PDF Content: Exercises 1 to 3
1 Composing Numbers
Exercise 1
Show different ways to make 5 using circles (PDF format)
Composing Numbers: Making 5
Grade 1 Mathematics - Place Value
Definition:
Composing numbers: Putting parts together to make a whole number.
Method:
- Start with a target number
- Find different combinations that equal the target
- Use visual models to show the parts
Visual Models:
5
2
3
OR
5
1
4
Ways to Make 5:
0+5, 1+4, 2+3, 3+2, 4+1, 5+0
Answer:
5 can be made in 6 different ways using number bonds.
Rules:
- Part-whole relationship: Parts combine to make the whole
- Commutative property: Order doesn't matter (2+3 = 3+2)
- Number flexibility: Same number can be made in multiple ways
Try This:
Find all the ways to make the number 6 using number bonds.
2 Decomposing Numbers
Exercise 2
Break apart 7 into two groups in different ways (PDF format)
Decomposing Numbers: Breaking Apart 7
Grade 1 Mathematics - Place Value
Definition:
Decomposing numbers: Breaking a number into smaller parts.
Visual Model:
7
3
4
OR
7
5
2
Decomposition Process:
1
1
1
1
1
1
1
7 circles total
→
1
1
1
Group 1: 3
1
1
1
1
Group 2: 4
Decompositions of 7:
0+7, 1+6, 2+5, 3+4, 4+3, 5+2, 6+1, 7+0
Answer:
7 can be broken into 8 different pairs of numbers.
Rules:
- Any number can be broken into parts
- Work systematically to find all combinations
- Check that parts add up to the whole
Try This:
Decompose the number 8 into all possible pairs.
3 Number Bonds
Exercise 3
Complete the number bond: 6 = 2 + ? (PDF format)
Number Bonds: Finding Missing Parts
Grade 1 Mathematics - Place Value
Definition:
Number bonds: Visual representations showing how numbers are related as parts of a whole.
Problem:
Complete the number bond: 6 = 2 + ?
Visual Solution:
6
2
?
→
6
2
4
Solution Steps:
- Identify what you know: Total is 6, one part is 2
- Use subtraction: 6 - 2 = 4
- Verify: 2 + 4 = 6 ✓
- Complete: 6 = 2 + 4
Answer:
The missing number is 4. 6 = 2 + 4
Rules:
- Whole minus known part = unknown part
- Number bonds help understand addition/subtraction
- Always verify that parts add to the whole
Try This:
Complete the number bond: 9 = 4 + ?
PDF Features & Educational Benefits
PDF = Portable Document Format
Educational Tool
Portable
PDF
Accessible anywhere
Printable
Hard copy
Physical worksheets
Shareable
Digital
Distributed easily
PDF Educational Benefits
Advantages:
- Consistent formatting: Looks the same on all devices
- Print-friendly: Easy to print for hands-on practice
- Shareable: Can be distributed to students and parents
- Archivable: Can be saved and referenced later
- Accessible: Works offline without internet
Best Practices:
- Include visual models and diagrams
- Provide clear step-by-step instructions
- Add practice exercises with solutions
- Use consistent formatting and fonts
- Include answer keys for self-checking
Interactive Elements:
- Fillable forms for student input
- QR codes linking to video tutorials
- Hyperlinks to related resources
- Embedded multimedia content
- Interactive quizzes and games
Composing & Decomposing Concepts
Core Concepts:
- Part-Whole Relationship: Understanding that numbers can be broken into parts and parts can be combined to make a whole
- Number Bonds: Visual representations showing how numbers are related
- Number Flexibility: Ability to see numbers in different ways
- Place Value: Understanding the value of digits based on their position
- Decomposition: Breaking larger numbers into smaller parts
Developmental Progression:
- Recognize small numbers (1-5)
- Understand number combinations
- Use visual models consistently
- Transition to abstract thinking
- Apply to problem-solving
PDF Content: Exercises 4 to 5
4 Problem Solving
Exercise 4
Word problem: Tom has 8 apples, puts 3 in backpack. How many in lunch box? (PDF format)
Word Problems: Applying Number Bonds
Grade 1 Mathematics - Place Value
Problem:
Tom has 8 apples. He puts some in his backpack and some in his lunch box. If he puts 3 in his backpack, how many does he put in his lunch box?
