You will learn
- Compare thousands first.
- Compare hundreds, tens and ones when needed.
- Use the signs and =.
- Explain how you know.
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
- Compare the thousands first.
- If they match, compare the hundreds, then tens, then ones.
- Use >, < or =.
- Explain how you know.
Words to know
More than. Sign: >.
Fewer than. Sign: <.
The same. Sign: =.
Say how numbers differ.
1. Discover: two crowds
4,523 people came to the market on Saturday and 4,532 on Sunday. Which day had more?
2. Understand: comparing four-digit numbers
Compare place by place from the left: thousands, then hundreds, then tens, then ones.
4,523 and 4,532: the thousands (4) and hundreds (5) are equal. Tens: 2 < 3. So 4,523 < 4,532.
7,001 > 6,999 because 7 thousands is more than 6 thousands. 5,050 < 5,500 because 0 hundreds is less than 5 hundreds.
Idea 1: Start at the left
Compare 3,215 and 3,251. Thousands: 3 and 3. Hundreds: 2 and 2. Tens: 1 and 5. So 3,215 < 3,251.
Idea 2: Signs
> means greater than, < means less than and = means equal. The sign points to the smaller number.
Idea 3: Zeros
5,050 > 5,005 because the hundreds are 0 and 0, then tens are 5 and 0.
Why start at the left? The biggest place decides first.
3. Worked examples
Example 1 (I show you): Thousands
8,000 __ 7,999
- 8 thousands is more than 7 thousands.
Answer: >
Example 2 (We do it together): Tens
3,215 __ 3,251
- Same thousands and hundreds. Tens: 1 and 5.
Answer: <
Example 3 (You try): Equal
2,468 __ 2,468
Show the steps and answer
- All digits match.
Answer: =
Did you know?
The sign always opens toward the greater number, like a hungry mouth.
Why this matters
Comparing numbers helps us order prices, distances and sizes.
4. Explore: compare cards
You need number cards.
- Pick two numbers: 4,523 and 4,532.
- Compare thousands, hundreds, tens.
- Write the sign.
- Repeat with 7,001 and 6,999.
Think about it: what did you notice?
4,523 < 4,532; 7,001 > 6,999.
5. Practise
Say it in a sentence
Use these starters when you talk about the lesson. Say them out loud.
- I compare the ___ first.
- ___ is greater than ___.
- The digits are the same so ___.
- I know because ___.
Guided practice
Question 1. 4,523 __ 4,532
<
Question 2. 7,001 __ 6,999
>
Question 3. 5,050 __ 5,500
<
Independent practice
Level 1: Start
- 3,215 __ 3,251
- 8,000 __ 7,999
- 5,050 __ 5,005
- 2,468 __ 2,468
- Greater: 6,789 or 6,798?
Level 2: Grow
- 4,812 __ 4,821
- 9,100 __ 9,010
- 3,333 __ 3,333
Level 3: Stretch
- Greatest: 2,999, 3,001 or 2,990?
- Smallest: 6,060, 6,006 or 6,600?
- Ali says 7,099 is greater than 7,100 because 99 is more than 1. What is wrong?
Answers are in the answer key below. Try first, then check.
6. Apply: everyday mathematics
School A has 1,254 pupils and School B 1,245. Which has more?
Show a sample answer
School A (1,254 > 1,245).
Another one. Write two numbers that differ only in the tens digit. Compare them.
Show a sample answer
for example 4,520 and 4,560; 4,520 < 4,560
7. Common mistakes
Fix: Always start from the thousands.
Fix: Start with the biggest place.
Fix: The sign opens toward the greater number.
8. Lesson summary and revision card
- I can compare four-digit numbers.
- I can use >, < and =.
- I can find the greatest and smallest.
- I can explain my answer.
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
- Compare from the left.
- Use <, > and =.
- Same digits, same value.
11. Next lesson
Next lesson: 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 >, < or =: 5,670 __ 5,607 [1 mark]
- Which is the smallest: 4,321, 4,123, 4,312? [1 mark]
- Put in order, smallest first: 3,050, 3,005, 3,500. [2 marks]
- Write >, < or =: 8,000 __ 7,999 [1 mark]
- Ben says 6,099 is more than 6,100. Is he right? Explain. [3 marks]
Total: 8 marks.
Marking guide and model answers
- > [1]
- 4,123 [1]
- 3,005 [1]; 3,050; 3,500 [1]
- > [1]
- No [1]. Compare hundreds first [1]. 6,100 has 1 hundred, 6,099 has 0 [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
- 3,215 __ 3,251
- 8,000 __ 7,999
- 5,050 __ 5,005
- 2,468 __ 2,468
- Greater: 6,789 or 6,798?
- 3,215 __ 3,251
- 8,000 __ 7,999
- 5,050 __ 5,005
- 2,468 __ 2,468
- Greater: 6,789 or 6,798?
Homework
Compare three pairs of prices from a shop. Write the sign each time.
Answer key and marking scheme
| Question | Expected response | Marks |
|---|---|---|
| 3,215 __ 3,251 | < | 2 |
| 8,000 __ 7,999 | > | 2 |
| 5,050 __ 5,005 | > | 2 |
| 2,468 __ 2,468 | = | 2 |
| Greater: 6,789 or 6,798? | 6,798 | 2 |
| Total | 10 |
Practice answers: Worksheet: 1 <; 2 >; 3 >; 4 =; 5 6,798.
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 <; 7 >; 8 >; 9 =; 10 6,798.
Independent practice answers. Level 1: 1 <; 2 >; 3 >; 4 =; 5 6,798. Level 2: 1 <; 2 >; 3 =. Level 3: 1 3,001; 2 6,006; 3 Compare the hundreds first. 7,100 has 1 hundred, 7,099 has 0..
Mastery and remediation
| Objective | Bronze (Developing) | Silver (Proficient) | Gold (Advanced) |
|---|---|---|---|
| O1 Compare thousands first | 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 Compare hundreds, tens and ones when 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 |
| O3 Use the signs <, > and = | 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 how you know | 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: Comparing the ones first. Always start from the thousands.
- Explain another way: use real objects first, then pictures.
- Show a simpler example: Line the digits up in a place value chart before comparing.
- 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 compares four-digit numbers using place value. You do not need to be good at mathematics to help.
- Compare prices together.
- Ask: which place decides?
- Use number cards and a sign card.
- 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: compare thousands first; compare hundreds, tens and ones when needed; use the signs <, > and =; explain how you know.
Prerequisite knowledge. Lessons 1 to 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 number 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. Which place do I compare first? Are the digits the same? Which is greater?
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. Comparing the ones first. Always start from the thousands.
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. Line the digits up in a place value chart before comparing. 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 2.NBT.A.4 and 3.NBT; Cambridge Primary Mathematics Stage 3 (comparing numbers). These sources informed the lesson.