You will learn
- Align points.
- Regroup across zeros.
- Subtract.
- Check by adding.
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
- Line up the decimal points.
- Add zeros as placeholders.
- Regroup across zeros when needed.
- Check by adding back.
Words to know
Start number.
Number taken away.
Answer.
Borrow.
1. Discover: change
You pay 10.00 for goods that cost 3.75. How much change?
2. Understand: subtracting decimals
- 10.00 − 3.75 = 6.25.
- 5.2 − 2.48 = 5.20 − 2.48 = 2.72.
- 8.003 − 2.5 = 8.003 − 2.500 = 5.503.
Check: 6.25 + 3.75 = 10.00.
Idea 1: Line up
7.50 − 2.25 = 5.25. 5.20 − 2.48 = 2.72.
Idea 2: Zeros
10.00 − 4.68 = 5.32. 3.000 − 0.125 = 2.875.
Idea 3: Mixed
8.003 − 2.500 = 5.503.
Why check? Adding the answer to the subtrahend should give the start.
3. Worked examples
Example 1 (I show you): Subtract
7.5 − 2.25
- 7.50 − 2.25.
Answer: 5.25
Example 2 (We do it together): Subtract
10 − 4.68
- Regroup across zeros.
Answer: 5.32
Example 3 (You try): Subtract
3 − 0.125
Show the steps and answer
- 3.000 − 0.125.
Answer: 2.875
Did you know?
Whole numbers have a hidden decimal point and can be written with zeros.
Why this matters
Subtracting decimals gives change, differences and what is left.
4. Explore: subtract
You need paper.
- Align 10.00 and 3.75.
- Regroup.
- Subtract.
- Check by adding.
Think about it: what did you notice?
6.25.
5. Practise
Say it in a sentence
Use these starters when you talk about the lesson. Say them out loud.
- I write ___ as ___.
- I regroup ___.
- The difference is ___.
- Check: ___ + ___ = ___.
Guided practice
Question 1. 10 − 3.75?
6.25.
Question 2. 5.2 − 2.48?
2.72.
Question 3. 8.003 − 2.5?
5.503.
Independent practice
Level 1: Start
- 7.5 − 2.25
- 10 − 4.68
- 5.2 − 2.48
- 3 − 0.125
- 8.003 − 2.5
Level 2: Grow
- 8.6 − 4.2
- 3.5 − 1.75
- 6 − 2.4
Level 3: Stretch
- 20.05 − 0.5
- 1 − 0.037
- Ben says 6.1 − 2.35 = 4.25. What is wrong?
Answers are in the answer key below. Try first, then check.
6. Apply: everyday mathematics
You pay 10 for goods of 3.75. What is the change?
Show a sample answer
6.25.
Another one. A rope is 10 m long. Ana cuts off 3.75 m. How much is left?
Show a sample answer
10.00 − 3.75 = 6.25 m
7. Common mistakes
Fix: Write 5.20.
Fix: Line up the points.
Fix: Trade from the next non-zero digit.
8. Lesson summary and revision card
- I can align decimal points.
- I can regroup across zeros.
- I can subtract decimals.
- 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 points.
- Add zeros.
- Check by adding.
11. Next lesson
Next lesson: Multiplying decimals. 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 7.5 − 2.25. [3 marks]
- Find 10 − 4.68. [3 marks]
- Find 5.2 − 2.48. [3 marks]
- Find 3 − 0.125. [3 marks]
- Ali says 8.003 − 2.5 = 5.998. Is he right? Explain. [3 marks]
Total: 15 marks.
Marking guide and model answers
- 7.50 − 2.25 [1]; regroup [1]; 5.25 [1]
- 10.00 − 4.68 [1]; regroup across zeros [1]; 5.32 [1]
- 5.20 − 2.48 [1]; regroup [1]; 2.72 [1]
- 3.000 − 0.125 [1]; regroup [1]; 2.875 [1]
- No [1]. Line up: 8.003 − 2.500 [1]. The answer is 5.503 [1].
Score guide: 13 to 15 = secure. 9 to 12 = nearly there, revise the parts you missed. Under 9 = work through the lesson again with a grown-up.
Printable worksheet
- 7.5 − 2.25
- 10 − 4.68
- 5.2 − 2.48
- 3 − 0.125
- 8.003 − 2.5
- 10 − 3.75 =
- 5.2 − 2.48 =
- 8.003 − 2.5 =
- 7.5 − 2.25 =
- 3 − 0.125 =
Homework
Subtract five pairs of decimals and check.
Answer key and marking scheme
| Question | Expected response | Marks |
|---|---|---|
| 7.5 − 2.25 | 5.25 | 2 |
| 10 − 4.68 | 5.32 | 2 |
| 5.2 − 2.48 | 2.72 | 2 |
| 3 − 0.125 | 2.875 | 2 |
| 8.003 − 2.5 | 5.503 | 2 |
| Total | 10 |
Practice answers: Worksheet: 1 5.25; 2 5.32; 3 2.72; 4 2.875; 5 5.503.
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 6.25; 7 2.72; 8 5.503; 9 5.25; 10 2.875.
Independent practice answers. Level 1: 1 5.25; 2 5.32; 3 2.72; 4 2.875; 5 5.503. Level 2: 1 4.4; 2 1.75; 3 3.6. Level 3: 1 19.55; 2 0.963; 3 He subtracted the smaller digit from the larger each time. 6.10 − 2.35 = 3.75..
Mastery and remediation
| Objective | Bronze (Developing) | Silver (Proficient) | Gold (Advanced) |
|---|---|---|---|
| O1 Align points | 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 Regroup across zeros | 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 | 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 |
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: Not adding zeros. Write 5.20.
- Explain another way: use real objects first, then pictures.
- Show a simpler example: Subtract hundredths.
- 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 from shopping.
- Ask: how many decimal places do we need?
- 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: align points; regroup across zeros; subtract; check by adding.
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. 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. Not adding zeros. Write 5.20.
13–15. Assessment questions, answer keys, marking scheme
Use the quiz and worksheet on this page. The 15-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. Subtract hundredths. 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.7; Cambridge Primary Mathematics Stage 5 (subtracting decimals). These sources informed the lesson; no official alignment is claimed.