Worksheets Part 1: Basic Place Value (Problems 1-10)
1 Identify place values
Problem 1
Circle the hundreds digit in 648.
Definition:
Place value positions: From right to left: ones, tens, hundreds.
Step 1: Identify positions
From right to left: 8 (ones), 4 (tens), 6 (hundreds)
Step 2: Locate hundreds digit
The hundreds digit is the third digit from the right
Step 3: Circle the answer
Circle the digit 6
Answer:
The hundreds digit in 648 is 6.
2 Calculate place values
Problem 2
What is the value of the tens digit in 379?
Definition:
Digit value: The actual worth of a digit based on its position (digit × place value).
Step 1: Identify the tens digit
In 379, the tens digit is 7
Step 2: Calculate its value
Tens value = 7 × 10 = 70
Answer:
The value of the tens digit in 379 is 70.
3 Expanded form
Problem 3
Write 524 in expanded form.
Definition:
Expanded form: Writing a number as the sum of each digit's value.
Step 1: Break down each digit
5 is in the hundreds place: 5 × 100 = 500
2 is in the tens place: 2 × 10 = 20
4 is in the ones place: 4 × 1 = 4
Step 2: Write in expanded form
524 = 500 + 20 + 4
524 = 500 + 20 + 4
Answer:
524 = 500 + 20 + 4
4 Ordering numbers
Problem 4
Put these numbers in order from least to greatest: 421, 124, 214
Definition:
Number ordering: Compare numbers by examining digits from left to right (highest place value first).
Step 1: Compare hundreds place first
421: 4 hundreds, 124: 1 hundred, 214: 2 hundreds
So 124 is smallest, then 214, then 421
5 Number composition
Problem 5
What number is made up of 7 hundreds, 3 tens, and 5 ones?
Definition:
Number composition: Building a number from its place value components.
Step 1: Convert each component to its value
7 hundreds = 7 × 100 = 700
3 tens = 3 × 10 = 30
5 ones = 5 × 1 = 5
Step 2: Add all values together
700 + 30 + 5 = 735
Answer:
The number is 735.
6 Missing digit
Problem 6
In the number 8_6, if the tens digit is 4, what is the number?
Definition:
Missing digit problems: Finding unknown digits based on given information.
Step 1: Identify known information
Number format: 8_6 (hundreds = 8, ones = 6)
Tens digit is given as 4
Step 2: Fill in the missing digit
Replace blank with the tens digit: 846
Answer:
The number is 846.
7 Compare place values
Problem 7
In 666, which digit has the greatest value?
Definition:
Digit value comparison: Compare the actual worth of each digit based on position.
Step 1: Calculate each digit's value
Hundreds digit: 6 × 100 = 600
Tens digit: 6 × 10 = 60
Ones digit: 6 × 1 = 6
Step 2: Compare the values
600 > 60 > 6
Answer:
The hundreds digit (6) has the greatest value (600).
8 Zero in place value
Problem 8
What is the value of each digit in 905?
Definition:
Zero in place value: Zero holds the place but contributes 0 to the total value.
Step 1: Identify each digit and its position
9 in hundreds place, 0 in tens place, 5 in ones place
Step 2: Calculate each digit's value
9 × 100 = 900
0 × 10 = 0 (zero still holds the tens place)
5 × 1 = 5
Answer:
Hundreds value: 900, Tens value: 0, Ones value: 5
9 Visual representation
Problem 9
Show 427 using base ten blocks.
Definition:
Base ten blocks: Visual tools representing units (ones), rods (tens), and flats (hundreds).
100
100
100
100
10
10
1
1
1
1
1
1
1
Step 1: Break down 427 by place value
4 hundreds: 4 × 100 = 400
2 tens: 2 × 10 = 20
7 ones: 7 × 1 = 7
Step 2: Represent with blocks
4 hundred blocks (flats)
2 ten blocks (rods)
7 one blocks (units)
Answer:
4 hundred blocks, 2 ten blocks, 7 one blocks
10 Subtraction with place value
Problem 10
Subtract: 573 - 241
Definition:
Place value subtraction: Subtracting numbers by working with hundreds, tens, and ones separately.
