You will learn
- Divide by whole numbers.
- Divide by powers of 10.
- Divide by a decimal.
- Place the point.
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 as normal and place the point.
- Move both numbers to make the divisor whole.
- Dividing by 10, 100, 1000 moves digits right.
- Dividing by a number less than 1 gives a bigger result.
Words to know
Number divided.
Number you divide by.
Answer.
Same value.
1. Discover: sharing equally
4.5 litres are shared equally by 3 jugs. How much in each?
2. Understand: dividing decimals
- 4.5 ÷ 3 = 1.5.
- 2.5 ÷ 5 = 0.5.
- 7.2 ÷ 0.9: multiply both by 10 → 72 ÷ 9 = 8.
- 12 ÷ 0.4 = 120 ÷ 4 = 30.
Idea 1: By whole
2.5 ÷ 5: 25 tenths ÷ 5 = 5 tenths, so 0.5. 4.5 ÷ 3 = 1.5.
Idea 2: By decimal
12 ÷ 0.4: multiply both by 10 to get 120 ÷ 4 = 30. 7.2 ÷ 0.9 = 72 ÷ 9 = 8.
Idea 3: Tenths
0.36 ÷ 0.6 = 3.6 ÷ 6 = 0.6.
Why multiply both? The answer stays the same but the divisor becomes whole.
3. Worked examples
Example 1 (I show you): Divide
2.5 ÷ 5
- 25 tenths ÷ 5.
Answer: 0.5
Example 2 (We do it together): Divide
12 ÷ 0.4
- ×10: 120 ÷ 4.
Answer: 30
Example 3 (You try): Divide
7.2 ÷ 0.9
Show the steps and answer
- ×10: 72 ÷ 9.
Answer: 8
Did you know?
Dividing by 0.5 is the same as multiplying by 2.
Why this matters
Dividing decimals shares money and measures equally.
4. Explore: divide
You need paper.
- Scale both numbers.
- Divide.
- Place the point.
- Check by multiplying.
Think about it: what did you notice?
8.
5. Practise
Say it in a sentence
Use these starters when you talk about the lesson. Say them out loud.
- I multiply both numbers by ___.
- Now I divide ___ ÷ ___.
- The quotient is ___.
- Check: ___ × ___ = ___.
Guided practice
Question 1. 4.5 ÷ 3?
1.5.
Question 2. 7.2 ÷ 0.9?
8.
Question 3. 12 ÷ 0.4?
30.
Independent practice
Level 1: Start
- 2.5 ÷ 5
- 0.36 ÷ 0.6
- 12 ÷ 0.4
- 4.5 ÷ 3
- 7.2 ÷ 0.9
Level 2: Grow
- 4.8 ÷ 2
- 6 ÷ 0.3
- 0.9 ÷ 3
Level 3: Stretch
- 0.45 ÷ 0.09
- 7.5 ÷ 0.5
- Ben says 12 ÷ 0.4 = 3. What is wrong?
Answers are in the answer key below. Try first, then check.
6. Apply: everyday mathematics
4.5 L is shared by 3 jugs. Each gets?
Show a sample answer
1.5 L.
Another one. 4.5 L of juice is shared equally into 3 jugs. How much in each?
Show a sample answer
1.5 L
7. Common mistakes
Fix: Check by multiplying.
Fix: Dividing by less than 1 makes bigger.
Fix: Move both numbers the same way.
8. Lesson summary and revision card
- I can divide by whole numbers.
- I can divide by powers of 10.
- I can divide by a decimal.
- I can place the point.
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 the divisor whole.
- Place the point.
- Check by multiplying.
11. Next lesson
Next lesson: Rounding and 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.
- Work out 2.5 ÷ 5. [2 marks]
- Work out 0.36 ÷ 0.6. [3 marks]
- Work out 12 ÷ 0.4. [3 marks]
- Work out 7.2 ÷ 0.9. [2 marks]
- Ali says 12 ÷ 0.4 = 3 because dividing makes numbers smaller. Is he right? Explain. [3 marks]
Total: 13 marks.
Marking guide and model answers
- 25 tenths ÷ 5 = 5 tenths [1]; 0.5 [1]
- Multiply both numbers by 10 to get 3.6 ÷ 6 [1]; 36 tenths ÷ 6 = 6 tenths [1]; 0.6 [1]
- Multiply both by 10 [1]; 120 ÷ 4 [1]; 30 [1]
- Multiply both by 10: 72 ÷ 9 [1]; 8 [1]
- No [1]. Dividing by a number less than 1 gives a bigger answer [1]. 12 ÷ 0.4 = 30 [1].
Score guide: 12 to 13 = secure. 8 to 11 = nearly there, revise the parts you missed. Under 8 = work through the lesson again with a grown-up.
Printable worksheet
- 2.5 ÷ 5
- 0.36 ÷ 0.6
- 12 ÷ 0.4
- 4.5 ÷ 3
- 7.2 ÷ 0.9
- 2.5 ÷ 5
- 0.36 ÷ 0.6
- 12 ÷ 0.4
- 4.5 ÷ 3
- 7.2 ÷ 0.9
Homework
Find 9.6 ÷ 4 and 3.6 ÷ 0.6.
Answer key and marking scheme
| Question | Expected response | Marks |
|---|---|---|
| 2.5 ÷ 5 | 0.5 | 2 |
| 0.36 ÷ 0.6 | 0.6 | 2 |
| 12 ÷ 0.4 | 30 | 2 |
| 4.5 ÷ 3 | 1.5 | 2 |
| 7.2 ÷ 0.9 | 8 | 2 |
| Total | 10 |
Practice answers: Worksheet: 1 0.5; 2 0.6; 3 30; 4 1.5; 5 8.
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 0.5; 7 0.6; 8 30; 9 1.5; 10 8.
Independent practice answers. Level 1: 1 0.5; 2 0.6; 3 30; 4 1.5; 5 8. Level 2: 1 2.4; 2 20; 3 0.3. Level 3: 1 5; 2 15; 3 Dividing by less than 1 gives a bigger answer: 12 ÷ 0.4 = 30..
Mastery and remediation
| Objective | Bronze (Developing) | Silver (Proficient) | Gold (Advanced) |
|---|---|---|---|
| O1 Divide by whole numbers | 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 Divide by powers of 10 | 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 Divide by a decimal | 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 Place the point | 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: Dividing and getting a larger answer wrongly. Check by multiplying.
- Explain another way: use real objects first, then pictures.
- Show a simpler example: Division facts.
- 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 decimals. You do not need to be good at mathematics to help.
- Share money or drinks equally.
- Ask: how many fit?
- Check by multiplying back.
- 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 whole numbers; divide by powers of 10; divide by a decimal; place the point.
Prerequisite knowledge. Lesson 5.
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. Is the divisor whole? Where does the point go?
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. Dividing and getting a larger answer wrongly. Check by multiplying.
13–15. Assessment questions, answer keys, marking scheme
Use the quiz and worksheet on this page. The 13-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. Division facts. 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 6 » Ratios & Proportional Relationships; Grade 6 » The Number System. These pages list the standards that cover this topic area; read them alongside the lesson.
Research used to shape this lesson. Common Core 5.NBT.B.7 and 6.NS.B.3; Cambridge Primary Mathematics Stage 6 (dividing decimals). These sources informed the lesson.