You will learn
- Partition a dividend.
- Use repeated subtraction.
- Use known facts.
- Choose a strategy.
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
- Break the dividend into easy parts.
- Divide each part.
- Add the partial quotients.
- Choose the strategy that suits the numbers.
Words to know
Break apart.
Subtract the divisor again and again.
A plan.
The answer.
1. Discover: bags of sweets
84 sweets are put into 4 equal bags. Can you split 84 into 80 and 4?
2. Understand: division strategies
- Partition: 84 ÷ 4 = (80 ÷ 4) + (4 ÷ 4) = 20 + 1 = 21.
- Partition: 96 ÷ 6 = (60 ÷ 6) + (36 ÷ 6) = 10 + 6 = 16.
- Repeated subtraction: 30 − 6 − 6 − 6 − 6 − 6 = 0, five times, so 30 ÷ 6 = 5.
Idea 1: Partition
72 ÷ 3: 60 ÷ 3 = 20 and 12 ÷ 3 = 4. 20 + 4 = 24.
Idea 2: Known facts
96 ÷ 4: 80 ÷ 4 = 20 and 16 ÷ 4 = 4. So 24. 75 ÷ 5: 50 ÷ 5 = 10 and 25 ÷ 5 = 5. So 15.
Idea 3: Repeated subtraction
52 ÷ 4: 40 ÷ 4 = 10 and 12 ÷ 4 = 3, so 13. Or take away 4 thirteen times.
Why choose the parts? Each part must divide exactly.
3. Worked examples
Example 1 (I show you): Partition
72 ÷ 3
- 60 ÷ 3 and 12 ÷ 3.
Answer: 24
Example 2 (We do it together): Partition
90 ÷ 6
- 60 ÷ 6 and 30 ÷ 6.
Answer: 15
Example 3 (You try): Partition
52 ÷ 4
Show the steps and answer
- 40 ÷ 4 and 12 ÷ 4.
Answer: 13
Did you know?
Partitioning also works for multiplication.
Why this matters
Having strategies makes division fast and flexible.
4. Explore: partition
You need paper.
- Write 84 ÷ 4.
- Split 84 into 80 and 4.
- Divide each part.
- Add the answers.
Think about it: what did you notice?
21.
5. Practise
Say it in a sentence
Use these starters when you talk about the lesson. Say them out loud.
- I split ___ into ___ and ___.
- ___ ÷ ___ = ___ and ___ ÷ ___ = ___.
- I add to get ___.
- So the quotient is ___.
Guided practice
Question 1. 84 ÷ 4?
21.
Question 2. 96 ÷ 6?
16.
Question 3. 30 ÷ 6?
5.
Independent practice
Level 1: Start
- 72 ÷ 3
- 96 ÷ 4
- 75 ÷ 5
- 90 ÷ 6
- 52 ÷ 4
Level 2: Grow
- 63 ÷ 3
- 92 ÷ 4
- 84 ÷ 6
Level 3: Stretch
- 135 ÷ 5
- 156 ÷ 6
- Kofi splits 52 ÷ 4 as 50 ÷ 4 and 2 ÷ 4 and gets stuck. What better split can he use?
Answers are in the answer key below. Try first, then check.
6. Apply: everyday mathematics
84 sweets in 4 bags equally. How many per bag?
Show a sample answer
21.
Another one. 78 stickers are shared equally among 6 children. How many does each child get?
Show a sample answer
60 ÷ 6 = 10 and 18 ÷ 6 = 3, so 13 stickers.
7. Common mistakes
Fix: Divide every part.
Fix: Choose parts that are multiples of the divisor.
Fix: Add the answers from each part.
8. Lesson summary and revision card
- I can partition a dividend.
- I can use repeated subtraction.
- I can use known facts.
- I can choose a strategy.
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
- Partition.
- Repeated subtraction.
- Add the parts.
11. Next lesson
Next lesson: Dividing larger numbers. 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 72 ÷ 3 by splitting. [2 marks]
- Find 96 ÷ 4 by splitting. [2 marks]
- Find 75 ÷ 5 by splitting. [2 marks]
- Find 90 ÷ 6 by splitting. [2 marks]
- Ali says 52 ÷ 4 = 14. Is he right? Explain. [3 marks]
Total: 11 marks.
Marking guide and model answers
- 60 ÷ 3 = 20 and 12 ÷ 3 = 4 [1]; 24 [1]
- 80 ÷ 4 = 20 and 16 ÷ 4 = 4 [1]; 24 [1]
- 50 ÷ 5 = 10 and 25 ÷ 5 = 5 [1]; 15 [1]
- 60 ÷ 6 = 10 and 30 ÷ 6 = 5 [1]; 15 [1]
- No [1]. 4 × 14 = 56, not 52 [1]. 40 ÷ 4 = 10 and 12 ÷ 4 = 3, so 13 [1].
Score guide: 10 to 11 = secure. 7 to 9 = nearly there, revise the parts you missed. Under 7 = work through the lesson again with a grown-up.
Printable worksheet
- 72 ÷ 3
- 96 ÷ 4
- 75 ÷ 5
- 90 ÷ 6
- 52 ÷ 4
- 84 ÷ 4 =
- 96 ÷ 6 =
- 72 ÷ 3 =
- 75 ÷ 5 =
- 90 ÷ 6 =
Homework
Divide five 2-digit numbers by partitioning.
Answer key and marking scheme
| Question | Expected response | Marks |
|---|---|---|
| 72 ÷ 3 | 24 | 2 |
| 96 ÷ 4 | 24 | 2 |
| 75 ÷ 5 | 15 | 2 |
| 90 ÷ 6 | 15 | 2 |
| 52 ÷ 4 | 13 | 2 |
| Total | 10 |
Practice answers: Worksheet: 1 24; 2 24; 3 15; 4 15; 5 13.
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 21; 7 16; 8 24; 9 15; 10 15.
Independent practice answers. Level 1: 1 24; 2 24; 3 15; 4 15; 5 13. Level 2: 1 21; 2 23; 3 14. Level 3: 1 27; 2 26; 3 40 ÷ 4 = 10 and 12 ÷ 4 = 3, so 13..
Mastery and remediation
| Objective | Bronze (Developing) | Silver (Proficient) | Gold (Advanced) |
|---|---|---|---|
| O1 Partition a dividend | 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 Use repeated subtraction | 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 known facts | 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 Choose a strategy | 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: Dividing only one part. Divide every part.
- Explain another way: use real objects first, then pictures.
- Show a simpler example: Use counters to share 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 uses partitioning and known facts to divide. You do not need to be good at mathematics to help.
- Share items equally and talk about the parts.
- Ask: how can you split it?
- Check with multiplication.
- 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: partition a dividend; use repeated subtraction; use known facts; choose a strategy.
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. 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 can I split the number into easy parts?
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. Dividing only one part. Divide every part.
13–15. Assessment questions, answer keys, marking scheme
Use the quiz and worksheet on this page. The 11-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. Use counters to share 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 4.NBT.B.6 (strategies for division); Cambridge Primary Mathematics Stage 4 (division strategies). These sources informed the lesson; no official alignment is claimed.