Compare Three-Digit Numbers

Understanding Number Comparison

Comparing numbers means determining which number is greater (larger), less (smaller), or if they are equal. When comparing three-digit numbers, we use our understanding of place value to make these determinations systematically and accurately.

What Does It Mean to Compare?

Comparing numbers answers questions like: - Which is bigger: 345 or 423? - Which is smaller: 789 or 698? - Are 567 and 567 the same?

We use special symbols to show these relationships: - > (greater than): 8 > 5 means "8 is greater than 5" - < (less than): 3 < 7 means "3 is less than 7" - = (equal to): 6 = 6 means "6 equals 6"

Why Comparing Numbers Matters

Learning to compare three-digit numbers helps you: - Make decisions - choose the larger or smaller quantity - Order numbers - arrange from least to greatest - Understand relationships - see how numbers relate to each other - Solve problems - determine which option is better - Develop number sense - build mathematical intuition - Work with money - compare prices and values

The Comparison Symbols

Greater Than: >

The symbol > means "greater than" or "is more than."

Think of it as an open mouth eating the bigger number!

Examples: - 456 > 234 (456 is greater than 234) - 800 > 750 (800 is greater than 750) - 999 > 100 (999 is greater than 100)

How to remember: The wide part opens toward the larger number.

Less Than: <

The symbol < means "less than" or "is fewer than."

The small point points to the smaller number!

Examples: - 234 < 456 (234 is less than 456) - 750 < 800 (750 is less than 800) - 100 < 999 (100 is less than 999)

How to remember: The small point aims at the smaller number.

Equal To: =

The symbol = means "equal to" or "the same as."

Both numbers are exactly the same!

Examples: - 456 = 456 (both numbers are identical) - 700 = 700 (equal amounts) - 123 = 123 (same value)

Memory Tricks for Symbols

Alligator mouth: The alligator's mouth opens wide to eat the bigger number!

789 > 234
(The mouth opens to 789, the bigger snack!)

L-trick: The symbol < looks like an L, and L is for Less than!

Number line: On a number line, larger numbers are to the right:

100 ---- 200 ---- 300 ---- 400 ---- 500
 ←less                      more→

Step-by-Step Comparison Process

Follow these steps to compare any two three-digit numbers correctly.

Step 1: Compare Hundreds First

Always start with the hundreds place!

Rule: The number with more hundreds is greater.

Example 1: Compare 523 and 381 - Hundreds: 5 vs. 3 - 5 > 3 - Result: 523 > 381 ✓

Example 2: Compare 742 and 856 - Hundreds: 7 vs. 8 - 7 < 8 - Result: 742 < 856 ✓

Example 3: Compare 299 and 901 - Hundreds: 2 vs. 9 - 2 < 9 - Result: 299 < 901 ✓

If hundreds are different, you're done! The comparison is determined.

Step 2: If Hundreds Are Equal, Compare Tens

If both numbers have the same hundreds digit, look at tens.

Rule: The number with more tens is greater.

Example 1: Compare 456 and 489 - Hundreds: 4 = 4 (equal, so check tens) - Tens: 5 vs. 8 - 5 < 8 - Result: 456 < 489 ✓

Example 2: Compare 732 and 715 - Hundreds: 7 = 7 (equal, so check tens) - Tens: 3 vs. 1 - 3 > 1 - Result: 732 > 715 ✓

Step 3: If Tens Are Also Equal, Compare Ones

If both hundreds AND tens are equal, look at ones.

Rule: The number with more ones is greater.

Example 1: Compare 567 and 563 - Hundreds: 5 = 5 (equal) - Tens: 6 = 6 (equal) - Ones: 7 vs. 3 - 7 > 3 - Result: 567 > 563 ✓

Example 2: Compare 821 and 828 - Hundreds: 8 = 8 (equal) - Tens: 2 = 2 (equal) - Ones: 1 vs. 8 - 1 < 8 - Result: 821 < 828 ✓

Step 4: If All Digits Are Equal

If hundreds, tens, AND ones are all the same, the numbers are equal!

