Worksheets on Composing and Decomposing Numbers in Grade 1

Master composing and decomposing numbers: place value, number bonds, addition/subtraction relationships, and visual representations through these 5 detailed worksheets.

Worksheet: Exercises 1 to 3
1 Number Bonds to 10
Exercise 1
Complete the number bonds for 10:
7 + ___ = 10
4 + ___ = 10
6 + ___ = 10
Definition:

Number Bond: A pair of numbers that add up to a target number (like 10).

Number Bond Method:
  1. Identify the known part of the bond
  2. Think: "What number added to the known part makes the target?"
  3. Use counting on or subtraction to find the missing part
  4. Verify by adding both parts together
10
7
3
Step 1: For 7 + ___ = 10

Think: "7 + ? = 10" or "10 - 7 = ?"

Step 2: Count up from 7 to 10

7, 8, 9, 10 → That's 3 more

Step 3: Verify the answer

7 + 3 = 10 ✓

Step 4: Complete all bonds

7 + 3 = 10, 4 + 6 = 10, 6 + 4 = 10

7 + 3 = 10, 4 + 6 = 10, 6 + 4 = 10
Final answers:

7 + 3 = 10, 4 + 6 = 10, 6 + 4 = 10

Applied rules:

• Bond Rule: Two numbers that add to the target

• Subtraction Rule: Target - known = unknown

• Verification Rule: Sum must equal the target

2 Decomposing Numbers
Exercise 2
Break apart these numbers into two parts:
8 = ___ + ___
12 = ___ + ___
15 = ___ + ___
Definition:

Decomposing: Breaking a number into smaller parts that add up to the original number.

8
5
3
Step 1: For 8 = ___ + ___

Find two numbers that add to 8: 5 + 3 = 8

Step 2: For 12 = ___ + ___

Think of 12 as 10 + 2, or find other pairs: 7 + 5 = 12

Step 3: For 15 = ___ + ___

15 can be 10 + 5, or 8 + 7, or 9 + 6

Step 4: Verify all decompositions

5 + 3 = 8 ✓, 7 + 5 = 12 ✓, 10 + 5 = 15 ✓

8 = 5 + 3, 12 = 7 + 5, 15 = 10 + 5
Final answers:

8 = 5 + 3, 12 = 7 + 5, 15 = 10 + 5

Applied rules:

• Decomposition Rule: Parts must sum to whole

• Flexibility Rule: Same number can be decomposed multiple ways

• Verification Rule: Check that parts add to original

3 Place Value Decomposition
Exercise 3
Decompose these numbers by place value:
24 = ___ tens + ___ ones
37 = ___ tens + ___ ones
50 = ___ tens + ___ ones
Definition:

Place Value Decomposition: Breaking a number into tens and ones based on digit positions.

24
→
2 TENS 4 ONES
10
10
1
1
1
1
Step 1: For 24

2 is in tens place (2 × 10 = 20), 4 is in ones place (4 × 1 = 4)

Step 2: For 37

3 tens (3 × 10 = 30), 7 ones (7 × 1 = 7)

Step 3: For 50

5 tens (5 × 10 = 50), 0 ones (0 × 1 = 0)

Step 4: Verify each decomposition

20 + 4 = 24 ✓, 30 + 7 = 37 ✓, 50 + 0 = 50 ✓

24 = 2 tens + 4 ones, 37 = 3 tens + 7 ones, 50 = 5 tens + 0 ones
Final answers:

24 = 2 tens + 4 ones, 37 = 3 tens + 7 ones, 50 = 5 tens + 0 ones

Applied rules:

• Place Value Rule: Left digit = tens, right digit = ones

• Multiplication Rule: Tens digit × 10, ones digit × 1

• Addition Rule: Tens + ones = original number

Composing and Decomposing Guide
Part + Part = Whole
Number Bond Formula
Composing
Part + Part = Whole
Building larger numbers
Decomposing
Whole = Part + Part
Breaking apart numbers
Place Value
AB = A×10 + B×1
Value based on position
Key definitions:

Composing: Putting together smaller numbers to make a larger number

Decomposing: Taking apart a number into smaller parts

Number Bond: Two numbers that combine to make a target number

Complete methodology:
  1. Identify the operation: Are you composing (adding) or decomposing (subtracting)?
  2. Find the relationship: What parts make up the whole?
  3. Apply the method: Use addition for composing, subtraction for decomposing
  4. Verify the result: Check that parts combine correctly
Tip 1: Use visual models like number bonds or ten frames to see the relationship.
Tip 2: Practice with number bonds to 10 first, then move to larger numbers.
Tip 3: Remember: composing is like putting puzzle pieces together.
Tip 4: Remember: decomposing is like taking apart a puzzle.
Common errors: Confusing composing with decomposing, forgetting to verify answers.
Memory aid: "Compose = Put Together, Decompose = Take Apart."
Essential Rules:

• Relationship Rule: Part + Part = Whole

• Commutative Rule: Order doesn't matter (3 + 4 = 4 + 3)

• Verification Rule: Always check that parts add to whole

• Place Value Rule: Position determines value

Number Bond Examples

10
7
3
15
8
7
Worksheet: Exercises 4 to 5
4 Composing Numbers
Exercise 4
Put together these parts to make whole numbers:
20 + 3 = ___
40 + 8 = ___
50 + 0 = ___
Definition:

Composing: Adding parts together to create a whole number.

