Mastering Math: The Power of Breaking Down Problems

One essential math strategy that all kids should know is the concept of “breaking down” complex problems into simpler, more manageable parts. This strategy, also known as “decomposition” or “chunking,” can be applied across various areas of mathematics, from basic arithmetic to more advanced algebra and geometry. Here’s how it can be useful in different contexts:

1. Addition and Subtraction

• Example: To solve 47 + 38, break it down into (40 + 30) + (7 + 8).
• Steps:
  1. Add the tens: 40 + 30 = 70
  2. Add the ones: 7 + 8 = 15
  3. Combine the results: 70 + 15 = 85

2. Multiplication

• Example: To solve 6 × 14, break it down into 6 × (10 + 4).
• Steps:
  1. Multiply 6 by 10: 6 × 10 = 60
  2. Multiply 6 by 4: 6 × 4 = 24
  3. Add the results: 60 + 24 = 84

3. Division

• Example: To solve 84 ÷ 4, break it down into 80 ÷ 4 and 4 ÷ 4.
• Steps:
  1. Divide 80 by 4: 80 ÷ 4 = 20
  2. Divide 4 by 4: 4 ÷ 4 = 1
  3. Combine the results: 20 + 1 = 21

4. Fractions

• Example: To add 3/4 + 2/8, break it down by finding a common denominator.
• Steps:
  1. Convert 3/4 to 6/8
  2. Add the fractions: 6/8 + 2/8 = 8/8 = 1

5. Algebra

• Example: To solve (x + 3)(x + 4), use the distributive property.
• Steps:
  1. Multiply x by each term in the second parenthesis: x(x + 4) = x² + 4x
  2. Multiply 3 by each term in the second parenthesis: 3(x + 4) = 3x + 12
  3. Combine like terms: x² + 4x + 3x + 12 = x² + 7x + 12

Benefits of Decomposition

• Reduces Cognitive Load: Simplifying problems into smaller steps makes them less intimidating and easier to handle.
• Enhances Understanding: By breaking problems down, students gain a deeper understanding of the mathematical concepts involved.
• Builds Confidence: Successfully solving smaller parts of a problem can boost a student’s confidence and encourage a positive attitude towards math.

Teaching kids to approach problems by breaking them down into smaller parts can significantly improve their mathematical thinking and problem-solving skills. This strategy is foundational and can be built upon as they encounter more complex mathematical concepts throughout their education.

Rachel Wise

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Rachel Wise is the author and founder of Education and Behavior. Rachel created Education and Behavior in 2014 for adults to have an easy way to access research-based information to support children in the areas of learning, behavior, and social-emotional development. As a survivor of abuse, neglect, and bullying, Rachel slipped through the cracks of her school and community. Education and Behavior hopes to play a role in preventing that from happening to other children. Rachel is also the author of Building Confidence and  Improving Behavior in Children: A Guide for Parents and Teachers.

"Children do best when there is consistency within and across settings (i.e., home, school, community). Education and Behavior allows us to maintain that consistency."

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