Parentheses Puzzles

5th Grade MathOrder of Operations4 pages

About this worksheet

An order of operations worksheet for 5th grade math built around grouping symbols (Common Core 5.OA.1 and 5.OA.2). A PEMDAS callout leads into four evaluations that nest parentheses inside brackets, such as 2 × [15 − (3 + 4)]. The Parentheses Puzzle flips the task: students place grouping symbols to force equations like 6 + 4 × 5 = 50 to come true. A translation table turns phrases such as subtract 4 from 20, then divide by 2 into expressions, and the final question compares 4 × (1,280 + 345) with the bare sum, no computing allowed.

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$Parentheses Puzzles: Order of Operations - page 1$

$Parentheses Puzzles: Order of Operations - page 2$

$Parentheses Puzzles: Order of Operations - page 3$

$Parentheses Puzzles: Order of Operations - page 4$

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 and construct expressions with parentheses and brackets, including the nested 2 × [15 − (3 + 4)].

5.OA.2

“Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, express the calculation "add 8 and 7, then multiply by 2" as 2 × (8 + 7). Recognize that 3 x (18932 + 921) is three times as large as 18932 + 921, without having to calculate the indicated sum or product.”

Questions 9 to 12 record calculations as expressions without evaluating, and question 13 mirrors the standard's own recognize-without-calculating example using 4 × (1,280 + 345).

What's inside this worksheet

Part 1: Evaluate the Expressions

Students work four expressions step by step: 14 + (8 × 3) − 5 = 33, (20 ÷ 4) + (7 × 2) = 19, the nested 2 × [15 − (3 + 4)] = 16, and [(18 − 6) ÷ 3] + 9 = 13.

Part 2: Parentheses Puzzle

Four equations are false as written until grouping symbols rescue them: 6 + 4 × 5 = 50, 24 ÷ 6 + 2 = 3, 30 − 10 ÷ 2 = 10, and 2 × 8 − 3 + 1 = 11.

Part 3: Words to Numerical Expressions

A table converts four phrases into expressions without evaluating, from add 9 and 7, then multiply by 3 to 6 × (15 − 9).

Part 4: Compare Without Calculating

Expression A, 4 × (1,280 + 345), stands against Expression B, the plain sum. Students state that A is 4 times larger and explain why no arithmetic is needed.

How teachers use it

Structured practice sequence

The four parts escalate cleanly: evaluate, repair, translate, reason. Weaker groups can stop after Part 2 and still have done a complete lesson's work.

Puzzle-first hook

Open class with Part 2's first equation on the board: 6 + 4 × 5 = 50, apparently false. The hunt for where the parentheses go teaches more about grouping than any restatement of PEMDAS.

No-calculator reasoning

Question 13's four-digit numbers are chosen to make computing painful. If a student starts adding 1,280 + 345, stop them and re-ask the question; the answer is in the structure.

More 5th Grade Math worksheets

Operations with Fractions Place Value and Decimals Measurement and Data Geometry

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