Free Printable WorksheetMathGrade 6Math Curriculum6.120

6.120 Construct and Critique Mathematical Arguments Worksheet

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Worksheet Overview & Skills Covered

Core academic competencies and curriculum alignment

This Grade 6 Math worksheet provides structured practice on 6.120 Construct and Critique Mathematical Arguments. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

Which statement correctly justifies the claim, or which critique correctly identifies the error in the argument? (CCSS Standards for Mathematical Practice 1-8; TX 19 TAC §111.26(b)(1)(A)-(G); FL Mathematical Thinking and Reasoning Standards; VA Process Standards)

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 6

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 6.120 Construct and Critique Mathematical Arguments skill assessments:

Problem 1Difficulty: Mastery

Student CJ tries to justify: “If P implies Q and Q implies R, then P implies R.” They make a truth table but check only the cases where P is true. Which critique is correct?

ATruth tables are not allowed for implication statements.

BYou should check only the cases where P is false.

CImplications can never be chained.

DA full truth table must check all possible truth values of P, Q, and R; skipping cases can miss a counterexample.

Solution & Explanation:Logical validity requires considering every case. Even if some cases seem irrelevant, omitting them means the argument has not been fully verified.

Problem 2Difficulty: Mastery

Claim: Points (x, y) that satisfy x squared + y squared = 25 are exactly the points 5 units from the origin. Which statement correctly justifies the claim?

ABecause 25 is a perfect square, all points form a line.

BBecause x² + y² is always 25, x and y must both be 5.

CBy the distance formula, distance from (0,0) is √(x² + y²); setting x² + y² = 25 makes the distance √25 = 5.

DBecause 25 ends in 5, the points must be in quadrant I.

Solution & Explanation:Distance from the origin is √(x²+y²). The equation x²+y²=25 means √(x²+y²)=√25=5, which is the definition of a circle of radius 5 centered at the origin.

Problem 3Difficulty: Mastery

Student CH says: “A one-to-one function always has an inverse function.” Which critique is correct?

AOne-to-one means the function is linear, so it has an inverse.

BTo have an inverse function from the stated outputs back to inputs, the function must also be onto the chosen codomain; otherwise the inverse may not be defined for all outputs.

COnto is never needed for inverses.

DOnly quadratic functions have inverses.

Solution & Explanation:An inverse function must take every value in the codomain back to some input. If the function is not onto that codomain, some outputs have no preimage, so an inverse function (on that codomain) does not exist.

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Frequently Asked Questions

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QWhat grade level and standards does this worksheet align with?

This worksheet is designed specifically for Grade 6 Math students. It aligns with educational standard 6.120 (Construct and Critique Mathematical Arguments).