You will learn
- Compare hundreds first.
- Compare 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 hundreds first.
- If they match, compare the tens, then the ones.
- Greater than is >. Less than is <.
- Equal means the same: =.
Words to know
More than. Sign: >.
Fewer than. Sign: <.
The same. Sign: =.
Say how numbers are alike or different.
1. Discover: two crowds
345 people came on Saturday and 354 on Sunday. Which day had more people? How can you tell without counting?
2. Understand: comparing numbers
To compare three-digit numbers, start with the hundreds. The one with more hundreds is bigger. If the hundreds are equal, compare the tens. If those are equal, compare the ones.
345 and 354: both have 3 hundreds. Tens: 4 and 5, so 354 is bigger. We write 345 < 354 and 354 > 345. The open side of the sign faces the bigger number.
Idea 1: Hundreds first
To compare two numbers, look at the hundreds first. 428 and 482 both have 4 hundreds, so look at the tens.
Idea 2: Tens, then ones
428 has 2 tens and 482 has 8 tens, so 428 < 482. If the tens match too, compare the ones.
Idea 3: The signs
> means greater than. < means less than. = means equal. The sign opens toward the bigger number.
Why hundreds first? A hundred is worth more than all the tens and ones that follow.
3. Worked examples
Example 1 (I show you): Compare
Compare 428 and 482.
- Same hundreds.
- Tens: 2 and 8.
Answer: 428 < 482
Example 2 (We do it together): Different hundreds
Compare 700 and 699.
- 7 hundreds is more than 6 hundreds.
Answer: 700 > 699
Example 3 (You try): Three numbers
Which is smallest: 540, 504 or 450?
Show the steps and answer
- Hundreds: 5, 5, 4.
- 450 has the fewest hundreds.
Answer: 450
Did you know?
The signs < and > look like a crocodile mouth. The mouth opens to the bigger number.
Why this matters
Comparing numbers helps us choose the cheaper price or the longer distance.
4. Explore: compare cards
You need number cards and a pencil.
- Pick two numbers: 428 and 482.
- Compare hundreds, then tens.
- Write the sign between them.
- Repeat with 507 and 570.
Think about it: what did you notice?
428 < 482 and 507 < 570.
5. Practise
Say it in a sentence
Use these starters when you talk about the lesson. Say them out loud.
- ___ is greater than ___.
- ___ is less than ___.
- I look at the ___ first.
- The tens are ___ so I look at the ___.
Guided practice
Question 1. Compare 345 and 354.
345 < 354.
Question 2. Compare 700 and 699.
700 > 699.
Question 3. Compare 250 and 250.
250 = 250.
Independent practice
Level 1: Start
- Compare 428 and 482.
- Compare 507 and 570.
- Compare 999 and 1,000.
- Which is greater: 612 or 621?
- Write < or >: 305 __ 350.
Level 2: Grow
- Which is greater: 306 or 360?
- Write <, > or =: 560 __ 506.
- Write <, > or =: 415 __ 415.
Level 3: Stretch
- Which is smallest: 540, 504 or 450?
- Write a number between 350 and 360.
- Ali says 98 is greater than 102 because 9 and 8 are big digits. What is wrong?
Answers are in the answer key below. Try first, then check.
6. Apply: everyday mathematics
School A has 428 pupils. School B has 482. Which school has fewer pupils?
Show a sample answer
School A has fewer (428 < 482).
Another one. School A has 468 pupils and School B has 486. Which has more? How many more?
Show a sample answer
School B; 486 − 468 = 18
7. Common mistakes
Fix: Always start with the hundreds.
Fix: Start with the hundreds.
Fix: The open side faces the bigger number.
8. Lesson summary and revision card
- I can compare hundreds first.
- I can compare tens and ones when needed.
- I can use <, > and =.
- I can explain how I know.
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
- Start with hundreds.
- Use <, > and =.
- The open side faces the bigger number.
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 =: 350 __ 305. [1 mark]
- Which is greater, 617 or 671? [1 mark]
- Put < or >: 999 __ 1,000. [1 mark]
- Which is smallest: 480, 408 or 804? [2 marks]
- Explain why 542 is greater than 459. [2 marks]
Total: 7 marks.
Marking guide and model answers
- > [1]
- 671 [1]
- < [1]
- 408 [2]. Give 1 mark for the method.
- 542 has 5 hundreds [1]; 459 has 4 hundreds [1]
Score guide: 6 to 7 = secure. 5 to 5 = nearly there, revise the parts you missed. Under 5 = work through the lesson again with a grown-up.
Printable worksheet
- 428 __ 482
- 507 __ 570
- 999 __ 1,000
- Greater: 612 or 621?
- 305 __ 350
- Which is greater: 543 or 534?
- Write <, > or =: 210 __ 201.
- What do we compare first?
- Which is smaller: 678 or 687?
- Write a number greater than 800.
Homework
Compare three pairs of prices from a shop receipt. Write the sign each time.
Answer key and marking scheme
| Question | Expected response | Marks |
|---|---|---|
| 428 __ 482 | < | 2 |
| 507 __ 570 | < | 2 |
| 999 __ 1,000 | < | 2 |
| Greater: 612 or 621? | 621 | 2 |
| 305 __ 350 | < | 2 |
| Total | 10 |
Practice answers: Worksheet: 1 <; 2 <; 3 <; 4 621; 5 <.
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): 6 543; 7 >; 8 The hundreds; 9 678; 10 Any number above 800.
Independent practice answers. Level 1: 1 428 < 482; 2 507 < 570; 3 999 < 1,000; 4 621; 5 <. Level 2: 1 360; 2 >; 3 =. Level 3: 1 450; 2 For example 355; 3 102 has 1 hundred. 98 has none, so 102 is greater..
Mastery and remediation
| Objective | Bronze (Developing) | Silver (Proficient) | Gold (Advanced) |
|---|---|---|---|
| O1 Compare hundreds 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 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 with the hundreds.
- Explain another way: use real objects first, then pictures.
- Show a simpler example: Compare with place value cards, hundreds first.
- 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 three-digit numbers and uses the signs. You do not need to be good at mathematics to help.
- Compare prices or house numbers.
- Ask: which is bigger, 420 or 402? How do you know?
- Play a game: draw two cards and compare.
- 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 hundreds first; compare tens and ones when needed; use the signs <, > and =; explain how you know.
Prerequisite knowledge. Lesson 5.
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 and a pencil. 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 digit do you compare first? Which is greater? How do you know?
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 with the hundreds.
13–15. Assessment questions, answer keys, marking scheme
Use the quiz and worksheet on this page. The 7-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. Compare with place value cards, hundreds first. 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.4 (compare three-digit numbers); Cambridge Primary Mathematics Stage 2. These sources informed the lesson.