Grade 6 - Mathematical Reasoning
Explanation and Free Practice Resources
Students analyze and decompose routine and non-routine problems by identifying relevant, irrelevant, and missing information; representing relationships with diagrams, tables, graphs, equations, expressions, and number lines; and working with whole numbers, integers, fractions, decimals, ratios, rates, percentages, and familiar measurements. They select efficient operations, tools, and strategies; work backward or use logical elimination; estimate before and after calculating; check precision, rounding, units, inverse operations, and algebraic solutions by substitution; and interpret results in context. They communicate complete justifications, compare and critique strategies and solutions, create related problems and statistical questions, recognize and generalize patterns, organize cases, and form, test, support, or disprove conjectures using examples and counterexamples.
On this page:
- Master skills like “Use logical elimination”, “Check units in a solution”, and “Critique another solution” with unlimited, free practice problems
- Download (or modify) free worksheets on Mathematical Reasoning you can use at home or in class with practice problems across all skills in this group including “Make and test conjectures”, “Analyze and correct errors”, “Choose tools appropriately”.
- Start working on adaptive units like “Multiplication - 2 Digit” or “Decimal Foundations - Intro” that include these skills and will introduce and scaffold the skills carefully for maximum learning.
Mathematical Reasoning: Individual Skills
Master 33 individual skills with free practice problems. Mouseover to see the skill's practice problems. Create a free account to track your progress.
Your results
- Analyze and correct errors
- Break a multi-step problem into parts
- Check calculations with inverse operations
- Check precision and rounding
- Check units in a solution
- Choose an appropriate representation
- Choose an efficient operation strategy
- Choose tools appropriately
- Communicate a solution clearly
- Compare two valid strategies
- Create a word problem for an equation
- Create a word problem for an expression
- Critique another solution
- Estimate before calculating
- Explain reasoning with mathematical vocabulary
- Identify efficient and inefficient strategies
- Identify irrelevant information
- Identify missing information
- Identify relevant information
- Interpret answers in context
- Make and test conjectures
- Organize cases systematically
- Recognize patterns and generalize
- Represent problems with diagrams
- Represent problems with equations
- Represent problems with tables
- Solve non-routine multi-step problems
- Use estimation to check reasonableness
- Use examples to support a conjecture
- Use logical elimination
- Verify algebraic solutions by substitution
- Work backward from a result
- Write a complete mathematical justification
Practice 'Analyze and correct errors'
Select any skill in this group by hovering over the list above. Unlimited free practice problems, automatically graded.
Hover a skill above to start practicing.
Download/Modify Free Grade 6 'Mathematical Reasoning' Worksheet
Print this free 'Mathematical Reasoning' worksheet to practice these skills away from the computer. Click 'Modify' to easily customize this worksheet to your exact needs.
This Worksheet Includes:
- Analyze and correct errors
- Break a multi-step problem into parts
- Check calculations with inverse operations
- Check precision and rounding
- Check units in a solution
- Choose an appropriate representation
- Choose an efficient operation strategy
- Choose tools appropriately
Units Teaching These Skills
These adaptive units introduce, teach, or reinforce skills in this group (Mathematical Reasoning) through scaffolded problems that grow in difficulty as concepts are understood.