When an expression contains more than one operation, the order in which you perform them matters: 3 + 4 x 2 equals 11 (multiply first) not 14 (add first). The conventional order is: (1) parentheses first, (2) multiplication and division from left to right, (3) addition and subtraction from left to right. At fourth grade, students work primarily with the first three operations and parentheses, saving exponents for later grades. The key understanding is that order of operations is a convention that ensures everyone interprets the same expression the same way -- it is the "grammar" of mathematical notation.
Start by showing that different orders give different answers: "Does 2 + 3 x 4 equal 20 or 14?" Establish the need for a shared convention. Introduce parentheses as "do this first" markers. Practice evaluating expressions step by step, underlining or circling the operation to perform next. Avoid over-relying on mnemonics (PEMDAS) without understanding -- students often misinterpret them.
You know how to add, subtract, and multiply multi-digit numbers. Now imagine reading the expression 3 + 4 × 2. Two people could reasonably get different answers: one might add first to get 7, then multiply to get 14; another might multiply first to get 8, then add to get 11. Both followed valid arithmetic steps — but they got different answers from the same expression. This is a problem. Math only works as a shared language if everyone reads the same expression the same way.
Order of operations is the agreement mathematicians made to fix this ambiguity. The rule: multiplication and division are performed before addition and subtraction. So 3 + 4 × 2 means 3 + (4 × 2) = 3 + 8 = 11, always. Think of multiplication as "tighter binding" than addition — it grabs its neighbors first. Addition and subtraction are weaker ties; they connect whatever is left after multiplication and division have been resolved.
Parentheses let you override the default order. Writing (3 + 4) × 2 means "add first, then multiply" — the parentheses announce: do this part first. Result: 7 × 2 = 14. Parentheses are the tool for saying "I really do want the addition done first here." Without them, multiplication wins. With them, you're in charge. Whenever you want to force a different order, use parentheses.
The mnemonic PEMDAS (Parentheses, Exponents, Multiplication, Division, Addition, Subtraction) can help you remember the hierarchy, but it hides an important detail: M and D are equal partners, evaluated left to right, not M before D always. Same for A and S. So 20 ÷ 4 × 2 is done left to right: (20 ÷ 4) × 2 = 5 × 2 = 10, not 20 ÷ (4 × 2) = 20 ÷ 8 = 2.5. Work through expressions step by step — circle the operation to do next, evaluate it, rewrite, repeat — until you build the habit of seeing priority before calculating.