Solved Exercises on Using Place Value Strategies in Grade 2

Master place value strategies: tens and ones, addition and subtraction within 100 with regrouping through these 5 detailed exercises.

Solution: Exercises 1 to 3
1 Adding with place value
Exercise 1
Add using place value strategies:
47 + 25
Definition:

Place value: Understanding that digits have different values based on their position (tens and ones)

Addition method:
  1. Break numbers into tens and ones
  2. Add tens together and ones together
  3. Combine the results
Expression
47 + 25
Break apart
40 + 7 + 20 + 5
Result
72
Step 1: Break numbers into tens and ones

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

25 = 20 + 5 (2 tens and 5 ones)

Step 2: Add tens together and ones together

Tens: 40 + 20 = 60

Ones: 7 + 5 = 12

Step 3: Combine the results

60 + 12 = 72

47 + 25 = 72
Final answer:

47 + 25 = 72

Applied rules:

• Place value: Separate tens and ones to make addition easier

• Regrouping: When adding ones gives 10 or more, convert to tens

• Combining: Add the final tens and ones together

Place Value Strategy Visual
📊
Tens Place

47 → 4 tens

25 → 2 tens

Total: 6 tens = 60

Ones Place

47 → 7 ones

25 → 5 ones

Total: 12 ones = 1 ten + 2 ones

Final Calculation

60 + 12 = 72

Or: 7 tens + 2 ones = 72

2 Subtracting with place value
Exercise 2
Subtract using place value strategies:
63 - 28
Definition:

Place value subtraction: Breaking numbers into tens and ones to perform subtraction

Expression
63 - 28
Break apart
60 + 3 - 20 - 8
Result
35
Step 1: Break numbers into tens and ones

63 = 60 + 3 (6 tens and 3 ones)

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

Step 2: Regroup when needed

We need to subtract 8 ones from 3 ones, but 3 < 8

Borrow 1 ten from 6 tens: 60 = 50 + 10

Now: 50 + 10 + 3 = 50 + 13 (5 tens and 13 ones)

Step 3: Subtract tens and ones separately

Tens: 50 - 20 = 30

Ones: 13 - 8 = 5

Step 4: Combine the results

30 + 5 = 35

63 - 28 = 35
Final answer:

63 - 28 = 35

Applied rules:

• Regrouping: When ones in minuend are less than ones in subtrahend, borrow from tens

• Place value: Separate tens and ones for easier calculation

• Subtraction: Subtract tens from tens and ones from ones

Subtraction Strategy Visual
📊
Original Numbers

63 → 6 tens + 3 ones

28 → 2 tens + 8 ones

Regrouping Needed

3 ones < 8 ones → Borrow 1 ten

63 → 5 tens + 13 ones

Final Calculation

Tens: 5 - 2 = 3 tens

Ones: 13 - 8 = 5 ones

Answer: 35

3 Mixed operations
Exercise 3
Solve using place value strategies:
56 + 17 - 24
Definition:

Mixed operations: Performing addition and subtraction in sequence using place value strategies

Expression
56 + 17 - 24
Step 1
56 + 17 = 73
Step 2
73 - 24 = 49
Step 1: Add 56 + 17

56 = 50 + 6 (5 tens and 6 ones)

17 = 10 + 7 (1 ten and 7 ones)

Tens: 50 + 10 = 60

Ones: 6 + 7 = 13 (1 ten + 3 ones)

60 + 13 = 73

Step 2: Subtract 73 - 24

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

24 = 20 + 4 (2 tens and 4 ones)

Need to regroup: 73 = 60 + 13 (6 tens and 13 ones)

Tens: 60 - 20 = 40

Ones: 13 - 4 = 9

40 + 9 = 49

Step 3: Final result

56 + 17 - 24 = 49

56 + 17 - 24 = 49
Final answer:

56 + 17 - 24 = 49

Applied rules:

• Order of operations: Perform operations from left to right

• Place value: Break numbers into tens and ones for each operation

• Regrouping: Apply when necessary in both addition and subtraction

Mixed Operations Strategy
📊
Step 1: Addition

56 + 17

50 + 6 + 10 + 7

= 60 + 13 = 73

Step 2: Subtraction

73 - 24

70 + 3 - 20 - 4

Regroup: 60 + 13 - 20 - 4

= 40 + 9 = 49

Final Answer

56 + 17 - 24 = 49

Place Value Rules and Methods
47 = 40 + 7
Breaking into Tens and Ones
Addition Strategy
T + O + T + O = (T + T) + (O + O)
Add tens and ones separately
Subtraction Strategy
T + O - T - O = (T - T) + (O - O)
Subtract tens and ones separately
Regrouping Rule
1 ten = 10 ones
Borrow when needed
Key definitions:

