Evaluating Expressions with Parentheses and Brackets

5th Grade MathOrder of Operations4 pages

About this worksheet

Eleven questions on evaluating numerical expressions with parentheses and brackets, written to the Common Core 5.OA.1 strand for 5th grade math. A callout sets the working order first: innermost parentheses, then brackets, then multiply and divide from left to right. Two guided items open the sheet with printed step lines, so students clear the parentheses in 3 × [14 - (2 + 7)] before touching the brackets. Six independent expressions follow, a detective section has students place the grouping symbols themselves, and a granola bar story asks for one expression that captures the whole problem. The key works each item through, ending at 3 bars per friend.

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Curriculum objectives covered

5.OA.1

Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols.

Questions 1 to 8 evaluate expressions that nest parentheses inside brackets, questions 9 and 10 have students place the symbols to hit a target value, and question 11 has them write and evaluate their own.

What's inside this worksheet

Guided Practice

Students evaluate 3 × [14 - (2 + 7)] and [(18 ÷ 2) + 6] ÷ 5 with the working scaffolded. Step 1 (Parentheses) and Step 2 (Brackets) each get a fill-in line before the boxed answer.

Independent Practice

Six expressions, questions 3 to 8, run from 50 - [4 × (3 + 5)] up to [(8 + 4) × 2] - (15 ÷ 3), the one item holding two separate grouped chunks. Lined space under each asks for every stage.

Grouping Symbol Detective

The task flips. Students insert parentheses and brackets to make 5 × 4 + 6 ÷ 2 = 25 and 30 - 2 × 5 + 3 = 14 true statements.

Real-World Numerical Expressions

Marcus buys 2 packs of 6 granola bars, receives 3 more, and shares them equally among 5 friends. Students write a single bracketed expression for the story, then evaluate it; the key gives [(2 × 6) + 3] ÷ 5 = 3.

Answer key

Full working for all eleven items, including the checks that verify both detective placements, such as 30 - [2 × (5 + 3)] = 14.

How teachers use it

Introducing brackets

Work question 1 on the document camera and let the printed step lines do the talking. Naming each stage, parentheses then brackets, is the habit questions 3 to 8 depend on.

Partner check

Pair students for the detective items. One partner places symbols in 5 × 4 + 6 ÷ 2 = 25, the other computes to verify, then they swap roles for question 10.

Exit ticket

Assign question 11 alone. A student who writes 2 × 6 + 3 ÷ 5 with no grouping symbols has told you exactly what to reteach tomorrow.

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