You will learn
- Decide if a story is sharing or grouping.
- Write a division sentence.
- Interpret the remainder.
- Check the answer.
Version 0.2 · expanded edition · built from cited public sources Content is based on the official frameworks and sources listed under Sources and standards. No official endorsement is claimed. Written in the style of common primary school assessments. No exam result is promised.
Student lesson
- Decide if the story is sharing or grouping.
- Write the division sentence.
- Think about what the remainder means.
- Check the answer.
Words to know
Share or group equally.
What is left over.
Give out equally.
Put into sets of the same size.
1. Discover: cars for the trip
29 children go on a trip. Each car holds 6. How many cars are needed?
2. Understand: division problems
First decide if the story is sharing or grouping, then divide and think about the remainder.
36 sweets shared among 4: 36 ÷ 4 = 9. 45 oranges in bags of 5: 45 ÷ 5 = 9 bags. 48 pupils into 6 teams: 8 each.
29 children, 6 per car: 29 ÷ 6 = 4 r 5. Four cars are full and 5 children are left, so we need 5 cars. The remainder tells us to round up here.
20 pencils, 3 per child: 6 children get 3, and 2 are left over.
Idea 1: Sharing
36 sweets shared among 4 children: 36 ÷ 4 = 9 each.
Idea 2: Grouping
45 oranges in bags of 5: 45 ÷ 5 = 9 bags.
Idea 3: Remainder
29 children, 6 per car: 29 ÷ 6 = 4 remainder 5. The 5 children still need a car, so 5 cars. 50 kg of rice in 8 kg sacks: 6 remainder 2, so 6 full sacks.
Why think about the remainder? Sometimes we round up, sometimes we ignore it.
3. Worked examples
Example 1 (I show you): Share
36 sweets shared among 4. Each gets?
- 36 ÷ 4.
Answer: 9
Example 2 (We do it together): Group
45 oranges in bags of 5. How many bags?
- 45 ÷ 5.
Answer: 9 bags
Example 3 (You try): Cars
29 children, 6 per car. Cars needed?
Show the steps and answer
- 29 ÷ 6 = 4 r 5.
- The 5 need a car.
Answer: 5 cars
Did you know?
A remainder can mean one more group is needed, or it can be ignored. It depends on the story.
Why this matters
Division problems appear in sharing, packing and planning.
4. Explore: story and remainder
You need paper and a pencil.
- Read: 29 children, 6 per car.
- Divide: 29 ÷ 6 = 4 r 5.
- Decide what to do with the 5 children.
- Write the answer: 5 cars.
Think about it: what did you notice?
5 cars are needed.
5. Practise
Say it in a sentence
Use these starters when you talk about the lesson. Say them out loud.
- This is sharing / grouping because ___.
- The division is ___ ÷ ___.
- The remainder means ___.
- The answer is ___.
Guided practice
Question 1. 36 sweets among 4?
9 each.
Question 2. 29 children, 6 per car: cars?
5.
Question 3. 20 pencils, 3 per child: left over?
2.
Independent practice
Level 1: Start
- 36 sweets shared among 4
- 45 oranges in bags of 5
- 48 pupils into 6 teams
- 50 kg of rice in 8 kg sacks
- 29 children, 6 per car
Level 2: Grow
- 24 books shared among 3 shelves
- 35 eggs in trays of 5
- 17 children in teams of 4
Level 3: Stretch
- 63 mangoes in baskets of 9
- 38 pupils, 5 to a bench. How many benches are needed?
- Ali says 29 children with 6 per car need 4 cars. What is wrong?
Answers are in the answer key below. Try first, then check.
6. Apply: everyday mathematics
A trader has 50 kg of rice and uses 8 kg sacks. How many full sacks and how many kg left?
Show a sample answer
6 full sacks with 2 kg left.
Another one. Write a division story with a remainder and say what the remainder means.
Show a sample answer
for example 26 sweets in bags of 5 make 5 bags with 1 sweet left
7. Common mistakes
Fix: Ask what the remainder means in the story.
Fix: Ask what the remainder means in the story.
Fix: Sharing and grouping are division.
8. Lesson summary and revision card
- I can tell sharing from grouping.
- I can write a division sentence.
- I can interpret the remainder.
- I can check the answer.
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
- Decide sharing or grouping.
- Divide.
- Think about the remainder.