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

Tens: The second digit from the right represents groups of ten

Ones: The rightmost digit represents individual units

Regrouping: Converting between tens and ones when performing operations

Complete methodology:
  1. Identify place values: Separate tens and ones in each number
  2. Perform operation: Add or subtract tens with tens, ones with ones
  3. Regroup if necessary: Convert between tens and ones when needed
  4. Combine results: Put tens and ones back together
Tip 1: Always write out the expanded form (tens + ones) to visualize the problem.
Tip 2: In subtraction, if ones in the top number are smaller than bottom ones, always regroup first.
Tip 3: Check your answer by adding the result to the subtracted number (if subtracting) or subtracting one addend from the sum.
Tip 4: Practice with base-10 blocks to physically see tens and ones.
Common errors: Forgetting to regroup in subtraction, mixing up tens and ones, not carrying over correctly.
Key concepts: 10 ones = 1 ten, place determines value, regrouping changes form but not value.
Formulas to know by heart:

• Expanded form: AB = A×10 + B

• Addition: (T₁ + O₁) + (T₂ + O₂) = (T₁ + T₂) + (O₁ + O₂)

• Subtraction: (T₁ + O₁) - (T₂ + O₂) = (T₁ - T₂) + (O₁ - O₂)

• Regrouping: When O₁ < O₂ in subtraction, borrow 1 ten = 10 ones

Solution: Exercises 4 to 5
4 Word problem with place value
Exercise 4
Sarah has 34 stickers. Her friend gives her 29 more stickers. How many stickers does Sarah have now?
Definition:

Word problems: Real-life situations requiring mathematical operations using place value strategies

Expression
34 + 29
Break apart
30 + 4 + 20 + 9
Result
63
Step 1: Identify the numbers

Sarah starts with 34 stickers

She gets 29 more stickers

This is an addition problem: 34 + 29

Step 2: Break numbers into tens and ones

34 = 30 + 4 (3 tens and 4 ones)

29 = 20 + 9 (2 tens and 9 ones)

Step 3: Add tens and ones separately

Tens: 30 + 20 = 50

Ones: 4 + 9 = 13

Step 4: Combine results

50 + 13 = 63

Step 5: State the answer in context

Sarah has 63 stickers now.

Sarah has 63 stickers.
Final answer:

Sarah has 63 stickers.

Applied rules:

• Problem solving: Identify operation needed from context

• Place value: Break numbers into tens and ones

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

Word Problem Strategy
📊
Given Information

Sarah: 34 stickers

Friend gives: 29 stickers

Operation: Addition

Break Apart

34 = 30 + 4

29 = 20 + 9

Calculate

Tens: 30 + 20 = 50

Ones: 4 + 9 = 13

Total: 50 + 13 = 63

5 Multi-step place value problem
Exercise 5
A store had 82 apples. They sold 35 apples in the morning and then received 18 more apples in the afternoon. How many apples does the store have now?
Definition:

Multi-step problems: Problems requiring multiple operations solved sequentially using place value strategies

Expression
82 - 35 + 18
Step 1
82 - 35 = 47
Step 2
47 + 18 = 65
Step 1: Start with initial amount

Store begins with 82 apples

Step 2: Subtract apples sold

82 - 35 (subtracting 35 apples)

82 = 80 + 2, 35 = 30 + 5

Need to regroup: 82 = 70 + 12

Tens: 70 - 30 = 40

Ones: 12 - 5 = 7

40 + 7 = 47 apples remaining

Step 3: Add apples received

47 + 18 (adding 18 apples)

47 = 40 + 7, 18 = 10 + 8

Tens: 40 + 10 = 50

Ones: 7 + 8 = 15

50 + 15 = 65 apples total

Step 4: Final answer in context

The store has 65 apples now.

The store has 65 apples.
Final answer:

The store has 65 apples.

