FL B.E.S.T. Standard MA.5.AR.2.2 | Grade 5 Mathematics
Evaluate multi-step numerical expressions using order of operations involving parentheses, exponents, multiplication and division (from left to right), and addition and subtraction (from left to right).
By the end of this lesson, students will be able to:
Students solve expressions strictly left to right, ignoring operation hierarchy.
Example Error: 3 + 4 x 2 = 7 x 2 = 14 (instead of 3 + 8 = 11)
Students think M always comes before D, and A always before S.
Example Error: 12 ÷ 4 x 3 = 12 ÷ 12 = 1 (instead of 3 x 3 = 9)
Students skip over exponents or don't know what they mean.
Example Error: 2 + 3² = 5² = 25 (instead of 2 + 9 = 11)
Students don't realize parentheses change the order of operations.
Write on board: "5 + 3 x 2 = ?" Ask students to solve. Some will say 16, some 11. Reveal that calculators give 11! Why? Because there's a special ORDER we follow.
Display the PEMDAS poster. Explain each letter with the mnemonic "Please Excuse My Dear Aunt Sally." Emphasize that M/D are partners (same level, left to right) and A/S are partners.
Solve 2 + 3² x (4 - 1) step by step: "First I look for Parentheses: 4 - 1 = 3. Next Exponents: 3² = 9. Then Multiply: 9 x 3 = 27. Finally Add: 2 + 27 = 29."
Solve together: 18 ÷ 6 + 2 x 5. Have students tell you what to do first (18 ÷ 6 = 3 and 2 x 5 = 10, then 3 + 10 = 13). Circle operations as you identify them.
Distribute practice worksheet. Remind students: "P-E-MD-AS. Check parentheses, then exponents, then multiply/divide left to right, then add/subtract left to right."
"When we have a problem with lots of different operations, we need to know which one to do first. We use a special order called PEMDAS. P is for Parentheses - always first! E is for Exponents - like 3 squared. Then M and D work together - Multiplication and Division, from left to right. Finally, A and S are partners - Addition and Subtraction, from left to right."
"Here's a tricky part: Multiplication doesn't always come before division! They're on the same level. When you see both, go left to right, like reading a book. Same with addition and subtraction - they're partners. If you see 8 - 3 + 2, go left to right: 8 - 3 = 5, then 5 + 2 = 7."
"I see you solved left to right. That's a good instinct for reading, but math has special rules. Let's use our PEMDAS checklist: Any parentheses? No. Any exponents? No. Any multiplication or division? Yes! Let's do those first, then come back for the addition."
| Step | Operation | What to Look For | Example |
|---|---|---|---|
| P | Parentheses | ( ), [ ], { } | (3 + 5) = 8 |
| E | Exponents | Small raised numbers | 4² = 16 |
| MD | Multiply/Divide | x, ÷ (left to right) | 12 ÷ 4 x 2 = 6 |
| AS | Add/Subtract | +, - (left to right) | 10 - 3 + 2 = 9 |
Assign skill 5.T.1 first to focus on parentheses, then 5.T.2 for exponents. Use 5.T.3 as a comprehensive review. SmartScore goal of 80+ indicates proficiency.