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7.75 Determining whether expressions are equivalent Worksheet

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Worksheet Overview & Skills Covered

Core academic competencies and curriculum alignment

This Grade 7 Math worksheet provides structured practice on 7.75 Determining whether expressions are equivalent. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

7.75 Determining whether expressions are equivalent - In multiple-choice items, students select whether two expressions are equivalent and choose the reasoning (simplify or evaluate) that confirms the decision. (CCSS 7.EE.A.2; FL MA.7.AR.1.2; VA 7.PFA.2)

Whether you are an educator preparing classroom handouts, a tutor reinforcing weekly topics, or a parent supporting homeschool learning, this printable resource gives students the deliberate practice required to achieve subject fluency and master state standards.

Grade

Grade 7

Subject

Math

Domain

Math Curriculum

Formats

PDF & DOCX

Sample Practice Problems

Preview the types of problems and questions covered in this worksheet

Below are sample questions representative of the exercises included on this worksheet and related 7.75 Determining whether expressions are equivalent skill assessments:

Problem 1Difficulty: Mastery

Are the expressions equivalent? Pick the choice that gives the correct decision and a correct check (simplify or evaluate). Expression 1: -x²-2x-22 Expression 2: -(x+4)²+3(2x-1)

AEquivalent; simplify: both become -x²-2x-22.

BEquivalent; evaluate at x = -1: Expr1 = -21, Expr2 = -21.

CNot equivalent; simplify: Expr1 → -x²-2x-22, Expr2 → -x²-2x-22.

DNot equivalent; evaluate at x = -1: Expr1 = -21, Expr2 = -18.

Solution & Explanation:Evaluate both expressions at x = -1. Expression 1 gives -21 and Expression 2 gives -18. Since the values are different, the expressions are not equivalent.

Problem 2Difficulty: Mastery

Select the statement that correctly tells whether the expressions are equivalent and how you can confirm it (by simplifying or by evaluating). Expression 1: -(x-1)(x+2)+(x+2)(2x+2) Expression 2: (x+2)(x+3)+2

AEquivalent; simplify: both become x²+5x+8.

BEquivalent; evaluate at x = 3: Expr1 = 30, Expr2 = 30.

CNot equivalent; simplify: Expr1 → x²+5x+6, Expr2 → x²+5x+8.

DNot equivalent; evaluate at x = 3: Expr1 = 30, Expr2 = 30.

Solution & Explanation:Simplify both expressions. Expression 1 simplifies to x²+5x+6 and Expression 2 simplifies to x²+5x+8. Since these are different, the expressions are not equivalent.

Problem 3Difficulty: Mastery

Determine whether the two expressions are equivalent. Choose the option that correctly states whether they are equivalent and names the reasoning (simplify or evaluate) that confirms it. Expression 1: (x+3)(x+4) Expression 2: -(x-1)(x+3)+(x+3)(2x+3)

AEquivalent; simplify: both become x²+7x+13.

BEquivalent; evaluate at x = 1: Expr1 = 20, Expr2 = 20.

CNot equivalent; simplify: Expr1 → x²+7x+12, Expr2 → x²+7x+10.

DNot equivalent; evaluate at x = 1: Expr1 = 20, Expr2 = 19.

Solution & Explanation:Evaluate both expressions at x = 1. They both give 20, so the expressions are equivalent.

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QWhat grade level and standards does this worksheet align with?

This worksheet is designed specifically for Grade 7 Math students. It aligns with educational standard 7.75 (Practice and review Grade 7 math skill 7.75: Determining Whether Expressions Are Equivalent.).