Solved Exercises on Comparing Numbers with Place Value in Grade 1

Master place value comparison: tens and ones, greater than less than, comparison strategies through these 5 detailed exercises.

Solution: Exercises 1 to 3
1 Compare numbers using tens and ones
Exercise 1
Compare 23 and 32. Which number is greater?
Write >, <, or =.
Definition:

Place value: Each digit in a number has a value based on its position. In two-digit numbers, the left digit is the TENS place and the right digit is the ONES place.

Comparison method:
  1. Look at the tens place first
  2. If tens are equal, compare the ones place
  3. Greater number has more tens, or same tens but more ones
Number 1
23 = 2 tens + 3 ones
Number 2
32 = 3 tens + 2 ones
Step 1: Identify tens place

23 has 2 tens, 32 has 3 tens

Step 2: Compare tens

Since 2 < 3, then 23 < 32

Step 3: Write the comparison

23 < 32

23 < 32
Final answer:

23 < 32 because 2 tens is less than 3 tens

Applied rules:

• Place value: Tens place is more important than ones place

• Comparison: Always compare from left to right (highest place value first)

• Symbols: > means greater than, < means less than, = means equal

2 Equal tens, compare ones
Exercise 2
Compare 45 and 48. Which number is greater?
Write >, <, or =.
Definition:

Equal tens comparison: When tens are the same, compare the ones place to determine which number is greater.

Number 1
45 = 4 tens + 5 ones
Number 2
48 = 4 tens + 8 ones
Comparison
45 < 48
Step 1: Identify tens place

45 has 4 tens, 48 has 4 tens

Step 2: Compare tens

Since 4 = 4, we move to ones place

Step 3: Compare ones

5 ones vs 8 ones, since 5 < 8, then 45 < 48

45 < 48
Final answer:

45 < 48 because tens are equal but 5 ones is less than 8 ones

Applied rules:

• Place value: When tens are equal, ones determine the greater number

• Sequential comparison: Compare higher place values first, then move to lower ones

• Equality check: If both tens and ones are equal, the numbers are equal

3 Greater tens comparison
Exercise 3
Compare 57 and 49. Which number is greater?
Write >, <, or =.
Definition:

Greater tens rule: When comparing two-digit numbers, the number with more tens is always greater, regardless of the ones place.

Number 1
57 = 5 tens + 7 ones
Number 2
49 = 4 tens + 9 ones
Result
57 > 49
Step 1: Identify tens place

57 has 5 tens, 49 has 4 tens

Step 2: Compare tens

Since 5 > 4, then 57 > 49

Step 3: Note about ones

Even though 49 has more ones (9 > 7), 57 is still greater because it has more tens

57 > 49
Final answer:

57 > 49 because 5 tens is greater than 4 tens

Applied rules:

• Tens dominance: Tens place is always more significant than ones place

• Comparison hierarchy: Tens first, then ones if needed

• Value comparison: More tens always means a greater number

Place Value Comparison Rules and Methods
23 = 2 tens + 3 ones
Place Value Breakdown
Rule 1
Compare TENS first
Tens place is more important
Rule 2
If TENS equal, compare ONES
Then check ones place
Rule 3
More TENS = Greater Number
Always compare left to right
Key definitions:

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

Tens place: The leftmost digit in a two-digit number represents groups of ten

Ones place: The rightmost digit in a two-digit number represents individual units

Complete methodology:
  1. Break down numbers: Identify tens and ones in each number
  2. Compare tens: Look at the tens place first
  3. Equal tens: If tens are equal, compare ones place
  4. Write comparison: Use >, <, or = symbols
Tip 1: Always start comparing from the left (tens place).
Tip 2: If tens are the same, only then look at ones.
Tip 3: Remember: 1 ten = 10 ones, so tens matter more!
Tip 4: Draw base-10 blocks to visualize the comparison.
Common errors: Forgetting to compare tens first, thinking more ones always means a greater number.
Key memory aid: "Tens come first, then ones - like reading words!"
Comparison symbols to remember:

• Greater than: > (opens toward the bigger number)

• Less than: < (points to the smaller number)

• Equal to: = (both sides are the same)

• Memory trick: The symbol looks like an alligator's mouth eating the bigger number!

