Exercises 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 exercises.

Solution: Exercises 1 to 3
1 Number Bonds to 10
Exercise 1
Complete these number bonds:
4 + ___ = 10
6 + ___ = 10
8 + ___ = 10
Definition:

Number Bond: Two numbers that add together to make another number (like 10).

Number Bond Method:
  1. Look at the first number in the bond
  2. Think: "How many more to get to 10?"
  3. Count on from the first number
  4. Write the missing number
10
4
6

Composition Process:

Adding two parts to make the whole number (10).

Step 1: For 4 + ___ = 10

Start at 4, count up to 10: 5, 6, 7, 8, 9, 10 → That's 6 more

Step 2: For 6 + ___ = 10

Start at 6, count up to 10: 7, 8, 9, 10 → That's 4 more

Step 3: For 8 + ___ = 10

Start at 8, count up to 10: 9, 10 → That's 2 more

Step 4: Verify all answers

4 + 6 = 10 ✓, 6 + 4 = 10 ✓, 8 + 2 = 10 ✓

4 + 6 = 10, 6 + 4 = 10, 8 + 2 = 10
Final answers:

4 + 6 = 10, 6 + 4 = 10, 8 + 2 = 10

Applied rules:

• Counting On Rule: Start from known number and count up

• Number Bond Rule: Two parts make the whole

• Verification Rule: Check that parts add to target

2 Simple Decomposing
Exercise 2
Break these numbers into two parts:
7 = ___ + ___
9 = ___ + ___
5 = ___ + ___
Definition:

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

7
3
4

Decomposition Process:

Breaking the whole number into two smaller parts.

Step 1: For 7 = ___ + ___

Think of two numbers that add to 7: 3 + 4 = 7

Step 2: For 9 = ___ + ___

Think of two numbers that add to 9: 5 + 4 = 9

Step 3: For 5 = ___ + ___

Think of two numbers that add to 5: 2 + 3 = 5

Step 4: Verify all decompositions

3 + 4 = 7 ✓, 5 + 4 = 9 ✓, 2 + 3 = 5 ✓

7 = 3 + 4, 9 = 5 + 4, 5 = 2 + 3
Final answers:

7 = 3 + 4, 9 = 5 + 4, 5 = 2 + 3

Applied rules:

• Part-Whole Rule: Parts must add to the whole

• Flexibility Rule: Same number can be broken differently

• Verification Rule: Always check that parts equal original

3 Place Value Composition
Exercise 3
Put together these parts to make numbers:
20 + 5 = ___
30 + 8 = ___
40 + 2 = ___
Definition:

Composing with Place Value: Adding tens and ones together to make a two-digit number.

20 + 5
→
2 tens + 5 ones = 25
10
10
1
1
1
1
1

Place Value Composition:

Combining tens and ones to form larger numbers.

Step 1: For 20 + 5

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

Step 2: For 30 + 8

30 (3 tens) + 8 (8 ones) = 3 tens and 8 ones = 38

Step 3: For 40 + 2

40 (4 tens) + 2 (2 ones) = 4 tens and 2 ones = 42

Step 4: Verify all compositions

20 + 5 = 25 ✓, 30 + 8 = 38 ✓, 40 + 2 = 42 ✓

20 + 5 = 25, 30 + 8 = 38, 40 + 2 = 42
Final answers:

20 + 5 = 25, 30 + 8 = 38, 40 + 2 = 42

Applied rules:

• Place Value Rule: Tens and ones add to make the number

• Composition Rule: Put parts together to make whole

• Addition Rule: Simple addition of tens and ones

Composing & Decomposing Concept Guide
Part + Part = Whole
Core Formula
Composing
Part + Part = Whole
Putting numbers together
Decomposing
Whole = Part + Part
Breaking numbers apart
Place Value
20 + 5 = 25
Tens and ones
Key definitions:

Composing: Putting together smaller numbers to make a bigger number

Decomposing: Taking apart a number into smaller parts

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

Place Value: Understanding tens and ones in numbers

Complete methodology:
  1. Look at the problem: Is it adding (composing) or breaking (decomposing)?
  2. Use your fingers or objects: Touch and count to help understand
  3. Count on or back: Use counting strategies
  4. Check your answer: Make sure it makes sense
Tip 1: Use your fingers to show number bonds - it helps visualize the concept.
Tip 2: Practice with number bonds to 10 every day - they're very important.
Tip 3: Remember: composing = putting together, decomposing = taking apart.
Tip 4: Draw pictures or use objects to help understand the problems.
Foundation Skill: These skills build the foundation for all future math learning.
Memory aid: "Put Together = Compose, Take Apart = Decompose."
Essential Rules:

• Part-Whole Rule: Part + Part = Whole

• Counting Rule: Use fingers or objects to count

• Verification Rule: Always check that parts add to whole

• Place Value Rule: Understand tens and ones

Number Bonds

10
7
3
8
5
3
Solution: Exercises 4 to 5
4 Addition Practice
Exercise 4
Solve these addition problems:
13 = 10 + ___
17 = 10 + ___
19 = 10 + ___
Definition:

Adding to 10: Understanding how numbers from 11-19 are made of 10 plus some more.

13 = 10 + 3
→
13 is 10 and 3 more
10
1
1
1

Teen Number Composition:

All teen numbers are 10 plus some ones.

