You will learn
- Write a number in expanded form.
- Put an expanded form back into a number.
- Use zeros correctly.
- Check expanded forms.
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 form shows the value of each digit.
- Add the hundreds, tens and ones.
- A zero place can be left out.
- Standard form is the usual way to write a number.
Words to know
A number written as the sum of its place values.
The answer to an addition.
The worth of a digit by its place.
The usual way to write a number, like 345.
1. Discover: taking a number apart
Take apart 345 like a puzzle: 300, 40 and 5. Put them back together. What do you get?
2. Understand: expanded form
In expanded form we show the value of each digit: 345 = 300 + 40 + 5.
If a place has 0, we skip it: 305 = 300 + 5. To put it back together, add the parts: 600 + 20 + 7 = 627.
Idea 1: Break a number up
345 in expanded form is 300 + 40 + 5. Each part is the value of a digit.
Idea 2: Put it back together
600 + 20 + 7 = 627. Add the parts. The usual way to write a number, like 627, is standard form.
Idea 3: Zeros
305 = 300 + 5. There are no tens, so we do not write 0 tens. In 900 + 9 = 909 the zero keeps the place.
Why? Expanded form shows what each digit is really worth.
3. Worked examples
Example 1 (I show you): Expand
Write 482 in expanded form.
- 4 is in the hundreds: 400.
- 8 is in the tens: 80.
- 2 is in the ones: 2.
Answer: 400 + 80 + 2
Example 2 (We do it together): Add the parts
What is 700 + 60 + 1?
- Add the hundreds, tens and ones.
Answer: 761
Example 3 (You try): With a zero
Write 509 in expanded form.
Show the steps and answer
- 5 hundreds: 500.
- 0 tens: leave out.
- 9 ones.
Answer: 500 + 9
Did you know?
Money works this way too. A note of 100, a note of 10 and 5 coins of 1 make 115.
Why this matters
Expanded form helps us add and subtract big numbers by place.
4. Explore: take apart and rebuild
You need paper, a pencil and place value cards.
- Write 482 in expanded form.
- Write 509 in expanded form.
- Add 700 + 60 + 1.
- Check by saying the number aloud.
Think about it: what did you notice?
482 = 400 + 80 + 2. 509 = 500 + 9. 700 + 60 + 1 = 761.
5. Practise
Say it in a sentence
Use these starters when you talk about the lesson. Say them out loud.
- ___ in expanded form is ___.
- ___ + ___ + ___ = ___.
- The zero means no ___.
- The standard form is ___.
Guided practice
Question 1. Expanded form of 345?
300 + 40 + 5.
Question 2. 600 + 20 + 7 = ?
627.
Question 3. Expanded form of 305?
300 + 5.
Independent practice
Level 1: Start
- Write 482 in expanded form.
- Write 509 in expanded form.
- Add 700 + 60 + 1.
- What number is 900 + 9?
- Is 200 + 30 + 4 the same as 234?
Level 2: Grow
- Write 365 in expanded form.
- 200 + 40 + 8 = ___.
- Write 703 in expanded form.
Level 3: Stretch
- 400 + 7 + 30 = ___.
- Write 990 in expanded form.
- Sade writes 405 as 400 + 50. What is wrong?
Answers are in the answer key below. Try first, then check.
6. Apply: everyday mathematics
A shop sold 400 + 50 + 6 mangoes. How many?
Show a sample answer
456 mangoes.
Another one. A shop has 2 boxes of 100 pens, 5 boxes of 10 pens and 6 loose pens. Write the total in expanded form and as a number.
Show a sample answer
200 + 50 + 6 = 256
7. Common mistakes
Fix: Skip the zero place or write it as 300 + 0 + 5; either way it is 305.
Fix: Check the place of each digit.
Fix: Hundreds, tens, ones in order.
8. Lesson summary and revision card
- I can write a number in expanded form.
- I can add the parts back to the number.
- I can use zeros correctly.
- I can check an expanded form.
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
- Show each value to expand.
- Add the parts to rebuild.
- A zero place is skipped.
11. Next lesson
Next lesson: Comparing three-digit 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 624 in expanded form. [2 marks]
- What is 800 + 30 + 9? [1 mark]
- Write 701 in expanded form. [2 marks]
- Is 300 + 20 + 5 the same as 352? Explain. [2 marks]
- What is 900 + 90 + 9? [1 mark]
Total: 8 marks.
Marking guide and model answers
- 600 + 20 + 4 [2]. Give 1 mark for two correct parts.
- 839 [1]
- 700 + 1 [2]. Give 1 mark if 0 tens are written.
- No [1]. 300 + 20 + 5 = 325 [1]
- 999 [1]
Score guide: 7 to 8 = secure. 5 to 6 = nearly there, revise the parts you missed. Under 5 = work through the lesson again with a grown-up.
Printable worksheet
- Expand 482.
- Expand 509.
- 700 + 60 + 1?
- 900 + 9?
- 200 + 30 + 4?
- Write 456 in expanded form.
- 300 + 10 + 2 = ___.
- Write 800 + 0 + 4 as a number.
- 500 + 70 = ___.
- Write 220 in expanded form.
Homework
Write the numbers 218, 540 and 603 in expanded form. Ask a family member to check.
Answer key and marking scheme
| Question | Expected response | Marks |
|---|---|---|
| Expand 482. | 400 + 80 + 2 | 2 |
| Expand 509. | 500 + 9 | 2 |
| 700 + 60 + 1? | 761 | 2 |
| 900 + 9? | 909 | 2 |
| 200 + 30 + 4? | 234 | 2 |
| Total | 10 |
Practice answers: Worksheet: 1 400 + 80 + 2; 2 500 + 9; 3 761; 4 909; 5 234.
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): 6 400 + 50 + 6; 7 312; 8 804; 9 570; 10 200 + 20.
Independent practice answers. Level 1: 1 400 + 80 + 2; 2 500 + 9; 3 761; 4 909; 5 yes, both are 234. Level 2: 1 300 + 60 + 5; 2 248; 3 700 + 3. Level 3: 1 437; 2 900 + 90; 3 There are no tens. 405 = 400 + 5..
Mastery and remediation
| Objective | Bronze (Developing) | Silver (Proficient) | Gold (Advanced) |
|---|---|---|---|
| O1 Write a number in expanded 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 |
| O2 Put an expanded form back into a number | 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 Use zeros correctly | 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 expanded forms | 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 305 as 300 + 0 + 5 but then reading it as 35. Skip the zero place or write it as 300 + 0 + 5; either way it is 305.
- Explain another way: use real objects first, then pictures.
- Show a simpler example: Build the number with place value cards and read each card.
- 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 and puts them back. You do not need to be good at mathematics to help.
- Write a number and break it into parts together.
- Use play money: how many hundreds, tens and ones?
- Ask: what is 400 + 30 + 2?
- 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 in expanded form; put an expanded form back into a number; use zeros correctly; check expanded forms.
Prerequisite knowledge. Lesson 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, a pencil and place value cards. 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? What do the parts add up to? What does the zero mean?
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 305 as 300 + 0 + 5 but then reading it as 35. Skip the zero place or write it as 300 + 0 + 5; either way it is 305.
13–15. Assessment questions, answer keys, marking scheme
Use the quiz and worksheet on this page. The 8-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. Build the number with place value cards and read each card. 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 2 » 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 2.NBT.A.3 (expanded form); Cambridge Primary Mathematics Stage 2. These sources informed the lesson.