Challenge Problems

This advanced math worksheet is designed to challenge high-performing students with complex expressions that require careful analysis and strategic problem solving. Learners work through problems involving multiple layers of parentheses, combined operations, and large numbers, often requiring five or more steps to complete accurately.

Instructional Objectives

• Skill Focus (Grades 6-8): Solve advanced multi-step expressions involving grouping symbols and multiple operations.
• Conceptual Understanding (Grades 6-8): Analyze expression structure to determine the correct order of operations and grouping strategy.
• Algebraic Reasoning (Grades 7-8): Apply logical, step-by-step reasoning to evaluate complex numerical and algebraic expressions.
• Curriculum Alignment (Grades 6-8): Supports advanced operations, higher-order thinking, and complex computational fluency standards.

Problems are intentionally rigorous, requiring persistence, precision, and thoughtful organization of work. Students must evaluate carefully, track each step, and use structured strategies to avoid common errors in lengthy computations.

Learning Benefits

• Ideal for advanced learners, enrichment, or challenge activities
• Strengthens perseverance and strategic problem-solving skills
• Encourages clear organization and justification of multi-step work
• Effective for independent practice, small groups, or extension lessons

This printable worksheet provides demanding, high-level practice that helps students build confidence and fluency with complex, multi-step mathematical expressions.

This worksheet is part of our 5-Step Order of Operations Worksheets collection.