Solved Exercises on Using Place Value Strategies in 2nd Grade

Master place value strategies: decomposing numbers, mental math, and computational strategies within 100 through these 5 detailed exercises with visual methods.

Solution: Exercises 1 to 3
1 Decomposing Numbers
Exercise 1
Decompose 47 into tens and ones. Then add 23 using place value strategies.
47 = 4 TENS
40
+ 7 ONES
7
47 = 40 + 7
4 TENS
7 ONES
+
2 TENS
3 ONES
47
+
23
70
Definition:

Place value decomposition: Breaking a number into its tens and ones components (e.g., 47 = 40 + 7).

Decomposition method:
  1. Identify the tens and ones in each number
  2. Separate tens and ones into different groups
  3. Add tens with tens and ones with ones
  4. Combine the results
Decompose
47 = 40 + 7
Decompose
23 = 20 + 3
Add
(40 + 20) + (7 + 3)
Step 1: Decompose each number

47 = 40 + 7 (4 tens + 7 ones)

23 = 20 + 3 (2 tens + 3 ones)

Step 2: Group by place value

Add tens with tens: 40 + 20 = 60

Add ones with ones: 7 + 3 = 10

Step 3: Combine the results

60 + 10 = 70

47 + 23 = 70
Final answer:

47 + 23 = 70 using place value decomposition.

Applied rules:

• Place value rule: Always add tens with tens and ones with ones

• Decomposition: Break numbers into tens and ones components

• Regrouping: When ones sum ≥ 10, combine with tens

2 Mental Math with Place Value
Exercise 2
Solve 56 + 18 mentally using place value strategies.
56 = 5 TENS
50
+ 6 ONES
6
18 = 1 TEN
10
+ 8 ONES
8
50 + 10
=
60
6 + 8
=
14
56
+
18
74
Definition:

Mental math with place value: Using place value understanding to perform calculations mentally by working with tens and ones separately.

Tens
50 + 10 = 60
Ones
6 + 8 = 14
Total
60 + 14 = 74
Step 1: Break down mentally

Think of 56 as 50 + 6 and 18 as 10 + 8

Step 2: Add tens mentally

50 + 10 = 60

Step 3: Add ones mentally

6 + 8 = 14

Step 4: Combine mentally

60 + 14 = 74

56 + 18 = 74
Final answer:

56 + 18 = 74 using mental place value strategies.

Applied rules:

• Mental decomposition: Break numbers into tens and ones mentally

• Separate operations: Work with tens and ones separately

• Regrouping: When ones sum ≥ 10, add to tens

3 Subtraction with Place Value
Exercise 3
Solve 73 - 28 using place value strategies.
73 = 7 TENS
70
+ 3 ONES
3
28 = 2 TENS
20
+ 8 ONES
8
70 - 20
=
50
3 - 8
=
Borrow!
73
-
28
45
Definition:

Subtraction with place value: Using place value understanding to subtract by working with tens and ones separately.

Decompose
73 = 70 + 3
Decompose
28 = 20 + 8
Subtract
(70 - 20) + (3 - 8)
Step 1: Decompose each number

73 = 70 + 3 (7 tens + 3 ones)

28 = 20 + 8 (2 tens + 8 ones)

Step 2: Attempt to subtract ones

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

Step 3: Regroup from tens

Borrow 1 ten from 7 tens: 73 = 60 + 13

Step 4: Complete the subtraction

(60 - 20) + (13 - 8) = 40 + 5 = 45

73 - 28 = 45
Final answer:

73 - 28 = 45 using place value regrouping strategies.

Applied rules:

• Place value rule: Subtract tens with tens and ones with ones

• Regrouping: When ones minuend < ones subtrahend, borrow from tens

• Conversion: 1 ten = 10 ones

Place Value Strategies Guide
AB = A×10 + B
Place Value Formula
Decomposition
Tens + Ones
Break Apart
Regrouping
1 Ten = 10 Ones
Borrow/Carry
Mental Math
Work Separately
Tens + Ones
AB = A TENS
+ B ONES
Solution: Exercises 4 to 5
4 Word Problem Application
Exercise 4
Sarah has 64 stickers. She gives 27 stickers to her friend. How many stickers does Sarah have left? Use place value strategies.
64 = 6 TENS
60
+ 4 ONES
4
27 = 2 TENS
20
+ 7 ONES
7
60 - 20
=
40
4 - 7
=
Borrow!
64
-
27
37
Definition:

Word problem solving with place value: Translating real-world scenarios into mathematical operations using place value understanding.

Initial
64
Given Away
27
Remaining
37
Step 1: Identify the numbers

Sarah has 64 stickers, gives away 27

Step 2: Decompose each number

64 = 60 + 4, 27 = 20 + 7

Step 3: Check for regrouping

4 < 7, so we need to borrow from tens

Step 4: Regroup

64 = 50 + 14 (borrow 1 ten)

Step 5: Subtract separately

(50 - 20) + (14 - 7) = 30 + 7 = 37

Step 6: State the answer

Sarah has 37 stickers remaining

Sarah has 37 stickers
Final answer:

Sarah has 37 stickers remaining.

