Solved Exercises on Place Value Strategy Examples in Grade 2

Master place value: decomposing numbers into tens and ones, regrouping, and using place value for addition and subtraction through these 5 detailed exercises.

Solution: Exercises 1 to 3
1 Decomposing Numbers
Exercise 1
Decompose 47 into tens and ones
Definition:

Decomposing Numbers: Breaking a number into its tens and ones components.

Decomposing Method:
  1. Identify the digit in the tens place
  2. Identify the digit in the ones place
  3. Express the number as the sum of tens and ones
  4. Verify by adding the components
Number
47
Tens
40
Ones
7
Step 1: Identify the tens digit

In 47, the tens digit is 4, which represents 4 tens = 40

Step 2: Identify the ones digit

In 47, the ones digit is 7, which represents 7 ones = 7

Step 3: Express as sum of tens and ones

47 = 40 + 7

47 = 40 + 7
Final answer:

47 = 40 + 7

Applied rules:

• Place Value: Each digit has a value based on its position

• Digit Recognition: Understanding that 4 in the tens place equals 40

• Number Composition: A two-digit number is the sum of its tens and ones

2 Addition Using Place Value
Exercise 2
Solve using place value: 34 + 25
Definition:

Place Value Addition: Add tens to tens and ones to ones separately, then combine.

Problem
34 + 25
Decompose
(30+4)+(20+5)
Add by place
50+9=59
Step 1: Decompose both numbers into tens and ones

34 = 30 + 4 and 25 = 20 + 5

Step 2: Add the tens together

30 + 20 = 50

Step 3: Add the ones together

4 + 5 = 9

Step 4: Combine the sums

50 + 9 = 59

34 + 25 = 59
Final answer:

34 + 25 = 59

Applied rules:

• Place Value Addition: Add digits with the same place value

• Regrouping: When ones sum to 10 or more, convert to tens and ones

• Number Composition: Reassemble the final sum from its components

3 Subtraction Using Place Value
Exercise 3
Solve using place value: 63 - 28
Definition:

Place Value Subtraction: Subtract tens from tens and ones from ones, regrouping when necessary.

Problem
63 - 28
Decompose
(60+3)-(20+8)
Regroup
60+3=50+13
Step 1: Decompose both numbers into tens and ones

63 = 60 + 3 and 28 = 20 + 8

Step 2: Check if ones can be subtracted

3 - 8 cannot be done, so we need to regroup

Step 3: Regroup from tens to ones

Take 1 ten from 60 (leaving 50) and add to 3 ones: 50 + 13

Step 4: Subtract tens and ones separately

50 - 20 = 30 and 13 - 8 = 5

Step 5: Combine the results

30 + 5 = 35

63 - 28 = 35
Final answer:

63 - 28 = 35

Applied rules:

• Place Value Subtraction: Subtract digits with the same place value

• Regrouping: When the top digit is smaller, borrow from the next higher place

• Number Composition: Reassemble the final difference from its components

Rules and methods, laws,...
47 = 40 + 7 (tens + ones)
Decomposing Numbers
Concept 1
Place Value
Each digit has value based on position
Concept 2
Decomposing
Breaking numbers into tens and ones
Concept 3
Regrouping
Borrowing from higher place value
Key definitions:

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

Tens: Groups of ten ones (10, 20, 30, etc.)

Ones: Individual units (1, 2, 3, etc.)

Regrouping: Converting from one place value to another (borrowing in subtraction, carrying in addition)

Complete methodology:
  1. Identify place values: Determine the tens and ones in each number
  2. Separate by place: Work with tens and ones separately
  3. Perform operations: Add or subtract digits in the same place
  4. Regroup when necessary: Borrow or carry between places
  5. Combine results: Put the tens and ones back together
Tip 1: Always start by identifying how many tens and ones are in each number.
Tip 2: In subtraction, if the top ones digit is smaller than the bottom ones digit, you must regroup.
Tip 3: When regrouping, remember: 1 ten = 10 ones.
Tip 4: Always check your answer by using the inverse operation.
Common errors: Forgetting to regroup when necessary, adding tens and ones together before completing operations, misidentifying place values.
Key strategies: Practice decomposing numbers, visualize with base-10 blocks, check answers with inverse operations.
Place value rules:

• In 2-digit numbers, the left digit is the tens place, right digit is the ones place

• When adding, add tens to tens and ones to ones

• When subtracting, subtract tens from tens and ones from ones

• Regroup when the top digit is smaller than the bottom digit in subtraction

• 1 ten = 10 ones (for regrouping purposes)

Solution: Exercises 4 to 5
4 Regrouping in Addition
Exercise 4
Solve using place value: 46 + 27
Definition:

Regrouping in Addition: When adding ones results in 10 or more, convert 10 ones to 1 ten.

