Created by Heidi Christy
14 questions
8th Grade
Math
Updated Sep 2025
This free printable Grade 8 mathematics worksheet gives students focused practice identifying the associative and commutative properties of addition and multiplication. Across 14 multiple-choice questions, students analyze changes in number order and grouping, match equations and definitions to the correct property, and distinguish these properties from the distributive property. The worksheet also moves from property recognition to pre-algebra application. Students identify the distributive property and simplify expressions such as 6 + 2(7x - 3), -2x - 4(4x - 8), and expressions involving subtraction and negative terms. This progression helps teachers check whether students can apply multiplication across parentheses, combine like terms, and manage signs accurately. It is suitable for Grade 8 review, guided practice, independent work, or a quick formative assessment, and includes a complete answer key.
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WorksheetsAnswer KeyCommutative Property
Associative Property
-2x - 12
This Grade 8 pre-algebra worksheet uses 14 multiple-choice questions to help students distinguish associative addition and multiplication from commutative addition and multiplication by analyzing equations, grouping, and order. It then connects property recognition to identifying the distributive property and simplifying linear expressions with parentheses, like terms, and positive or negative coefficients. The format lets teachers assess both vocabulary and the accurate application of these properties.
Introduce the worksheet by having students compare each equation’s order of factors or addends with its grouping, then ask them to explain what changed and what stayed the same. Use the definition-based items to build precise language before students work through the equation-identification questions. After reviewing the distributive-property item, model one final expression step by step so students connect the property names to simplifying algebraic expressions.
Students may confuse commutative property, which changes the order of numbers, with associative property, which changes their grouping or parentheses. In the simplifying items, watch for errors when distributing a negative sign or coefficient, such as changing the signs inside 3x - (x - 6), and for failing to combine like terms after expanding. Some students may also select a property based only on seeing parentheses without checking whether the operation is addition or multiplication.
This worksheet is available as a printable PDF and as a digital quiz on Wayground, so you can assign the 14 multiple-choice questions in the format that fits your lesson. It includes a complete answer key for checking property classifications and simplified expressions. Printable submissions can also be graded by scanning student work with the Wayground for Teachers app.
The final questions assess whether students can use the distributive property to expand expressions and then combine like terms correctly. They include expressions with positive coefficients, subtraction before parentheses, and negative terms, such as -6x + 4(x - 3). These items reveal whether students can preserve signs while moving from a factored expression to a simplified linear expression.
Wayground offers a broad collection of free printable worksheets and practice problems across all subjects, with downloadable PDFs and answer keys to support essential skill development. Teachers can browse more resources at https://wayground.com/en-us/worksheets.