Composing and Decomposing Numbers Assessment for Grade 1 Students

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

Complete Summary: Compose and Decompose 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
Assessment
Testing understanding of number composition
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

Assessment: Testing and evaluating understanding of mathematical concepts

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 4 tens and 7 ones.
What number do you get?
Step 1: Identify the parts
Tens
4 tens
Ones
7 ones
Step 2: Convert tens to value

4 tens = 4 × 10 = 40

Step 3: Keep ones as value

7 ones = 7 × 1 = 7

Step 4: Add together

40 + 7 = 47

Step 5: Visual representation
47 =
4 tens + 7 ones = 47
4 tens + 7 ones = 47
Explanation:

When we compose 4 tens (40) and 7 ones (7), we get 47. The 4 goes in the tens place and the 7 goes in the ones place.

2 Decompose numbers
Exercise 2
Decompose the number 63 into tens and ones.
How many tens and how many ones?
Step 1: Identify the number
6
3

Number: 63

Step 2: Identify tens and ones
Tens Place
6
Ones Place
3

63 has 6 tens and 3 ones

Step 3: Visual representation
63 =
6 tens + 3 ones = 63
Step 4: Write the decomposition

63 = 60 + 3

63 = 6 tens + 3 ones

63 = 6 tens + 3 ones
Explanation:

When we decompose 63, we break it into 6 tens (60) and 3 ones (3). The 6 in the tens place represents 60, and the 3 in the ones place represents 3.

3 Compose and verify
Exercise 3
If you have 5 tens and 2 ones, what number do you get?
Then decompose that number back to check your work.
Step 1: Compose the number
Tens
5 tens = 50
+
Ones
2 ones = 2
=
Result
52

5 tens + 2 ones = 50 + 2 = 52

Step 2: Verify by decomposing
5
2

52 has 5 tens and 2 ones

Step 3: Check the values

5 tens = 50

2 ones = 2

50 + 2 = 52 ✓

Step 4: Visual verification
52 =
5 tens + 2 ones = 52
5 tens + 2 ones = 52
52 = 5 tens + 2 ones
Explanation:

We composed 5 tens (50) and 2 ones (2) to get 52. Then we decomposed 52 back to 5 tens and 2 ones to verify our answer is correct.

Exercises 4 to 5 Solutions
4 Mixed operations
Exercise 4
Decompose 89, then compose the parts back together to verify.
Show both processes clearly.
Step 1: Decompose 89
8
9

89 has 8 tens and 9 ones

89 = 80 + 9

89 = 8 tens + 9 ones

Step 2: Visual decomposition
89 =
8 tens + 9 ones = 89
Step 3: Compose back together
8 tens
80
+
9 ones
9
=
Result
89
Step 4: Final verification

89 = 80 + 9 = 89 ✓

89 = 8 tens + 9 ones
8 tens + 9 ones = 89
Explanation:

We decomposed 89 into 8 tens (80) and 9 ones (9), then composed those parts back to get 89. This confirms our understanding of place value.

5 Assessment challenge
Exercise 5
If 3 tens and 4 ones make a number, and that number is decomposed, what parts would you get?
Show the full cycle: compose → decompose → verify.
Step 1: Compose 3 tens and 4 ones
3 tens
30
+
4 ones
4
=
Result
34

3 tens + 4 ones = 30 + 4 = 34

Step 2: Decompose the result (34)
3
4

34 has 3 tens and 4 ones

34 = 30 + 4

34 = 3 tens + 4 ones

Step 3: Visual representation
34 =
3 tens + 4 ones = 34
Step 4: Verification cycle

Original: 3 tens + 4 ones → Compose → 34

Then: 34 → Decompose → 3 tens + 4 ones

Full cycle completed successfully!

3 tens + 4 ones = 34
34 = 3 tens + 4 ones
Explanation:

This exercise demonstrates the inverse relationship between composing and decomposing. Starting with 3 tens and 4 ones, we composed them to get 34. Then we decomposed 34 back to 3 tens and 4 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: 3 tens + 5 ones = 35
  • Decompose: Like taking apart a block structure. For numbers: 47 = 4 tens + 7 ones
  • Real example: If you have 2 tens (20) and 8 ones (8), you compose them to make 28
  • Reverse: If you have 28, you can decompose it to 2 tens 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!