Example: Compare 456 and 456 - Hundreds: 4 = 4 - Tens: 5 = 5 - Ones: 6 = 6 - Result: 456 = 456 ✓

Practice Examples

Example Set 1: Hundreds Decide

Compare 625 and 814

  6 2 5
  8 1 4
  ↓
  6 < 8

Answer: 625 < 814

Compare 950 and 467

  9 5 0
  4 6 7
  ↓
  9 > 4

Answer: 950 > 467

Example Set 2: Tens Decide

Compare 532 and 589

  5 3 2
  5 8 9
  ↓ ↓
  5=5
    3 < 8

Answer: 532 < 589

Compare 478 and 421

  4 7 8
  4 2 1
  ↓ ↓
  4=4
    7 > 2

Answer: 478 > 421

Example Set 3: Ones Decide

Compare 765 and 768

  7 6 5
  7 6 8
  ↓ ↓ ↓
  7=7
    6=6
      5 < 8

Answer: 765 < 768

Compare 849 and 842

  8 4 9
  8 4 2
  ↓ ↓ ↓
  8=8
    4=4
      9 > 2

Answer: 849 > 842

Comparing Numbers with Zeros

Zeros can be tricky, but remember: zero has value (or lack of value)!

Zero in the Tens Place

Compare 405 and 456 - Hundreds: 4 = 4 - Tens: 0 vs. 4 - 0 < 4 - Answer: 405 < 456

Compare 708 and 680 - Hundreds: 7 vs. 6 - 7 > 6 - Answer: 708 > 680

Zero in the Ones Place

Compare 450 and 456 - Hundreds: 4 = 4 - Tens: 5 = 5 - Ones: 0 vs. 6 - 0 < 6 - Answer: 450 < 456

Zero in Multiple Places

Compare 300 and 305 - Hundreds: 3 = 3 - Tens: 0 = 0 - Ones: 0 vs. 5 - 0 < 5 - Answer: 300 < 305

Compare 700 and 600 - Hundreds: 7 vs. 6 - 7 > 6 - Answer: 700 > 600

Ordering Three-Digit Numbers

Ordering means arranging numbers from least to greatest (or greatest to least).

Ordering from Least to Greatest

Problem: Order these numbers: 567, 234, 589, 199

Strategy: 1. Compare hundreds first to get rough groups: - 199 (1 hundred) - smallest - 234 (2 hundreds) - 567 and 589 (5 hundreds) - largest group

1. Within groups with same hundreds, compare tens:
2. 567 has 6 tens
3. 589 has 8 tens

4. 589 > 567

5. Final order: 199, 234, 567, 589 ✓

Ordering from Greatest to Least

Problem: Order these numbers: 432, 876, 421, 890

Strategy: 1. Find the largest (highest hundreds): - 890 (8 hundreds) - 876 (8 hundreds) - Between these, 890 > 876 (compare tens: 9 > 7)

1. Continue with remaining:
2. 432 (4 hundreds)
3. 421 (4 hundreds)

4. Between these, 432 > 421 (compare tens: 3 > 2)

5. Final order: 890, 876, 432, 421 ✓

Using a Number Line

A number line helps visualize which numbers are larger or smaller.

Number Line for Three-Digit Numbers

100 --- 200 --- 300 --- 400 --- 500 --- 600 --- 700 --- 800 --- 900 --- 1000
  ↑                               ↑                                   ↑
 150                             520                                 875

Numbers to the RIGHT are GREATER
Numbers to the LEFT are LESS

Examples: - 520 > 150 (520 is to the right of 150) - 875 > 520 (875 is to the right of 520) - 150 < 875 (150 is to the left of 875)

Plotting Numbers to Compare

Problem: Compare 345 and 378

Number line:

300 ---- 320 ---- 340 ---- 360 ---- 380 ---- 400
              ↑                  ↑
             345                378

378 is to the right, so 378 > 345 ✓

Real-World Comparisons

Comparing numbers helps in many everyday situations.

Money and Shopping

Comparing prices: - Item A costs $456 - Item B costs $423 - Which costs more? - 456 > 423, so Item A costs more

Saving goals: - Goal: $600 - Saved so far: $578 - Have you reached your goal? - 578 < 600, so not yet!

Measurements

Heights: - Building A: 325 feet - Building B: 389 feet - Which is taller? - 389 > 325, Building B is taller

Distances: - Route 1: 567 miles - Route 2: 542 miles - Which is shorter? - 542 < 567, Route 2 is shorter

Scores and Quantities

Test scores: - Your score: 892 points - Friend's score: 876 points - Who scored higher? - 892 > 876, you scored higher!

