Composing and Decomposing Numbers for Grade 1 Students

Master composing and decomposing numbers up to 100 using place value: tens and ones, number breakdown, and understanding relationships.

Complete Summary: Composing and Decomposing Numbers
Core Concepts Explained
Compose
Put together tens and ones to make a number
Decompose
Break apart a number into tens and ones
Place Value
Value of a digit based on its position
Inverse Operations
Opposite operations that undo each other
Key Definitions:

Compose: To put together parts to make a whole number (e.g., 3 tens + 5 ones = 35)

Decompose: To break apart a number into its parts (e.g., 47 = 4 tens + 7 ones)

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

Tens Place: The leftmost digit in a 2-digit number representing groups of 10

Ones Place: The rightmost digit in a 2-digit number representing individual units

Inverse Operations: Operations that undo each other (compose and decompose)

Base-10: Our number system based on groups of 10

Core Rules and Laws:

• Rule 1: 1 ten = 10 ones (10 individual units = 1 group of 10)

• Rule 2: The position of a digit determines its value

• Rule 3: Tens place value is 10 times the ones place value

• Rule 4: Every 10 ones can be regrouped as 1 ten

• Rule 5: Numbers can be decomposed into tens + ones

• Law: Composition and decomposition are inverse operations

Compose Method:
  1. Step 1: Identify the tens and ones parts
  2. Step 2: Convert tens to their value (tens × 10)
  3. Step 3: Keep ones as their value
  4. Step 4: Add tens and ones together
  5. Step 5: Write the final number
Decompose Method:
  1. Step 1: Identify the number to decompose
  2. Step 2: Look at the tens digit (left digit)
  3. Step 3: Look at the ones digit (right digit)
  4. Step 4: Express as: number = tens + ones
  5. Step 5: Verify by recomposing
Tip 1: Remember: compose = put together, decompose = take apart!
Tip 2: Use base-10 blocks to visualize the process.
Tip 3: Always check your work by going both directions.
Tip 4: Count by tens first, then add the ones.
Common Pitfalls: Confusing tens and ones positions, forgetting to multiply tens by 10, miscounting groups.
Memory Aids: "Tens on the left, ones on the right", "10 ones make 1 ten", "Position tells the value".
Key Takeaways:

• Compose and decompose are opposite operations

• Tens place value is always 10 times the ones place

• 10 individual units can be grouped as 1 ten

• Practice both operations to strengthen understanding

• Always verify your answers by checking both directions

Exercises 1 to 3 Solutions
1 Compose numbers
Exercise 1
Compose the number from 2 tens and 8 ones.
What number do you get?
Step 1: Identify the parts
Tens
2 tens
→
Value
20
Ones
8 ones
→
Value
8
Step 2: Convert tens to value

2 tens = 2 × 10 = 20

Step 3: Keep ones as value

8 ones = 8 × 1 = 8

Step 4: Add together

20 + 8 = 28

Step 5: Visual representation
28 =
2 tens + 8 ones = 28
2 tens + 8 ones = 28
Explanation:

When we compose 2 tens (20) and 8 ones (8), we get 28. The 2 goes in the tens place and the 8 goes in the ones place.

2 Decompose numbers
Exercise 2
Decompose the number 54 into tens and ones.
How many tens and how many ones?
Step 1: Identify the number
5
4

Number: 54

Step 2: Identify tens and ones
Tens Place
5
Ones Place
4

54 has 5 tens and 4 ones

Step 3: Visual representation
54 =
5 tens + 4 ones = 54
Step 4: Write the decomposition

54 = 50 + 4

54 = 5 tens + 4 ones

54 = 5 tens + 4 ones
Explanation:

When we decompose 54, we break it into 5 tens (50) and 4 ones (4). The 5 in the tens place represents 50, and the 4 in the ones place represents 4.

