Overview
This lecture covers mental math strategies for quick addition, subtraction, multiplication, and division, using number breakdowns and distributive properties for easier mental calculations.
Mental Math Addition Techniques
- Break numbers into parts (e.g., 34 = 30 + 4) to add each part separately.
- Add each corresponding place value, then combine the subtotals for the final answer.
- Works with both two-digit and three-digit numbers.
Mental Math Subtraction Techniques
- Decompose both numbers (e.g., 75 = 70 + 5; 38 = 30 + 8) and apply subtraction to each part.
- Watch for negative results in units/tens and combine appropriately.
- Confirm results with traditional subtraction if needed.
Mental Math Multiplication Techniques
- View multiplication as repeated addition if tables are not memorized.
- Break down multi-digit numbers using the distributive property (e.g., 20 × 13 = (20 × 10) + (20 × 3)).
- Use substitution (e.g., 49 = 50 – 1) for easier mental calculation with numbers near multiples of 10 or 100.
Mental Math Division Techniques
- Break the dividend into parts divisible by the divisor (e.g., 168 ÷ 4 → 100 + 40 + 16).
- Divide each part separately and sum the results.
- For numbers not obviously divisible, find nearby multiples.
Key Terms & Definitions
- Distributive Property — Multiplying a number by a sum is the same as multiplying by each addend and adding the results: a(b + c) = ab + ac.
- Repeated Addition — Viewing multiplication as adding the same number multiple times.
- Place Value Breakdown — Splitting numbers into hundreds, tens, and units to simplify operations.
Action Items / Next Steps
- Practice these mental math techniques with additional problems.
- Review multiplication tables up to twelve for faster calculations.
- Confirm answers using traditional written methods when necessary.