Step 1: Align numbers by place value
573
- 241
-----
Step 2: Subtract ones place
3 - 1 = 2
Step 3: Subtract tens place
7 - 4 = 3
Step 4: Subtract hundreds place
5 - 2 = 3
Worksheets Part 2: Intermediate Problems (Problems 11-20)
11 Comparison
Problem 11
Which is greater: 634 or 643?
Definition:
Number comparison: Compare numbers by examining digits from left to right.
Step 1: Compare hundreds place
Both have 6 hundreds → Equal so far
Step 2: Compare tens place
634: 3 tens, 643: 4 tens
Since 4 > 3, 643 > 634
Answer:
643 is greater than 634.
12 Addition with place value
Problem 12
Add: 247 + 158
Definition:
Place value addition: Adding numbers by working with hundreds, tens, and ones separately.
ONES
7 + 8 = 15 → Write 5, carry 1
Step 1: Add ones place
7 + 8 = 15 → Write 5, carry 1 to tens
Step 2: Add tens place
4 + 5 + 1 (carry) = 10 → Write 0, carry 1 to hundreds
Step 3: Add hundreds place
2 + 1 + 1 (carry) = 4
13 Word problem
Problem 13
Sarah has 356 stickers. She gives 124 stickers to her friend. How many stickers does she have left?
Definition:
Word problem solving: Translating story problems into mathematical operations.
Step 1: Identify the operation
"Gives" indicates subtraction: 356 - 124
Step 2: Subtract each place
Hundreds: 3 - 1 = 2
Tens: 5 - 2 = 3
Ones: 6 - 4 = 2
Answer:
Sarah has 232 stickers left.
14 Pattern recognition
Problem 14
Complete the pattern: 300, 400, 500, __, __
Definition:
Number patterns: Identifying the rule by finding the difference between consecutive numbers.
Step 1: Find the pattern
400 - 300 = 100
500 - 400 = 100
The pattern is adding 100 each time
Step 2: Continue the pattern
500 + 100 = 600
600 + 100 = 700
Answer:
The next two numbers are 600 and 700.
15 Equation solving
Problem 15
Find the missing number: 684 - __ = 452
Definition:
Missing number problems: Using inverse operations to find unknown values.
Step 1: Set up the equation
684 - ? = 452
This means ? = 684 - 452
Step 2: Perform the subtraction
684 - 452 = 232
Step 3: Verify
684 - 232 = 452 ✓
Answer:
The missing number is 232.
16 Addition with regrouping
Problem 16
Add: 389 + 247
Definition:
Regrouping: When a sum in any place value is 10 or more, carry over to the next place value.
Step 1: Add ones place
9 + 7 = 16 → Write 6, carry 1 to tens
HUNDREDS
3 + 2 + 1 (carry) = 6
TENS
8 + 4 + 1 (carry) = 13 → Write 3, carry 1
ONES
9 + 7 = 16 → Write 6, carry 1
Step 2: Add tens place
8 + 4 + 1 (carry) = 13 → Write 3, carry 1 to hundreds
Step 3: Add hundreds place
3 + 2 + 1 (carry) = 6
17 Subtraction with borrowing
Problem 17
Subtract: 523 - 287
Definition:
Borrowing: When the top digit is smaller than the bottom digit, borrow from the next higher place value.
Step 1: Check ones place
3 < 7, so borrow from tens: 523 → 5[11][13]
Step 2: Check tens place
After borrowing: 1 < 8, so borrow from hundreds: 5[11][13] → 4[11][13]
Step 3: Subtract each place
Hundreds: 4 - 2 = 2
Tens: 11 - 8 = 3
Ones: 13 - 7 = 6
18 Ordering with zeros
Problem 18
Put these numbers in order from greatest to least: 608, 680, 806
Definition:
Number ordering: Compare numbers by examining digits from left to right, paying attention to zeros.