Applied rules:

• Order of operations: Work from left to right for addition/subtraction

• Place value: Break each number into tens and ones

• Regrouping: Apply when necessary in each operation

Multi-Step Problem Strategy
📊
Initial Amount

Start: 82 apples

First Operation

82 - 35

82 = 70 + 12

35 = 30 + 5

Result: 47 apples

Second Operation

47 + 18

47 = 40 + 7

18 = 10 + 8

Result: 65 apples

Place Value Laws, Methods, Rules, and Definitions
AB = A×10 + B
Place Value Formula
Key definitions:

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

Tens place: The second digit from the right, representing groups of ten

Ones place: The rightmost digit, representing individual units

Regrouping: Converting between tens and ones when performing operations

Expanded form: Writing a number as the sum of its place values

Complete methodology:
  1. Recognize the problem: Determine if addition or subtraction is needed
  2. Break apart numbers: Write each number in expanded form (tens + ones)
  3. Perform operation: Add or subtract tens with tens, ones with ones
  4. Regroup if necessary: Convert between tens and ones when needed
  5. Combine results: Add the tens and ones results together
  6. Verify answer: Check by performing the inverse operation
Tip 1: Draw tens and ones using base-10 blocks or sticks to visualize problems.
Tip 2: Always check your work by adding the difference to the subtrahend in subtraction.
Tip 3: In word problems, underline key numbers and operations to identify what to do.
Tip 4: Remember that 10 ones always equal 1 ten when regrouping.
Tip 5: Practice skip counting by 10s to strengthen understanding of tens place.
Common errors: Forgetting to regroup in subtraction, adding instead of subtracting, misaligning digits.
Key concepts: Position determines value, 10 ones = 1 ten, regrouping preserves value.
Memorization tips: "More ones? Need to regroup!" for subtraction.
Visual aids: Use place value charts, base-10 blocks, or drawings to support learning.
Formulas to know by heart:

• Place value: Two-digit number AB = A×10 + B

• Addition: (T₁ + O₁) + (T₂ + O₂) = (T₁ + T₂) + (O₁ + O₂)

• Subtraction: (T₁ + O₁) - (T₂ + O₂) = (T₁ - T₂) + (O₁ - O₂)

• Regrouping: When O₁ < O₂ in subtraction, 1T₁ = 10O₁

• Checking: Add result to subtrahend to verify difference

Questions & Answers

Question: I don't understand why we need to break numbers into tens and ones. Why can't I just add them normally?

Answer: Great question! Breaking numbers into tens and ones helps you understand what you're really doing when you add or subtract. Let me explain:

  • When you see 23 + 15, you're actually adding 2 tens + 1 ten = 3 tens, and 3 ones + 5 ones = 8 ones
  • This equals 30 + 8 = 38
  • Breaking it apart makes it easier to see why 23 + 15 = 38
  • It also helps when you need to regroup: like when adding 27 + 15, the ones (7 + 5 = 12) create a new ten

Think of it like having bags of 10 marbles and loose marbles. It's easier to count 2 full bags + 1 full bag = 3 full bags, plus 7 loose + 5 loose = 12 loose (which becomes 1 more full bag + 2 loose).

Question: My child struggles with regrouping in subtraction. How can I help them understand when to borrow?

Answer: Regrouping in subtraction can be tricky! Here's a helpful approach:

  • Always check the ones first: "Do I have enough ones to subtract?"
  • If the top number's ones are smaller than the bottom number's ones, you MUST regroup
  • Think of it as "asking your neighbor for help": take 1 ten from the tens place and convert it to 10 ones
  • For example, in 42 - 17: 2 ones is less than 7 ones, so we regroup 42 to 3 tens and 12 ones

Use manipulatives like base-10 blocks or draw representations. Have your child say "I need to ask my tens place for help" when regrouping.

Practice with simple problems first: 21 - 13, 32 - 18, etc., before moving to larger numbers.

Question: I want to get faster at place value problems. Are there any shortcuts I can learn?

Answer: Once you master the basics, here are some mental math shortcuts for advanced learners:

  • Compensation: Instead of 48 + 27, think 50 + 25 (add 2 to 48 and subtract 2 from 27)
  • Decomposition: Break numbers strategically: 36 + 48 = 36 + 40 + 8 = 76 + 8 = 84
  • Make tens: In 17 + 8, think 17 + 3 + 5 = 20 + 5 = 25
  • Patterns: Notice that adding 9 is like adding 10 and subtracting 1

But remember, these shortcuts work because of place value! Always understand the underlying concept first.

Practice with timed drills once you're comfortable with the basic strategies to build speed and accuracy.