Problem
46 + 27
Decompose
(40+6)+(20+7)
Add by place
60+13=60+10+3
Step 1: Decompose both numbers into tens and ones

46 = 40 + 6 and 27 = 20 + 7

Step 2: Add the tens together

40 + 20 = 60

Step 3: Add the ones together

6 + 7 = 13

Step 4: Regroup when ones sum to 10+

13 ones = 10 ones + 3 ones = 1 ten + 3 ones

Step 5: Add the regrouped ten to the tens sum

60 + 10 = 70, then 70 + 3 = 73

46 + 27 = 73
Final answer:

46 + 27 = 73

Applied rules:

• Place Value Addition: Add digits with the same place value

• Regrouping: When ones sum to 10 or more, convert to tens and ones

• Number Composition: Reassemble the final sum from its components

5 Mixed Operations with Place Value
Exercise 5
Solve using place value: 52 + 19 - 24
Definition:

Mixed Operations with Place Value: Perform operations sequentially using place value strategy.

Problem
52 + 19 - 24
First: 52 + 19
70 + 11 = 81
Then: 81 - 24
70 + 11 - 24 = 57
Step 1: First perform 52 + 19 using place value

52 = 50 + 2, 19 = 10 + 9, so (50 + 10) + (2 + 9) = 60 + 11 = 71

Step 2: Now perform 71 - 24 using place value

71 = 70 + 1, 24 = 20 + 4

Step 3: Since 1 < 4, regroup 70 + 1 to 60 + 11

Now we have (60 + 11) - (20 + 4)

Step 4: Subtract tens and ones separately

60 - 20 = 40, and 11 - 4 = 7

Step 5: Combine the results

40 + 7 = 47

52 + 19 - 24 = 47
Final answer:

52 + 19 - 24 = 47

Applied rules:

• Order of Operations: Perform operations from left to right

• Place Value Strategy: Use decomposition for each operation

• Regrouping: Apply when needed in each step

Place Value Strategy Concepts and Techniques
47 = 40 + 7 (decomposing into tens and ones)
Place Value Decomposition
Key definitions:

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

Decomposing: Breaking a number into its component parts (tens and ones)

Regrouping: Converting between place values (1 ten = 10 ones)

Composing: Combining parts to make a whole number

Complete methodology:
  1. Identify place values: Look at each digit and determine its value
  2. Separate by place: Group tens and ones separately
  3. Perform operations: Work with tens and ones separately
  4. Regroup when necessary: Convert between places when needed
  5. Combine results: Put the final answer together
Tip 1: Think of tens as bundles of 10 ones - this helps visualize regrouping
Tip 2: Use base-10 blocks or drawings to physically represent the numbers
Tip 3: In subtraction, always check if you need to regroup BEFORE subtracting
Tip 4: Practice with number lines to see how place value affects the magnitude of numbers
Common errors: Forgetting to regroup when necessary, adding tens and ones together before completing operations, misidentifying place values.
Success habits: Regular practice with decomposing numbers, visualizing with manipulatives, checking answers.
Place value strategies:

• Decompose numbers into tens and ones before operating

• Add/subtract digits with the same place value

• Regroup when necessary (10 ones = 1 ten)

• Check your answer by using the inverse operation

• Use visual models to support understanding

Place Value Strategy Workflow

🔢
Step-by-Step Process
1
Identify place values
2
Separate by place
3
Operate by place
4
Regroup if needed
5
Combine results
Place Value Visualization
Understanding place value helps us see that 47 is actually 4 tens and 7 ones, making operations easier to manage.
Master Place Value for Strong Math Foundation!

Questions & Answers

Question: I don't understand why we need to regroup. Can't I just subtract the numbers as they are?

Answer: Great question! Regrouping is necessary when you can't perform an operation directly. Let's look at 63 - 28:

  • If we try to subtract the ones directly: 3 - 8, we can't because 3 is smaller than 8
  • Regrouping allows us to "borrow" from the tens place: 63 = 60 + 3 = 50 + 13
  • Now we can subtract the ones: 13 - 8 = 5
  • And subtract the tens: 50 - 20 = 30
  • So the answer is 30 + 5 = 35

Think of it like money: if you have 63 cents (6 dimes and 3 pennies) and need to pay 28 cents, you can't give 8 pennies because you only have 3. So you change one of your dimes (10 pennies) to get enough pennies to pay.

Question: My child is struggling with place value. How can I help them practice at home?

Answer: Here are effective ways to practice place value at home:

  • Use manipulatives: Base-10 blocks, straws bundled in tens, or even groups of 10 beans
  • Play number games: Have your child build numbers with place value cards
  • Real-world connections: Use money to show tens and ones (dimes and pennies)
  • Drawings: Have your child draw sticks for tens and dots for ones

Start with simple numbers like 12, 23, 34 and practice decomposing them: 12 = 10 + 2. Once comfortable, move to larger numbers and operations.

Make it visual and hands-on - the more concrete experiences your child has with tens and ones, the better they'll understand abstract place value concepts.

Question: Why do we need to separate tens and ones? Can't I just add the numbers together?

Answer: Separating tens and ones makes addition and subtraction much easier! Here's why:

  • It's organized: Instead of trying to add 34 + 25 all at once, you add 30 + 20 = 50, then 4 + 5 = 9, then 50 + 9 = 59
  • It prevents mistakes: You won't accidentally add 4 tens to 5 ones
  • It builds number sense: You understand that 34 really means 3 tens and 4 ones
  • It prepares you for bigger numbers: This same strategy works for hundreds and thousands later

Think of it like organizing your toys - it's easier to count if you group similar items together!