Step 1: Compare hundreds place first
608: 6 hundreds, 680: 6 hundreds, 806: 8 hundreds
So 806 is greatest
Step 2: Compare 608 and 680
Both have 6 hundreds, compare tens: 608 has 0 tens, 680 has 8 tens
So 680 > 608
19 Place value challenge
Problem 19
What is the difference between the value of the hundreds digit and the tens digit in 749?
Definition:
Digit value difference: Calculate the value of each specified digit and find the difference.
Step 1: Identify the digits
Hundreds digit: 7, Tens digit: 4
HUNDREDS VALUE
7 × 100 = 700
Step 2: Calculate the difference
700 - 40 = 660
Answer:
The difference is 660.
20 Mixed operations
Problem 20
Calculate: 456 + 234 - 89
Definition:
Mixed operations: Perform operations from left to right following order of operations.
Step 1: Perform addition first
456 + 234 = 690
Step 2: Perform subtraction next
690 - 89
Ones: 0 - 9 → Need to borrow: 10 - 9 = 1
Tens: 8 - 8 = 0
Hundreds: 6 - 0 = 6
Answer:
456 + 234 - 89 = 601
Worksheets Part 3: Advanced Problems (Problems 21-25)
21 Complex ordering
Problem 21
Put these numbers in order from least to greatest: 503, 350, 530, 305
Definition:
Complex number ordering: Compare numbers by examining digits from left to right with multiple zeros.
Step 1: Compare hundreds place first
503: 5 hundreds, 350: 3 hundreds, 530: 5 hundreds, 305: 3 hundreds
So 350 and 305 are smaller than 503 and 530
Step 2: Compare 350 vs 305
Both have 3 hundreds, compare tens: 350 has 5 tens, 305 has 0 tens
So 305 < 350
Step 3: Compare 503 vs 530
Both have 5 hundreds, compare tens: 503 has 0 tens, 530 has 3 tens
So 503 < 530
Answer:
305, 350, 503, 530
22 Multiple zeros
Problem 22
What is the value of each digit in 800?
Definition:
Multiple zeros: Understanding place value when multiple positions have zeros.
Step 1: Identify each digit and its position
8 in hundreds place, 0 in tens place, 0 in ones place
Step 2: Calculate each digit's value
8 × 100 = 800
0 × 10 = 0 (zero still holds the tens place)
0 × 1 = 0 (zero still holds the ones place)
Answer:
Hundreds value: 800, Tens value: 0, Ones value: 0
23 Complex visual representation
Problem 23
Show 508 using base ten blocks.
Definition:
Complex visual representation: Using base ten blocks to represent numbers with zeros in middle positions.
100
100
100
100
100
1
1
1
1
1
1
1
1
Step 1: Break down 508 by place value
5 hundreds: 5 × 100 = 500
0 tens: 0 × 10 = 0 (no ten blocks needed)
8 ones: 8 × 1 = 8
Step 2: Represent with blocks
5 hundred blocks (flats)
0 ten blocks (rods)
8 one blocks (units)
Answer:
5 hundred blocks, 0 ten blocks, 8 one blocks
24 Multi-step word problem
Problem 24
Tom has 425 marbles. He gives 138 marbles to his friend and then finds 57 more marbles. How many marbles does he have now?
Definition:
Multi-step word problem: Solving problems that require multiple operations in sequence.
Step 1: Identify the operations
Start with 425, subtract 138, then add 57: 425 - 138 + 57
Step 2: Perform subtraction first
425 - 138
Ones: 5 < 8 → Borrow: 15 - 8 = 7
Tens: 1 < 3 (after borrowing) → Borrow: 11 - 3 = 8
Hundreds: 3 - 1 = 2
Result: 287
Step 3: Add the remaining amount
287 + 57 = 344
Answer:
Tom has 344 marbles now.
25 Challenge problem
Problem 25
What is the sum of the values of all digits in 674?
