Comparing and Ordering Numbers - Second Grade
What is Comparing and Ordering?
Concept: Comparing means finding which number is bigger or smaller. Ordering means arranging numbers from smallest to biggest or biggest to smallest!
What We'll Learn:
✓ Using comparison symbols: <, >, =
✓ Comparing numbers up to 100
✓ Putting numbers in order (ascending & descending)
✓ Finding greatest and least in word problems
💡 Tip: When comparing numbers, always look at place values from left to right!
Comparison Symbols
Concept: We use special symbols to show how numbers compare to each other!
<
Less Than
Means: Smaller than
5 < 8
5 is less than 8
🐊 The alligator eats the bigger number!
>
Greater Than
Means: Bigger than
9 > 3
9 is greater than 3
🐊 The alligator eats the bigger number!
=
Equal To
Means: Same as
7 = 7
7 is equal to 7
Both sides have the same value!
Memory Trick: The Alligator Rule 🐊
The open mouth always points to the BIGGER number!
3 < 7
Mouth opens to 7
9 > 5
Mouth opens to 9
💡 Tip: The small end of the symbol points to the smaller number!
1. Comparing Numbers up to 100
Concept: To compare numbers up to 100, we use place value! Compare tens first, then ones.
Steps to Compare Numbers:
Step 1: Count the number of digits
More digits = bigger number
Step 2: If same digits, compare the TENS place
Larger tens digit = bigger number
Step 3: If tens are equal, compare the ONES place
Larger ones digit = bigger number
📝 Example 1: Comparing Two-Digit Numbers
Compare: 45 and 52
Tens
4
Ones
5
<
Tens
5
Ones
2
Solution:
Compare tens: 4 < 5
So 45 < 52
Answer: 45 < 52
Compare: 67 and 63
Tens
6
Ones
7
>
Tens
6
Ones
3
Solution:
Tens are equal: 6 = 6
Compare ones: 7 > 3
Answer: 67 > 63
Quick Comparison Rules:
✓ Any two-digit number > any one-digit number (45 > 9)
✓ 100 is greater than all two-digit numbers
✓ Always start comparing from the left (highest place value)
✓ If all digits are equal, numbers are equal
💡 Tip: Tens place is more important than ones place when comparing!
2. Put Numbers up to 100 in Order
Concept: Ordering means arranging numbers from smallest to biggest (ascending) or biggest to smallest (descending)!
⬆️ ASCENDING Order
From SMALLEST to BIGGEST
12, 25, 48, 67, 89
Numbers get LARGER ↗️
⬇️ DESCENDING Order
From BIGGEST to SMALLEST
95, 71, 53, 36, 14
Numbers get SMALLER ↘️
Steps to Order Numbers:
Step 1: Look at all the numbers
Step 2: Compare using place values (tens, then ones)
Step 3: Find the smallest (or biggest) number first
Step 4: Continue finding next smallest (or biggest)
Step 5: Write numbers in correct order
📝 Example: Ascending Order
Put these numbers in order from smallest to biggest:
43
18
75
29
Solution:
Compare tens place: 1, 2, 4, 7
Smallest tens = 18 (1 ten)
Next = 29 (2 tens)
Next = 43 (4 tens)
Biggest = 75 (7 tens)
Answer: 18, 29, 43, 75
📝 Example: Descending Order
Put these numbers in order from biggest to smallest:
56
82
34
67
Solution:
Compare tens place: 3, 5, 6, 8
Biggest tens = 82 (8 tens)
Next = 67 (6 tens)
Next = 56 (5 tens)
Smallest = 34 (3 tens)
Answer: 82, 67, 56, 34
💡 Tip: Use a number line or hundred chart to help you see the order!
3. Greatest and Least - Word Problems up to 100
Concept: In word problems, we need to find the greatest (biggest) or least (smallest) number from a group!
Important Vocabulary:
GREATEST / LARGEST / BIGGEST
Means: The highest number
Also called: Maximum
LEAST / SMALLEST / LOWEST
Means: The lowest number
Also called: Minimum
📖 Word Problem Examples
Problem 1: Finding the Greatest
Three friends collected stamps. Amit has 45 stamps, Priya has 62 stamps, and Ravi has 38 stamps. Who has the GREATEST number of stamps?
Solution:
Amit: 45 stamps
Priya: 62 stamps
Ravi: 38 stamps
Compare: 38 < 45 < 62
Answer: Priya has the greatest number (62 stamps)
Problem 2: Finding the Least
A shop has three boxes of pencils. Box A has 73 pencils, Box B has 56 pencils, and Box C has 81 pencils. Which box has the LEAST number of pencils?
Solution:
Box A: 73 pencils
Box B: 56 pencils
Box C: 81 pencils
Compare: 56 < 73 < 81
Answer: Box B has the least number (56 pencils)
Problem 3: Order from Greatest to Least
Four students scored the following marks in a test: Sara: 67, Tom: 89, Maya: 54, Ali: 76. Arrange their scores from greatest to least.
Solution:
Compare all scores: 54, 67, 76, 89
Greatest to least order: 89, 76, 67, 54
Answer: Tom (89), Ali (76), Sara (67), Maya (54)
Steps to Solve Word Problems:
Step 1: Read the problem carefully
Step 2: Find all the numbers
Step 3: Look for keywords (greatest, least, order)
Step 4: Compare the numbers
Step 5: Write your answer clearly
💡 Tip: Circle or underline all numbers in the problem before comparing!
Important Comparison Rules
Place Value Rule
Compare from LEFT to RIGHT
(Tens → Ones)
Greater Than
If a > b
Then b < a
Ordering Rule
Ascending: ↗️
Smallest → Biggest
Descending: ↘️
Biggest → Smallest
Quick Reference Guide
| Symbol | Name | Meaning | Example |
|---|---|---|---|
| < | Less Than | First number is smaller | 23 < 56 |
| > | Greater Than | First number is bigger | 78 > 45 |
| = | Equal To | Both numbers are the same | 64 = 64 |
🎯 Tips for Comparing & Ordering Success 🎯
- ✓ Always compare tens place first, then ones place
- ✓ Remember the alligator rule - mouth opens to bigger number
- ✓ Use a number line to visualize comparisons
- ✓ Circle keywords in word problems (greatest, least, order)
- ✓ Practice with real-life examples (prices, scores, ages)
- ✓ Check your answer by comparing again
⭐ You're a Comparing & Ordering Champion! ⭐
Excellent work learning to compare and order numbers! You now know how to use the symbols <, >, and =, can compare any numbers up to 100 using place value, can put numbers in ascending or descending order, and can solve word problems about greatest and least. These skills are super important for all future math. Keep practicing and you'll be a comparison expert! You're doing amazing!