You will learn
- Line up decimals.
- Subtract with regrouping.
- Subtract from a whole number.
- Check by adding.
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
- Line up the decimal points.
- Fill empty places with zeros.
- Subtract from the right and regroup.
- Check by adding back.
Words to know
Result of subtracting.
Borrow.
Line up.
Opposite operation.
1. Discover: change
You pay with 10 for something costing 3.60. What is your change?
2. Understand: subtracting decimals
- 10.00 − 3.60 = 6.40.
- 5.2 − 1.75 = 5.20 − 1.75 = 3.45.
- 4.5 − 2.25 = 2.25.
- Check: 3.45 + 1.75 = 5.20.
Idea 1: Line up
0.9 − 0.35: write 0.90 − 0.35 = 0.55.
Idea 2: Regroup
8.05 − 2.9 = 8.05 − 2.90 = 5.15. 5.2 − 1.75 = 5.20 − 1.75 = 3.45.
Idea 3: Whole
10 − 3.6 = 10.0 − 3.6 = 6.4. Check: 6.4 + 3.6 = 10.
Why add back? Adding is the inverse of subtracting.
3. Worked examples
Example 1 (I show you): Subtract
0.9 − 0.35
- 0.90 − 0.35.
Answer: 0.55
Example 2 (We do it together): Subtract
8.05 − 2.9
- 8.05 − 2.90.
- Regroup.
Answer: 5.15
Example 3 (You try): Subtract
10 − 3.6
Show the steps and answer
- 10.0 − 3.6.
Answer: 6.4
Did you know?
Subtracting decimals is just subtracting whole numbers with a point in place.
Why this matters
Subtracting decimals finds change, differences in length and time.
4. Explore: subtract
You need paper.
- Line up points.
- Add zeros.
- Subtract right to left.
- Check by adding.
Think about it: what did you notice?
6.40.
5. Practise
Say it in a sentence
Use these starters when you talk about the lesson. Say them out loud.
- I line up the ___.
- I write ___ as ___.
- I regroup the ___.
- The difference is ___.
Guided practice
Question 1. 10 − 3.60?
6.40.
Question 2. 5.2 − 1.75?
3.45.
Question 3. 4.5 − 2.25?
2.25.
Independent practice
Level 1: Start
- 0.9 − 0.35
- 8.05 − 2.9
- 10 − 3.6
- 4.5 − 2.25
- 5.2 − 1.75
Level 2: Grow
- 0.8 − 0.3
- 5 − 1.5
- 2.4 − 1.15
Level 3: Stretch
- 12.3 − 4.75
- 1 − 0.064
- Ben says 5.2 − 1.75 = 4.55. What is wrong?
Answers are in the answer key below. Try first, then check.
6. Apply: everyday mathematics
You pay 10 for a 3.60 item. Change?
Show a sample answer
6.40.
Another one. Ama has 20.50 and spends 7.75. How much is left?
Show a sample answer
12.75
7. Common mistakes
Fix: Regroup when needed.
Fix: Regroup when the top digit is smaller.
Fix: Use zeros to fill gaps.
8. Lesson summary and revision card
- I can line up decimals.
- I can subtract with regrouping.
- I can subtract from a whole number.
- I can check by adding.
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
- Align the points.
- Add zeros.
- Check by adding.
11. Next lesson
Next lesson: Decimal multiplication. 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 0.9 − 0.35. [3 marks]
- Work out 8.05 − 2.9. [3 marks]
- Work out 10 − 3.6. [2 marks]
- Work out 4.5 − 2.25. [2 marks]
- Ali says 5.2 − 1.75 = 4.55. Is he right? Explain. [3 marks]
Total: 13 marks.
Marking guide and model answers
- 0.90 − 0.35 [1]; subtract the columns with regrouping [1]; 0.55 [1]
- 8.05 − 2.90 [1]; subtract with regrouping [1]; 5.15 [1]
- 10.0 − 3.6 [1]; 6.4 [1]
- 4.50 − 2.25 [1]; 2.25 [1]
- No [1]. Line up the points: 5.20 − 1.75 [1]. The answer is 3.45 [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
- 0.9 − 0.35
- 8.05 − 2.9
- 10 − 3.6
- 4.5 − 2.25
- 5.2 − 1.75
- 0.9 − 0.35
- 8.05 − 2.9
- 10 − 3.6
- 4.5 − 2.25
- 5.2 − 1.75
Homework
Find the change when paying 20 for three items you choose.
Answer key and marking scheme
| Question | Expected response | Marks |
|---|---|---|
| 0.9 − 0.35 | 0.55 | 2 |
| 8.05 − 2.9 | 5.15 | 2 |
| 10 − 3.6 | 6.4 | 2 |
| 4.5 − 2.25 | 2.25 | 2 |
| 5.2 − 1.75 | 3.45 | 2 |
| Total | 10 |
Practice answers: Worksheet: 1 0.55; 2 5.15; 3 6.4; 4 2.25; 5 3.45.
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 0.55; 7 5.15; 8 6.4; 9 2.25; 10 3.45.
Independent practice answers. Level 1: 1 0.55; 2 5.15; 3 6.4; 4 2.25; 5 3.45. Level 2: 1 0.5; 2 3.5; 3 1.25. Level 3: 1 7.55; 2 0.936; 3 Line up and regroup: 5.20 − 1.75 = 3.45..
Mastery and remediation
| Objective | Bronze (Developing) | Silver (Proficient) | Gold (Advanced) |
|---|---|---|---|
| O1 Line up decimals | 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 Subtract with regrouping | 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 Subtract from a whole 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 |
| O4 Check by adding | 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: Subtracting the smaller digit from the larger. Regroup when needed.
- Explain another way: use real objects first, then pictures.
- Show a simpler example: Money subtraction.
- 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 subtracts decimals. You do not need to be good at mathematics to help.
- Work out change when shopping.
- Ask: are the points lined up?
- Check by adding 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: line up decimals; subtract with regrouping; subtract from a whole number; check by adding.
Prerequisite knowledge. Lesson 3.
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. Are the points lined up? Do I need to regroup?
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. Subtracting the smaller digit from the larger. Regroup when needed.
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. Money subtraction. 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; Cambridge Primary Mathematics Stage 6 (subtracting decimals). These sources informed the lesson.