Worksheets Part 1: Basic Place Value (Problems 1-10)
1 Identify place values
Problem 1
Circle the hundreds digit in 342.
Definition:
Place value positions: From right to left: ones, tens, hundreds.
Grade 1 concept: Learning that each position in a number has a special name and value.
Step 1: Look at the number
342 has three digits
Step 2: Find the hundreds place
Count from the right: 2 (ones), 4 (tens), 3 (hundreds)
Step 3: Circle the answer
Circle the digit 3
Answer:
The hundreds digit in 342 is 3.
2 Count tens and ones
Problem 2
How many tens and ones are in 27?
Definition:
Counting tens and ones: Breaking apart a number into groups of ten and leftover ones.
Grade 1 concept: Understanding that numbers like 27 are made of 2 tens and 7 ones.
Step 1: Look at the number
27 has two digits: 2 and 7
Step 2: Identify the tens digit
The first digit (2) tells us how many tens
Step 3: Identify the ones digit
The second digit (7) tells us how many ones
Answer:
27 has 2 tens and 7 ones.
3 Expanded form
Problem 3
Write 145 in expanded form.
Definition:
Expanded form: Writing a number as the sum of each digit's value.
Grade 1 concept: Seeing how numbers are built from smaller parts.
Step 1: Break down each digit
1 is in the hundreds place: 1 × 100 = 100
4 is in the tens place: 4 × 10 = 40
5 is in the ones place: 5 × 1 = 5
Step 2: Write in expanded form
145 = 100 + 40 + 5
145 = 100 + 40 + 5
Answer:
145 = 100 + 40 + 5
4 Ordering numbers
Problem 4
Put these numbers in order from least to greatest: 231, 132, 321
Definition:
Number ordering: Compare numbers by examining digits from left to right (highest place value first).
Grade 1 concept: Learning that the leftmost digit tells us which number is bigger.
Step 1: Compare hundreds place first
231: 2 hundreds, 132: 1 hundred, 321: 3 hundreds
So 132 is smallest, then 231, then 321
5 Number composition
Problem 5
What number is made up of 1 hundred, 3 tens, and 4 ones?
Definition:
Number composition: Building a number from its place value components.
Grade 1 concept: Putting together hundreds, tens, and ones to make a number.
Step 1: Convert each component to its value
1 hundred = 1 × 100 = 100
3 tens = 3 × 10 = 30
4 ones = 4 × 1 = 4
Step 2: Add all values together
100 + 30 + 4 = 134
Answer:
The number is 134.
6 Missing digit
Problem 6
In the number 2_7, if the tens digit is 5, what is the number?
Definition:
Missing digit problems: Finding unknown digits based on given information.
Grade 1 concept: Filling in the missing piece of a number.
Step 1: Look at what we know
Number format: 2_7 (hundreds = 2, ones = 7)
Tens digit is given as 5
Step 2: Put it together
Replace blank with the tens digit: 257
Answer:
The number is 257.
7 Compare place values
Problem 7
In 111, which digit has the greatest value?
Definition:
Digit value comparison: Compare the actual worth of each digit based on position.
Grade 1 concept: Even when digits are the same, their position makes them different.
Step 1: Look at each digit's value
Hundreds digit: 1 × 100 = 100
Tens digit: 1 × 10 = 10
Ones digit: 1 × 1 = 1
Step 2: Compare the values
100 > 10 > 1
Answer:
The hundreds digit (1) has the greatest value (100).
8 Zero in place value
Problem 8
What is the value of each digit in 105?
Definition:
Zero in place value: Zero holds the place but contributes 0 to the total value.
Grade 1 concept: Zero is important - it holds a place in the number!
Step 1: Look at each digit
1 in hundreds place, 0 in tens place, 5 in ones place
Step 2: Calculate each digit's value
1 × 100 = 100
0 × 10 = 0 (zero still holds the tens place)
5 × 1 = 5
Answer:
Hundreds value: 100, Tens value: 0, Ones value: 5
9 Visual representation
Problem 9
Show 134 using base ten blocks.
