You will learn
- Use objects to divide.
- Read and write the sign ÷.
- Read 12 ÷ 3 = 4 as a sentence.
- Say what a leftover is.
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
- Divide means share or group equally.
- The sign ÷ means divide.
- 12 ÷ 3 = 4 means 12 shared into 3 groups gives 4.
- A leftover is what remains.
Words to know
Share or group equally.
The sign that means divide.
What remains when it does not divide exactly.
The answer to a division.
1. Discover: dividing bottle tops
You have 12 bottle tops. Divide them into 3 equal piles. How many are in each pile? Write it with the sign ÷.
2. Understand: division sign
The sign ÷ means divide. 12 ÷ 3 = 4 is read “12 divided by 3 is 4”.
With objects: put 12 tops in 3 piles, one at a time. Each pile has 4.
Sometimes there is a leftover: 13 sweets shared among 4 children is 3 each and 1 left over.
Idea 1: The sign ÷
The sign ÷ means divide. 12 ÷ 3 = 4 is read “12 divided by 3 is 4”. The answer is the quotient.
Idea 2: Use objects
Take 12 counters. Make 3 equal groups. Each group has 4. So 12 ÷ 3 = 4.
Idea 3: Leftovers
13 sweets shared among 4 children: 3 each and 1 left over.
Why? 4 × 3 = 12, and 13 − 12 = 1.
3. Worked examples
Example 1 (I show you): Divide
12 ÷ 3 = ?
- 12 shared into 3 equal groups.
- Each group has 4.
Answer: 4
Example 2 (We do it together): Use the table
15 ÷ 5 = ?
- 5 × 3 = 15.
Answer: 3
Example 3 (You try): Leftover
14 sweets shared among 4 children. How many each? How many left over?
Show the steps and answer
- 4 × 3 = 12.
- 14 − 12 = 2.
Answer: 3 each, 2 left over
Did you know?
The division sign ÷ has a dot above and below a line, like a fraction.
Why this matters
Division is the opposite of multiplication, and it answers sharing questions.
4. Explore: piles of tops
You need 12 tops.
- Put them in 3 piles equally.
- Write 12 ÷ 3 = 4.
- Do 20 ÷ 5 with tops.
- Try 13 tops in 4 piles and see what is left.
Think about it: what did you notice?
12 ÷ 3 = 4; 20 ÷ 5 = 4; 13 ÷ 4 is 3 with 1 left over.
5. Practise
Say it in a sentence
Use these starters when you talk about the lesson. Say them out loud.
- ___ ÷ ___ = ___.
- 12 divided by 3 is ___.
- There are ___ left over.
- I check with ___ × ___.
Guided practice
Question 1. 12 ÷ 3?
4.
Question 2. 14 ÷ 2?
7.
Question 3. 13 shared among 4?
3 each, 1 left.
Independent practice
Level 1: Start
- 12 ÷ 3
- 20 ÷ 5
- 14 ÷ 2
- 10 ÷ 10
- 18 ÷ 2
Level 2: Grow
- 18 ÷ 3 = ___.
- 15 ÷ 3 = ___.
- 10 ÷ 5 = ___.
Level 3: Stretch
- 17 sweets are shared among 5 children. How many each? How many left over?
- Write a ÷ sentence for 20 shared among 4.
- Ali says 12 ÷ 3 = 36. What is wrong?
Answers are in the answer key below. Try first, then check.
6. Apply: everyday mathematics
18 mangoes shared between 2 children. How many each?
Show a sample answer
9 mangoes.
Another one. 21 books are put equally on 3 shelves. How many are on each shelf?
Show a sample answer
7
7. Common mistakes
Fix: The total (12) comes first.
Fix: ÷ means share or group.
Fix: Say how many are left over.
8. Lesson summary and revision card
- I can use objects to divide.
- I can read and write the sign ÷.
- I can read 12 ÷ 3 = 4 as a sentence.
- I can say what a leftover is.
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
- ÷ means divide.
- Total first, then the divisor.
- Some divisions have a leftover.
11. Next lesson
Next lesson: Division using pictures. 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 ÷ 3 = ? [1 mark]
- 20 ÷ 5 = ? [1 mark]
- 10 ÷ 10 = ? [1 mark]
- 13 sweets are shared among 4 children. How many each? How many left over? [3 marks]
- Kofi says 14 ÷ 2 = 12. Is he right? Explain. [3 marks]
Total: 9 marks.
Marking guide and model answers
- 4 [1]
- 4 [1]
- 1 [1]
- 3 each [1]; 1 left over [1]; 4 × 3 + 1 = 13 [1]
- No [1]. 14 − 2 is not division [1]. 2 × 7 = 14 so 14 ÷ 2 = 7 [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 ÷ 3
- 20 ÷ 5
- 14 ÷ 2
- 10 ÷ 10
- 18 ÷ 2
- 12 ÷ 3 = ___.
- 20 ÷ 5 = ___.
- 14 ÷ 2 = ___.
- 18 ÷ 2 = ___.
- 10 ÷ 10 = ___.
Homework
Use stones to show 12 ÷ 4. Write the division sentence.
Answer key and marking scheme
| Question | Expected response | Marks |
|---|---|---|
| 12 ÷ 3 | 4 | 2 |
| 20 ÷ 5 | 4 | 2 |
| 14 ÷ 2 | 7 | 2 |
| 10 ÷ 10 | 1 | 2 |
| 18 ÷ 2 | 9 | 2 |
| Total | 10 |
Practice answers: Worksheet: 1 4; 2 4; 3 7; 4 1; 5 9.
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 4; 8 7; 9 9; 10 1.
Independent practice answers. Level 1: 1 4; 2 4; 3 7; 4 1; 5 9. Level 2: 1 6; 2 5; 3 2. Level 3: 1 3 each, 2 left over; 2 20 ÷ 4 = 5; 3 ÷ means share, not multiply. 12 ÷ 3 = 4..
Mastery and remediation
| Objective | Bronze (Developing) | Silver (Proficient) | Gold (Advanced) |
|---|---|---|---|
| O1 Use objects to divide | 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 Read and write the sign ÷ | 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 Read 12 ÷ 3 = 4 as a 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 |
| O4 Say what a leftover is | 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: Writing 12 ÷ 3 as 3 ÷ 12. The total (12) comes first.
- Explain another way: use real objects first, then pictures.
- Show a simpler example: Use counters and rings; count what is in each ring.
- 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 objects to divide and learns the sign ÷. You do not need to be good at mathematics to help.
- Share snacks equally and say the ÷ sentence.
- Ask: 12 shared among 3 is how many?
- Talk about leftovers.
- 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: use objects to divide; read and write the sign ÷; read 12 ÷ 3 = 4 as a sentence; say what a leftover is.
Prerequisite knowledge. Lessons 1 and 2.
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 tops. 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 do we divide? How many in each group? Is there a leftover?
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. Writing 12 ÷ 3 as 3 ÷ 12. The total (12) comes first.
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. Use counters and rings; count what is in each ring. 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 3.OA.A.2 (division); Cambridge Primary Mathematics Stage 2. These sources informed the lesson.