Expanded Form with Addition for Grade 1

Master expanded form with addition: place value understanding, step-by-step methods, and detailed solutions through these 5 exercises.

Expanded Form with Addition

Visual Guide to Understanding Place Value Addition

🔟
Tens Place
Groups of 10
1️⃣
Ones Place
Individual units
📝
Expanded Form
Break numbers into parts
➕
Addition
Combine the parts
1
Expand Both Numbers
2
Group Tens Together
3
Group Ones Together
4
Add and Combine
(20 + 5) + (10 + 3)
+
= (20 + 10) + (5 + 3)
=
30 + 8 = 38
Worksheet: Exercises 1 to 3
1 Basic Addition
Exercise 1
Solve: 25 + 13 using expanded form addition
Definition:

Expanded Form Addition: Adding numbers by breaking them into tens and ones, then adding like place values separately

Addition Method:
  1. Write both numbers in expanded form
  2. Add the tens together
  3. Add the ones together
  4. Combine the sums
  5. Write final answer in standard form
Step 1: Write in expanded form

25 = 20 + 5

13 = 10 + 3

Step 2: Group like place values

(20 + 5) + (10 + 3) = (20 + 10) + (5 + 3)

Step 3: Add tens together

20 + 10 = 30

Step 4: Add ones together

5 + 3 = 8

Step 5: Combine results

30 + 8 = 38

25 + 13 = 38
Final Answer:

25 + 13 = 38

Applied Rules:

• Place Value Addition: Add tens to tens and ones to ones

• Expanded Form: Break numbers into tens and ones

• Verification: Check by adding directly: 25 + 13 = 38 ✓

2 Intermediate Addition
Exercise 2
Solve: 34 + 25 using expanded form addition
Step 1: Write in expanded form

34 = 30 + 4

25 = 20 + 5

Step 2: Group like place values

(30 + 4) + (20 + 5) = (30 + 20) + (4 + 5)

Step 3: Add tens together

30 + 20 = 50

Step 4: Add ones together

4 + 5 = 9

Step 5: Combine results

50 + 9 = 59

34 + 25 = 59
Final Answer:

34 + 25 = 59

Applied Rules:

• Place Value Addition: Add tens to tens and ones to ones

• Expanded Form: Break numbers into tens and ones

• Verification: Check by adding directly: 34 + 25 = 59 ✓

3 Practice Addition
Exercise 3
Solve: 42 + 17 using expanded form addition
Step 1: Write in expanded form

42 = 40 + 2

17 = 10 + 7

Step 2: Group like place values

(40 + 2) + (10 + 7) = (40 + 10) + (2 + 7)

Step 3: Add tens together

40 + 10 = 50

Step 4: Add ones together

2 + 7 = 9

Step 5: Combine results

50 + 9 = 59

42 + 17 = 59
Final Answer:

42 + 17 = 59

Applied Rules:

• Place Value Addition: Add tens to tens and ones to ones

• Expanded Form: Break numbers into tens and ones

• Verification: Check by adding directly: 42 + 17 = 59 ✓

Worksheet: Exercises 4 to 5
4 Advanced Addition
Exercise 4
Solve: 56 + 23 using expanded form addition
Step 1: Write in expanded form

56 = 50 + 6

23 = 20 + 3

Step 2: Group like place values

(50 + 6) + (20 + 3) = (50 + 20) + (6 + 3)

Step 3: Add tens together

50 + 20 = 70

Step 4: Add ones together

6 + 3 = 9

Step 5: Combine results

70 + 9 = 79

56 + 23 = 79
Final Answer:

56 + 23 = 79

Applied Rules:

• Place Value Addition: Add tens to tens and ones to ones

• Expanded Form: Break numbers into tens and ones

• Verification: Check by adding directly: 56 + 23 = 79 ✓

5 Challenge Problem
Exercise 5
Solve: 64 + 35 using expanded form addition
Step 1: Write in expanded form

64 = 60 + 4

35 = 30 + 5

Step 2: Group like place values

(60 + 4) + (30 + 5) = (60 + 30) + (4 + 5)

Step 3: Add tens together

60 + 30 = 90

Step 4: Add ones together

4 + 5 = 9

Step 5: Combine results

90 + 9 = 99

64 + 35 = 99
Final Answer:

64 + 35 = 99

Applied Rules:

• Place Value Addition: Add tens to tens and ones to ones

• Expanded Form: Break numbers into tens and ones

• Verification: Check by adding directly: 64 + 35 = 99 ✓

Comprehensive Summary: Expanded Form with Addition

Complete Guide to Expanded Form with Addition

This summary provides a comprehensive overview of expanded form addition, covering all essential concepts, methods, and practice strategies.