Definition:
Base ten blocks: Visual tools representing units (ones), rods (tens), and flats (hundreds).
Grade 1 concept: Using blocks to see how numbers are built.
Step 1: Break down 134 by place value
1 hundred: 1 × 100 = 100
3 tens: 3 × 10 = 30
4 ones: 4 × 1 = 4
Step 2: Represent with blocks
1 hundred block (flat)
3 ten blocks (rods)
4 one blocks (units)
Answer:
1 hundred block, 3 ten blocks, 4 one blocks
10 Subtraction with place value
Problem 10
Subtract: 245 - 123
Definition:
Place value subtraction: Subtracting numbers by working with hundreds, tens, and ones separately.
Grade 1 concept: Taking away hundreds from hundreds, tens from tens, and ones from ones.
Step 1: Align numbers by place value
245
- 123
-----
Step 2: Subtract ones place
5 - 3 = 2
Step 3: Subtract tens place
4 - 2 = 2
Step 4: Subtract hundreds place
2 - 1 = 1
Worksheets Part 2: Advanced Problems (Problems 11-20)
11 Comparison
Problem 11
Which is greater: 345 or 354?
Definition:
Number comparison: Compare numbers by examining digits from left to right.
Grade 1 concept: Start comparing from the leftmost digit.
Step 1: Compare hundreds place
Both have 3 hundreds → Equal so far
Step 2: Compare tens place
345: 4 tens, 354: 5 tens
Since 5 > 4, 354 > 345
Answer:
354 is greater than 345.
12 Addition with place value
Problem 12
Add: 124 + 132
Definition:
Place value addition: Adding numbers by working with hundreds, tens, and ones separately.
Grade 1 concept: Adding hundreds to hundreds, tens to tens, and ones to ones.
Step 1: Add ones place
4 + 2 = 6
Step 2: Add tens place
2 + 3 = 5
Step 3: Add hundreds place
1 + 1 = 2
13 Word problem
Problem 13
Lily has 156 stickers. She gives 123 stickers to her friend. How many stickers does she have left?
Definition:
Word problem solving: Translating story problems into mathematical operations.
Grade 1 concept: "Gives" means we subtract from the total.
Step 1: Identify the operation
"Gives" indicates subtraction: 156 - 123
Step 2: Subtract each place
Hundreds: 1 - 1 = 0
Tens: 5 - 2 = 3
Ones: 6 - 3 = 3
Answer:
Lily has 33 stickers left.
14 Pattern recognition
Problem 14
Complete the pattern: 100, 200, 300, __, __
Definition:
Number patterns: Identifying the rule by finding the difference between consecutive numbers.
Grade 1 concept: Looking for what's the same and what's changing.
Step 1: Find the pattern
200 - 100 = 100
300 - 200 = 100
The pattern is adding 100 each time
Step 2: Continue the pattern
300 + 100 = 400
400 + 100 = 500
Answer:
The next two numbers are 400 and 500.
15 Equation solving
Problem 15
Find the missing number: 234 - __ = 111
Definition:
Missing number problems: Using inverse operations to find unknown values.
Grade 1 concept: If we took away something and got 111, we can add back to find what we started with.
Step 1: Set up the equation
234 - ? = 111
This means ? = 234 - 111
Step 2: Perform the subtraction
234 - 111 = 123
Step 3: Verify
234 - 123 = 111 ✓
Answer:
The missing number is 123.
16 Addition with regrouping
Problem 16
Add: 147 + 128
Definition:
Regrouping: When a sum in any place value is 10 or more, carry over to the next place value.
Grade 1 concept: When we have 10 or more ones, we make a group of ten.
Step 1: Add ones place
7 + 8 = 15 → Write 5, carry 1 to tens
TENS
4 + 2 + 1 (carry) = 7
ONES
7 + 8 = 15 → Write 5, carry 1
Step 2: Add tens place
4 + 2 + 1 (carry) = 7
Step 3: Add hundreds place
1 + 1 = 2
17 Subtraction with borrowing
Problem 17
Subtract: 243 - 127
Definition:
Borrowing: When the top digit is smaller than the bottom digit, borrow from the next higher place value.
