You will learn
- Write expanded form with addition.
- Write expanded form with multiplication.
- Convert back to standard form.
- Handle zeros in the middle.
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
- Expanded form adds the value of each digit.
- Zeros hold places but are not written.
- Expanded form can use multiplication.
- Convert back to standard form by adding.
Words to know
Sum of place values.
Normal way to write a number.
Value by position.
Total.
1. Discover: taking it apart
3,456,789 can be taken apart place by place. How would you write it as a sum?
2. Understand: expanded form
- 3,456,789 = 3,000,000 + 400,000 + 50,000 + 6,000 + 700 + 80 + 9.
- With multiplication: 3×1,000,000 + 4×100,000 + 5×10,000 + 6×1,000 + 7×100 + 8×10 + 9×1.
- Zeros: 2,050,300 = 2,000,000 + 50,000 + 300.
Idea 1: Addition
4,300,060 = 4,000,000 + 300,000 + 60. 1,000,001 = 1,000,000 + 1.
Idea 2: Back to standard
900,000 + 8,000 + 20 = 908,020. The zero holds the empty place.
Idea 3: Multiplication
5 × 10,000 + 3 × 1,000 + 7 = 50,000 + 3,000 + 7 = 53,007. The 7 in 3,456,789 is worth 700.
Why leave out zeros? They add nothing to the total.
3. Worked examples
Example 1 (I show you): Expand
4,300,060
- Millions, hundred-thousands, tens.
Answer: 4,000,000 + 300,000 + 60
Example 2 (We do it together): Standard
900,000 + 8,000 + 20
- Add them.
Answer: 908,020
Example 3 (You try): Value
7 in 3,456,789
Show the steps and answer
- Hundreds place.
Answer: 700
Did you know?
Expanded form shows exactly what each digit is worth.
Why this matters
Expanded form shows why we carry and borrow when we calculate.
4. Explore: expand
You need paper.
- Write 3,456,789.
- Write each digit with its value.
- Add to check.
- Do 2,050,300.
Think about it: what did you notice?
2,000,000 + 50,000 + 300.
5. Practise
Say it in a sentence
Use these starters when you talk about the lesson. Say them out loud.
- The digits are worth ___.
- In expanded form: ___ + ___ + ___.
- Added together they make ___.
- The zero holds the ___ place.
Guided practice
Question 1. Expand 2,050,300.
2,000,000 + 50,000 + 300.
Question 2. Standard: 6,000,000 + 20,000 + 5?
6,020,005.
Question 3. Value of 5 in 3,456,789?
50,000.
Independent practice
Level 1: Start
- Expand 4,300,060
- Standard: 900,000 + 8,000 + 20
- Expand 1,000,001
- Standard: 5×10,000 + 3×1,000 + 7
- Value of 7 in 3,456,789
Level 2: Grow
- Expand 3,200,500
- Write 700,000 + 40 + 6 as a number
- Value of 9 in 8,923,456
Level 3: Stretch
- Expand 7,070,707
- Write 4 × 1,000,000 + 6 × 1,000 + 2 × 10 as a number
- Ana writes 600,000 + 3 as 60,003. What is wrong?
Answers are in the answer key below. Try first, then check.
6. Apply: everyday mathematics
A stadium has 45,208 seats. Write this in expanded form.
Show a sample answer
40,000 + 5,000 + 200 + 8.
Another one. There are 86,400 seconds in a day. Write 86,400 in expanded form.
Show a sample answer
80,000 + 6,000 + 400
7. Common mistakes
Fix: Skip zero places.
Fix: Every place needs a digit.
Fix: The value of 7 in 700 is 700.
8. Lesson summary and revision card
- I can write expanded form with addition.
- I can write it with multiplication.
- I can convert back to standard form.
- I can handle zeros in the middle.
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
- Digit times place.
- Skip zeros.
- Check by adding.
11. Next lesson
Next lesson: Comparing and ordering 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 4,300,060 in expanded form. [3 marks]
- Write 900,000 + 8,000 + 20 as a number. [2 marks]
- Write 1,000,001 in expanded form. [2 marks]
- Write 5 × 10,000 + 3 × 1,000 + 7 as a number. [2 marks]
- Kofi says the value of 7 in 3,456,789 is 7. Is he right? Explain. [3 marks]
Total: 12 marks.
Marking guide and model answers
- 4,000,000 [1]; 300,000 [1]; 60 [1]
- Add the place values [1]; 908,020 [1]
- 1,000,000 [1]; 1 [1]
- 50,000 + 3,000 + 7 [1]; 53,007 [1]
- No [1]. 7 is in the hundreds place [1]. It is worth 700 [1].
Score guide: 11 to 12 = secure. 8 to 10 = nearly there, revise the parts you missed. Under 8 = work through the lesson again with a grown-up.
Printable worksheet
- Expand 4,300,060
- 900,000 + 8,000 + 20
- Expand 1,000,001
- 5×10,000 + 3×1,000 + 7
- Value of 7 in 3,456,789
- 2,050,300 in expanded form
- 6,000,000 + 20,000 + 5 =
- Value of 5 in 3,456,789
- 900,000 + 8,000 + 20 =
- 5 × 10,000 + 3 × 1,000 + 7 =
Homework
Expand five large numbers.
Answer key and marking scheme
| Question | Expected response | Marks |
|---|---|---|
| Expand 4,300,060 | 4,000,000 + 300,000 + 60 | 2 |
| 900,000 + 8,000 + 20 | 908,020 | 2 |
| Expand 1,000,001 | 1,000,000 + 1 | 2 |
| 5×10,000 + 3×1,000 + 7 | 53,007 | 2 |
| Value of 7 in 3,456,789 | 700 | 2 |
| Total | 10 |
Practice answers: Worksheet: 1 4,000,000 + 300,000 + 60; 2 908,020; 3 1,000,000 + 1; 4 53,007; 5 700.
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 2,000,000 + 50,000 + 300; 7 6,020,005; 8 50,000; 9 908,020; 10 53,007.
Independent practice answers. Level 1: 1 4,000,000 + 300,000 + 60; 2 908,020; 3 1,000,000 + 1; 4 53,007; 5 700. Level 2: 1 3,000,000 + 200,000 + 500; 2 700,046; 3 900,000. Level 3: 1 7,000,000 + 70,000 + 700 + 7; 2 4,006,020; 3 600,000 + 3 = 600,003. A zero is needed in each empty place..
Mastery and remediation
| Objective | Bronze (Developing) | Silver (Proficient) | Gold (Advanced) |
|---|---|---|---|
| O1 Write expanded form with 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 |
| O2 Write expanded form with multiplication | 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 Convert back to standard form | 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 Handle zeros in the middle | 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: Writing 0 for missing places. Skip zero places.
- Explain another way: use real objects first, then pictures.
- Show a simpler example: Use place value cards.
- 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 numbers in expanded form. You do not need to be good at mathematics to help.
- Break phone numbers or prices into place values.
- Ask: what is each digit worth?
- Use place value cards.
- 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 expanded form with addition; write expanded form with multiplication; convert back to standard form; handle zeros in the middle.
Prerequisite knowledge. Lessons 1 and 2.
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. What is each digit worth? Is there a zero?
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 missing places. Skip zero places.
13–15. Assessment questions, answer keys, marking scheme
Use the quiz and worksheet on this page. The 12-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. 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.A.3a; Cambridge Primary Mathematics Stage 5 (expanded form). These sources informed the lesson; no official alignment is claimed.