Solved Exercises on Comparing Numbers Using Place Value in Grade 1

Master comparing numbers using place value: greater than, less than, equal to with visual representations through these 3 detailed exercises.

Solution: Exercises 1 to 3
1 Comparing Numbers with Different Tens
Exercise 1
Compare 45 and 37 using place value. Which number is greater?
Explain your reasoning.
Definition:

Comparing numbers: Determining if one number is greater than (>), less than (<), or equal to (=) another number using place value.

Comparison method:
  1. Compare the tens digits first
  2. If tens are different, the number with more tens is greater
  3. If tens are the same, compare the ones digits
Number 1
45
TENS DIGIT
4
ONES DIGIT
5
Number 2
37
TENS DIGIT
3
ONES DIGIT
7
vs
Step 1: Compare tens digits

45 has 4 tens, 37 has 3 tens

Since 4 > 3, then 45 > 37

Step 2: Since tens are different, no need to compare ones

When tens are different, the number with more tens is always greater

Step 3: Write the comparison

45 > 37 (45 is greater than 37)

45 > 37
Final answer:

45 is greater than 37 because 45 has 4 tens and 37 has 3 tens. Since 4 > 3, then 45 > 37.

Applied rules:

• Place value comparison: Compare tens first, then ones if needed

• Greater than: When tens differ, the number with more tens is greater

• Comparison logic: 4 tens (40) is more than 3 tens (30)

2 Comparing Numbers with Same Tens
Exercise 2
Compare 63 and 68 using place value. Which number is smaller?
Explain your reasoning.
Definition:

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

63
<
68
NUMBER
63
TENS
6
ONES
3
NUMBER
68
TENS
6
ONES
8
vs
Step 1: Compare tens digits

63 has 6 tens, 68 has 6 tens

Since 6 = 6, move to ones digits

Step 2: Compare ones digits

63 has 3 ones, 68 has 8 ones

Since 3 < 8, then 63 < 68

Step 3: Write the comparison

63 < 68 (63 is less than 68)

63 < 68
Final answer:

63 is smaller than 68 because both have 6 tens, but 63 has 3 ones while 68 has 8 ones. Since 3 < 8, then 63 < 68.

Applied rules:

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

• Less than: When ones differ and are in the same tens group

• Comparison logic: 63 = 60 + 3, 68 = 60 + 8, since 3 < 8, then 63 < 68

3 Equal Numbers
Exercise 3
Compare 54 and 54 using place value. Are these numbers equal?
Explain your reasoning.
Definition:

Equal numbers: Two numbers are equal when both their tens and ones digits are the same.

54
=
54
NUMBER
54
TENS
5
ONES
4
NUMBER
54
TENS
5
ONES
4
=
Step 1: Compare tens digits

Both numbers have 5 tens

Since 5 = 5, continue to ones

Step 2: Compare ones digits

Both numbers have 4 ones

Since 4 = 4, the numbers are equal

Step 3: Write the comparison

54 = 54 (54 is equal to 54)

Final answer:

54 and 54 are equal because both have 5 tens and 4 ones. When both tens and ones digits are the same, the numbers are equal.

Applied rules:

• Equality rule: Numbers are equal when both tens and ones digits match

• Comparison logic: 54 = 50 + 4 and 54 = 50 + 4, so they are identical

• Reflexive property: Any number is equal to itself

Comparison Rules and Methods
45 > 37 because 4 > 3 (tens)
Tens Comparison
Greater Than
58 > 43
More tens
Less Than
24 < 27
Same tens, fewer ones
Equal
65 = 65
Same tens and ones
Key Rule: Always compare tens first, then ones if needed.
Comparison Logic: More tens = greater number (unless ones compensate).
Tip 1: Think of tens as "big" groups and ones as "small" units.
Tip 2: Use visual aids like base-10 blocks to compare numbers.
Tip 3: Remember that 1 ten equals 10 ones (10 > 9).
Key Rules to Remember:

• Tens first: Always compare tens digits before ones digits

• Greater than: More tens means greater number

• Same tens: Compare ones digits when tens are equal

• Equal numbers: Both tens and ones digits must match

AB ? CD where A,C=tens, B,D=ones
General Comparison
Numbers Tens Comparison Ones Comparison Result 45 vs 37 4 > 3 Not needed 45 > 37 63 vs 68 6 = 6 3 < 8 63 < 68 54 vs 54 5 = 5 4 = 4 54 = 54 72 vs 69 7 > 6 Not needed 72 > 69
Additional Practice
4 Mixed Comparison Practice
Exercise 4
Compare the following pairs using place value:
a) 28 ___ 31
b) 45 ___ 42
c) 67 ___ 67
Definition:

Mixed practice: Combining different types of comparisons to strengthen understanding.

