You will learn
- Divide by a 2-digit number.
- Interpret remainders.
- Check by multiplying.
- Estimate the quotient.
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
- Divide by a 2-digit number step by step.
- Estimate how many times the divisor fits.
- Remainders must be less than the divisor.
- Check by multiplying and adding.
Words to know
Number divided.
Number we divide by.
Answer.
Left over.
1. Discover: sharing equally
1,584 books are shared among 12 schools. How many each?
2. Understand: long division
- 1,584 ÷ 12 = 132 (12 × 132 = 1,584).
- 7,350 ÷ 15 = 490.
- 4,096 ÷ 32 = 128.
- 1,000 ÷ 12 = 83 r4 (12 × 83 = 996).
Estimate first: 1,584 ÷ 12 ≈ 1,600 ÷ 10 = 160. Close.
Idea 1: Exact
925 ÷ 25 = 37 because 25 × 37 = 925. 4,096 ÷ 32 = 128.
Idea 2: Remainder
1,000 ÷ 12 = 83 r4 because 12 × 83 = 996 and 1,000 − 996 = 4.
Idea 3: Check
3,150 ÷ 18 = 175. Check: 18 × 175 = 3,150. 2,400 ÷ 16 = 150.
Why check? Multiplication undoes division.
3. Worked examples
Example 1 (I show you): Divide
925 ÷ 25
- How many 25s?
Answer: 37
Example 2 (We do it together): Remainder
1,000 ÷ 12
- 12 × 83 = 996.
Answer: 83 r4
Example 3 (You try): Check
3,150 ÷ 18
Show the steps and answer
- 18 × 175.
Answer: 175
Did you know?
The remainder is always smaller than the divisor.
Why this matters
Division by 2-digit numbers shares costs and packs items.
4. Explore: divide
You need paper.
- Write 1,584 ÷ 12.
- Divide step by step.
- Multiply back.
- Do 1,000 ÷ 12.
Think about it: what did you notice?
132; 83 r4.
5. Practise
Say it in a sentence
Use these starters when you talk about the lesson. Say them out loud.
- The divisor is ___.
- It fits ___ times.
- The remainder is ___.
- I check: ___ × ___ + ___ = ___.
Guided practice
Question 1. 1,584 ÷ 12?
132.
Question 2. 7,350 ÷ 15?
490.
Question 3. 1,000 ÷ 12?
83 r4.
Independent practice
Level 1: Start
- 925 ÷ 25
- 4,096 ÷ 32
- 2,400 ÷ 16
- 1,000 ÷ 12
- 3,150 ÷ 18
Level 2: Grow
- 288 ÷ 12
- 750 ÷ 25
- 100 ÷ 12
Level 3: Stretch
- 4,500 ÷ 15
- 1,000 ÷ 15
- Ben says 612 ÷ 12 = 41. Check by multiplying.
Answers are in the answer key below. Try first, then check.
6. Apply: everyday mathematics
1,584 books to 12 schools. Each gets?
Show a sample answer
132.
Another one. A shop packs 850 sweets into bags of 25. How many bags?
Show a sample answer
850 ÷ 25 = 34 bags
7. Common mistakes
Fix: Divide again.
Fix: Divide again.
Fix: Multiply back and add the remainder.
8. Lesson summary and revision card
- I can divide by a 2-digit number.
- I can interpret remainders.
- I can check by multiplying.
- I can estimate the quotient.
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
- Divide, multiply, subtract, bring down.
- Check by multiplying.
- Remainder < divisor.
11. Next lesson
Next lesson: Estimation. 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 925 ÷ 25. [2 marks]
- Find 4,096 ÷ 32. [2 marks]
- Find 2,400 ÷ 16. [2 marks]
- Find 1,000 ÷ 12 with a remainder. [3 marks]
- Ali says 3,150 ÷ 18 = 165. Is he right? Check. [3 marks]
Total: 12 marks.
Marking guide and model answers
- 25 × 37 [1]; 37 [1]
- 32 × 128 = 4,096 [1]; 128 [1]
- 16 × 150 = 2,400 [1]; 150 [1]
- 12 × 83 = 996 [1]; 83 [1]; remainder 4 [1]
- No [1]. 18 × 165 = 2,970 [1]. The answer is 175 [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
- 925 ÷ 25
- 4,096 ÷ 32
- 2,400 ÷ 16
- 1,000 ÷ 12
- 3,150 ÷ 18
- 1,584 ÷ 12 =
- 7,350 ÷ 15 =
- 4,096 ÷ 32 =
- 925 ÷ 25 =
- 1,000 ÷ 12 =
Homework
Divide four 4-digit numbers by 12 and check.
Answer key and marking scheme
| Question | Expected response | Marks |
|---|---|---|
| 925 ÷ 25 | 37 | 2 |
| 4,096 ÷ 32 | 128 | 2 |
| 2,400 ÷ 16 | 150 | 2 |
| 1,000 ÷ 12 | 83 r4 | 2 |
| 3,150 ÷ 18 | 175 | 2 |
| Total | 10 |
Practice answers: Worksheet: 1 37; 2 128; 3 150; 4 83 r4; 5 175.
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): 6 132; 7 490; 8 128; 9 37; 10 83 r4.
Independent practice answers. Level 1: 1 37; 2 128; 3 150; 4 83 r4; 5 175. Level 2: 1 24; 2 30; 3 8 r4. Level 3: 1 300; 2 66 r10; 3 12 × 41 = 492, not 612. The answer is 51..
Mastery and remediation
| Objective | Bronze (Developing) | Silver (Proficient) | Gold (Advanced) |
|---|---|---|---|
| O1 Divide by a 2-digit number | 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 Interpret remainders | 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 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 |
| O4 Estimate the quotient | 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: A remainder bigger than the divisor. Divide again.
- Explain another way: use real objects first, then pictures.
- Show a simpler example: Practise dividing by 1-digit numbers.
- 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 2-digit numbers. You do not need to be good at mathematics to help.
- Share a bill among friends.
- Ask: what does the remainder mean?
- 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: divide by a 2-digit number; interpret remainders; check by multiplying; estimate the quotient.
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 many times does it fit? What is left over?
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. A remainder bigger than the divisor. Divide again.
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. Practise dividing by 1-digit numbers. 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 5.NBT.B.6; Cambridge Primary Mathematics Stage 5 (division). These sources informed the lesson; no official alignment is claimed.