Grade 6Mathhard
Advanced Order of Operations - Grade 6
A challenging worksheet covering complex order of operations with exponents, nested parentheses, and multiple operations using PEMDAS rules
Download Free PDF
No signup required — instant download
order-of-operationsPEMDASexponentsgrade-6math-worksheetadvancedparentheseschallenging
Worksheet Preview
What Your Child Will Learn
- Apply PEMDAS rules correctly to solve multi-step expressions containing exponents, parentheses, multiplication, division, addition, and subtraction
- Evaluate expressions with nested parentheses by working from the innermost groupings outward
- Calculate expressions involving exponents with bases greater than 10 and exponents up to 3
- Solve complex order of operations problems containing at least 5 different mathematical operations in a single expression
- Identify and correct common order of operations errors when multiple operations of the same priority level appear together
How to Use This Worksheet
- Step 1: Have students read through all 15 problems first and identify which ones contain nested parentheses, exponents, and multiple operation types
- Step 2: For each problem, students should underline or circle parentheses first, then mark exponents, and finally identify multiplication/division and addition/subtraction operations in order
- Step 3: Work through the first 3-4 problems together, verbalizing each step of PEMDAS and showing how to handle operations of equal priority from left to right
- Step 4: Allow students to complete problems 5-10 independently while checking their work step-by-step rather than just final answers
- Step 5: Review problems 11-15 together, focusing on the most complex expressions and discussing any common errors or misconceptions that arose
Tips for Parents & Teachers
Students often forget that multiplication and division have equal priority and should be solved left to right - use the phrase 'MD twins' and 'AS twins' to help them remember to work horizontally when operations have equal rank
When teaching nested parentheses like ((3+2)×4)-6, have students use different colored pencils for each level of parentheses to visually track which groupings to solve first
Many 6th graders rush through exponents - remind them that 2³ means 2×2×2, not 2×3, and have them write out the multiplication before calculating
Create a 'PEMDAS checkpoint' system where students circle each operation type in different colors before solving, helping them visualize the correct sequence for complex expressions
Frequently Asked Questions
Why does my child keep getting different answers when there are multiple multiplication and division operations in one problem?
This is a very common issue! When multiplication and division appear together, they have equal priority and must be solved from left to right, not in the order they appear in PEMDAS. For example, in 24÷4×3, you solve 24÷4=6 first, then 6×3=18, not 4×3=12 then 24÷12=2.
How can I help my child remember to solve nested parentheses correctly?
Teach them to work from the 'inside out' like peeling an onion. In expressions like ((5+3)×2)+4, they should solve the innermost parentheses (5+3=8) first, then the next level (8×2=16), and finally add 4. Using different colored pencils for each level helps visualize this process.
My 6th grader struggles with exponents in order of operations problems - what's the best way to practice this?
Have them write out what the exponent means before calculating. For 2⁴, they should write 2×2×2×2=16 rather than jumping to the answer. This prevents confusion with multiplication (2×4=8) and builds understanding of what exponents actually represent.
Should my child use a calculator for these complex order of operations problems?
At the 6th grade level, it's better to work through these problems by hand to build number sense and ensure they truly understand PEMDAS. However, they can use a calculator to check their final answers after showing all their work step-by-step.
What should I do if my child consistently makes errors on problems with both addition/subtraction and multiplication/division?
Related Worksheets
More Math Worksheets
Related Articles
How to Teach Fractions to Kids: A Parent's Complete Guide
Learn how to teach fractions to kids in grades 2–5 with proven strategies, visual models, and hands-on methods that build real understanding — not just memorized rules.
How to Teach Ratios and Proportions: A Middle School Parent's Guide
Learn how to teach ratios and proportions to middle schoolers with step-by-step strategies, real-world examples, and hands-on activities for grades 6–8.
How to Teach Geometry to Kids: Angles, Shapes, and Lines
A practical parent guide to teaching geometry from kindergarten through 8th grade — covering shapes, angles, lines, and symmetry with hands-on activities and free worksheets.
Get Free Worksheets in Your Inbox
Subscribe for new worksheets and homeschool tips. No spam, unsubscribe anytime.