Comparing Numbers

For Elementary Students

Why Do We Compare Numbers?

Every day you compare things: which toy costs more, who is taller, which snack has more pieces!

Comparing numbers helps you figure out which is bigger, smaller, or if they're the same.

Think about it like this: If you have 5 stickers and your friend has 8 stickers, who has more? Comparing helps you know!

The Comparison Symbols

We use special symbols to compare:

Greater than >

• 7 > 3 means "7 is greater than 3"
• Read as: "Seven is greater than three"
• The open mouth eats the bigger number!

Less than <

• 3 < 7 means "3 is less than 7"
• Read as: "Three is less than seven"
• The open mouth still eats the bigger number!

Equal to =

• 5 = 5 means "5 is equal to 5"
• Read as: "Five equals five"

Alligator Trick!

Think of the symbols as an alligator's mouth. The alligator is hungry and always wants to eat the bigger number!

9  >  2    (Alligator eats 9 because it's bigger)
   👄→

2  <  9    (Alligator eats 9 from the other side)
  ←👄

Comparing Small Numbers (0-10)

For small numbers, think about counting:

0 ─── 1 ─── 2 ─── 3 ─── 4 ─── 5 ─── 6 ─── 7 ─── 8 ─── 9 ─── 10

Numbers to the right are bigger!

• 2 < 5 (2 is to the left of 5)
• 8 > 3 (8 is to the right of 3)
• 4 = 4 (same number!)

Comparing Two-Digit Numbers

Example: Compare 47 and 52

Look at the tens place first:

• 47 has 4 tens
• 52 has 5 tens
• 5 tens is more than 4 tens!

Answer: 47 < 52

What If the Tens Are the Same?

Example: Compare 34 and 37

Tens place: Both have 3 tens (same!)

Ones place: 4 vs 7

• 4 is less than 7

Answer: 34 < 37

For Junior High Students

Why Comparing Numbers Matters

In real life, you compare numbers all the time:

• Prices (which costs more?)
• Scores (who won?)
• Distances (which is farther?)
• Quantities (who has more?)

The Three Comparison Symbols

Memory tip: The open end of > or < always points to the larger number.

Comparing Numbers: Step-by-Step

Step 1: Count the digits

More digits usually means a bigger number.

• 456 (3 digits) > 78 (2 digits)
• 1,234 (4 digits) > 999 (3 digits)

Step 2: If same number of digits, compare left to right

Start with the leftmost digit (highest place value) and compare.

Example 1: Different First Digits

Compare 342 and 489

• Hundreds place: 3 vs 4
• 4 > 3, so 489 is bigger

Answer: 342 < 489

Example 2: Same First Digit, Check Next

Compare 672 and 645

• Hundreds: 6 = 6 (same, move on)
• Tens: 7 vs 4
• 7 > 4, so 672 is bigger

Answer: 672 > 645

Example 3: Check All the Way to the End

Compare 834 and 837

• Hundreds: 8 = 8 (same)
• Tens: 3 = 3 (same)
• Ones: 4 vs 7
• 4 < 7, so 834 is smaller

Answer: 834 < 837

Comparing Larger Numbers

The same rules apply!

Compare 12,456 and 12,389

• Ten thousands: 1 = 1 (same)
• Thousands: 2 = 2 (same)
• Hundreds: 4 vs 3
• 4 > 3, so 12,456 is bigger

Answer: 12,456 > 12,389

Ordering Numbers

Ascending order: Smallest to largest

• Example: 23, 45, 67, 89

Descending order: Largest to smallest

• Example: 89, 67, 45, 23

Comparing with Different Numbers of Digits

Example: Compare 999 and 1,000

• 999 has 3 digits (hundreds)
• 1,000 has 4 digits (thousands)

Answer: 999 < 1,000

Tip: One thousand is always bigger than nine hundred ninety-nine!

Using Number Lines

Number lines help visualize comparisons:

smaller                                   larger
   ←                                         →
100 ─── 200 ─── 300 ─── 400 ─── 500 ─── 600 ─── 700

Numbers further to the right are always greater.

Real-Life Comparisons

Shopping: "Is $45 < $52?" → Yes, $45 costs less

Scores: "Did you score > 80?" → If you scored 85, yes!

Age: "Is 12 years old > 10 years old?" → Yes

Distance: "Is 250 miles < 300 miles?" → Yes, 250 is shorter

Common Mistakes

❌ Mistake: "34 > 8 because 34 has two digits" ✓ Correct: Compare the values, not the number of digits. 34 > 8 is correct, but think about value (34 is thirty-four, 8 is eight).

❌ Mistake: Confusing the symbols ✓ Remember: The open mouth eats the bigger number!

Practice