Grade 6 Integers - Hard Practice
A hard grade 6 worksheet for Integer Operations.
Worksheet snapshot
- Integer Operations
- Key concepts: Understanding core integer operations concepts for Grade 6; Applying integer operations strategies appropriate to Grade 6
- Students master integer operations at Grade 6 level, working with challenging problems, explaining their reasoning, and applying concepts to new situations.
- Apply it: Integer Operations at the Grade 6 level connects to everyday situations students encounter: problem-solving in daily life, making sense of quantities and relationships, and building mathematical literacy for future learning.
- -1 + -49 =
- 46 - 47 =
- 32 + 19 =
About Integer Operations
Integer operations extend arithmetic to include negative numbers, introducing the complete set of positive and negative whole numbers. Students learn to add, subtract, multiply, and divide integers using models and rules.
Integers are essential for representing temperatures, elevations, financial situations (debt), and many mathematical concepts. Understanding integers is crucial for algebra, coordinate graphing, and mathematical reasoning about quantity and change.
Integer Operations
Add/subtract/multiply/divide integers using number lines, counters, and rules; apply to real contexts.
This hard level worksheet:
Multi-step problems with mixed integer operations and order of operations; justify sign rules with models or patterns.
Key Concepts
- Opposites and zero pairs
- Number line models for +/-
- Sign rules for × and ÷
- Order of operations with integers
Prerequisite skills
Add/subtract whole numbers; understand opposites on a number line; basic order of operations.
Teaching Strategies
Use number lines/counters to ground sign rules; show patterns (e.g., repeated subtraction) for multiplication/division signs; mix contexts (temperature, elevation, debt).
Assessment ideas
Test integer operation fluency with mixed problems. Include word problems in temperature, elevation, or financial contexts. Have students model integer operations on number lines. Ask students to explain integer operation rules.
Common Challenges
Dropping negative signs; overgeneralizing sign rules; order of operations errors.
Real-World Applications
Temperatures, elevations, bank balances/debt, and score changes.
Extension Activities
Explain why (-a)×(-b) is positive using patterns; solve a word problem two ways (model and rule).
Parent Tips
When you see negative temperatures or balances, ask your child to describe the change using integer language.