Comparing Numbers Using Place Value for Grade 1 Students

Master comparing numbers up to 100 using place value: tens and ones, comparison symbols, and step-by-step methods.

Complete Summary: Comparing Using Place Value
Core Concepts Explained
Place Value
Value of a digit depends on its position in the number
Tens Place
Left digit in 2-digit numbers (groups of 10)
Ones Place
Right digit in 2-digit numbers (individual units)
Comparison
Determining greater, lesser, or equal relationships
Key Definitions:

Place Value: The value of a digit based on its position in a number (tens, ones)

Comparison: Determining the relationship between two numbers using symbols

Tens Place: The leftmost digit in a 2-digit number representing groups of 10

Ones Place: The rightmost digit in a 2-digit number representing individual units

Greater Than (>): Symbol indicating the first number is larger

Less Than (<): Symbol indicating the first number is smaller

Equal (=): Symbol indicating both numbers have the same value

Core Rules and Laws:

• Rule 1: Always compare tens first when comparing 2-digit numbers

• Rule 2: If tens are equal, compare the ones digits

• Rule 3: More tens always means a greater number

• Rule 4: When tens are the same, more ones determine the greater number

• Rule 5: Equal tens and equal ones mean equal numbers

• Law: Place value priority: tens > ones (tens have higher priority)

Step-by-Step Method:
  1. Step 1: Identify tens and ones in each number
  2. Step 2: Compare tens digits (left to right)
  3. Step 3: If tens are equal, compare ones digits
  4. Step 4: Select appropriate comparison symbol
  5. Step 5: Verify by checking actual values
Tip 1: Remember: 1 ten = 10 ones, so tens matter more!
Tip 2: The comparison symbol opens toward the larger number.
Tip 3: Draw base-10 blocks to visualize numbers.
Tip 4: Say numbers out loud: "thirty-four" vs "twenty-seven".
Common Pitfalls: Comparing ones first, forgetting tens priority, mixing up symbols.
Memory Aids: "Tens come first!", "More tens win!", "Symbol mouth eats bigger number".
Key Takeaways:

• Always start comparing from the left (tens place)

• Tens have higher priority than ones in comparison

• Use visual models like base-10 blocks for understanding

• Practice regularly to build number sense

• Remember: 25 = 20 + 5 (2 tens + 5 ones)

Exercises 1 to 3 Solutions
1 Basic comparison
Exercise 1
Compare 56 and 48. Which number is greater?
Use the symbols >, <, or =
Step 1: Identify place values
5
6
?
4
8

56 = 5 tens + 6 ones

48 = 4 tens + 8 ones

Step 2: Compare tens first

56 has 5 tens, 48 has 4 tens

Since 5 > 4, then 56 > 48

Step 3: Visual representation
56 =
5 tens + 6 ones
48 =
4 tens + 8 ones
Step 4: Write the answer

56 > 48

56 > 48
Explanation:

56 is greater than 48 because 5 tens (50) is greater than 4 tens (40), even though 56 has fewer ones than 48.

2 Equal numbers
Exercise 2
Compare 37 and 37. Are they equal?
Use the symbols >, <, or =
Step 1: Identify place values
3
7
?
3
7

37 = 3 tens + 7 ones

37 = 3 tens + 7 ones

Step 2: Compare tens

Both numbers have 3 tens

3 = 3 (tens are equal)

Step 3: Compare ones

Both numbers have 7 ones

7 = 7 (ones are equal)

Step 4: Write the answer

Since both tens and ones are equal, 37 = 37

37 = 37
Explanation:

37 equals 37 because both numbers have identical tens and ones digits.

3 Same tens, different ones
Exercise 3
Compare 42 and 45. Which number is smaller?
Use the symbols >, <, or =
Step 1: Identify place values
4
2
?
4
5

42 = 4 tens + 2 ones

45 = 4 tens + 5 ones

Step 2: Compare tens

Both numbers have 4 tens

4 = 4 (tens are equal)

Step 3: Compare ones

42 has 2 ones, 45 has 5 ones

Since 2 < 5, then 42 < 45

Step 4: Write the answer

42 < 45

42 < 45
Explanation:

42 is less than 45 because they have the same tens (4), but 2 ones is less than 5 ones.