11. Next lesson
Next lesson: Equal Parts of a Whole. 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.
- 36 sweets are shared among 4. How many each? [2 marks]
- 45 oranges in bags of 5. How many bags? [2 marks]
- 29 children, 6 per car. How many cars? [3 marks]
- 50 kg rice in 8 kg sacks. How many full sacks? [2 marks]
- Kofi says 48 pupils in 6 teams gives 8 teams. Is he right? Explain. [3 marks]
Total: 12 marks.
Marking guide and model answers
- 36 ÷ 4 [1] = 9 [1]
- 45 ÷ 5 [1] = 9 [1]
- 29 ÷ 6 = 4 remainder 5 [1]; the 5 need a car [1]; 5 cars [1]
- 50 ÷ 8 = 6 remainder 2 [1]; 6 full sacks [1]
- No [1]. 48 ÷ 6 = 8 is the number in each team [1]. There are 6 teams [1].
Score guide: 11 to 12 = secure. 8 to 10 = nearly there, revise the parts you missed. Under 8 = work through the lesson again with a grown-up.
Printable worksheet
- 36 sweets among 4
- 45 oranges in bags of 5
- 48 pupils into 6 teams
- 50 kg in 8 kg sacks, full sacks
- 29 children, 6 per car, cars needed
- 36 sweets shared among 4. Each gets ___.
- 45 oranges in bags of 5 make ___ bags.
- 48 pupils into 6 teams gives ___ each.
- 29 children, 6 per car. Cars needed: ___
- 50 kg rice in 8 kg sacks gives ___ full sacks.
Homework
Write a division story about sharing food at home, with a remainder.
Answer key and marking scheme
| Question | Expected response | Marks |
|---|---|---|
| 36 sweets among 4 | 9 | 2 |
| 45 oranges in bags of 5 | 9 | 2 |
| 48 pupils into 6 teams | 8 | 2 |
| 50 kg in 8 kg sacks, full sacks | 6 | 2 |
| 29 children, 6 per car, cars needed | 5 | 2 |
| Total | 10 |
Practice answers: Worksheet: 1 9; 2 9; 3 8; 4 6; 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 9; 7 9; 8 8; 9 5; 10 6.
Independent practice answers. Level 1: 1 9 each; 2 9 bags; 3 8 pupils in each team; 4 5 cars; 5 6 full sacks with 2 kg left. Level 2: 1 8 books; 2 7 trays; 3 4 teams and 1 child left. Level 3: 1 7 baskets; 2 8 benches; 3 29 ÷ 6 = 4 remainder 5. The 5 children need another car, so 5 cars..
Mastery and remediation
| Objective | Bronze (Developing) | Silver (Proficient) | Gold (Advanced) |
|---|---|---|---|
| O1 Decide if a story is sharing or grouping | 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 division sentence | 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 Interpret the remainder | 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 the answer | 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 |
Courseversity badge thresholds (overall quiz score): Gold = 90–100%; Silver = 80–89.9%; Bronze = 70–79.9%. A badge is never a full record of progress.
If a learner struggles
- Find the misconception: Ignoring the remainder. Ask what the remainder means in the story.
- Explain another way: use real objects first, then pictures.
- Show a simpler example: Act the story 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 solves division word problems and decides what to do with a remainder. You do not need to be good at mathematics to help.
- Make up sharing and grouping stories.
- Ask: what does the remainder mean?
- Use real objects.
- 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: decide if a story is sharing or grouping; write a division sentence; interpret the remainder; check the answer.
Prerequisite knowledge. Lessons 1 to 6.
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 and a pencil. 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. Sharing or grouping? What is the division? What does the remainder mean?
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. Ignoring the remainder. Ask what the remainder means in the story.
13–15. Assessment questions, answer keys, marking scheme
Use the quiz and worksheet on this page. The 12-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. Act the story 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
This lesson is based on the sources below, and no official 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. Where a standard code is named, it points to the official framework.
Official standards for this topic area. Common Core State Standards for Mathematics (official site): Grade 3 » Operations & Algebraic Thinking; Grade 3 » Number & Operations in Base Ten. These pages list the standards that cover this topic area; read them alongside the lesson.
Research used to shape this lesson. Common Core 3.OA.A.3 and 4.OA.A.3; Cambridge Primary Mathematics Stage 3 (division word problems). These sources informed the lesson.