Visual Model:
8
3
?
→
8
3
5
Solution Steps:
- Total apples = 8
- Apples in backpack = 3
- Apples in lunch box = 8 - 3 = 5
- Check: 3 + 5 = 8 ✓
Answer:
Tom puts 5 apples in his lunch box.
Real-World Connection:
- Apply math to everyday situations
- Use subtraction to find missing parts
- Verify answers make sense in context
Try This:
Sarah has 10 stickers. She gives 4 to her friend. How many does she have left?
5 Number Puzzles
Exercise 5
Number puzzle: I'm thinking of a number made with 4 and 6. What am I? (PDF format)
Number Puzzles: Flexible Thinking
Grade 1 Mathematics - Place Value
Puzzle:
I am thinking of a number. When I break it apart, I can make it with 4 and 6. What number am I thinking of? Show 3 other ways to make this number.
Visual Model:
?
4
6
→
10
4
6
Solution Steps:
- If 4 and 6 make the number, then 4 + 6 = 10
- Find other combinations for 10: 0+10, 1+9, 2+8, 3+7, 5+5
- Select 3 additional combinations: 1+9, 2+8, 3+7
- Verify: 1+9=10, 2+8=10, 3+7=10
Answer:
The number is 10. Three other ways: 1+9, 2+8, 3+7
Number Flexibility:
- Same number can be made in multiple ways
- Work systematically to find all possibilities
- Check that all combinations equal the target number
Try This:
I'm thinking of a number that can be made with 3 and 5. What number am I? Show 4 other ways.
Complete PDF Summary: Composing and Decomposing Numbers
Complete Summary: Composing and Decomposing Numbers
Grade 1 Mathematics - Place Value
Key Definitions:
- Composing numbers: Putting smaller numbers together to make a larger number
- Decomposing numbers: Breaking a larger number into smaller parts
- Number bonds: Visual tools showing the relationship between a number and its parts
- Part-whole relationship: A mathematical concept that a whole number can be divided into parts
- Number flexibility: The ability to see numbers in different ways and understand their relationships
Core Methods:
- Identify the target number: Determine what number you're working with
- Find all possible combinations: Systematically explore different ways to compose/decompose
- Use visual models: Draw circles, groups, or number bonds to represent relationships
- Verify results: Check that all parts add up to the whole
Essential Rules:
- Part + Part = Whole (composition)
- Whole - Part = Other Part (decomposition)
- For any number n: n = 0+n, 1+(n-1), 2+(n-2), ..., n+0
- Commutative property: a + b = b + a
- Number bonds show the relationship between parts and whole
Teaching Tips:
- Use your hands! Hold up fingers to show number bonds
- Think of numbers as "friends" that like to play together
- Look for patterns: as one number gets bigger, the other gets smaller
- Practice every day with small numbers (up to 10) to build strong foundations
- Use concrete objects like blocks or toys to visualize concepts
Common Mistakes:
- Forgetting to include the combination where one part is zero
- Mixing up the concept of parts and whole
- Not working systematically when finding all combinations
- Forgetting to verify that parts add up to the whole
Success Strategies:
- Start with all objects in one group, then move them one by one
- Use visual models consistently to build understanding
- Practice with manipulatives before moving to abstract thinking
- Connect concepts to real-world situations
- Encourage multiple representations of the same number
Practice Problems:
- Find all ways to make 8 using number bonds
- Complete the number bond: 9 = 4 + ?
- Decompose 12 into two equal parts
- Solve: Tom has 7 cookies. He eats 3. How many are left?
PDF Learning Guide
PDF Benefits
Consistent: Same appearance across all devices
Printable: Physical copies for hands-on practice
Accessible: Works offline without internet
Learning Path
Visual: Start with concrete models
Conceptual: Understand part-whole relationships
Abstract: Apply to problem-solving
Key Points
Flexibility: Same number, different parts
Patterns: As one part increases, the other decreases
Verification: Always check that parts add to whole
PDF Learning Process
1
Read
2
Practice
3
Apply
4
Verify
Master Numbers: PDF Guides Build Strong Foundations!