Free Printable Properties of Integers Worksheets for Year 6

In 6th grade, students are typically introduced to the formal names for the properties of operations (commutative, associative, distributive). The focus is on recognizing these properties and understanding how they apply to the newly expanded number system that now includes negative integers.

Start with familiar operations on positive whole numbers to demonstrate a property, then test if the same rule holds true when negative numbers are included. For example, ask "Does 3 + 5 = 5 + 3? Now, let's check if -3 + 5 = 5 + (-3)." This helps them generalize the rules.

Focus on exercises that ask students to identify the property shown in an equation, such as recognizing `4 × (5+2) = (4×5) + (4×2)` as the distributive property. Fill-in-the-blank problems that require applying a property to complete an equation are also highly effective at this stage.

A frequent error is confusing the commutative and associative properties. The commutative property involves changing the order of numbers, while the associative property involves changing their grouping (using parentheses) without changing the order. Using clear, simple examples for each can help distinguish them.

The Common Core standards for 6th grade (6.NS) focus on extending number sense to the full system of rational numbers. These worksheets directly support this by helping students understand the fundamental structure and rules that govern operations with positive and negative integers, a critical foundation for algebra.

You can assign this resource as a printable PDF for hands-on practice or as an interactive digital quiz on the Wayground platform. Each worksheet includes a full answer key, and for paper assignments, you can use the Wayground for Teachers app to quickly scan and grade student work.