Solved Exercises on Ordering Numbers in Grade 1

Master number ordering: arranging from least to greatest and greatest to least through these 5 detailed exercises.

Solution: Exercises 1 to 3
1 Ordering from least to greatest
Exercise 1
Put these numbers in order from least to greatest:
42, 28, 56, 31, 42
Definition:

Least to greatest: Arranging numbers from smallest to largest value

Ordering method:
  1. Compare all numbers using place value
  2. Find the number with the smallest tens digit
  3. If tens are equal, compare ones digits
  4. Arrange from smallest to largest
1
Compare tens: 28(tens=2), 31(tens=3), 42(tens=4), 42(tens=4), 56(tens=5)
2
Smallest tens is 2, so 28 is first
3
Next smallest tens is 3, so 31 is second
4
Next tens is 4, compare 42 and 42 (equal, so both next)
5
Largest tens is 5, so 56 is last
Step 1: Identify place values

28: 2 tens, 8 ones; 31: 3 tens, 1 one; 42: 4 tens, 2 ones; 56: 5 tens, 6 ones

Step 2: Compare tens first

2 < 3 < 4 < 5, so 28 < 31 < 42 < 56

Step 3: Arrange in order

28, 31, 42, 42, 56

28
→
31
→
42
→
42
→
56
28, 31, 42, 42, 56
Final answer:

28, 31, 42, 42, 56

Applied rules:

• Place value priority: Compare tens first, then ones

• Ascending order: Numbers increase from left to right

• Equality: Equal numbers can appear consecutively

2 Ordering from greatest to least
Exercise 2
Put these numbers in order from greatest to least:
73, 68, 73, 59, 81
Definition:

Greatest to least: Arranging numbers from largest to smallest value

1
Compare tens: 59(tens=5), 68(tens=6), 73(tens=7), 73(tens=7), 81(tens=8)
2
Largest tens is 8, so 81 is first
3
Next largest tens is 7, compare 73 and 73 (equal)
4
Next tens is 6, so 68 is next
5
Smallest tens is 5, so 59 is last
Step 1: Identify place values

81: 8 tens, 1 one; 73: 7 tens, 3 ones; 68: 6 tens, 8 ones; 59: 5 tens, 9 ones

Step 2: Compare tens first

8 > 7 > 6 > 5, so 81 > 73 > 68 > 59

Step 3: Arrange in descending order

81, 73, 73, 68, 59

81
→
73
→
73
→
68
→
59
81, 73, 73, 68, 59
Final answer:

81, 73, 73, 68, 59

Applied rules:

• Descending order: Numbers decrease from left to right

• Place value priority: Compare tens first, then ones

• Equality: Equal numbers can appear consecutively

3 Mixed ordering with same tens
Exercise 3
Put these numbers in order from least to greatest:
47, 43, 49, 41, 45
Definition:

Same tens comparison: When tens digits are equal, compare ones digits

Number Tens Ones Position
41 4 1 1st
43 4 3 2nd
45 4 5 3rd
47 4 7 4th
49 4 9 5th
Step 1: Notice all have same tens

All numbers have 4 tens: 41, 43, 45, 47, 49

Step 2: Compare ones digits

Ones: 1 < 3 < 5 < 7 < 9

Step 3: Arrange by ones

41, 43, 45, 47, 49

41
→
43
→
45
→
47
→
49
41, 43, 45, 47, 49
Final answer:

41, 43, 45, 47, 49

Applied rules:

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

• Ones comparison: Use ascending order for ones

• Consistent pattern: Numbers follow logical sequence

Ordering Rules and Strategies
Least to Greatest: A < B < C < D...
Ascending Order
Ascending
Smallest → Largest
Least to greatest
Descending
Largest → Smallest
Greatest to least
Place Value
Tens > Ones
Compare priority
Key definitions:

Ordering: Arranging numbers in a specific sequence based on their value

Ascending order: From smallest to largest (least to greatest)

Descending order: From largest to smallest (greatest to least)

