Solved Exercises on Breaking Apart Numbers for Grade 1

Master breaking apart numbers: addition and subtraction strategies with visual infographics, step-by-step solutions, and practice problems.

Breaking Apart Numbers Concepts & Visuals
BREAK APART NUMBERS SUMMARY

Definition: Breaking apart numbers means splitting a number into two or more smaller parts that add up to the original number.

Core Rules:

  • Any number can be broken into different parts
  • The parts must add up to the original number
  • There are often multiple ways to break apart a number
  • Breaking apart helps with addition and subtraction

Methods: Use visual models, number bonds, or mental partitioning to break numbers into parts.

Examples: 7 can be broken into 3 + 4, 2 + 5, 1 + 6, or 7 + 0

Tips: Practice with small numbers first, use manipulatives, and connect to real-life situations.

🧩 Breaking Apart Numbers
Split numbers into smaller parts that add up to the whole
Definition:

Breaking Apart Numbers: Splitting a number into two or more smaller numbers that add together to equal the original number.

Breaking Apart Method:
  1. Identify the number to break apart (the whole)
  2. Decide how many parts you want to create
  3. Choose the values for each part ensuring they add up to the whole
  4. Verify the parts add up to the original number
5 = 2 + 3
6 = 4 + 2
7 = 3 + 4
8 = 5 + 3
Key Rules:

• Parts must sum to whole: All parts added together equal the original number

• Multiple combinations: There are often several ways to break apart a number

• Strategic breaking: Break numbers in ways that help solve problems

• Visual representation: Use models to show the relationship between parts and whole

Tip 1: Use objects like blocks or counters to physically separate numbers.
Tip 2: Practice number bonds to understand how numbers relate to each other.
Tip 3: Connect breaking apart to real-life scenarios (sharing, grouping, etc.).
Solution: Exercises 1 to 3
1 Basic Number Breaking
Exercise 1
Break apart 5 into two parts
Strategy:

Breaking Apart: Split 5 into two smaller numbers that add up to 5.

2
Part 1
+
3
Part 2
Step 1: Identify the number to break apart

We need to break apart 5

Step 2: Choose two numbers that add to 5

2 + 3 = 5

Step 3: Verify the parts add up correctly

2 + 3 = 5 ✓

5 = 2 + 3
Final answer:

5 can be broken into 2 and 3

Applied rules:

• Part-Whole Relationship: Parts must sum to the whole number

• Decomposition: Split the number into smaller components

• Verification: Check that parts add up to the original number

2 Different Ways to Break
Exercise 2
Show two different ways to break apart 7
Strategy:

Multiple Decompositions: Show different ways to split 7 into parts.

Step 1: First way to break apart 7

7 = 4 + 3

Step 2: Second way to break apart 7

7 = 2 + 5

Step 3: Verify both decompositions

4 + 3 = 7 ✓ and 2 + 5 = 7 ✓

7 = 4 + 3
7 = 2 + 5
Final answer:

7 can be broken into 4 and 3, or 2 and 5

Applied rules:

• Multiple Representations: Same number can be decomposed differently

• Flexibility: Numbers have multiple valid decompositions

• Verification: All parts must sum to the original number

3 Breaking for Addition
Exercise 3
Break apart 6 to help solve 6 + 4
Strategy:

Strategic Breaking: Break 6 to make 10 with 4, then add the remainder.

Step 1: Identify what's needed to make 10

4 needs 6 more to make 10, but we have 6

Step 2: Break apart 6 strategically

Break 6 into 6 and 0 (6 = 6 + 0)

Step 3: Use the breaking to solve

4 + 6 = 4 + 6 = 10

Step 4: Alternative approach

Break 6 into 4 + 2 to make 10 with 4: (4 + 4) + 2 = 8 + 2 = 10

6 + 4 = 10
Final answer:

Break 6 into 4 + 2 to make 10 with 4, then add 2: 10 + 2 = 12

Applied rules:

• Strategic Decomposition: Break numbers to make calculations easier

• Number Relationships: Understand how numbers combine

• Problem Solving: Use decomposition to simplify operations

Solution: Exercises 4 to 5
4 Breaking for Subtraction
Exercise 4
Break apart 8 to help solve 8 - 3
Strategy:

Subtraction Breaking: Break 8 into 3 and 5 to make subtraction easier.

Step 1: Identify the subtraction problem

8 - 3 = ?

Step 2: Break apart 8 into 3 and 5

8 = 3 + 5

Step 3: Subtract the matching part

8 - 3 = (3 + 5) - 3 = 5

Step 4: Verify the answer

5 + 3 = 8 ✓

8 - 3 = 5
Final answer:

Break 8 into 3 + 5, then 8 - 3 = 5

Applied rules:

• Subtraction Strategy: Use decomposition to visualize subtraction

• Part-Whole Understanding: Know how parts relate to the whole

• Verification: Check answer by adding back

5 Advanced Breaking
Exercise 5
Break apart 9 into three parts
Strategy:

Multi-Part Breaking: Split 9 into three smaller numbers that add to 9.

Step 1: Choose three numbers that add to 9

Let's use 3, 3, and 3

Step 2: Verify the sum

3 + 3 + 3 = 9 ✓

Step 3: Show alternative breakdown

9 = 2 + 3 + 4 (also equals 9)

Step 4: Another combination

9 = 1 + 4 + 4 (also equals 9)

9 = 3 + 3 + 3
9 = 2 + 3 + 4
9 = 1 + 4 + 4
Final answer:

9 can be broken into 3 + 3 + 3, or 2 + 3 + 4, or 1 + 4 + 4

Applied rules:

• Multiple Parts: Numbers can be broken into more than two parts

• Flexible Decomposition: Many valid ways to break numbers

• Sum Verification: All parts must add to the original number

Questions & Answers

Question: Why do we need to break apart numbers? Can't we just use them as they are?

Answer: Breaking apart numbers is like having a superpower for math! Here's why it helps:

Benefits of breaking apart:

  • It makes hard problems easier (like breaking 8 into 5 + 3)
  • It helps us add and subtract faster
  • It builds understanding of how numbers work together
  • It prepares you for bigger math later

Just like breaking a big cookie into smaller pieces to share, breaking numbers helps us work with them better!

Question: My child doesn't understand that numbers can be broken apart in different ways. How can I help?

Answer: This concept can be tricky! Here are hands-on activities to help your child understand:

Teaching approaches:

  • Use physical objects: Give 6 blocks and have them separate into 2 groups
  • Try different groupings: 6 blocks can be 1+5, 2+4, 3+3
  • Draw pictures: Draw 6 circles and color them in different groups
  • Play games: Hide some objects and ask how many are left

The key is showing that the same total can be organized in different ways!

Question: What if I break a number wrong? How do I know if I did it right?

Answer: Easy check - just add your parts together! If they equal the original number, you got it right:

Checking method:

  • Add your parts: If you broke 7 into 2 and 4, add 2 + 4 = 6
  • Compare to original: 6 ≠ 7, so that's wrong
  • Try again: Break 7 into 3 and 4, then 3 + 4 = 7 ✓
  • Use objects: Count out the original number and separate them

Always add your parts to make sure they equal the number you started with!