Part a: 28 ___ 31

28 has 2 tens, 31 has 3 tens

Since 2 < 3, then 28 < 31

Part b: 45 ___ 42

45 and 42 both have 4 tens

45 has 5 ones, 42 has 2 ones

Since 5 > 2, then 45 > 42

Part c: 67 ___ 67

Both numbers have 6 tens and 7 ones

Since both digits match, 67 = 67

Final answers:

a) 28 < 31

b) 45 > 42

c) 67 = 67

Applied rules:

• Consistency: Apply the same method to all parts of the problem

• Place value: Position determines the value of each digit

• Verification: Check each answer by reviewing place values

5 Problem Solving
Exercise 5
Sarah has 5 tens blocks and 3 ones blocks. Jake has 4 tens blocks and 8 ones blocks. Who has more blocks in total? Use place value to compare.
Definition:

Problem solving: Applying comparison concepts to real-world scenarios with visual representations.

Sarah's Number
53
TENS
5
ONES
3
Jake's Number
48
TENS
4
ONES
8
vs
Step 1: Determine Sarah's number

Sarah has 5 tens blocks and 3 ones blocks = 50 + 3 = 53

Step 2: Determine Jake's number

Jake has 4 tens blocks and 8 ones blocks = 40 + 8 = 48

Step 3: Compare using place value

Sarah's number (53) has 5 tens, Jake's number (48) has 4 tens

Since 5 > 4, then 53 > 48

Final answer:

Sarah has more blocks. Sarah has 53 blocks and Jake has 48 blocks. Since 53 > 48, Sarah has more.

Applied rules:

• Visual representation: Blocks help understand the concept concretely

• Place value comparison: Compare tens first, then ones if needed

• Application: Connect abstract math to real-world problems

Comprehensive Summary: Comparing Numbers Using Place Value
AB ? CD → Compare A vs C first, then B vs D if A=C
Comparison Algorithm
Key Definitions:

Comparing numbers: Determining if one number is greater than (>), less than (<), or equal to (=) another number.

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

Tens: Groups of 10 (1 ten = 10, 2 tens = 20, etc.).

Ones: Single units (1 one = 1, 2 ones = 2, etc.).

Greater than (>): One number is larger than another.

Less than (<): One number is smaller than another.

Equal (=): Two numbers have the same value.

Complete Methodology:
  1. Identify place values: Determine tens and ones in each number
  2. Compare tens first: Look at the tens digits of both numbers
  3. Make decision if different: If tens differ, greater tens means greater number
  4. Compare ones if equal: If tens are the same, compare the ones digits
  5. Write the comparison: Use >, <, or = symbols appropriately
Tip 1: Always start with tens - they are more significant than ones.
Tip 2: Think of tens as "big" groups of 10 and ones as "small" units.
Tip 3: Use visual aids like base-10 blocks to compare numbers.
Tip 4: Remember: 1 ten = 10 ones, so tens matter more than ones.
Common errors: Comparing ones before tens, forgetting to compare both places, misreading symbols.
Key insights: Place value comparison is fundamental for ordering numbers and arithmetic.
Core Rules and Principles:

• Primary rule: Always compare tens digits first

• Secondary rule: Only compare ones digits if tens are equal

• Greater than principle: More tens = greater number

• Same tens principle: Compare ones when tens are equal

• Equality principle: Both tens and ones must match for equality

Examples: 45>37, 63<68, 54=54
Concrete Examples
Memory aid: "Tens first, then ones if needed" - like looking at the bigger picture first.
Success check: If 45 > 37, then 45 should be further along the number line than 37. ✓
Golden Rule: When comparing two-digit numbers, the number with more tens is always greater, regardless of the ones digit. Only compare ones when tens are equal.

Questions & Answers

Question: Why do we compare the tens first? Why not the ones?

Answer: We compare tens first because tens are more valuable than ones. Think of it like this:

  • 1 ten = 10 ones, so tens are worth more
  • 4 tens (40) is more than 3 tens (30), even if the ones are different
  • It's like comparing bags of 10 marbles vs single marbles

For example: 41 vs 39

  • 41 has 4 tens (40) and 1 one (1) = 41 total
  • 39 has 3 tens (30) and 9 ones (9) = 39 total

Even though 39 has more ones (9 > 1), 41 is still greater because 4 tens (40) is more than 3 tens (30).

Question: My child is having trouble understanding the greater than (>) and less than (<) symbols. How can I help them remember which is which?

Answer: Here are some helpful memory tricks for the symbols:

  • Alligator method: The alligator mouth opens toward the bigger number (the alligator wants to eat the bigger meal!)
  • Arrow method: Think of the symbol as pointing to the smaller number
  • Character method: > looks like a "greater" g, < looks like an "less" l

Examples:

  • 5 > 3 (the alligator eats the 5 because it's bigger)
  • 2 < 7 (the alligator eats the 7 because it's bigger)

Practice with real objects: place 5 blocks on one side and 3 blocks on the other, then use the alligator mouth to show which is greater.

Question: What happens when two numbers have the same tens but different ones? Like 64 and 67?

Answer: When two numbers have the same tens digit, you compare the ones digits to determine which is greater:

For 64 and 67:

  • Both numbers have 6 tens (60)
  • 64 has 4 ones (4)
  • 67 has 7 ones (7)
  • Since 4 < 7, then 64 < 67

Think of it like having the same number of bags of 10 marbles (6 bags each), but one person has 4 extra marbles and the other has 7 extra marbles. The person with 7 extra marbles has more total marbles.

Rule: When tens are equal, the number with more ones is greater.