Grade 6Mathhard

Mathematical Mastery Challenge

Mathematical Mastery Challenge — Order of Operations worksheet for Grade 6.

Download Free PDF

No signup required — instant download

mathorder-of-operationsG6hard

Worksheet Preview

Grade 6 Order of Operations Worksheet - 10 Problems

What Your Child Will Learn

Apply PEMDAS rules to evaluate complex expressions containing nested parentheses, exponents, and all four arithmetic operations in the Mathematical Mastery Challenge worksheet
Solve 10 hard-level order-of-operations problems by correctly prioritizing exponents before multiplication or division and performing left-to-right calculations
Demonstrate step-by-step simplification of expressions that combine multiple sets of parentheses with exponents and mixed operations at Grade 6 difficulty
Identify and correct errors in expressions where students commonly skip exponents or mishandle left-to-right multiplication and division

How to Use This Worksheet

Step 1: Review the PEMDAS acronym together and model one hard sample expression from the worksheet by writing every intermediate step
Step 2: Let the student complete the first three problems independently while showing all calculations on the page
Step 3: Compare answers and discuss any order-of-operations errors, focusing on exponent placement and left-to-right rules
Step 4: Have the student finish the remaining seven problems, then self-check using the answer key while explaining corrections aloud
Step 5: Extend practice by asking the student to create one new hard expression similar to those on the worksheet and solve it using the same process

Tips for Parents & Teachers

Watch for students forgetting to resolve exponents first in problems like 3 + 2^4 × (5 - 1); have them circle exponents before any other operations on this worksheet

Address the common left-to-right mistake by requiring students to rewrite each multiplication or division step in order before moving to addition or subtraction

For nested parentheses, instruct students to work from the inside out and number each pair on the page to avoid skipping layers in the harder problems

Use the 10 problems to practice checking final answers by plugging results back into the original expression to verify order-of-operations accuracy

Frequently Asked Questions

How should Grade 6 students handle exponents when parentheses are also present in a hard order-of-operations problem?

Always resolve exponents after parentheses but before multiplication or division; for example, in 2 × (3 + 4)^2, first simplify inside the parentheses to get 2 × 7^2, then calculate the exponent to reach 2 × 49.

What is the best way to remember left-to-right order for multiplication and division in complex expressions?

Treat multiplication and division as equal priority and work strictly left to right; students can underline each pair of operations in sequence on the worksheet to avoid jumping ahead to addition or subtraction.

Why do many Grade 6 students struggle with nested parentheses on hard worksheets?

They often skip the innermost set or miscount layers; encourage numbering each parenthesis pair from the inside out and solving one layer completely before moving outward.

How can parents check if their child has mastered hard order-of-operations problems at this level?

Ask the student to explain each step aloud while solving a problem from the Mathematical Mastery Challenge and verify that exponents are done before multiplication or division and that all operations follow left-to-right rules.

What common mistake occurs when expressions include both exponents and division?

Students frequently divide before calculating the exponent; practice circling every exponent first on the worksheet to ensure it is handled immediately after parentheses.