Visual Place Value Comparison
Understanding Place Value Visually
Visual representation of comparing 24 and 31:
24 = 2 tens + 4 ones
31 = 3 tens + 1 one
Since 3 tens > 2 tens, then 31 > 24

Analysis: The chart shows how place value affects the overall value of numbers.

  • 24 = 20 + 4 = 24 total units
  • 31 = 30 + 1 = 31 total units
  • Even though 24 has more ones (4 > 1), 31 is greater because it has more tens

Questions & Answers

Question: I don't understand why 19 is less than 21 even though 9 is bigger than 1. Shouldn't the number with the bigger last digit be greater?

Answer: Great question! This is a common confusion about place value. Let me explain:

  • In the number 19: 1 is in the tens place and 9 is in the ones place
  • In the number 21: 2 is in the tens place and 1 is in the ones place
  • The tens place is worth much more than the ones place (1 ten = 10 ones)

So when comparing 19 and 21:

  • 19 = 1 ten + 9 ones = 10 + 9 = 19 total
  • 21 = 2 tens + 1 one = 20 + 1 = 21 total

Even though 9 ones is more than 1 one, having 2 tens (20) is more valuable than having 1 ten (10). That's why 21 > 19.

Think of it like money: $21 is more than $19 because the "2" in the tens place represents $20, which is more than the $10 represented by the "1" in the tens place of $19.

Question: My child is struggling with the concept of place value. How can I help them understand that the position of a digit matters?

Answer: Here are effective ways to teach place value to young learners:

  • Use manipulatives: Base-10 blocks, where a single cube represents 1 and a stick of 10 cubes represents 10
  • Draw representations: Show 23 as 2 groups of 10 sticks and 3 individual dots
  • Real-world examples: Use money ($1 bills vs $10 bills) or grouping objects (eggs in cartons of 10)
  • Position games: Have your child physically move digits to different positions and see how the value changes

Try this activity: Give your child 23 objects and have them group them into sets of 10. They'll see 2 full groups of 10 and 3 remaining, helping them visualize "2 tens and 3 ones."

Remember, the key concept is that the same digit has different values depending on where it sits in the number. The "2" in 23 is worth 20, while the "2" in 32 is worth only 2.

Question: How do I remember which way the greater than and less than signs go? I keep mixing them up.

Answer: Here are some fun memory tricks to remember the symbols:

  • Alligator method: The symbol looks like an alligator's mouth that always wants to eat the bigger number!
  • Less than sign (<): It looks like the letter "L" for "Less than"
  • Greater than sign (>): It does NOT look like "L", so it's not less than
  • Arrow pointing: The narrow end of the symbol points to the smaller number

Examples:

  • 15 > 12 (the alligator eats 15 because it's bigger)
  • 8 < 14 (the arrow points to 8, the smaller number)

Practice drawing the symbols while saying "the big end goes to the big number" until it becomes automatic!

Question: What activities can I use in class to reinforce place value comparison skills?

Answer: Here are engaging classroom activities for place value comparison:

  • Place value war: Students draw two cards, make the largest number possible, then compare with a partner
  • Base-10 building: Give students base-10 blocks to build numbers and compare their values
  • Number line walks: Have students physically move along a number line to compare values
  • Place value charts: Fill in charts showing tens and ones, then compare
  • Real-world connections: Compare prices, ages, or quantities using place value

Interactive games work especially well: create a "greater than" and "less than" alligator puppet that "eats" the larger number. Also try digital tools where students drag and drop symbols between numbers.

Consistent practice with visual aids helps students internalize the concept that position determines value.

Question: How do I help my child practice place value comparison at home?

Answer: Here are practical home activities for practicing place value comparison:

  1. Daily number practice: Each day, pick two numbers and compare them using place value
  2. Card games: Use playing cards to create two-digit numbers and compare
  3. Coin counting: Count coins by tens and ones, then compare totals
  4. Household items: Count groups of items (forks, books, toys) and compare quantities
  5. Calendar math: Compare dates, ages, or room numbers using place value

Make it fun with these ideas:

  • Create a "number comparison journal" with daily challenges
  • Use food items like raisins or crackers to represent tens and ones
  • Play "guess my number" games where you give clues about place value

Regular practice with concrete materials makes abstract concepts more accessible!