Key Definitions
  • Expanded Form: Writing a number as the sum of its place values (e.g., 25 = 20 + 5)
  • Place Value: The value of a digit based on its position in a number
  • Tens Place: The second digit from the right; represents groups of 10
  • Ones Place: The rightmost digit; represents individual units
  • Expanded Form Addition: Adding numbers by breaking them into tens and ones, then adding like place values separately
  • Like Place Values: Adding tens with tens and ones with ones
Core Rules & Principles
  • Place Value Rule: Each position has a specific value (ones, tens, hundreds, etc.)
  • Tens Rule: Tens digit × 10 = tens value
  • Ones Rule: Ones digit × 1 = ones value
  • Addition Rule: Add like place values together (tens with tens, ones with ones)
  • Verification Rule: Adding expanded parts gives the original number
Step-by-Step Method
  1. Expand Both Numbers: Write each number in expanded form (tens + ones)
  2. Group Like Values: Rearrange to group tens together and ones together
  3. Add Tens: Add all the tens values together
  4. Add Ones: Add all the ones values together
  5. Combine Results: Add the tens sum to the ones sum
  6. Verify: Check by adding original numbers directly
Examples & Practice

Simple Examples:

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

15 + 22: (10 + 5) + (20 + 2) = (10 + 20) + (5 + 2) = 30 + 7 = 37

Intermediate Examples:

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

46 + 13: (40 + 6) + (10 + 3) = (40 + 10) + (6 + 3) = 50 + 9 = 59

Advanced Examples:

57 + 32: (50 + 7) + (30 + 2) = (50 + 30) + (7 + 2) = 80 + 9 = 89

68 + 21: (60 + 8) + (20 + 1) = (60 + 20) + (8 + 1) = 80 + 9 = 89

Tips & Tricks
  • Always Expand First: Break both numbers into tens and ones before adding
  • Group Together: Put all tens in one group and all ones in another
  • Add Separately: Add tens to tens, then ones to ones
  • Combine Carefully: Add the tens sum to the ones sum
  • Verify Always: Check by adding original numbers directly
Common Pitfalls
  • Mixing Place Values: Adding tens to ones instead of like values
  • Forgetting Expansion: Trying to add without breaking into place values
  • Grouping Error: Not organizing tens and ones separately
  • Combining Mistakes: Adding the wrong sums together
  • Verification Neglect: Not checking the final answer
Memory Aids
  • "Tens with Tens, Ones with Ones": Always add like place values
  • "Expand First": Break numbers into tens and ones before adding
  • "Group and Add": Group like values, then add each group
  • "Combine Last": Add the group totals together
  • "Check Always": Verify by direct addition
Key Takeaways
  • Expanded form addition helps understand place value relationships
  • Adding like place values separately makes addition clearer
  • Every two-digit number can be broken into tens and ones
  • Verification builds confidence and prevents errors
  • Practice with various numbers strengthens place value understanding

Questions & Answers

Question: Why do we need to break numbers into tens and ones for addition? Can't I just add them directly?

Answer: You can add directly, but expanded form addition helps you understand what's really happening. When you break numbers into tens and ones, you see that you're adding groups of 10 separately from individual units. This builds a strong foundation for understanding place value, which makes harder math much easier later. It's like learning to walk before running - it might seem slower now, but it makes everything else easier!

Question: How do I know which numbers to add together when using expanded form?

Answer: Always add like place values together! This means you add all the tens with other tens, and all the ones with other ones. For example, in (20 + 5) + (10 + 3), you add 20 + 10 (both are tens) and 5 + 3 (both are ones). Then combine the results: 30 + 8 = 38. Remember: "Tens with tens, ones with ones!"

Question: How can I check if I did the expanded form addition correctly?

Answer: The best way to check your expanded form addition is to add the original numbers directly and see if you get the same answer. For example, if you calculated 25 + 13 = 38 using expanded form, check by adding 25 + 13 directly to see if you still get 38. You can also use base-10 blocks or drawings to verify your answer visually.