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.

Solution: Exercises 1 to 3
1 Comparing 2-digit numbers
Exercise 1
Compare 34 and 27. Which number is greater?
Use the symbols >, <, or =
Definition:

Place value: In a 2-digit number, the left digit represents tens and the right digit represents ones.

Comparison method:
  1. Compare the tens digits first
  2. If tens are equal, compare the ones digits
  3. Use comparison symbols: > (greater than), < (less than), = (equal)
3
4
?
2
7
3 tens 4 ones
2 tens 7 ones
Step 1: Compare tens digits

34 has 3 tens, 27 has 2 tens

Since 3 > 2, then 34 > 27

Step 2: Visual representation
34 =
3 tens + 4 ones
27 =
2 tens + 7 ones
Step 3: Write the comparison

34 > 27

34 > 27
Final answer:

34 is greater than 27 because 3 tens is greater than 2 tens.

Applied rules:

• Place value rule: Tens come first when comparing 2-digit numbers

• Comparison rule: Start from the left (highest place value)

• Symbol rule: > means greater than, < means less than

2 Equal numbers comparison
Exercise 2
Compare 45 and 45. Are they equal?
Use the symbols >, <, or =
Definition:

Equal numbers: Two numbers are equal if they have the same value in every place.

4
5
?
4
5
4 tens 5 ones
4 tens 5 ones
Step 1: Compare tens digits

45 has 4 tens, 45 has 4 tens

Tens are equal: 4 = 4

Step 2: Compare ones digits

45 has 5 ones, 45 has 5 ones

Ones are equal: 5 = 5

Step 3: Write the comparison

Since both tens and ones are equal, 45 = 45

45 = 45
Final answer:

45 equals 45 because both numbers have the same tens and ones.

Applied rules:

• Equality rule: Numbers are equal when all place values match

• Comparison sequence: Tens first, then ones

• Symbol usage: = means equal value

3 Same tens, different ones
Exercise 3
Compare 63 and 68. Which number is smaller?
Use the symbols >, <, or =
Definition:

Same tens comparison: When tens are equal, compare ones to determine which number is greater.

6
3
?
6
8
6 tens 3 ones
6 tens 8 ones
Step 1: Compare tens digits

63 has 6 tens, 68 has 6 tens

Tens are equal: 6 = 6

Step 2: Compare ones digits

63 has 3 ones, 68 has 8 ones

Since 3 < 8, then 63 < 68

Step 3: Visual representation
63 =
6 tens + 3 ones
68 =
6 tens + 8 ones
Step 4: Write the comparison

63 < 68

63 < 68
Final answer:

63 is less than 68 because they have the same tens but 3 ones is less than 8 ones.

Applied rules:

• Same tens rule: When tens are equal, compare ones

• Comparison order: Always compare from highest place value

• Symbol meaning: < means smaller number comes first

Place Value Rules and Methods
25 = 2 tens + 5 ones
Place Value Representation
Rule 1
Compare TENS first
Start from the left
Rule 2
If tens equal, compare ONES
Move to next place
Rule 3
Use >, <, or =
Comparison symbols
Key definitions:

Tens place: The left digit in a 2-digit number (represents groups of 10)

Ones place: The right digit in a 2-digit number (represents individual units)

Comparison: Determining which number is greater, lesser, or equal

Complete methodology:
  1. Identify place values: Separate tens and ones in each number
  2. Compare tens: Look at the tens digits first
  3. If tens equal: Compare the ones digits
  4. Select symbol: Choose >, <, or = based on comparison
Tip 1: Always start comparing from the left (tens place).
Tip 2: More tens always mean a bigger number.
Tip 3: When tens are same, more ones make the bigger number.
Common errors: Comparing ones first, forgetting to compare tens, mixing up symbols.
Memory aid: "Biggest tens win!" If tens tie, "biggest ones win!"
Place Value Comparison Rules:

• Rule 1: Compare tens digits first (left to right)

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

• Rule 3: 35 > 25 because 3 > 2 (more tens)

• Rule 4: 42 < 47 because 4 = 4 (same tens) but 2 < 7 (fewer ones)

• Rule 5: 58 = 58 because 5 = 5 and 8 = 8 (all digits match)

Solution: Exercises 4 to 5
4 Mixed comparison
Exercise 4
Compare 71 and 69. Which number is greater?
Use the symbols >, <, or =
Definition:

Mixed comparison: Comparing numbers where one has more tens but fewer ones than the other.

7
1
?
6
9
7 tens 1 one
6 tens 9 ones
Step 1: Compare tens digits

71 has 7 tens, 69 has 6 tens

Since 7 > 6, then 71 > 69 (tens decide the outcome)

Step 2: Note about ones

Even though 71 has only 1 one and 69 has 9 ones, the tens determine the comparison

7 tens = 70, while 6 tens = 60, so 71 > 69

Step 3: Verification

71 = 70 + 1 = 71

69 = 60 + 9 = 69

Since 71 > 69, our comparison is correct

71 > 69
Final answer:

71 is greater than 69 because 7 tens is greater than 6 tens, even though 71 has fewer ones.

