You will learn
- Name the place of each digit.
- Say the value of each digit.
- Build a number from thousands, hundreds, tens and ones.
- Explain why a zero is needed.
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
- Name the place of each digit.
- The value depends on the place.
- Build numbers from thousands, hundreds, tens and ones.
- A zero holds a place.
Words to know
Groups of 1,000.
Groups of 100.
Groups of 10.
Single units.
1. Discover: a place value chart
In the number 3,742, what does the 7 mean? What would happen to its value if the 3 and the 7 swapped places?
2. Understand: thousands, hundreds, tens, ones
In 4,523 the 4 is in the thousands place (4,000), the 5 in the hundreds place (500), the 2 in the tens place (20) and the 3 in the ones place (3).
The same digit has different values in different places. In 2,222 the digits are worth 2,000, 200, 20 and 2.
6 thousands, 0 hundreds, 4 tens and 9 ones is 6,049. The 0 keeps the hundreds place.
Idea 1: Places
In 3,742 the 3 is in the thousands place, 7 in the hundreds, 4 in the tens and 2 in the ones.
Idea 2: Value
The 7 in 3,742 is worth 700. The same digit is worth more in a higher place.
Idea 3: Build
2 Th, 3 H, 0 T, 5 O make 2,305. The 0 shows there are no tens.
Why a zero? It keeps the other digits in their correct places.
3. Worked examples
Example 1 (I show you): Value
What is the value of the 7 in 3,742?
- 7 is in the hundreds place.
Answer: 700
Example 2 (We do it together): Place
What is the thousands digit in 8,106?
- Look at the first digit.
Answer: 8
Example 3 (You try): Build
Build 2 Th, 3 H, 0 T, 5 O.
Show the steps and answer
- Write each digit in its place.
Answer: 2,305
Did you know?
In 2,222 each 2 has a different value: 2,000, 200, 20 and 2.
Why this matters
Place value tells us how big a number really is.
4. Explore: place value chart
Draw a chart with columns Th, H, T, O.
- Write 4,523 in the chart.
- Say the value of each digit.
- Build 6,049.
- Swap two digits and say how the number changes.
Think about it: what did you notice?
4,523: 4,000, 500, 20, 3. 6,049 keeps a zero in the hundreds.
5. Practise
Say it in a sentence
Use these starters when you talk about the lesson. Say them out loud.
- The digit ___ is in the ___ place.
- Its value is ___.
- ___ thousands and ___ ones make ___.
- We write 0 so that ___.
Guided practice
Question 1. Value of 5 in 4,523?
500.
Question 2. Hundreds digit in 9,206?
2.
Question 3. 6 Th, 0 H, 4 T, 9 O?
6,049.
Independent practice
Level 1: Start
- Value of 7 in 3,742
- Thousands digit in 8,106
- Tens digit in 5,689
- Build 2 Th, 3 H, 0 T, 5 O
- Value of the second 2 in 2,222
Level 2: Grow
- Value of the 6 in 4,613
- Tens digit in 7,284
- Build 5 Th, 0 H, 3 T, 1 O
Level 3: Stretch
- Value of the 9 in 9,009
- Build 3 thousands, 4 tens
- Ben says the 5 in 5,420 is worth 5. What is wrong?
Answers are in the answer key below. Try first, then check.
6. Apply: everyday mathematics
A farm has 3 thousands, 7 hundreds, 4 tens and 2 ones of eggs. How many eggs?
Show a sample answer
3,742 eggs.
Another one. Write a number with 4 in the hundreds place and 0 in the tens place. Say the value of the 4.
Show a sample answer
for example 3,405; the 4 is worth 400
7. Common mistakes
Fix: It is in the hundreds place so it is worth 700.
Fix: Check its place first.
Fix: Write 0 where there is none.
8. Lesson summary and revision card
- I can name the place of each digit.
- I can say the value of a digit.
- I can build a number from its parts.
- I can explain why we need a zero.
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
- Place decides value.
- Th, H, T, O.
- Zero is a place holder.
11. Next lesson
Next lesson: Expanded form. 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.
- What is the value of the 8 in 5,184? [1 mark]
- Build 6 Th, 0 H, 4 T, 9 O. [2 marks]
- What digit is in the hundreds place of 3,926? [1 mark]
- Why do we write a 0 in 5,007? [2 marks]
- Ama says the 2 in 2,222 is always worth 2. Is she right? Explain. [3 marks]
Total: 9 marks.
Marking guide and model answers
- 80 [1]
- 6,049 [2]
- 9 [1]
- To hold the empty hundreds and tens [1]; so the 5 stays in the thousands place [1]
- No [1]. Value depends on place [1]. The 2s are worth 2,000, 200, 20 and 2 [1].
Score guide: 8 to 9 = secure. 6 to 7 = nearly there, revise the parts you missed. Under 6 = work through the lesson again with a grown-up.
Printable worksheet
- Value of 7 in 3,742
- Thousands digit in 8,106
- Tens digit in 5,689
- 2 Th, 3 H, 0 T, 5 O
- Value of the tens 2 in 2,222
- Value of the 5 in 4,523
- Hundreds digit in 9,206
- 6 Th, 0 H, 4 T, 9 O = ___
- In 2,222 the tens digit is worth ___.
- 7 Th, 0 H, 0 T, 5 O = ___
Homework
Write a four-digit number and ask someone at home to say each digit’s value.
Answer key and marking scheme
| Question | Expected response | Marks |
|---|---|---|
| Value of 7 in 3,742 | 700 | 2 |
| Thousands digit in 8,106 | 8 | 2 |
| Tens digit in 5,689 | 8 | 2 |
| 2 Th, 3 H, 0 T, 5 O | 2,305 | 2 |
| Value of the tens 2 in 2,222 | 20 | 2 |
| Total | 10 |
Practice answers: Worksheet: 1 700; 2 8; 3 8; 4 2,305; 5 20.
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): 6 500; 7 2; 8 6,049; 9 20; 10 7,005.
Independent practice answers. Level 1: 1 700; 2 8; 3 8; 4 2,305; 5 200 (the second 2 from the left is in the hundreds place). Level 2: 1 600; 2 8; 3 5,031. Level 3: 1 9,000 for the first 9, and 9 for the last; 2 3,040; 3 It is in the thousands place, so it is worth 5,000..
Mastery and remediation
| Objective | Bronze (Developing) | Silver (Proficient) | Gold (Advanced) |
|---|---|---|---|
| O1 Name the place of each 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 Say the value of each 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 |
| O3 Build a number from thousands, hundreds, tens and ones | 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 Explain why a zero is needed | 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: Saying the 7 in 3,742 is worth 7. It is in the hundreds place so it is worth 700.
- Explain another way: use real objects first, then pictures.
- Show a simpler example: Use place value cards and a Th H T O chart.
- 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 names the place and value of each digit in four-digit numbers. You do not need to be good at mathematics to help.
- Use number cards to build four-digit numbers.
- Ask: what is the value of this digit?
- Use coins of 1, 10, 100 and 1,000 to model numbers.
- 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: name the place of each digit; say the value of each digit; build a number from thousands, hundreds, tens and ones; explain why a zero is needed.
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. 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). Draw a chart with columns Th, H, T, O. 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. Which place is the digit in? What is it worth?
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 in 3,742 is worth 7. It is in the hundreds place so it is worth 700.
13–15. Assessment questions, answer keys, marking scheme
Use the quiz and worksheet on this page. The 9-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 and a Th H T O chart. 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 3 » 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 3.NBT.A and 2.NBT.A.1 (place value); Cambridge Primary Mathematics Stage 3 (place value). These sources informed the lesson.