You will learn
- Write a number as a sum of place values.
- Write expanded notation for numbers with zeros.
- Write the standard form from expanded notation.
- 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
- Expanded notation is a sum of place values.
- Skip zero places.
- Rebuild the number from the parts.
- Check by adding.
Words to know
A number written as a sum of place values.
The usual way to write a number.
The answer to an addition.
The position of a digit.
1. Discover: breaking apart
45,208 can be taken apart by place: 40,000 and 5,000 and 200 and 8. Is it still the same number if you add the parts?
2. Understand: expanded notation
Expanded notation writes a number as a sum of place values.
- 45,208 = 40,000 + 5,000 + 200 + 8.
- Skip places with zero: there is no tens digit, so we write no tens.
- 3,507 = 3,000 + 500 + 7.
To go back: 60,000 + 700 + 4 = 60,704.
Idea 1: Expand
7,052 = 7,000 + 50 + 2. 28,300 = 20,000 + 8,000 + 300.
Idea 2: Rebuild
20,000 + 900 + 5 = 20,905. 100,000 + 40,000 + 6 = 140,006.
Idea 3: Zeros
90,090 = 90,000 + 90. Zero places have no part.
Why expand? It shows the value of every digit.
3. Worked examples
Example 1 (I show you): Expand
Expand 7,052.
- 7,000, 50, 2.
Answer: 7,000 + 50 + 2
Example 2 (We do it together): Rebuild
20,000 + 900 + 5
- No thousands, no tens.
Answer: 20,905
Example 3 (You try): Zero
Expand 90,090.
Show the steps and answer
- No thousands, no hundreds, no ones.
Answer: 90,000 + 90
Did you know?
Expanded notation is also called expanded form.
Why this matters
Expanded notation helps us add and subtract big numbers.
4. Explore: take it apart
You need paper and a pencil.
- Write 45,208.
- Write each digit with its value.
- Add to check.
- Try 60,704.
Think about it: what did you notice?
60,000 + 700 + 4.
5. Practise
Say it in a sentence
Use these starters when you talk about the lesson. Say them out loud.
- The expanded notation is ___.
- Adding the parts gives ___.
- There is no ___ so I skip it.
- The standard form is ___.
Guided practice
Question 1. Expand 3,507.
3,000 + 500 + 7.
Question 2. Write 60,000 + 700 + 4.
60,704.
Question 3. Expand 45,208.
40,000 + 5,000 + 200 + 8.
Independent practice
Level 1: Start
- Expand 7,052
- Expand 28,300
- Write 20,000 + 900 + 5
- Write 100,000 + 40,000 + 6
- Expand 90,090
Level 2: Grow
- Expand 5,308
- 40,000 + 600 + 2
- Expand 62,040
Level 3: Stretch
- 300,000 + 20,000 + 7
- Expand 408,010
- Ana writes 60,704 as 60,000 + 700 + 40. What is wrong?
Answers are in the answer key below. Try first, then check.
6. Apply: everyday mathematics
A van costs 82,400. Write this in expanded notation.
Show a sample answer
80,000 + 2,000 + 400.
Another one. Write 345,206 in expanded notation and add the parts to check.
Show a sample answer
300,000 + 40,000 + 5,000 + 200 + 6 = 345,206
7. Common mistakes
Fix: Write the digits carefully.
Fix: Zero places have no part.
Fix: Check the place of each digit.
8. Lesson summary and revision card
- I can write a number as a sum of place values.
- I can handle zeros.
- I can write the standard form.
- 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
- Expanded notation adds place values.
- Skip zeros.
- Check by adding.
11. Next lesson
Next lesson: Comparing large numbers. 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.
- Write 3,507 in expanded notation. [2 marks]
- 60,000 + 700 + 4 = ? [1 mark]
- Write 28,300 in expanded notation. [2 marks]
- Write 90,090 in expanded notation. [2 marks]
- Kofi writes 100,000 + 40,000 + 6 as 14,006. Is he right? Explain. [3 marks]
Total: 10 marks.
Marking guide and model answers
- 3,000 + 500 + 7 [2]
- 60,704 [1]
- 20,000 + 8,000 [1] + 300 [1]
- 90,000 + 90 [2]
- No [1]. 100,000 + 40,000 = 140,000 [1]. The number is 140,006 [1].
Score guide: 9 to 10 = secure. 6 to 8 = nearly there, revise the parts you missed. Under 6 = work through the lesson again with a grown-up.
Printable worksheet
- Expand 7,052
- Expand 28,300
- 20,000 + 900 + 5
- 100,000 + 40,000 + 6
- Expand 90,090
- 3,507 =
- 60,000 + 700 + 4 =
- 28,300 =
- 20,000 + 900 + 5 =
- 100,000 + 40,000 + 6 =
Homework
Pick three numbers from a newspaper and expand them.
Answer key and marking scheme
| Question | Expected response | Marks |
|---|---|---|
| Expand 7,052 | 7,000 + 50 + 2 | 2 |
| Expand 28,300 | 20,000 + 8,000 + 300 | 2 |
| 20,000 + 900 + 5 | 20,905 | 2 |
| 100,000 + 40,000 + 6 | 140,006 | 2 |
| Expand 90,090 | 90,000 + 90 | 2 |
| Total | 10 |
Practice answers: Worksheet: 1 7,000 + 50 + 2; 2 20,000 + 8,000 + 300; 3 20,905; 4 140,006; 5 90,000 + 90.
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 3,000 + 500 + 7; 7 60,704; 8 20,000 + 8,000 + 300; 9 20,905; 10 140,006.
Independent practice answers. Level 1: 1 7,000 + 50 + 2; 2 20,000 + 8,000 + 300; 3 20,905; 4 140,006; 5 90,000 + 90. Level 2: 1 5,000 + 300 + 8; 2 40,602; 3 60,000 + 2,000 + 40. Level 3: 1 320,007; 2 400,000 + 8,000 + 10; 3 The 4 is in the ones place: 60,000 + 700 + 4..
Mastery and remediation
| Objective | Bronze (Developing) | Silver (Proficient) | Gold (Advanced) |
|---|---|---|---|
| O1 Write a number as a sum of place values | 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 Write expanded notation for numbers with 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 Write the standard form from expanded notation | 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: Writing 0 for a missing place and getting the number wrong. Write the digits carefully.
- Explain another way: use real objects first, then pictures.
- Show a simpler example: Use place value cards that you can stack.
- 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 writes big numbers as a sum of place values. You do not need to be good at mathematics to help.
- Write the date or a phone number in expanded form.
- Ask: how much is each digit worth?
- Use a place value chart.
- 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: write a number as a sum of place values; write expanded notation for numbers with zeros; write the standard form from expanded notation; 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 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. What is each digit worth? Is there a zero? Do the parts add back?
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. Writing 0 for a missing place and getting the number wrong. Write the digits carefully.
13–15. Assessment questions, answer keys, marking scheme
Use the quiz and worksheet on this page. The 10-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. Use place value cards that you can stack. 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 4 » Number & Operations in Base Ten. These pages list the standards that cover this topic area; read them alongside the lesson.
Research used to shape this lesson. Common Core 4.NBT.A.2 (expanded form); Cambridge Primary Mathematics Stage 4 (place value). These sources informed the lesson.