Step 1: For 13 = 10 + ___

13 is made of 10 and 3 more, so 13 = 10 + 3

Step 2: For 17 = 10 + ___

17 is made of 10 and 7 more, so 17 = 10 + 7

Step 3: For 19 = 10 + ___

19 is made of 10 and 9 more, so 19 = 10 + 9

Step 4: Verify all answers

10 + 3 = 13 ✓, 10 + 7 = 17 ✓, 10 + 9 = 19 ✓

13 = 10 + 3, 17 = 10 + 7, 19 = 10 + 9
Final answers:

13 = 10 + 3, 17 = 10 + 7, 19 = 10 + 9

Applied rules:

• Teen Number Rule: Numbers 11-19 are 10 + ones

• Place Value Rule: 10 is the base for teen numbers

• Addition Rule: Simple addition with 10

5 Mixed Practice
Exercise 5
Complete these mixed problems:
5 + ___ = 9
14 = 10 + ___
8 = ___ + ___
Definition:

Mixed Practice: Problems that mix composing and decomposing skills.

Mixed Practice
5 + 4 = 9 14 = 10 + 4 8 = 3 + 5
Step 1: For 5 + ___ = 9

Start at 5, count up to 9: 6, 7, 8, 9 → That's 4 more

Step 2: For 14 = 10 + ___

14 is 10 and 4 more, so 14 = 10 + 4

Step 3: For 8 = ___ + ___

Think of two numbers that add to 8: 3 + 5 = 8

Step 4: Verify all answers

5 + 4 = 9 ✓, 10 + 4 = 14 ✓, 3 + 5 = 8 ✓

5 + 4 = 9, 14 = 10 + 4, 8 = 3 + 5
Final answers:

5 + 4 = 9, 14 = 10 + 4, 8 = 3 + 5

Applied rules:

• Missing Addend Rule: Count up from known to target

• Place Value Rule: Teen numbers are 10 + ones

• Decomposition Rule: Find two numbers that add to target

Complete Summary: Composing & Decomposing Numbers
Part + Part = Whole
Foundation Formula
Key definitions:

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

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: Understanding that numbers have tens and ones parts

Complete methodology:
  1. Read the problem carefully: Understand if you're adding or breaking apart
  2. Use visual aids: Fingers, objects, or drawings to help
  3. Apply the operation: Use addition for composing, think of parts for decomposing
  4. Check your work: Make sure your answer makes sense
Tip 1: Practice number bonds to 10 every day - they're the building blocks of math.
Tip 2: Use your fingers to show the numbers - it helps you see the math.
Tip 3: Remember: numbers 11-19 are always 10 plus some more ones.
Tip 4: Draw pictures or use toys to help understand the problems.

Foundation Skill: These concepts are essential for all future math and beyond.
Real-world use: Helps with counting money, telling time, and solving problems.
Essential Rules:

• Part-Whole Rule: Part + Part = Whole

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

• Place Value Rule: Numbers have tens and ones places

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

• Teen Number Rule: Numbers 11-19 are 10 + ones

Examples

Type Problem Answer Explanation
Composing 10 + 5 15 1 ten and 5 ones = 15
Decomposing 8 = ___ + ___ 5 + 3 8 can be broken into 5 and 3
Number Bond 4 + ___ = 10 4 + 6 = 10 4 and 6 make 10
Place Value 17 = 10 + ___ 10 + 7 = 17 17 is 10 and 7 more

Questions & Answers

Question: My child is struggling with number bonds. What's the best way to practice them?

Answer: Number bonds are crucial for math success! Try these approaches:

  • Daily practice: Just 5-10 minutes with number bonds to 10
  • Hands-on materials: Use fingers, blocks, or counters to physically see the bonds
  • Games: Make it fun with dice games or card matching
  • Stories: Create simple stories like "I had 7 apples, ate some, now have 3 left"

Start with smaller numbers (to 5), then progress to 10. Use visual aids constantly - students learn best through concrete experiences before moving to abstract thinking.

Question: How can I help students understand that the same number can be decomposed in different ways?

Answer: Show flexibility through hands-on exploration:

  1. Use manipulatives: Give 6 blocks and have students separate them differently each time
  2. Show all possibilities: 6 = 0+6, 1+5, 2+4, 3+3, 4+2, 5+1, 6+0
  3. Real-life examples: "6 cookies could be 2 for me and 4 for you, or 3 each"
  4. Pattern recognition: Notice that as one part increases, the other decreases
  5. Regular practice: Daily exploration with different numbers

This flexibility is essential for students to develop number sense. It prepares them for mental math strategies and problem-solving flexibility.

Question: Some students confuse composing and decomposing. How can I clarify the difference?

Answer: Use clear action words and physical demonstrations:

  • Composing = PUTTING TOGETHER: Like building with blocks - combining parts
  • Decomposing = TAKING APART: Like breaking down a tower - separating into parts
  • Physical actions: Use hands to show coming together vs. moving apart
  • Visual cues: Arrows pointing together vs. arrows pointing away

Practice with real objects: "Let's COMPOSE 5 and 3 to make 8" (put together) vs. "Let's DECOMPOSE 8 into 5 and 3" (take apart). The physical action reinforces the concept for learners.