Applied rules:

• Problem translation: Convert words to mathematical operations

• Place value decomposition: Break numbers into tens and ones

• Regrouping rule: Borrow when needed for subtraction

5 Mixed Operations Strategy
Exercise 5
Solve: 45 + 28 - 16 using place value strategies. Which approach works best?
45 = 4 TENS
40
+ 5 ONES
5
28 = 2 TENS
20
+ 8 ONES
8
40 + 20
=
60
5 + 8
=
13
60 - 10
=
50
13 - 6
=
7
45
+
28
-
16
57
Definition:

Mixed operations with place value: Solving problems involving multiple operations using place value strategies.

First
45 + 28
Then
73 - 16
Final
57
Step 1: Solve 45 + 28

(40 + 20) + (5 + 8) = 60 + 13 = 73

Step 2: Solve 73 - 16

(70 - 10) + (3 - 6) → Regroup: (60 - 10) + (13 - 6) = 50 + 7 = 57

Step 3: Verify with place value

57 = 50 + 7 (5 tens + 7 ones)

Step 4: Alternative approach

Work with tens and ones separately: (40+20-10) + (5+8-6) = 50 + 7 = 57

45 + 28 - 16 = 57
Final answer:

45 + 28 - 16 = 57 using place value strategies.

Applied rules:

• Sequential operations: Perform operations from left to right

• Place value maintenance: Keep track of tens and ones separately

• Regrouping: Apply borrowing/carrying as needed

Place Value Strategy Properties
(A×10 + B) + (C×10 + D) = (A+C)×10 + (B+D)
Addition Formula
Key definitions:

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

Decomposition: Breaking a number into its place value components.

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

Mental math: Performing calculations mentally using place value understanding.

Place value strategy selection:
  1. Decomposition: Break numbers into tens and ones
  2. Separate operations: Work with tens and ones separately
  3. Regrouping: Apply borrowing or carrying as needed
  4. Recombination: Join the results together
Tip 1: Always identify tens and ones before starting calculations.
Tip 2: Work with tens and ones separately to avoid confusion.
Tip 3: Remember to regroup when ones sum ≥ 10 or when subtracting needs borrowing.
Tip 4: Use place value understanding to verify your answers.
Common errors: Mixing tens and ones, forgetting to regroup, misplacing digits.
Key insight: Place value understanding is fundamental to all arithmetic operations.
Important rules:

• Decomposition: 47 = 40 + 7 (4 tens + 7 ones)

• Addition: 34 + 25 = (30 + 20) + (4 + 5) = 50 + 9 = 59

• Subtraction: 62 - 28 = (60 - 20) + (2 - 8) → Regroup: (50 - 20) + (12 - 8) = 34

• Regrouping: When ones ≥ 10, convert to tens; when ones minuend < subtrahend, borrow

Place Value Strategy Comparison Chart
Place Value Strategies
Visual comparison of different place value strategies:
Strategy 1
Decomposition
Strategy 2
Mental Math
Strategy 3
Regrouping

Observation: All strategies use place value understanding but in different ways.

  • Decomposition: Break numbers into tens and ones components
  • Mental math: Work with tens and ones separately mentally
  • Regrouping: Convert between place values when needed
  • All strategies reinforce place value concepts and number relationships

Questions & Answers

Question: My child struggles to understand why we need to decompose numbers using place value. How can I help them see the benefit?

Answer: Here are ways to help children understand the benefit:

  • Concrete examples: Use manipulatives like base-10 blocks to show how numbers break apart
  • Simplification: Explain that breaking big problems into smaller parts makes them easier
  • Visualization: Draw groups of tens and ones to make the concept visual
  • Real-world connections: Compare to organizing objects into groups

The key is showing that place value decomposition makes complex problems more manageable.

Question: How can I help students develop fluency with place value strategies?

Answer: Focus on these approaches:

  • Repeated practice: Provide multiple opportunities with different numbers
  • Variety of representations: Use visual models, manipulatives, and symbolic notation
  • Progressive difficulty: Start with simple problems and increase complexity
  • Regular review: Reinforce concepts regularly to build fluency

Fluency develops through consistent practice with meaningful contexts.

Question: Are there any games or activities that can help practice place value strategies?

Answer: Absolutely! Here are engaging activities:

  • Place value dice: Roll dice to generate numbers and decompose them
  • Base-10 block challenges: Build numbers and perform operations with blocks
  • Number line hops: Use number lines to visualize place value operations
  • Place value puzzles: Match decomposed forms with standard forms

Make it interactive and fun - children learn best when actively engaged!