Solved Exercises on Using Place Value Strategies to Add in Grade 2

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

Solution: Exercises 1 to 3
1 Basic addition with place value
Exercise 1
Add using place value strategies:
34 + 25
Definition:

Place value addition: Adding numbers by breaking them into tens and ones, then combining like place values

Addition method:
  1. Break each number into tens and ones
  2. Add the tens together
  3. Add the ones together
  4. Combine the results
Expression
34 + 25
Break apart
30 + 4 + 20 + 5
Result
59
Step 1: Break numbers into tens and ones

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

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

Step 2: Add the tens together

30 + 20 = 50

Step 3: Add the ones together

4 + 5 = 9

Step 4: Combine the results

50 + 9 = 59

34 + 25 = 59
Final answer:

34 + 25 = 59

Applied rules:

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

• Like place values: Only add tens to tens and ones to ones

• Combining: Add the final tens and ones together

Place Value Addition Visual
📊
Tens Place

34 → 3 tens

25 → 2 tens

Total: 3 + 2 = 5 tens = 50

Ones Place

34 → 4 ones

25 → 5 ones

Total: 4 + 5 = 9 ones

Final Calculation

50 + 9 = 59

Or: 5 tens + 9 ones = 59

2 Addition with regrouping
Exercise 2
Add using place value strategies:
48 + 37
Definition:

Regrouping: Converting 10 or more ones into a new ten when adding

Expression
48 + 37
Break apart
40 + 8 + 30 + 7
Result
85
Step 1: Break numbers into tens and ones

48 = 40 + 8 (4 tens and 8 ones)

37 = 30 + 7 (3 tens and 7 ones)

Step 2: Add the tens together

40 + 30 = 70

Step 3: Add the ones together

8 + 7 = 15 ones

Since 15 ≥ 10, we need to regroup!

Step 4: Regroup the ones

15 ones = 1 ten + 5 ones

Add this extra ten to our tens: 70 + 10 = 80

Step 5: Combine the results

80 + 5 = 85

48 + 37 = 85
Final answer:

48 + 37 = 85

Applied rules:

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

• Place value: Separate tens and ones for easier calculation

• Combining: Add final tens and ones together

Addition with Regrouping
📊
Original Numbers

48 → 4 tens + 8 ones

37 → 3 tens + 7 ones

Regrouping Needed

8 ones + 7 ones = 15 ones

15 ones = 1 ten + 5 ones

Final Calculation

Tens: 4 + 3 + 1 = 8 tens

Ones: 5 ones

Answer: 85

3 Adding multiples of 10
Exercise 3
Add using place value strategies:
50 + 20
Definition:

Adding multiples of 10: Adding numbers that only have tens place values (no ones)

Expression
50 + 20
Break apart
5 tens + 2 tens
Result
70
Step 1: Recognize the place values

50 = 5 tens + 0 ones

20 = 2 tens + 0 ones

Step 2: Add the tens together

5 tens + 2 tens = 7 tens

Step 3: Add the ones together

0 ones + 0 ones = 0 ones

Step 4: Combine the results

7 tens + 0 ones = 70

50 + 20 = 70
Final answer:

50 + 20 = 70

Applied rules:

• Place value: Understand that multiples of 10 only have tens place

• Like place values: Only add tens to tens and ones to ones

• Zero ones: When adding multiples of 10, the ones place remains zero

Adding Multiples of 10
📊
Tens Place

50 → 5 tens

20 → 2 tens

Total: 5 + 2 = 7 tens = 70

Ones Place

50 → 0 ones

20 → 0 ones

Total: 0 + 0 = 0 ones

Final Answer

7 tens + 0 ones = 70

Complete Summary: Using Place Value Strategies to Add
AB + CD = (A×10 + B) + (C×10 + D)
Place Value Addition 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 10 or more ones into a new ten when adding

Expanded form: Writing a number as the sum of its place values (e.g., 45 = 40 + 5)

Complete methodology:
  1. Recognize the numbers: Look at each number and identify tens and ones
  2. Break apart numbers: Write each number in expanded form (tens + ones)
  3. Add tens with tens: Combine all the tens together
  4. Add ones with ones: Combine all the ones together
  5. Check for regrouping: If ones total is 10 or more, convert to tens
  6. Combine results: Add the final tens and ones together
Tip 1: Always write out the expanded form (tens + ones) to visualize the problem.
Tip 2: When adding ones, if the sum is 10 or more, remember to regroup into tens.
Tip 3: Check your answer by counting up from one number by the value of the other.
Tip 4: Use base-10 blocks or drawings to physically represent tens and ones.
Tip 5: Remember that adding 10 means adding 1 to the tens place.
Common errors: Adding tens to ones, forgetting to regroup when ones sum to 10+, misaligning digits.
Key concepts: 10 ones = 1 ten, only add like place values, regrouping preserves value.
Memorization tip: "More than 9 ones? Make a new ten!" for regrouping.
Essential rules to remember:

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

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

• Regrouping rule: When O₁ + O₂ ≥ 10, convert to tens and ones

• Like place values: Only add tens to tens and ones to ones

Examples progression
Simple addition (no regrouping):

23 + 14 = (20 + 3) + (10 + 4) = (20 + 10) + (3 + 4) = 30 + 7 = 37

Addition with regrouping:

38 + 27 = (30 + 8) + (20 + 7) = (30 + 20) + (8 + 7) = 50 + 15 = 50 + 10 + 5 = 65

Adding multiples of 10:

40 + 30 = (4 tens) + (3 tens) = 7 tens = 70

Solution: Exercises 4 to 5
4 Word problem with place value addition
Exercise 4
Emma has 26 red marbles and 48 blue marbles. How many marbles does Emma have altogether?
Definition:

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

Expression
26 + 48
Break apart
20 + 6 + 40 + 8
Result
74
Step 1: Identify the numbers in the problem

Emma has 26 red marbles

Emma has 48 blue marbles

This is an addition problem: 26 + 48

Step 2: Break numbers into tens and ones

26 = 20 + 6 (2 tens and 6 ones)

48 = 40 + 8 (4 tens and 8 ones)

Step 3: Add tens and ones separately

Tens: 20 + 40 = 60

Ones: 6 + 8 = 14

Step 4: Regroup if necessary

14 ones = 1 ten + 4 ones

Add this extra ten to our tens: 60 + 10 = 70

Step 5: Combine results and state answer

70 + 4 = 74

Emma has 74 marbles altogether.

Emma has 74 marbles altogether.
Final answer:

Emma has 74 marbles altogether.

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

Red marbles: 26

Blue marbles: 48

Operation: Addition

Break Apart

26 = 20 + 6

48 = 40 + 8

Calculate

Tens: 20 + 40 = 60

Ones: 6 + 8 = 14

Regroup: 14 = 1 ten + 4 ones

Total: 60 + 10 + 4 = 74

5 Multi-step place value addition
Exercise 5
A school library has 35 books in the fiction section and 47 books in the non-fiction section. Then they receive 18 more books. How many books are in the library now?
Definition:

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

Expression
35 + 47 + 18
Step 1
35 + 47 = 82
Step 2
82 + 18 = 100
Step 1: Find the initial number of books

Fiction books: 35

Non-fiction books: 47

Total initially: 35 + 47

Step 2: Add the initial books (35 + 47)

35 = 30 + 5, 47 = 40 + 7

Tens: 30 + 40 = 70

Ones: 5 + 7 = 12

Since 12 ≥ 10, regroup: 12 = 1 ten + 2 ones

70 + 10 = 80, plus 2 ones = 82 books initially

Step 3: Add the new books

Now add the 18 new books: 82 + 18

82 = 80 + 2, 18 = 10 + 8

Tens: 80 + 10 = 90

Ones: 2 + 8 = 10

Since 10 ≥ 10, regroup: 10 = 1 ten + 0 ones

90 + 10 = 100, plus 0 ones = 100 books total

Step 4: Final answer in context

The library has 100 books now.

The library has 100 books.
Final answer:

The library has 100 books.

Applied rules:

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

• Place value: Break each number into tens and ones

• Regrouping: Apply when necessary in each operation

Multi-Step Problem Strategy
📊
Initial Books

Fiction: 35 books

Non-fiction: 47 books

Total: 35 + 47

First Addition

35 + 47

35 = 30 + 5

47 = 40 + 7

Result: 82 books

Second Addition

82 + 18

82 = 80 + 2

18 = 10 + 8

Result: 100 books

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. 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 addition. How can I help them understand when to regroup?

Answer: Regrouping in addition happens when the ones add up to 10 or more! Here's a helpful approach:

  • Always check the ones first: "What do I get when I add the ones?"
  • If the ones add to 10 or more, you need to regroup
  • Think of it as "making a new group of 10": every 10 ones becomes 1 ten
  • For example, in 28 + 17: 8 ones + 7 ones = 15 ones, which becomes 1 ten + 5 ones

Use manipulatives like base-10 blocks or draw representations. Have your child say "I made a new ten!" when regrouping.

Practice with simple problems first: 15 + 18, 27 + 16, etc., before moving to larger numbers.

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

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

  • Adding multiples of 10: Just add the tens digits and keep zeros (e.g., 40 + 30 = 70)
  • Compensation: Instead of 39 + 25, think 40 + 24 (add 1 to 39 and subtract 1 from 25)
  • Make tens: In 27 + 8, think 27 + 3 + 5 = 30 + 5 = 35
  • 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.