Exercises 4 to 5 Solutions
4 Advanced comparison
Exercise 4
Compare 73 and 69. Which number is greater?
Use the symbols >, <, or =
Step 1: Identify place values
7
3
?
6
9

73 = 7 tens + 3 ones

69 = 6 tens + 9 ones

Step 2: Compare tens first

73 has 7 tens, 69 has 6 tens

Since 7 > 6, then 73 > 69

Step 3: Note about ones

Even though 73 has only 3 ones and 69 has 9 ones, the tens determine the comparison

7 tens = 70, while 6 tens = 60

Step 4: Write the answer

73 > 69

73 > 69
Explanation:

73 is greater than 69 because 7 tens (70) is greater than 6 tens (60), regardless of the ones digits.

5 Ordering numbers
Exercise 5
Arrange these numbers from least to greatest: 54, 47, 54, 61, 47
Use place value to order them correctly
Step 1: Identify place values for each number

54 = 5 tens + 4 ones

47 = 4 tens + 7 ones

54 = 5 tens + 4 ones

61 = 6 tens + 1 one

47 = 4 tens + 7 ones

Step 2: Group by tens

Numbers with 4 tens: 47, 47

Numbers with 5 tens: 54, 54

Numbers with 6 tens: 61

Step 3: Order within each group

Within 4 tens group: 47 = 47

Within 5 tens group: 54 = 54

Within 6 tens group: just 61

Step 4: Combine in ascending order

Start with lowest tens (4), then 5, then 6

Final order: 47, 47, 54, 54, 61

47, 47, 54, 54, 61
Explanation:

From least to greatest: 47, 47, 54, 54, 61. We ordered by tens first (4, 5, 6), then considered the repeated numbers.

Questions & Answers

Question: I don't understand why 28 is bigger than 35 sometimes. Can you explain?

Answer: Actually, 28 is NEVER bigger than 35! Let me explain why 35 is always greater than 28:

  • 35 = 3 tens + 5 ones = 30 + 5 = 35
  • 28 = 2 tens + 8 ones = 20 + 8 = 28
  • Compare tens first: 3 tens > 2 tens, so 35 > 28
  • Visual: 35 has 3 groups of 10 (30) plus 5 more, while 28 has only 2 groups of 10 (20) plus 8 more

The key rule: Always compare tens first! Since 3 > 2, then 35 > 28. The ones digits (5 vs 8) don't matter here because the tens already determine the answer.

Remember: 1 ten = 10 ones, so tens have much more value than ones!

Question: My child struggles with the comparison symbols. How can I make this easier?

Answer: Here are effective strategies to help with comparison symbols:

  • Alligator Method: Imagine the symbol is an alligator's mouth that always wants to eat the bigger number: 5 > 3 (mouth opens to 5) and 2 < 8 (mouth opens to 8)
  • L Method: The less than symbol < looks like the letter L for "Less than"
  • Point Method: The pointy end always points to the smaller number: 4 < 7 (pointy end points to 4)
  • Hands Method: Make > with your right hand and < with your left hand

Practice with real objects: Give your child 5 blocks and 3 blocks, ask which pile is bigger, then introduce the symbol 5 > 3.

Use everyday comparisons: "I have 3 cookies, you have 5 cookies. Who has more? 5 > 3!"

Question: Why do we need to learn place value? It seems too hard.

Answer: Place value is super important! Here's why:

  • Real-world connections: Money (tens of dollars, ones of dollars), ages, house numbers
  • Number sense: Helps you understand what numbers really mean (54 = 50 + 4)
  • Easier math: Makes adding and subtracting much simpler
  • Future success: Needed for bigger numbers and more complex math

Think of place value like organizing your room - everything has a place, so it's easier to find what you need!

Practice tip: Count by tens first (10, 20, 30...) then add the ones. This builds good habits!

It might seem hard now, but with practice, place value becomes natural and very helpful!