3 Compose and verify
Exercise 3
If you have 7 tens and 3 ones, what number do you get?
Then decompose that number back to check your work.
Step 1: Compose the number
7 tens
70
+
3 ones
3
=
Result
73

7 tens + 3 ones = 70 + 3 = 73

Step 2: Verify by decomposing
7
3

73 has 7 tens and 3 ones

Step 3: Check the values

7 tens = 70

3 ones = 3

70 + 3 = 73 ✓

Step 4: Visual verification
73 =
7 tens + 3 ones = 73
7 tens + 3 ones = 73
73 = 7 tens + 3 ones
Explanation:

We composed 7 tens (70) and 3 ones (3) to get 73. Then we decomposed 73 back to 7 tens and 3 ones to verify our answer is correct.

Exercises 4 to 5 Solutions
4 Mixed operations
Exercise 4
Decompose 91, then compose the parts back together to verify.
Show both processes clearly.
Step 1: Decompose 91
9
1

91 has 9 tens and 1 one

91 = 90 + 1

91 = 9 tens + 1 one

Step 2: Visual decomposition
91 =
9 tens + 1 one = 91
Step 3: Compose back together
9 tens
90
+
1 one
1
=
Result
91
Step 4: Final verification

91 = 90 + 1 = 91 ✓

91 = 9 tens + 1 one
9 tens + 1 one = 91
Explanation:

We decomposed 91 into 9 tens (90) and 1 one (1), then composed those parts back to get 91. This confirms our understanding of place value.

5 Challenge exercise
Exercise 5
If 4 tens and 6 ones make a number, and that number is decomposed, what parts would you get?
Show the full cycle: compose → decompose → verify.
Step 1: Compose 4 tens and 6 ones
4 tens
40
+
6 ones
6
=
Result
46

4 tens + 6 ones = 40 + 6 = 46

Step 2: Decompose the result (46)
4
6

46 has 4 tens and 6 ones

46 = 40 + 6

46 = 4 tens + 6 ones

Step 3: Visual representation
46 =
4 tens + 6 ones = 46
Step 4: Verification cycle

Original: 4 tens + 6 ones → Compose → 46

Then: 46 → Decompose → 4 tens + 6 ones

Full cycle completed successfully!

4 tens + 6 ones = 46
46 = 4 tens + 6 ones
Explanation:

This exercise demonstrates the inverse relationship between composing and decomposing. Starting with 4 tens and 6 ones, we composed them to get 46. Then we decomposed 46 back to 4 tens and 6 ones, completing the full cycle and verifying our understanding.

Questions & Answers

Question: I don't understand what "compose" and "decompose" mean. Can you explain?

Answer: Great question! Think of it like building with blocks:

  • Compose: Like putting blocks together to build something. For numbers: 2 tens + 5 ones = 25
  • Decompose: Like taking apart a block structure. For numbers: 37 = 3 tens + 7 ones
  • Real example: If you have 1 ten (10) and 8 ones (8), you compose them to make 18
  • Reverse: If you have 18, you can decompose it to 1 ten and 8 ones

Compose = put together, Decompose = take apart. They are opposite operations that help you understand how numbers work!

Question: My child is struggling with place value. How can I help them practice composing and decomposing?

Answer: Here are effective practice strategies:

  • Use manipulatives: Base-10 blocks, straws bundled in tens, or legos grouped in tens
  • Draw pictures: Draw lines for tens and dots for ones
  • Play games: "What's my number?" where you give tens and ones and they guess
  • Daily practice: Pick random numbers and have them compose/decompose

Practice tip: Start with simple numbers like 10-20, then gradually increase. Always have your child explain their thinking to ensure understanding.

Make it fun with songs, rhymes, or story problems that involve real-life scenarios.

Question: Why do we need to learn to compose and decompose numbers? It seems hard.

Answer: Learning to compose and decompose numbers is very important! Here's why:

  • Real-world connections: Money, shopping, counting items
  • Easier addition/subtraction: 25 + 30 becomes 2 tens + 5 ones + 3 tens = 5 tens + 5 ones = 55
  • Future math: Needed for multiplication, division, and larger numbers
  • Problem solving: Helps you understand what numbers really mean

Think of it like understanding how a toy works - once you know how the pieces fit together, you can build anything!

Practice with everyday items: count your fingers (10 ones = 1 ten), group crayons in tens, or count coins in groups of 10.

It might seem hard now, but with practice, it becomes natural and very helpful!