20 + 3 = 23
10
10
1
1
1
Step 1: For 20 + 3

20 (2 tens) + 3 (3 ones) = 2 tens and 3 ones = 23

Step 2: For 40 + 8

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

Step 3: For 50 + 0

50 (5 tens) + 0 (0 ones) = 5 tens and 0 ones = 50

Step 4: Verify all compositions

20 + 3 = 23 ✓, 40 + 8 = 48 ✓, 50 + 0 = 50 ✓

20 + 3 = 23, 40 + 8 = 48, 50 + 0 = 50
Final answers:

20 + 3 = 23, 40 + 8 = 48, 50 + 0 = 50

Applied rules:

• Composing Rule: Add tens and ones separately

• Place Value Rule: Combine tens with tens, ones with ones

• Addition Rule: Simple addition of parts

5 Mixed Practice
Exercise 5
Complete the following:
35 = ___ + ___ (tens + ones)
6 + ___ = 12
18 = 10 + ___
Definition:

Mixed Practice: Problems that require both composing and decomposing skills.

35
→
30 + 5
10
10
10
1
Step 1: For 35 = ___ + ___

35 = 3 tens + 5 ones = 30 + 5

Step 2: For 6 + ___ = 12

Think: 12 - 6 = 6, so 6 + 6 = 12

Step 3: For 18 = 10 + ___

Think: 18 - 10 = 8, so 10 + 8 = 18

Step 4: Verify all answers

30 + 5 = 35 ✓, 6 + 6 = 12 ✓, 10 + 8 = 18 ✓

35 = 30 + 5, 6 + 6 = 12, 18 = 10 + 8
Final answers:

35 = 30 + 5, 6 + 6 = 12, 18 = 10 + 8

Applied rules:

• Decomposition Rule: Separate tens and ones

• Addition Rule: Missing addend calculation

• Verification Rule: Always check final answers

Complete Summary: Composing and Decomposing Numbers
Part + Part = Whole
Core Relationship
Key definitions:

Composing: Combining two or more numbers to make a larger number

Decomposing: Breaking a number into smaller parts that add up to the original

Number Bond: A pair of numbers that add up to a specific total

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

Complete methodology:
  1. Identify the task: Determine if you're composing (adding) or decomposing (breaking apart)
  2. Recognize the structure: Look for tens and ones, or missing addends
  3. Apply the operation: Use addition for composing, subtraction for decomposing
  4. Verify your work: Check that your answer makes sense and adds up correctly
Tip 1: Use visual models like base-10 blocks to physically compose and decompose numbers.
Tip 2: Practice number bonds daily to build fluency with addition facts.
Tip 3: Remember that decomposing can be done in multiple ways (e.g., 8 = 5+3 or 4+4).
Tip 4: Use counting strategies: "count on" for composing, "count back" for decomposing.
Foundation Skill: These concepts are essential for future addition and subtraction.
Real-world use: Helps with money counting, measuring, and problem-solving.
Essential Rules:

• Part-Whole Rule: Part + Part = Whole

• Commutative Rule: Order of parts doesn't change the whole

• Place Value Rule: Position determines the value of digits

• Verification Rule: Always check that parts add to the original number

• Flexibility Rule: Same number can be decomposed multiple ways

Examples of Composing and Decomposing

Type Problem Answer Verification
Composing 20 + 7 27 20 + 7 = 27 ✓
Decomposing 15 = ___ + ___ 10 + 5 10 + 5 = 15 ✓
Place Value 43 = ___ tens + ___ ones 4 tens + 3 ones 40 + 3 = 43 ✓
Number Bond 6 + ___ = 10 6 + 4 = 10 6 + 4 = 10 ✓

Questions & Answers

Question: My child is struggling to understand the difference between composing and decomposing numbers. How can I make this clearer?

Answer: Think of it in terms of building and taking apart:

  • Composing = Building: Like putting puzzle pieces together to make a picture (20 + 3 = 23)
  • Decomposing = Taking apart: Like breaking down a LEGO structure into individual pieces (23 = 20 + 3)

Use concrete objects: Give your child 8 blocks and ask them to put them into 2 groups. Then ask them to put the groups back together. This hands-on experience helps them see that composing and decomposing are opposite actions that preserve the total amount.

Remember: composing is putting together, decomposing is taking apart. Both result in the same total number!

Question: How can I help students who are having trouble with number bonds to 10? They seem to forget them quickly.

Answer: Building number bond fluency requires multiple approaches:

  1. Visual representation: Use ten frames, fingers, or manipulatives to see the relationships
  2. Pattern recognition: Notice that 7 + 3 = 10 and 3 + 7 = 10 (commutative property)
  3. Story connections: Create stories like "7 birds were sitting on a branch, 3 more flew over"
  4. Regular practice: 5-10 minutes daily with different activities
  5. Games and songs: Make it fun and memorable

Focus on one family at a time (like bonds to 5 first, then 10), and connect to real-life situations. The more senses involved, the better the retention!

Question: Some students think there's only one way to decompose a number. How can I show them flexibility?

Answer: Demonstrate with hands-on activities that the same total can be broken into different parts:

  • Give 8 blocks and have students separate them into different pairs (5+3, 4+4, 6+2, 7+1)
  • Show that 8 = 8+0, 7+1, 6+2, 5+3, 4+4, 3+5, 2+6, 1+7, 0+8
  • Use the same number in different contexts (8 apples could be 3 red + 5 green, or 2 big + 6 small)

Emphasize that while the parts can vary, the whole always stays the same. This flexibility is crucial for developing number sense and later mathematical reasoning. Show them that being able to see numbers in multiple ways is a strength, not a weakness!