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

Ordering methodology:
  1. Identify all numbers: List the numbers to be ordered
  2. Compare place values: Start with tens, then ones
  3. Determine sequence: Decide if ascending or descending
  4. Arrange systematically: Place from smallest/largest to largest/smallest
Tip 1: Always compare tens first, then ones if needed.
Tip 2: Use a number line to visualize the order.
Tip 3: Circle or highlight the smallest/largest number first.
Tip 4: Practice with physical objects to build intuition.
Comparison priority: Tens place > Ones place in determining order.
Equal numbers: Identical numbers can appear consecutively in order.
Ordering rules to remember:

• Compare tens digits first in two-digit numbers

• If tens are equal, compare ones digits

• Ascending: smallest to largest (increasing)

• Descending: largest to smallest (decreasing)

• Equal numbers maintain their relative position

Ordering Strategy Guide
📊
Least to Greatest
Numbers increase from left to right
23 < 45 < 67 < 89
Greatest to Least
Numbers decrease from left to right
89 > 67 > 45 > 23
Place Value First
Always compare tens before ones
52 vs 48 → 5 > 4 → 52 > 48
Systematic Approach
Find smallest/largest, then next, etc.
23, 45, 12 → 12, 23, 45
Solution: Exercises 4 to 5
4 Ordering with zeros in ones place
Exercise 4
Put these numbers in order from greatest to least:
60, 58, 62, 55, 60
Definition:

Zero in ones place: Zero still represents a value in the ones position

Number Tens Ones Position (Desc)
62 6 2 1st
60 6 0 2nd
60 6 0 3rd
58 5 8 4th
55 5 5 5th
Step 1: Compare tens digits

62, 60, 60 have 6 tens; 58, 55 have 5 tens

Step 2: Among 6 tens, compare ones

62: ones=2, 60: ones=0, 60: ones=0 → 62 > 60 = 60

Step 3: Among 5 tens, compare ones

58: ones=8, 55: ones=5 → 58 > 55

Step 4: Arrange in descending order

62, 60, 60, 58, 55

62
→
60
→
60
→
58
→
55
62, 60, 60, 58, 55
Final answer:

62, 60, 60, 58, 55

Applied rules:

• Zero placeholder: Zero in ones place still has value

• Descending priority: Higher tens first, then higher ones

• Equality handling: Equal numbers maintain consecutive positions

5 Complex ordering challenge
Exercise 5
Put these numbers in order from least to greatest:
84, 79, 84, 72, 81, 79
Definition:

Complex ordering: Multiple occurrences of same numbers requiring careful systematic arrangement

Number Tens Ones Group Position
72 7 2 70s 1st
79 7 9 70s 2nd
79 7 9 70s 3rd
81 8 1 80s 4th
84 8 4 80s 5th
84 8 4 80s 6th
Step 1: Group by tens

70s group: 72, 79, 79; 80s group: 81, 84, 84

Step 2: Order within each group

70s: 72 < 79 = 79; 80s: 81 < 84 = 84

Step 3: Combine groups in order

70s group first, then 80s group

Step 4: Final arrangement

72, 79, 79, 81, 84, 84

72
→
79
→
79
→
81
→
84
→
84
72, 79, 79, 81, 84, 84
Final answer:

72, 79, 79, 81, 84, 84

Applied rules:

• Grouping strategy: Organize by tens place first

• Within-group ordering: Order numbers within each tens group

• Sequential combination: Join groups in ascending tens order

Comprehensive Summary: Ordering Numbers
A₁ < A₂ < A₃ < ... < Aₙ (ascending)
Ordered Sequence
Key definitions:

Ordering: The process of arranging numbers in a specific sequence based on their value

Ascending order: Numbers arranged from smallest to largest (least to greatest)

Descending order: Numbers arranged from largest to smallest (greatest to least)

