You will learn
- Line up digits by place value.
- Add with regrouping.
- Add numbers with different digit counts.
- Check an addition.
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 digits by place value.
- Add column by column from the right.
- Regroup when a column makes 10 or more.
- Check with an estimate.
Words to know
A number being added.
The answer to addition.
Carry ten of one place to the next.
Digits lined up by place.
1. Discover: two harvests
A farm harvested 45,678 kg of cassava and 23,456 kg of yams. How much in all?
2. Understand: column addition
Line up the digits by place and add from the right. If a column makes 10 or more, regroup.
- Ones: 8 + 6 = 14. Write 4, carry 1.
- Tens: 7 + 5 + 1 = 13. Write 3, carry 1.
- Hundreds: 6 + 4 + 1 = 11. Write 1, carry 1.
- Thousands: 5 + 3 + 1 = 9. Ten-thousands: 4 + 2 = 6.
Sum: 69,134.
Idea 1: Line up
23,456 + 12,345: ones 6 + 5 = 11, carry 1; tens 5 + 4 + 1 = 10, carry 1; hundreds 4 + 3 + 1 = 8; thousands 3 + 2 = 5; ten-thousands 2 + 1 = 3. The sum is 35,801.
Idea 2: Different digits
56,789 + 4,321 = 61,110. Line up 4,321 so its ones are under the ones.
Idea 3: Check
48,900 + 9,876: estimate 49,000 + 10,000 = 59,000. The exact sum 58,776 is close.
Why estimate? It catches big mistakes.
3. Worked examples
Example 1 (I show you): Add
23,456 + 12,345
- Carry in the ones and tens.
Answer: 35,801
Example 2 (We do it together): Different digits
56,789 + 4,321
- Line up the places.
Answer: 61,110
Example 3 (You try): Check
Estimate 48,900 + 9,876.
Show the steps and answer
- 49,000 + 10,000.
Answer: about 59,000
Did you know?
We always start adding from the ones.
Why this matters
Adding large numbers is used in business and science.
4. Explore: add and check
You need paper and a pencil.
- Write 45,678 and 23,456 in columns.
- Add from the right.
- Carry where needed.
- Check by adding 23,456 + 45,678.
Think about it: what did you notice?
69,134 both ways.
5. Practise
Say it in a sentence
Use these starters when you talk about the lesson. Say them out loud.
- The ones column makes ___.
- I write ___ and carry ___.
- The sum is ___.
- My estimate is ___.
Guided practice
Question 1. 45,678 + 23,456?
69,134.
Question 2. 8 + 6 in the ones: write and carry?
Write 4, carry 1.
Question 3. 12,000 + 3,500?
15,500.
Independent practice
Level 1: Start
- 23,456 + 12,345
- 48,900 + 9,876
- 56,789 + 4,321
- 100 + 99,900
- 7,408 + 2,592
Level 2: Grow
- 45,300 + 12,400
- 29,865 + 1,135
- 6,789 + 8,765
Level 3: Stretch
- 56,789 + 43,211
- 78,909 + 12,091
- Ana adds 48,900 + 9,876 and gets 57,776. Check it.
Answers are in the answer key below. Try first, then check.
6. Apply: everyday mathematics
A school collected 28,450 and 31,675 bottle tops. How many in all?
Show a sample answer
60,125.
Another one. A school collects 45,678 in term 1 and 23,456 in term 2. How much altogether?
Show a sample answer
69,134
7. Common mistakes
Fix: Write the carry above the next column.
Fix: Ones under ones.
Fix: Add the carry.
8. Lesson summary and revision card
- I can line up digits by place value.
- I can add with regrouping.
- I can add numbers with different digit counts.
- I can check an addition.
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
- Line up places.
- Carry when 10 or more.
- Check by switching the order.
11. Next lesson
Next lesson: Large-number subtraction. 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 23,456 + 12,345. [2 marks]
- Find 48,900 + 9,876. [2 marks]
- Find 56,789 + 4,321. [2 marks]
- Estimate 48,900 + 9,876. [2 marks]
- Kofi says 7,408 + 2,592 = 9,900. Is he right? Explain. [3 marks]
Total: 11 marks.
Marking guide and model answers
- Line up and add [1]; 35,801 [1]
- Line up [1]; 58,776 [1]
- Line up [1]; 61,110 [1]
- 49,000 + 10,000 [1] = 59,000 [1]
- No [1]. 408 + 592 = 1,000 [1]. The sum is 10,000 [1].
Score guide: 10 to 11 = secure. 7 to 9 = nearly there, revise the parts you missed. Under 7 = work through the lesson again with a grown-up.
Printable worksheet
- 23,456 + 12,345
- 48,900 + 9,876
- 56,789 + 4,321
- 100 + 99,900
- 7,408 + 2,592
- 45,678 + 23,456 =
- 23,456 + 12,345 =
- 48,900 + 9,876 =
- 56,789 + 4,321 =
- 7,408 + 2,592 =
Homework
Add the populations of two towns. Check your answer.
Answer key and marking scheme
| Question | Expected response | Marks |
|---|---|---|
| 23,456 + 12,345 | 35,801 | 2 |
| 48,900 + 9,876 | 58,776 | 2 |
| 56,789 + 4,321 | 61,110 | 2 |
| 100 + 99,900 | 100,000 | 2 |
| 7,408 + 2,592 | 10,000 | 2 |
| Total | 10 |
Practice answers: Worksheet: 1 35,801; 2 58,776; 3 61,110; 4 100,000; 5 10,000.
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 69,134; 7 35,801; 8 58,776; 9 61,110; 10 10,000.
Independent practice answers. Level 1: 1 35,801; 2 58,776; 3 61,110; 4 100,000; 5 10,000. Level 2: 1 57,700; 2 31,000; 3 15,554. Level 3: 1 100,000; 2 91,000; 3 The estimate is 59,000. The hundreds 9 + 8 = 17 carries 1. The sum is 58,776..
Mastery and remediation
| Objective | Bronze (Developing) | Silver (Proficient) | Gold (Advanced) |
|---|---|---|---|
| O1 Line up digits by place value | 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 digit counts | 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 an addition | 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: Forgetting the carried 1. Write the carry above the next column.
- Explain another way: use real objects first, then pictures.
- Show a simpler example: Practise 4-digit addition.
- 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 numbers up to hundreds of thousands. You do not need to be good at mathematics to help.
- Add bill totals on paper.
- Ask: did you carry?
- Always 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 digits by place value; add with regrouping; add numbers with different digit counts; check an addition.
Prerequisite knowledge. Grade 3 addition to 10,000.
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 and a pencil. 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 places lined up? Did I carry? Does it match my estimate?
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. Forgetting the carried 1. Write the carry above the next column.
13–15. Assessment questions, answer keys, marking scheme
Use the quiz and worksheet on this page. The 11-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 4-digit addition. 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 4.NBT.B.4 (add multi-digit numbers); Cambridge Primary Mathematics Stage 4 (addition). These sources informed the lesson; no official alignment is claimed.