Instructions:
Draw circles to show different ways to make the number 5.
Example: Ways to make 5
5 = 2 + 3, 5 = 1 + 4, 5 = 0 + 5, 5 = 3 + 2, 5 = 4 + 1, 5 = 5 + 0
Visual Models:
5 circles = 5
5 = 2 + 3
5 = 1 + 4
Answer:
5 can be made in 6 different ways: 0+5, 1+4, 2+3, 3+2, 4+1, 5+0
Practice Problems:
Find ways to make 4: _______, _______, _______, _______, _______, _______
Find ways to make 6: _______, _______, _______, _______, _______, _______, _______, _______
Instructions:
Circle the number and then separate it into two groups.
Decomposing 7:
7 circles total
Group 1: 3
Group 2: 4
7 = 3 + 4
All Ways to Decompose 7:
7 = 0 + 7, 1 + 6, 2 + 5, 3 + 4, 4 + 3, 5 + 2, 6 + 1, 7 + 0
Answer:
7 can be decomposed into 8 different pairs of numbers.
Additional Practice:
Decompose 8: _______, _______, _______, _______, _______, _______, _______, _______, _______, _______
Decompose 9: _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______, _______,......
Composing and Decomposing Numbers Worksheet for Kindergarten - Grade 1
Learning to compose and decompose numbers through kindergarten-level worksheets: exploring number bonds, part-whole relationships, and number flexibility with these 5 detailed exercises.
Instructions:
Circle the groups of objects to show different ways to make the number 5.
Ways to Make 5:
5 = 5
5 = 2 + 3
5 = 1 + 4
Number Bonds:
Answer:
5 can be made as: 0+5, 1+4, 2+3, 3+2, 4+1, 5+0
Practice:
Find all ways to make 6: _______, _______, _______, _______, _______, _______
Instructions:
Separate the circles into two groups to show how 7 can be broken apart.
Decomposing 7:
7 circles total
Group 1: 3
Group 2: 4
All Combinations:
7 = 0+7, 1+6, 2+5, 3+4, 4+3, 5+2, 6+1, 7+0
Answer:
There are 8 different ways to make 7.
Practice:
Decompose 8: _______, _______, _______, _______, _______, _______, _______, _______, _______
Instructions:
Find the missing number to complete each number bond.
Problem 1: 6 = 2 + ?
6 - 2 = 4, so 6 = 2 + 4
Problem 2: 8 = 4 + ?
8 - 4 = 4, so 8 = 4 + 4
Problem 3: 5 = ? + 2
5 - 2 = 3, so 5 = 3 + 2
Answers:
6 = 2 + 4, 8 = 4 + 4, 5 = 3 + 2
Practice:
Complete: 9 = 3 + ?, 7 = 5 + ?, 4 = ? + 1
Composing numbers: Combining smaller numbers to make a larger number.
Decomposing numbers: Breaking a larger number into smaller parts.
Number bonds: Visual representations showing how numbers are related as parts of a whole.
Part-whole relationship: Understanding that numbers can be broken into parts and parts can be combined to make a whole.
Number flexibility: Ability to see numbers in different ways.
- Identify the whole: Determine the target number
- Find the parts: Look for combinations that make the whole
- Use visual models: Circles, groups, or number bonds to show relationships
- Verify: Check that parts add up to the whole
• Any number can be decomposed into different pairs of parts
• The order of parts doesn't change the whole (commutative property)
• To find a missing part: Whole - Known Part = Missing Part
• Number bonds help visualize part-whole relationships
• Practice with numbers up to 10 builds strong number sense
Word Problems:
Problem 1: Tom has 8 apples. He puts 3 in his backpack. How many does he put in his lunch box?
Solution:
8 - 3 = 5, so Tom puts 5 apples in his lunch box.
More Problems:
Problem 2: Sarah has 6 stickers. She gives 2 to her friend. How many does she have left?
Problem 3: There are 9 birds on a tree. 4 fly away. How many are left?
Answers:
Problem 1: 5 apples, Problem 2: 4 stickers, Problem 3: 5 birds
Number Puzzles:
Puzzle 1: I am thinking of a number. When I break it apart, I can make it with 4 and 3. What number am I?
Solution:
4 + 3 = 7, so the number is 7.
More Puzzles:
Puzzle 2: What two numbers make 9 if one of them is 5?
Puzzle 3: I have 6. One part is 2. What is the other part?
Answers:
Puzzle 1: 7, Puzzle 2: 4 (5 + 4 = 9), Puzzle 3: 4 (2 + 4 = 6)
Key Definitions:
Composing numbers: Putting parts together to make a whole number.
Decomposing numbers: Breaking a number into smaller parts.
Number bonds: Visual representations showing how numbers are related as parts of a whole.
Part-whole relationship: Understanding that numbers can be broken into parts and parts can be combined to make a whole.
Number flexibility: Ability to see numbers in different ways.
Core 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
Step-by-Step Methods:
- Identify the whole 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: Check that your parts add up to the whole
Examples:
Simple: 5 = 2 + 3, 5 = 1 + 4, 5 = 0 + 5
Advanced: 8 = 3 + 5, 8 = 2 + 6, 8 = 1 + 7, 8 = 0 + 8
Tips and Tricks:
- Use your 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 with concrete objects like blocks or toys
Common Pitfalls:
- 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
Key Takeaways:
- Numbers are flexible and can be broken apart and put back together
- Same number can be made in multiple ways
- Number bonds help visualize relationships
- Practice builds number sense and flexibility
Number Bonds Guide
Top circle: The whole number
Bottom circles: The parts that make up the whole
6 = 2 + 4
Same number, different parts:
5 = 0+5, 1+4, 2+3, 3+2, 4+1, 5+0
8 = 0+8, 1+7, 2+6, 3+5, 4+4, etc.
Pattern: As one part increases by 1, the other decreases by 1
Order doesn't matter: 2+3 = 3+2
All combinations: Include 0+number and number+0
Questions & Answers
Question: Why do we need to break numbers apart? Can't we just count them all together?
Answer: Great question! Breaking numbers apart helps us in many ways:
- It makes addition easier: 7 + 6 = 7 + 3 + 3 = 10 + 3 = 13
- It helps with subtraction: 10 - 4 = think of 10 as 6 + 4, so 10 - 4 = 6
- It builds number sense: understanding how numbers fit together
- It prepares you for bigger math: multiplication, division, and fractions
Think of it like having a puzzle - sometimes it's easier to work with smaller pieces than the whole thing!
Question: How can I help my child practice composing and decomposing numbers at home?
Answer: Here are some fun activities for home practice:
- Use toys: Have your child sort toys into two groups and count each group
- Play with food: Count crackers, then separate into two bowls
- Finger games: Show numbers on fingers and ask "How many on this hand?"
- Story problems: "You have 5 cookies. You eat 2. How many left?"
- Draw pictures: Draw circles and color them in different groups
Keep it playful and connected to real life - children learn best through hands-on activities!
Question: Sometimes I forget all the ways to make a number. How can I remember?
Answer: Here are some helpful strategies:
- Start with 0: Begin with 0 + the number, then 1 + ?, 2 + ?, etc.
- Use your fingers: Hold up the number of fingers, then fold some down
- Look for patterns: As one number goes up, the other goes down
- Practice regularly: Do a few minutes each day with the same numbers
- Use visual aids: Draw circles or use objects to represent the numbers
Remember, it takes practice! Start with smaller numbers like 5 or 6 before moving to bigger ones.