You will learn
- Line up decimal points.
- Add with regrouping.
- Add numbers with different decimal places.
- Estimate to check.
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.
- Add from the right and regroup.
- Estimate to check.
Words to know
Number added.
Answer.
Separator.
Carry.
1. Discover: adding lengths
A rope is 3.45 m and another is 2.8 m. How long together?
2. Understand: adding decimals
- 3.45 + 2.80 = 6.25.
- 12.07 + 4.936: 12.070 + 4.936 = 17.006.
Line up the decimal points. Write zeros so the numbers have the same decimal places. Estimate: 12 + 5 = 17.
Idea 1: Line up
1.25 + 3.40 = 4.65. 0.75 + 0.80 = 1.55.
Idea 2: Different places
12.070 + 4.936 = 17.006. 5.50 + 3.75 = 9.25.
Idea 3: Carry
9.99 + 0.01 = 10.00, which is 10.
Why line up points? So tenths add to tenths and hundredths to hundredths.
3. Worked examples
Example 1 (I show you): Add
1.25 + 3.4
- 1.25 + 3.40.
Answer: 4.65
Example 2 (We do it together): Add
12.07 + 4.936
- 12.070 + 4.936.
Answer: 17.006
Example 3 (You try): Add
9.99 + 0.01
Show the steps and answer
- Carry up.
Answer: 10
Did you know?
Money is a decimal with two places, so addition works the same way.
Why this matters
Adding decimals is used in shopping, measuring and sport.
4. Explore: add
You need paper.
- Line up 3.45 and 2.80.
- Add from the right.
- Place the point.
- Estimate to check.
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 line up the ___.
- I add zeros so that ___.
- I regroup ___.
- The sum is ___.
Guided practice
Question 1. 3.45 + 2.8?
6.25.
Question 2. 12.07 + 4.936?
17.006.
Question 3. Why line up the points?
So places match.
Independent practice
Level 1: Start
- 1.25 + 3.4
- 0.75 + 0.8
- 12.07 + 4.936
- 5.5 + 3.75
- 9.99 + 0.01
Level 2: Grow
- 4.6 + 2.7
- 0.25 + 0.5
- 6.08 + 1.9
Level 3: Stretch
- 12.345 + 0.655
- 100 + 0.99
- Ana says 2.5 + 1.25 = 1.50 because she lined up the left digits. What is wrong?
Answers are in the answer key below. Try first, then check.
6. Apply: everyday mathematics
Two ropes of 3.45 m and 2.8 m are joined. Length?
Show a sample answer
6.25 m.
Another one. Ben buys 3.45 kg of rice and 2.8 kg of beans. How many kg altogether?
Show a sample answer
3.45 + 2.80 = 6.25 kg
7. Common mistakes
Fix: Align decimal points.
Fix: Line up the decimal points.
Fix: Carry to the next place.
8. Lesson summary and revision card
- I can line up decimal points.
- I can add with regrouping.
- I can add numbers with different decimal places.
- I can estimate to check.
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.
- Estimate.
11. Next lesson
Next lesson: Subtracting 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 1.25 + 3.4. [3 marks]
- Find 0.75 + 0.8. [2 marks]
- Find 12.07 + 4.936. [3 marks]
- Find 5.5 + 3.75. [2 marks]
- Ali says 9.99 + 0.01 = 9.100. Is he right? Explain. [3 marks]
Total: 13 marks.
Marking guide and model answers
- 1.25 + 3.40 [1]; add place by place [1]; 4.65 [1]
- 0.75 + 0.80 [1]; 1.55 [1]
- 12.070 + 4.936 [1]; regroup [1]; 17.006 [1]
- 5.50 + 3.75 [1]; 9.25 [1]
- No [1]. 9.99 + 0.01 carries up [1]. The answer is 10.00 [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
- 1.25 + 3.4
- 0.75 + 0.8
- 12.07 + 4.936
- 5.5 + 3.75
- 9.99 + 0.01
- 3.45 + 2.8 =
- 12.07 + 4.936 =
- 1.25 + 3.4 =
- 0.75 + 0.8 =
- 9.99 + 0.01 =
Homework
Add the prices of five items.
Answer key and marking scheme
| Question | Expected response | Marks |
|---|---|---|
| 1.25 + 3.4 | 4.65 | 2 |
| 0.75 + 0.8 | 1.55 | 2 |
| 12.07 + 4.936 | 17.006 | 2 |
| 5.5 + 3.75 | 9.25 | 2 |
| 9.99 + 0.01 | 10 | 2 |
| Total | 10 |
Practice answers: Worksheet: 1 4.65; 2 1.55; 3 17.006; 4 9.25; 5 10.
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 17.006; 8 4.65; 9 1.55; 10 10.
Independent practice answers. Level 1: 1 4.65; 2 1.55; 3 17.006; 4 9.25; 5 10. Level 2: 1 7.3; 2 0.75; 3 7.98. Level 3: 1 13; 2 100.99; 3 Line up the decimal points: 2.50 + 1.25 = 3.75..
Mastery and remediation
| Objective | Bronze (Developing) | Silver (Proficient) | Gold (Advanced) |
|---|---|---|---|
| O1 Line up decimal 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 Add 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 Add numbers with different decimal places | 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 to check | 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 lining up the points. Align decimal points.
- Explain another way: use real objects first, then pictures.
- Show a simpler example: Add 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 adds decimals. You do not need to be good at mathematics to help.
- Add prices on a receipt.
- Ask: are the decimal points lined up?
- Estimate first.
- 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 decimal points; add with regrouping; add numbers with different decimal places; estimate to check.
Prerequisite knowledge. Lessons 1 to 4.
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 decimal 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 lining up the points. Align decimal points.
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. Add 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 (adding decimals). These sources informed the lesson; no official alignment is claimed.