Grade 1 concept: When we don't have enough to subtract, we take from the next place.
Step 1: Check ones place
3 < 7, so we need to borrow from tens
Step 2: Borrow from tens
Take 1 ten from 4 tens: 4 - 1 = 3 tens
Add 10 ones to 3 ones: 3 + 10 = 13 ones
Step 3: Subtract each place
Hundreds: 2 - 1 = 1
Tens: 3 - 2 = 1
Ones: 13 - 7 = 6
18 Ordering with zeros
Problem 18
Put these numbers in order from greatest to least: 107, 170, 105
Definition:
Number ordering: Compare numbers by examining digits from left to right, paying attention to zeros.
Grade 1 concept: Even though zeros are small, they still matter in place value.
Step 1: Compare hundreds place first
All have 1 hundred → Equal so far
Step 2: Compare tens place
107: 0 tens, 170: 7 tens, 105: 0 tens
So 170 is greatest
Step 3: Compare 107 and 105
Both have 0 tens, compare ones: 7 > 5
So 107 > 105
19 Place value challenge
Problem 19
What is the difference between the value of the hundreds digit and the tens digit in 234?
Definition:
Digit value difference: Calculate the value of each specified digit and find the difference.
Grade 1 concept: Even the same digit has different values in different places.
Step 1: Identify the digits
Hundreds digit: 2, Tens digit: 3
HUNDREDS VALUE
2 × 100 = 200
Step 2: Calculate the difference
200 - 30 = 170
Answer:
The difference is 170.
20 Mixed operations
Problem 20
Calculate: 156 + 123 - 78
Definition:
Mixed operations: Perform operations from left to right following order of operations.
Grade 1 concept: Do the operations in the order they appear.
Step 1: Perform addition first
156 + 123 = 279
Step 2: Perform subtraction next
279 - 78
Ones: 9 - 8 = 1
Tens: 7 - 7 = 0
Hundreds: 2 - 0 = 2
Answer:
156 + 123 - 78 = 201
Grade 1 Place Value Concepts Review
ONES PLACE
1
Rightmost position
Value = Digit × 1
TENS PLACE
10
Second from right
Value = Digit × 10
HUNDREDS PLACE
100
Third from right
Value = Digit × 100
Key Grade 1 Concepts:
Place value: The value of a digit based on its position in a number
Digit: Any of the symbols 0, 1, 2, 3, 4, 5, 6, 7, 8, 9
Standard form: Normal way of writing numbers (e.g., 134)
Expanded form: Showing the value of each digit (e.g., 100+30+4)
Base ten blocks: Visual tools for understanding place value
Grade 1 Place Value Methods:
- Identify positions: Count from right (ones, tens, hundreds)
- Determine values: Multiply digit by its place value
- Compare values: Higher positions have greater value
- Compose numbers: Add place values to get total
- Decompose numbers: Break down into place values
Tip 1: Remember the acronym HTU (Hundreds, Tens, Units/Ones).
Tip 2: Each place is 10 times greater than the place to its right.
Tip 3: Zero digits hold place but contribute zero value.
Tip 4: When comparing, start with the highest place value.
Common errors for Grade 1: Confusing digit with its place value, misidentifying positions, forgetting zeros' role in maintaining structure.
Grade 1 learning tips: Practice with visual aids like base ten blocks, use place value charts, work with expanded forms regularly.
Grade 1 Place Value Rules:
• Right-to-left pattern: Ones, tens, hundreds
• Multiplication rule: Digit × Place value gives actual value
• Position importance: Same digit has different value in different positions
• Zero function: Holds place but adds no value
• Comparison rule: Start comparing from highest place value
Detailed Summary: Hundreds, Tens and Ones Concepts for Grade 1
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., 145 = 100 + 40 + 5).
Standard form: The normal way of writing numbers (e.g., 145).
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: 134 = 1 hundred, 3 tens, 4 ones
Intermediate: 205 = 2 hundreds, 0 tens, 5 ones
Advanced: 345 - 123 = 222 (place value subtraction)
Challenge: 156 + 123 - 78 = 201 (mixed operations)
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