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

Sequence: An ordered list of numbers following a specific pattern

Complete ordering methodology:
  1. Identify all numbers: List all numbers to be ordered
  2. Determine place values: Separate tens and ones digits
  3. Decide order type: Ascending (least to greatest) or descending (greatest to least)
  4. Compare systematically: Use place value to determine relationships
  5. Arrange in sequence: Place numbers in the correct order
  6. Verify accuracy: Double-check that the sequence is correct
Tip 1: Always compare tens digits first - they have greater value than ones.
Tip 2: Use the "grouping method" - organize by tens, then order within groups.
Tip 3: Equal numbers can appear consecutively in the ordered sequence.
Tip 4: Practice with number lines to visualize the ordering process.
Place value hierarchy: Tens place > Ones place in determining numerical order.
Zero significance: Zero in ones place still contributes to the number's value.
Essential ordering rules:

• Tens priority: Always compare tens digits first in two-digit numbers

• Ones tiebreaker: Only compare ones digits when tens are equal

• Ascending order: Each number is greater than or equal to the previous

• Descending order: Each number is less than or equal to the previous

• Equality handling: Equal numbers maintain consecutive positions in sequence

Ordering Success Framework
📊
Place Value First
Compare tens before ones
47 vs 52 → 4 < 5 → 47 < 52
Ascending Order
Numbers increase left to right
23 < 45 < 67 < 89
Descending Order
Numbers decrease left to right
89 > 67 > 45 > 23
Grouping Method
Organize by tens, then order within
23,45,27 → 23,27,45
Key takeaways:

• Place value understanding is fundamental to accurate ordering

• Systematic approaches prevent missing numbers or incorrect sequences

• Both ascending and descending orders require the same comparison logic

• Practice with varied number sets builds confidence and fluency

Questions & Answers

Question: Why do we put 40 before 39 when ordering from least to greatest? Isn't 4 smaller than 3?

Answer: Great question! You're looking at just the digits, but we need to consider the whole number:

  • 40 means: 4 tens and 0 ones (40 total)
  • 39 means: 3 tens and 9 ones (39 total)
  • Comparison: 40 is greater than 39 because 4 tens (40) is more than 3 tens (30)

Think of it like having 4 bags of 10 candies vs 3 bags of 10 candies plus 9 loose candies. The 4 bags have more!

Always compare the tens first, then the ones if the tens are the same!

Question: My child gets confused when there are repeated numbers in the list. How should they handle that?

Answer: Repeated numbers are perfectly normal in ordering! Here's how to handle them:

  • Equal treatment: Numbers that are the same have equal value
  • Consecutive placement: Equal numbers appear next to each other in the sequence
  • No skipping: Don't eliminate duplicate numbers
  • Example: For 23, 27, 23 → order is 23, 23, 27

Practice with lists that have repeated numbers to build comfort with this concept.

Tip: Have your child circle or underline repeated numbers to identify them easily!

Question: How do I know if I should go from smallest to biggest or biggest to smallest?

Answer: Look for key words in the question:

  • Least to greatest: Start with smallest, end with largest
  • Greatest to least: Start with largest, end with smallest
  • Smallest to largest: Same as least to greatest
  • Largest to smallest: Same as greatest to least

Think of it like a race: "least to greatest" means the slowest runner first, fastest last.

"Greatest to least" means the fastest runner first, slowest last!

Always read the instructions carefully to see which order they want!

Question: How can I make ordering numbers more engaging for my child?

Answer: Make it hands-on and fun:

  • Number cards: Write numbers on cards and have your child physically arrange them
  • Race tracks: Use toy cars to "race" numbers from start to finish
  • Staircase: Arrange numbers like steps going up (ascending) or down (descending)
  • Real objects: Use toys, snacks, or household items to represent numbers

Turn it into a game: "Help the numbers find their homes in order!"

Tip: Start with smaller numbers and gradually increase complexity!

Question: How does ordering numbers connect to other mathematical concepts?

Answer: Number ordering is foundational for many advanced concepts:

  • Number sense: Understanding the relative magnitude of numbers
  • Estimation: Placing numbers on number lines and benchmarks
  • Operations: Understanding that addition increases and subtraction decreases
  • Data interpretation: Reading graphs and charts
  • Algebra: Solving inequalities and understanding variable relationships

Students who master ordering develop stronger mathematical reasoning skills.

Example: Understanding that 45 < 67 helps with problems like "What number is between 45 and 67?"

This skill supports all future mathematical learning!