You will learn
- Make groups of a given size.
- Count the number of groups.
- Tell sharing from grouping.
- Check by multiplying.
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
- Make groups of a given size.
- Count the groups.
- Sharing asks how many in each. Grouping asks how many groups.
- Check by multiplying.
Words to know
A set of the same size.
Finding how many groups.
Share or group equally.
The answer to a division.
1. Discover: packing eggs
There are 24 eggs. A tray holds 6. How many trays do we need?
2. Understand: division as grouping
Sometimes we know the size of each group and need the number of groups.
24 eggs in trays of 6: 24 ÷ 6 = 4 trays, because 4 × 6 = 24.
30 ÷ 5 = 6 groups. 45 ÷ 9 = 5. 36 ÷ 4 = 9. 64 ÷ 8 = 8.
Repeated subtraction also works: 24 − 6 − 6 − 6 − 6 = 0, four 6s.
Idea 1: Groups
24 eggs in trays of 6: 24 ÷ 6 = 4 trays.
Idea 2: Counting groups
30 in groups of 5: 30 ÷ 5 = 6 groups.
Idea 3: Sharing or grouping?
100 oranges in bags of 25: 100 ÷ 25 = 4 bags. We know the size of each bag, and we find the number of bags.
Why two kinds? The sum is the same, but the question is different.
3. Worked examples
Example 1 (I show you): Trays
24 eggs in trays of 6. How many trays?
- 24 ÷ 6.
Answer: 4 trays
Example 2 (We do it together): Groups
30 in groups of 5. How many groups?
- 30 ÷ 5.
Answer: 6
Example 3 (You try): Bags
100 oranges in bags of 25. How many bags?
Show the steps and answer
- 100 ÷ 25.
Answer: 4 bags
Did you know?
Sharing and grouping give the same quotient but ask different questions.
Why this matters
Grouping tells us how many boxes, trays or teams we need.
4. Explore: group them
You need 24 counters.
- Make groups of 6.
- Count the groups.
- Make groups of 4 with the same counters.
- Compare the number of groups.
Think about it: what did you notice?
Groups of 6 make 4; groups of 4 make 6.
5. Practise
Say it in a sentence
Use these starters when you talk about the lesson. Say them out loud.
- I put ___ in groups of ___.
- There are ___ groups.
- The division is ___ ÷ ___ = ___.
- I check by ___ × ___.
Guided practice
Question 1. 24 eggs in trays of 6?
4 trays.
Question 2. 30 in groups of 5?
6 groups.
Question 3. 64 ÷ 8?
8.
Independent practice
Level 1: Start
- 24 in groups of 6
- 30 in groups of 5
- 45 ÷ 9
- 36 ÷ 4
- 100 in groups of 25
Level 2: Grow
- 12 in groups of 3
- 35 ÷ 7
- 20 in groups of 4
Level 3: Stretch
- 72 ÷ 8
- 60 in groups of 20
- Ben says 30 sweets in groups of 6 make 24 groups. What is wrong?
Answers are in the answer key below. Try first, then check.
6. Apply: everyday mathematics
A trader packs 100 oranges in bags of 25. How many bags?
Show a sample answer
4 bags.
Another one. A farmer packs 48 eggs in trays of 6. How many trays?
Show a sample answer
8 trays
7. Common mistakes
Fix: Count how many groups are made.
Fix: Read the question: how many groups?
Fix: Use division.
8. Lesson summary and revision card
- I can make groups of a given size.
- I can count the groups.
- I can tell sharing from grouping.
- I can check by multiplying.
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
- Grouping finds the number of groups.
- Repeated subtraction works.
- Check by multiplying.
11. Next lesson
Next lesson: Relationship between multiplication and division. 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.
- 24 eggs in trays of 6. How many trays? [2 marks]
- 30 ÷ 5 = ? [1 mark]
- 100 oranges in bags of 25. How many bags? [2 marks]
- Check 36 ÷ 4 = 9. [2 marks]
- Ama says sharing and grouping are the same question. Is she right? Explain. [3 marks]
Total: 10 marks.
Marking guide and model answers
- 24 ÷ 6 [1] = 4 [1]
- 6 [1]
- 100 ÷ 25 [1] = 4 [1]
- 9 × 4 [1] = 36 [1]
- No [1]. Sharing asks how many in each share [1]. Grouping asks how many groups [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
- 24 in groups of 6
- 30 in groups of 5
- 45 ÷ 9
- 36 ÷ 4
- 100 in groups of 25
- 24 eggs in trays of 6 need ___ trays.
- 30 ÷ 5 =
- 45 ÷ 9 =
- 36 ÷ 4 =
- 100 oranges in bags of 25 make ___ bags.
Homework
Group 24 stones in 3 different sizes. Count the groups each time.
Answer key and marking scheme
| Question | Expected response | Marks |
|---|---|---|
| 24 in groups of 6 | 4 | 2 |
| 30 in groups of 5 | 6 | 2 |
| 45 ÷ 9 | 5 | 2 |
| 36 ÷ 4 | 9 | 2 |
| 100 in groups of 25 | 4 | 2 |
| Total | 10 |
Practice answers: Worksheet: 1 4; 2 6; 3 5; 4 9; 5 4.
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 4; 7 6; 8 5; 9 9; 10 4.
Independent practice answers. Level 1: 1 4; 2 6; 3 5; 4 9; 5 4. Level 2: 1 4; 2 5; 3 5. Level 3: 1 9; 2 3; 3 He subtracted. 30 ÷ 6 = 5 because 5 × 6 = 30..
Mastery and remediation
| Objective | Bronze (Developing) | Silver (Proficient) | Gold (Advanced) |
|---|---|---|---|
| O1 Make groups of a given size | 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 Count the number of groups | 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 Tell sharing from 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 |
| O4 Check by multiplying | 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: Counting items instead of groups. Count how many groups are made.
- Explain another way: use real objects first, then pictures.
- Show a simpler example: Move counters into rings of equal size.
- 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 divides by making groups of a given size. You do not need to be good at mathematics to help.
- Ask: how many bags do we need for 20 apples if each holds 4?
- Use counters to make groups.
- Check by multiplying.
- 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: make groups of a given size; count the number of groups; tell sharing from grouping; check by multiplying.
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 24 counters. 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. What is the size of each group? How many groups? Does it check?
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. Counting items instead of groups. Count how many groups are made.
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. Move counters into rings of equal size. 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.2 and 3.OA.A.3; Cambridge Primary Mathematics Stage 3 (division as grouping). These sources informed the lesson.