Applied rules:

• Priority rule: Tens place has higher priority than ones

• Override rule: More tens always beats fewer tens

• Verification rule: Check by converting to total value

5 Multiple comparisons
Exercise 5
Arrange these numbers from least to greatest: 42, 38, 42, 51, 38
Use place value to order them correctly
Definition:

Ordering numbers: Arranging numbers from smallest to largest (ascending) or largest to smallest (descending).

Step 1: Organize numbers with place values
38 =
3
8
3 tens 8 ones
42 =
4
2
4 tens 2 ones
42 =
4
2
4 tens 2 ones
51 =
5
1
5 tens 1 one
38 =
3
8
3 tens 8 ones
Step 2: Group by tens

Numbers with 3 tens: 38, 38

Numbers with 4 tens: 42, 42

Numbers with 5 tens: 51

Step 3: Order within each group

Within 3 tens group: 38 = 38 (both equal)

Within 4 tens group: 42 = 42 (both equal)

Within 5 tens group: just 51

Step 4: Combine in ascending order

Start with lowest tens (3), then 4, then 5

Final order: 38, 38, 42, 42, 51

38, 38, 42, 42, 51
Final answer:

From least to greatest: 38, 38, 42, 42, 51

Applied rules:

• Grouping rule: Group numbers by tens to organize comparison

• Ascending order: Smallest to largest

• Place value priority: Tens determine major ordering

Place Value Comparison Laws and Methods
23 = 2 tens + 3 ones
Place Value Decomposition
Key definitions:

Place value: The value of a digit based on its position in a number

Comparison: Determining the relationship between two numbers using >, <, or =

Ascending order: Arranging numbers from smallest to largest

Descending order: Arranging numbers from largest to smallest

Complete methodology:
  1. Analyze each number: Identify tens and ones in each number
  2. Compare systematically: Start with tens, then ones if needed
  3. Select appropriate symbol: Use >, <, or = based on comparison
  4. Verify result: Double-check by considering actual value
Tip 1: Draw ten sticks and one dots to visualize numbers.
Tip 2: Remember: 1 ten = 10 ones, so tens matter more.
Tip 3: Count by tens first: 10, 20, 30, etc., then add ones.
Tip 4: Practice saying numbers: "thirty-four" has more tens than "twenty-seven".
Key insight: The number of tens determines the primary comparison.
Visual aid: Use base-10 blocks or drawings to represent numbers.
Memory trick: "More tens, more wins!" unless tens are equal.
Place Value Comparison Laws:

• Law 1: Tens place has priority over ones place

• Law 2: If tens differ, the number with more tens is greater

• Law 3: If tens are equal, compare ones to determine greater number

• Law 4: Equal tens and equal ones mean equal numbers

• Law 5: The comparison symbol opens toward the larger number

Place Value Comparison Infographic
📊
Comparison Strategy

1. Look at tens digit first

2. If tens equal, check ones

3. Use comparison symbols:

> (opens to larger)

< (points to smaller)

= (numbers equal)

Base-10 Model

34 = 3 tens blocks + 4 ones

27 = 2 tens blocks + 7 ones

34 > 27 (more tens)

Common Mistakes

❌ Comparing ones first

❌ Forgetting to check tens

❌ Mixing up symbols

✅ Always tens first!

Memory Aid

"Tens come first!"

"Bigger tens win!"

"If tens tie, ones decide"

Symbol mouth eats bigger number

Questions & Answers

Question: I have trouble remembering which way the > and < symbols go. How can I remember which is which?

Answer: Great question! Here are some helpful memory tricks:

  • Alligator Method: Think of the symbol as an alligator's mouth that always wants to eat the bigger number: 5 > 3 (mouth opens to 5) and 3 < 5 (mouth opens to 5)
  • L Method: The less than symbol < looks like the letter L for "Less than"
  • Arrow Method: The pointy end always points to the smaller number: 2 < 8 (arrow points to 2)

Practice with examples: 7 > 4 (7 is bigger, so mouth opens to 7) and 4 < 7 (mouth still opens to 7, the bigger number).

The equal sign = means both sides have the same value.

Question: My child keeps comparing the ones digit first instead of the tens. How can I help them remember the correct order?

Answer: This is a very common mistake! Try these strategies:

  • Left-to-right rule: "Always start reading from the left, like reading words!"
  • Value importance: Explain that tens are worth more (1 ten = 10 ones), so they matter more
  • Visual aids: Use base-10 blocks - show that 1 ten stick is longer than 10 individual ones
  • Rhyme method: "Tens first, then ones, that's how the comparison's done!"

Practice with examples like 29 vs 31: "Which has more tens? 2 or 3? So 31 is bigger, even though 9 > 1 in the ones place."

Consistent practice with the "tens first" mantra will help build the habit.

Question: Why do we need to learn place value? It seems hard to compare numbers this way.

Answer: Great question! Place value helps us understand numbers better and makes math easier! Here's why it's important:

  • Real-world applications: Money (tens of dollars, ones of dollars), age, counting objects
  • Better number sense: Understanding that 45 is made of 40 + 5 helps with addition/subtraction
  • Faster comparisons: Once you know place value, you can quickly see that 63 is bigger than 58
  • Foundation for future math: You'll need place value for adding, subtracting, and working with bigger numbers

Think of place value like organizing your toys - it's easier to find what you need when things are in the right place!

Practice with fun activities like counting groups of 10 and leftover ones.