Mastering Order of Operations with GEMA
Year 7 Mathematics New Zealand Curriculum Building Mathematical Problem-Solving Skills
What is GEMA?
G - Grouping symbols (brackets, parentheses) E - Exponents (powers, indices) M - Multiplication A - Addition and Subtraction (left to right)
Why Do We Need Order of Operations?
What happens if we solve 2 + 3 × 4 without rules? Method 1: (2 + 3) × 4 = 20 Method 2: 2 + (3 × 4) = 14 Which answer is correct?
G - Grouping Symbols First
Brackets ( ) Square brackets [ ] Curly braces { } Always solve what's inside grouping symbols first Work from innermost to outermost brackets
Bracket Practice
Solve: (5 + 3) × 2 Solve: 4 × (7 - 3) Solve: (2 + 4) ÷ (9 - 7) Challenge: 3 × [(8 + 2) - (4 + 1)]
E - Exponents (Powers)
Exponents come after grouping symbols Examples: 2³ = 2 × 2 × 2 = 8 5² = 5 × 5 = 25 Remember: exponents are repeated multiplication
M - Multiplication (and Division)
Multiplication and division have equal priority Work from left to right Examples: 12 ÷ 3 × 2 = 4 × 2 = 8 Not: 12 ÷ (3 × 2) = 12 ÷ 6 = 2
GEMA in Action
{"left":"Example: 2 + 3² × (4 - 1)\nStep 1: Grouping (4 - 1) = 3\nStep 2: Exponents 3² = 9","right":"Step 3: Multiplication 9 × 3 = 27\nStep 4: Addition 2 + 27 = 29"}
GEMA Challenge
Solve these using GEMA: 1) 5 + 2³ × 3 2) (8 - 3) × 2² + 1 3) 24 ÷ 4 + 3 × (5 - 2) 4) 2 × [3 + (4² - 10)]
Remember GEMA
"Mathematics is not about numbers, equations, computations, or algorithms: it is about understanding." - William Paul Thurston GEMA helps us understand the logical order of mathematical operations