Order of Operations

Order of operations is one of those topics that looks tiny on paper — a few rules about which operation goes first — but it trips up kids for years if it’s taught as a memory trick instead of a reason. This nine-week program teaches it as a reason. The whole thing rests on a simple question every kid should ask: if three different people compute 8 − 3 + 2 and get three different answers, who’s right? The order of operations is the answer to that question. It’s the rule that lets everyone get the same number from the same expression.

Week 1 starts with addition and subtraction only, building the left-to-right habit. Week 2 brings multiplication and division into the mix and introduces the PEMDAS hierarchy — the idea that × and ÷ outrank + and − no matter where they sit. Week 3 adds parentheses, and the famous comparison kids never forget once they’ve seen it: 3 + 5 × 2 = 13, but (3 + 5) × 2 = 16. Same numbers. Same operations. Different answer. That single example does more work than any acronym.

Week 4 extends to nested parentheses and longer expressions. The habit we drill here is rewrite-after-every-step: once you replace what you just calculated with its value, the line in front of you gets shorter, and a six-operation expression becomes a series of small easy problems. Week 5 turns the lens around — instead of evaluating expressions, students write them from word descriptions. Sum, difference, product, quotient. And the trickier phrasing like “twice the sum of 3 and 7” that signals parentheses.

Week 6 introduces comparing expressions without fully evaluating them, plus the distributive property — a × (b + c) = a × b + a × c — which doubles as a mental-math tool (6 × 99 becomes 6 × 100 − 6, which any 4th grader can do in their head). Weeks 7 and 8 are application weeks: multi-step word problems with the discipline of write-first-solve-second, then error analysis and puzzles that ask kids to find the broken rule in a wrong answer. Week 9 is the capstone — five cumulative worksheets that pull everything together.

What sets these worksheets apart from the usual PEMDAS drill packs is the concept passages. Before each set of problems, students read a short instructional passage that explains the rule with examples and counter-examples. The passages tell kids what mistake they’re most likely to make and why it happens. That up-front teaching is what builds understanding instead of just memorization.

This program is built on Common Core standards 5.OA.A.1 (parentheses, brackets, or braces in numerical expressions) and 5.OA.A.2 (writing expressions from words), and aligns with how order of operations is taught in most 4th and 5th grade classrooms. All worksheets are free, print-ready PDFs with full answer keys.