You will learn
- Find the value of a digit.
- Write expanded form.
- Write standard form.
- Compare place values.
Version 0.1 · published for early use · expert review pending Standards alignment: pending verification. Not yet reviewed against the Courseversity scorecard.
Student lesson
Words to know
What a digit is worth.
Sum of place values.
The usual way.
Digit times its place.
1. Discover: what is 7 worth?
In 3,725,410 the digit 7 is not worth 7. What is it worth?
2. Understand: place value
- In 3,725,410 the 7 is in the hundred-thousands place: value 700,000.
- Expanded: 3,000,000 + 700,000 + 20,000 + 5,000 + 400 + 10.
- The 5 is worth 5,000 and the 2 is worth 20,000.
- The 0 holds the ones place.
3. Explore: expand
You need paper.
- Name each place.
- Multiply digit by place.
- Write the sum.
- Check by adding.
Think about it: what did you notice?
3,725,410.
4. Practise
Guided practice
Question 1. Value of 7?
700,000.
Question 2. Value of 5?
5,000.
Question 3. Value of 2?
20,000.
Independent practice
- Value of 4 in 3,725,410
- Value of 3 in 3,725,410
- Expanded form of 6,208
- Standard form of 40,000 + 300 + 5
- Value of 8 in 8,450,000
Answers are in the answer key below. Try first, then check.
5. Apply: everyday mathematics
A prize is 1,250,000. What does the 2 stand for?
Show a sample answer
200,000.
6. Common mistake
Fix: It is worth 700,000.
7. Check and master
Answer all questions. You will see feedback after each one.
Your result appears here after you answer every question.
8. Key takeaways
- Digit value depends on place.
- Expanded form adds the values.
- Zero holds a place.
9. Next lesson
Next lesson: Factors and multiples. Keep going with the next idea in this course.
Printable worksheet
- Value of 4 in 3,725,410
- Value of 3 in 3,725,410
- 6,208 expanded
- 40,000 + 300 + 5
- Value of 8 in 8,450,000
Homework
Write your phone number’s digits with their place values (for a 6-digit number).
Answer key and marking scheme
| Question | Expected response | Marks |
|---|---|---|
| Value of 4 in 3,725,410 | 400 | 2 |
| Value of 3 in 3,725,410 | 3,000,000 | 2 |
| 6,208 expanded | 6,000 + 200 + 8 | 2 |
| 40,000 + 300 + 5 | 40,305 | 2 |
| Value of 8 in 8,450,000 | 8,000,000 | 2 |
| Total | 10 |
Practice answers: Worksheet: 1 400; 2 3,000,000; 3 6,000 + 200 + 8; 4 40,305; 5 8,000,000.
Quiz answers: 1 A, 2 B, 3 C, 4 A, 5 B, challenge C.
Mastery and remediation
| Objective | Bronze (Developing) | Silver (Proficient) | Gold (Advanced) |
|---|---|---|---|
| O1 Find the value of a digit | 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 | 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 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 Compare 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 |
Proposed Courseversity thresholds for this page: Bronze = at least 3 of 5 core questions correct; Silver = all 5; Gold = all 5 plus the challenge. A badge is never a full record of progress.
If a learner struggles
- Find the misconception: Saying the 7 is worth 7. It is worth 700,000.
- Explain another way: use real objects first, then pictures.
- Show a simpler example: Place value to 10,000.
- 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.
Teacher package
1–5. Objectives, prerequisites, materials, preparation, duration
Lesson objectives. Learners will: find the value of a digit; write expanded form; write standard form; compare place values.
Prerequisite knowledge. Lesson 1.
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. 35–45 minutes.
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.
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. Saying the 7 is worth 7. It is worth 700,000.
13–15. Assessment questions, answer keys, marking scheme
Use the quiz and worksheet on this page. The 10-mark scheme and all answers are in the answer key above. Re-check every answer and the marking scheme before publication.
16–19. Remediation, enrichment, homework, teacher reflection
Remediation. Place value to 10,000. 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.