6 × 8 = 48.
Answer: 8
Example 2 (We do it together): Reverse
108 ÷ 12
- 12 × 9 = 108.
Answer: 9
Example 3 (You try): Reverse
132 ÷ 11
Show the steps and answer
- 11 × 12 = 132.
Answer: 12
Did you know?
In 48 ÷ 6 = 8, 48 is the dividend, 6 the divisor and 8 the quotient.
Why this matters
Quick division facts help in sharing and long division.
4. Explore: fact family
You need paper.
- Write 7 × 8 = 56.
- Write the two division facts.
- Do the same for 9 × 8.
- Name the dividend, divisor and quotient.
Think about it: what did you notice?
56 ÷ 7 = 8, 56 ÷ 8 = 7.
5. Practise
Say it in a sentence
Use these starters when you talk about the lesson. Say them out loud.
- I think of ___ × ___ = ___.
- So ___ ÷ ___ = ___.
- The dividend is ___.
- The quotient is ___.
Guided practice
Question 1. 56 ÷ 7?
8.
Question 2. 72 ÷ 9?
8.
Question 3. 144 ÷ 12?
12.
Independent practice
Level 1: Start
- 48 ÷ 6
- 81 ÷ 9
- 108 ÷ 12
- 63 ÷ 7
- 132 ÷ 11
Level 2: Grow
- 54 ÷ 6
- 77 ÷ 7
- 96 ÷ 8
Level 3: Stretch
- 121 ÷ 11
- Write the fact family for 7, 9 and 63.
- Ana says 48 ÷ 6 = 9 because 6 × 9 = 54. What is wrong?
Answers are in the answer key below. Try first, then check.
6. Apply: everyday mathematics
72 books are shared among 9 shelves equally. How many each?
Show a sample answer
8 books.
Another one. 72 sweets are shared equally among 8 children. How many does each get?
Show a sample answer
72 ÷ 8 = 9 sweets
7. Common mistakes
Fix: The dividend is the number being shared.
Fix: The dividend is the number being divided.
Fix: Think of the multiplication fact.
8. Lesson summary and revision card
- I can recall division facts to 144 ÷ 12.
- I can link division to multiplication.
- I can use fact families.
- I can solve quick division problems.
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
- Division undoes multiplication.
- Fact families.
- Name the parts.
11. Next lesson
Next lesson: Division strategies. 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.
- Find 48 ÷ 6. [2 marks]
- Find 81 ÷ 9. [1 mark]
- Find 108 ÷ 12. [2 marks]
- Find 63 ÷ 7. [2 marks]
- Ben says 132 ÷ 11 = 11. Is he right? Explain. [3 marks]
Total: 10 marks.
Marking guide and model answers
- 6 × 8 = 48 [1]; 8 [1]
- 9 [1]
- 12 × 9 = 108 [1]; 9 [1]
- 7 × 9 = 63 [1]; 9 [1]
- No [1]. 11 × 11 = 121, not 132 [1]. The answer is 12 [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
- 48 ÷ 6
- 81 ÷ 9
- 108 ÷ 12
- 63 ÷ 7
- 132 ÷ 11
- 56 ÷ 7 =
- 72 ÷ 9 =
- 144 ÷ 12 =
- In 56 ÷ 7 = 8 the divisor is
- 132 ÷ 11 =
Homework
Write a fact family for 8, 9 and 72.
Answer key and marking scheme
| Question | Expected response | Marks |
|---|---|---|
| 48 ÷ 6 | 8 | 2 |
| 81 ÷ 9 | 9 | 2 |
| 108 ÷ 12 | 9 | 2 |
| 63 ÷ 7 | 9 | 2 |
| 132 ÷ 11 | 12 | 2 |
| Total | 10 |
Practice answers: Worksheet: 1 8; 2 9; 3 9; 4 9; 5 12.
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 8; 7 8; 8 12; 9 7; 10 12.
Independent practice answers. Level 1: 1 8; 2 9; 3 9; 4 9; 5 12. Level 2: 1 9; 2 11; 3 12. Level 3: 1 11; 2 7 × 9 = 63; 9 × 7 = 63; 63 ÷ 7 = 9; 63 ÷ 9 = 7; 3 6 × 8 = 48, so the answer is 8..
Mastery and remediation
| Objective | Bronze (Developing) | Silver (Proficient) | Gold (Advanced) |
|---|---|---|---|
| O1 Recall division facts to 144 ÷ 12 | 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 Link division to multiplication | 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 fact families | 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 quick division 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 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: Mixing dividend and divisor. The dividend is the number being shared.
- Explain another way: use real objects first, then pictures.
- Show a simpler example: Share objects equally.
- 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 recalls division facts using multiplication facts. You do not need to be good at mathematics to help.
- Say a fact family out loud together.
- Ask: which multiplication fact helps?
- Practise in short daily bursts.
- 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: recall division facts to 144 ÷ 12; link division to multiplication; use fact families; solve quick division problems.
Prerequisite knowledge. Multiplication facts review.
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. Which multiplication fact gives this division?
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. Mixing dividend and divisor. The dividend is the number being shared.
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. Share objects equally. 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 3.OA.C.7 and 4.NBT.B.6; Cambridge Primary Mathematics Stage 4 (division facts). These sources informed the lesson; no official alignment is claimed.