Lesson Description
This lesson introduces the order of operations for whole numbers, guiding students through the use of parentheses, exponents, multiplication, division, addition, and subtraction (PEMDAS) to solve arithmetic problems correctly.
Learning Objectives
- Apply the correct order of operations to solve arithmetic problems with whole numbers.
- Understand and use parentheses and exponents in calculations.
- Identify common errors when applying PEMDAS rules.
Topics Covered
- Parentheses and grouping symbols
- Exponents
- Multiplication and Division
- Addition and Subtraction
- PEMDAS hierarchy for whole numbers
Key Terms
- PEMDAS: An acronym representing the order of operations—Parentheses, Exponents, Multiplication/Division, Addition/Subtraction.
- Parentheses: Symbols used to group parts of a mathematical expression and indicate priority in calculation.
- Exponent: A number that indicates how many times a base is multiplied by itself.
Lesson Examples
Example 1: Simple PEMDAS Problem
- Problem: 5 + 3 × 2
- Step 1: Identify operations—multiplication comes before addition.
- Step 2: Multiply 3 × 2 = 6
- Step 3: Add 5 + 6 = 11 → Answer: 11
Example 2: Using Parentheses
- Problem: (5 + 3) × 2
- Step 1: Solve inside parentheses first: 5 + 3 = 8
- Step 2: Multiply by 2: 8 × 2 = 16 → Answer: 16
Practice Problems
- 7 + 4 × 3
- (6 + 2) × 5
- 9 × 2 + 8 ÷ 4
- (3 + 5)² - 4
Tips & Common Mistakes
- Always perform operations inside parentheses first.
- Remember that multiplication and division are performed left to right.
- Addition and subtraction also follow left-to-right order.
Summary
Mastering PEMDAS with whole numbers ensures accurate arithmetic calculations. Always follow the hierarchy: parentheses, exponents, multiplication/division, and addition/subtraction.
Challenge Problems
- 12 + 3 × (4 + 2)
- (8 - 3) × (2 + 5)²
- 18 ÷ (3 × 2) + 5