You will learn
- Put objects into groups of a given size.
- Count the number of groups.
- Tell sharing from grouping.
- Check the total.
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
- Grouping means putting objects into groups of a given size.
- Count how many groups there are.
- Sharing finds the size of each share. Grouping finds the number of groups.
- Check the total.
Words to know
A set of things together.
A fixed number in each group.
What we find when grouping.
All of them.
1. Discover: packing eggs
There are 12 eggs. A tray holds 4 eggs. How many trays do we need?
2. Understand: making equal groups
Sometimes we know the size of each group and want to find how many groups.
12 eggs in trays of 4: take away 4, 4, 4. That is 3 trays. We write 12 ÷ 4 = 3.
In sharing, we know the number of groups and find how many in each. In grouping, we know how many in each and find the number of groups. Both are division.
Idea 1: Make groups
12 eggs in trays of 4. Put 4 eggs in each tray. You fill 3 trays.
Idea 2: Sharing and grouping
When we share, we know the number of groups and find how many in each. When we group, we know how many in each group and find the number of groups.
Idea 3: Check
3 trays of 4 is 3 × 4 = 12. It matches.
Why check? Multiplying undoes grouping.
3. Worked examples
Example 1 (I show you): Eggs in trays
12 eggs go in trays of 4. How many trays?
- 4, 8, 12.
- 3 trays.
Answer: 3
Example 2 (We do it together): Groups of 5
10 in groups of 5 make how many groups?
- 5, 10.
Answer: 2 groups
Example 3 (You try): Check
Check: 5 groups of 3 make 15?
Show the steps and answer
- 5 × 3 = 15.
Answer: Yes
Did you know?
Shopkeepers group goods all the time, such as 6 eggs in a box.
Why this matters
Grouping shows how many equal parts fit into a total.
4. Explore: group them
You need 12 counters.
- Make groups of 4.
- Count the groups.
- Now make groups of 3 with the same counters.
- Compare the number of groups.
Think about it: what did you notice?
Groups of 4 make 3 groups. Groups of 3 make 4 groups.
5. Practise
Say it in a sentence
Use these starters when you talk about the lesson. Say them out loud.
- ___ in groups of ___ make ___ groups.
- I count ___ groups.
- ___ × ___ = ___.
- This is grouping because ___.
Guided practice
Question 1. 12 eggs in trays of 4?
3 trays.
Question 2. 10 in groups of 5?
2 groups.
Question 3. 15 in groups of 3?
5 groups.
Independent practice
Level 1: Start
- 12 in groups of 4
- 10 in groups of 5
- 15 in groups of 3
- 20 in groups of 10
- 8 in groups of 2
Level 2: Grow
- 18 in groups of 2 = ___ groups.
- 25 in groups of 5 = ___ groups.
- 16 in groups of 4 = ___ groups.
Level 3: Stretch
- 24 in groups of 4 = ___ groups.
- A trader has 30 mangoes and puts 5 in each bag. How many bags?
- Ben says 12 in groups of 4 make 8 groups. What is wrong?
Answers are in the answer key below. Try first, then check.
6. Apply: everyday mathematics
A trader packs 20 oranges in bags of 10. How many bags?
Show a sample answer
2 bags.
Another one. 20 children make teams of 5. How many teams are there?
Show a sample answer
4
7. Common mistakes
Fix: Count how many groups are made.
Fix: Ask: do I know the groups or the size of each?
Fix: Keep making groups of 4 until none are left.
8. Lesson summary and revision card
- I can put objects into groups of a given size.
- I can count the number of groups.
- I can tell sharing from grouping.
- I can check the total.
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
- Make equal-sized groups.
- Count the groups.
- Sharing and grouping are both division.
11. Next lesson
Next lesson: Division using objects. 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.
- 12 eggs go in trays of 4. How many trays? [2 marks]
- Put 20 in groups of 10. How many groups? [1 mark]
- Put 15 sweets in bags of 3. How many bags? [2 marks]
- What is the difference between sharing and grouping? [2 marks]
- Check that 6 groups of 3 make 18. [2 marks]
Total: 9 marks.
Marking guide and model answers
- 12 in groups of 4 [1]; 3 [1]
- 2 [1]
- 5 [2]. Give 1 mark for the method.
- Sharing: find how many in each [1]; grouping: find how many groups [1]
- 6 × 3 [1] = 18 [1]
Score guide: 8 to 9 = secure. 6 to 7 = nearly there, revise the parts you missed. Under 6 = work through the lesson again with a grown-up.
Printable worksheet
- 12 in groups of 4
- 10 in groups of 5
- 15 in groups of 3
- 20 in groups of 10
- 8 in groups of 2
- 12 in groups of 4 = ___ groups.
- 10 in groups of 5 = ___ groups.
- 8 in groups of 2 = ___ groups.
- 18 in groups of 3 = ___ groups.
- 20 in groups of 10 = ___ groups.
Homework
Put 12 stones into groups of 2, then groups of 3, then groups of 4. Count each time.
Answer key and marking scheme
| Question | Expected response | Marks |
|---|---|---|
| 12 in groups of 4 | 3 | 2 |
| 10 in groups of 5 | 2 | 2 |
| 15 in groups of 3 | 5 | 2 |
| 20 in groups of 10 | 2 | 2 |
| 8 in groups of 2 | 4 | 2 |
| Total | 10 |
Practice answers: Worksheet: 1 3; 2 2; 3 5; 4 2; 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 3; 7 2; 8 4; 9 6; 10 2.
Independent practice answers. Level 1: 1 3; 2 2; 3 5; 4 2; 5 4. Level 2: 1 9; 2 5; 3 4. Level 3: 1 6; 2 6; 3 12 − 4 = 8 is not grouping. 3 groups of 4 make 12..
Mastery and remediation
| Objective | Bronze (Developing) | Silver (Proficient) | Gold (Advanced) |
|---|---|---|---|
| O1 Put objects into 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 the total | 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 the objects instead of the 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 the same 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 puts objects into equal groups and counts the groups. You do not need to be good at mathematics to help.
- Put beans into cups of a given size and count the cups.
- Ask: 12 sweets in bags of 3. How many bags?
- Check using 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: put objects into groups of a given size; count the number of groups; tell sharing from grouping; check the total.
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 12 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. How many in each group? How many groups? Can you 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 the objects instead of the groups. Count how many groups are made.
13–15. Assessment questions, answer keys, marking scheme
Use the quiz and worksheet on this page. The 9-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 the same 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 2 » Operations & Algebraic Thinking; Grade 2 » 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 2.OA.C.3 and 3.OA.A.2 (division as grouping); Cambridge Primary Mathematics Stage 2. These sources informed the lesson.