Collections: - Collection A: 345 stamps - Collection B: 354 stamps - Which is larger? - 354 > 345, Collection B is larger

Problem-Solving Strategies

Strategy 1: Use Place Value Charts

Problem: Which is greater: 678 or 687?

Place value chart:

┌───┬───┬───┐    ┌───┬───┬───┐
│ 6 │ 7 │ 8 │    │ 6 │ 8 │ 7 │
└───┴───┴───┘    └───┴───┴───┘
  ↓   ↓   ↓        ↓   ↓   ↓
  6 = 6            6 = 6
      7 < 8            8 > 7

Answer: 687 > 678

Strategy 2: Line Up Vertically

Problem: Compare 523 and 589

Line up the places:

  5 2 3
  5 8 9

Compare column by column, left to right. - Hundreds equal - Tens: 2 < 8 Answer: 523 < 589

Strategy 3: Think About Real Objects

Problem: Which is more: 299 apples or 301 apples?

Think: - 299 = almost 300 - 301 = just over 300 - 301 > 299 Answer: 301 > 299

Strategy 4: Use Benchmarks

Problem: Compare 478 and 521

Think: - 478 is less than 500 - 521 is more than 500 - So 521 > 478 Answer: 521 > 478

Practice Activities

Activity 1: Number Card Comparison War

Materials: Cards with three-digit numbers

How to play: 1. Each player draws a card 2. Compare numbers 3. Player with larger number wins both cards 4. Explain WHY your number is larger!

Activity 2: Greater Than/Less Than Sort

Materials: Paper plates labeled >, <, =

Activity: 1. Write pairs of numbers on cards 2. Compare each pair 3. Place the card on the correct plate 4. Explain your reasoning

Activity 3: Number Line Hop

Materials: Large number line on floor (100-1000)

Activity: 1. Teacher calls two numbers 2. Students stand at those positions 3. Class determines who is "greater" (farther right) 4. Use correct symbol to write the comparison

Activity 4: Create Your Own Comparisons

Create comparison challenges: 1. Write two three-digit numbers 2. Trade with a partner 3. Partner compares using >, <, or = 4. Check each other's work

Activity 5: Ordering Race

Materials: Index cards with numbers

Challenge: 1. Get 5-10 cards with different numbers 2. Race to put them in order (least to greatest) 3. Explain your strategy 4. Switch to greatest to least

Common Mistakes and Solutions

Mistake 1: Comparing from the right

Problem: Comparing 456 and 489, starting with ones (6 vs 9) and concluding 456 < 489 for wrong reason

Solution: Always start comparing from the LEFT (hundreds place first)!

Mistake 2: Confusing the symbols

Problem: Writing 789 < 234 (backwards)

Solution: Remember the alligator—mouth opens to the BIGGER number! 789 > 234

Mistake 3: Ignoring place value with zeros

Problem: Thinking 305 > 350 because 5 > 0

Solution: Compare systematically! 305 vs 350: hundreds equal (3=3), tens different (0 < 5), so 305 < 350

Mistake 4: Rushing through comparison

Problem: Not checking all places systematically

Solution: Use the step-by-step process: hundreds, then tens, then ones.

Assessment Checkpoints

You've mastered comparing three-digit numbers when you can: - ✓ Use >, <, and = symbols correctly - ✓ Compare numbers by starting with hundreds place - ✓ Continue to tens and ones when needed - ✓ Order numbers from least to greatest - ✓ Order numbers from greatest to least - ✓ Explain your comparison reasoning - ✓ Compare numbers with zeros correctly - ✓ Apply comparison to real-world situations

Looking Ahead

Mastering number comparison prepares you for: - Rounding: Deciding which benchmark is closer - Inequalities: Using comparison in algebra - Graphing: Plotting and comparing values - Estimation: Determining if answers are reasonable - Negative numbers: Extending comparison below zero - Decimals: Comparing numbers with parts

Conclusion

Comparing three-digit numbers is an essential skill that builds on your understanding of place value. By learning to systematically compare hundreds, then tens, then ones, you develop a reliable method for determining which numbers are greater, lesser, or equal. The symbols >, <, and = become powerful tools for expressing mathematical relationships. Practice comparing numbers in everyday situations—prices, distances, scores, quantities—and you'll see that comparison is one of the most practical and frequently used mathematical skills. Remember: start with hundreds, proceed left to right, and let place value guide your thinking!