Definition:
Sum of digit values: Calculate the value of each digit based on its position and add them together.
Step 1: Calculate each digit's value
Hundreds digit: 6 × 100 = 600
Tens digit: 7 × 10 = 70
Ones digit: 4 × 1 = 4
Step 2: Add all values together
600 + 70 + 4 = 674
Answer:
The sum of the values of all digits in 674 is 674.
Detailed Summary: Hundreds, Tens and Ones Concepts for Grade 2
Key Concepts and Definitions:
Place value: The value of a digit based on its position in a number. Each position represents a power of 10.
Hundreds place: The third digit from the right, representing groups of 100.
Tens place: The second digit from the right, representing groups of 10.
Ones place: The rightmost digit, representing individual units.
Expanded form: Writing a number as the sum of each digit's value (e.g., 345 = 300 + 40 + 5).
Standard form: The normal way of writing numbers (e.g., 345).
Base ten blocks: Visual tools representing units (ones), rods (tens), and flats (hundreds).
Regrouping: Exchanging between place values (10 ones = 1 ten, 10 tens = 1 hundred).
Borrowing: Taking 1 from a higher place value when the top digit is smaller than the bottom digit.
Zero placeholder: Zero holds the place in a number but contributes 0 to the total value.
Core Rules and Principles:
• Position rule: From right to left: ones, tens, hundreds
• Multiplication rule: Digit × Place value gives actual value
• Comparison rule: Start comparing from highest place value
• Zero rule: Zero holds place but adds no value
• Regrouping rule: 1 hundred = 10 tens, 1 ten = 10 ones
• Order of operations: Perform calculations from left to right
• Borrowing rule: When top digit < bottom digit, borrow from next higher place
• Carrying rule: When sum ≥ 10, carry to next higher place
Step-by-Step Methods:
- Identifying place values: Count positions from right (ones, tens, hundreds)
- Calculating digit values: Multiply digit by its place value (100, 10, or 1)
- Writing expanded form: Express each digit's value as a sum
- Number comparison: Compare digits starting from the highest place value
- Number composition: Add place values to form the complete number
- Visual representation: Use base ten blocks to model numbers
- Regrouping: Exchange between place values when needed
- Word problem solving: Identify operation and apply place value concepts
- Subtraction with borrowing: Borrow from higher place when needed
- Addition with carrying: Carry to higher place when sum ≥ 10
Examples (Simple to Advanced):
Basic: 234 = 2 hundreds, 3 tens, 4 ones
Intermediate: 507 = 5 hundreds, 0 tens, 7 ones
Advanced: 456 - 234 = 222 (place value subtraction)
Challenge: 345 + 123 - 78 = 390 (mixed operations)
Expert: 674 → 600 + 70 + 4 = 674 (sum of digit values)
Tips and Tricks:
• Use the acronym HTU (Hundreds, Tens, Units) to remember position order
• Remember: each place is 10 times greater than the place to its right
• When comparing, start with the leftmost digit (highest place value)
• Zero digits hold place but contribute zero value
• Practice with base ten blocks for visual understanding
• Always check your work by adding back or verifying with expanded form
Common Pitfalls:
• Confusing digit with its place value (the digit 5 in 500 represents 500, not 5)
• Misidentifying positions when zeros are present
• Forgetting that the same digit has different values in different positions
• Starting comparisons from the wrong end (always start from highest place value)
• Forgetting to regroup when performing addition or subtraction
• Not borrowing correctly when the next place has 0
Key Notes for Memorization:
• Memory aid: "Houses, Tents, Units" - H (hundreds), T (tens), U (ones)
• Value calculation: Always multiply the digit by its place value
• Comparison strategy: Highest place value determines which number is larger
• Zero function: Maintains number structure even when contributing zero value
• Regrouping concept: 10 of a smaller unit equals 1 of the next larger unit
• Visual learning: Use base ten blocks to reinforce abstract concepts
• Verification: Always check your answer by adding or subtracting back