Free Printable WorksheetMathAlgebra IMath CurriculumA-REI connections (course-model dependent)

ALG1.105 Absolute Value as Distance and Magnitude Worksheet

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Worksheet Overview & Skills Covered

Core academic competencies and curriculum alignment

This Algebra I Math worksheet provides structured practice on ALG1.105 Absolute Value as Distance and Magnitude. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

ALG1.105 Absolute Value as Distance and Magnitude - Select the statement that correctly interprets absolute value as distance from zero and as magnitude of change; Select the option that shows how to use distance interpretations to set up simple equations and inequalities. (CCSS: A-REI connections (course-model dependent); TEKS: §111.39(c)(2)(B) (inequalities) and local curricula; VA SOL: A.EI.1 (method reasoning); FL B.E.S.T.: MA.912.AR.4.1; NY-NGLS: AI-F.IF.7b connections; CA CCSSM: F-IF.7b; MA 2017: HS.F-IF.7b; DoDEA CCRSM; NAEP: Algebra—equations; NCTM P2A: Practices 1, 3.)

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

Algebra I

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 ALG1.105 Absolute Value as Distance and Magnitude skill assessments:

Problem 1Difficulty: Mastery
For r > 0, which option gives the most complete distance interpretation of |x - c| <= r?
Ax is at least r units from c, so x <= c - r or x >= c + r.
Bx is no more than r units from c, so c - r <= x <= c + r.
Cx is exactly r units from zero, so x = -r or x = r.
Dx is no more than c units from r, so r - c <= x <= r + c.
Solution & Explanation:The expression |x - c| measures distance from x to c. At most r units from c gives all values between c - r and c + r, inclusive.
Problem 2Difficulty: Mastery
A tracker changes a runner's position reading from 8 miles to -2 miles. The signed change is -10 miles. What is the magnitude of the change?
A-10 miles, because the signed change is negative
B6 miles, because ∣8∣ - ∣-2∣ = 6
C10 miles, because ∣-2 - 8∣ = 10
D2 miles, because the final reading is -2
Solution & Explanation:Magnitude is the absolute value of signed change. Since -2 - 8 = -10, the magnitude is |-10| = 10 miles.
Problem 3Difficulty: Mastery
Which statement correctly connects the interval -6 < x < 6 with absolute value?
AIt means ∣x∣ > 6 because every value has a sign.
BIt means ∣x - 6∣ < 0 because x is below 6.
CIt means ∣x + 6∣ = 6 because the interval starts at -6.
DIt means ∣x∣ < 6 because every value in the interval is less than 6 units from zero.
Solution & Explanation:The interval from -6 to 6 contains exactly the values whose distance from zero is less than 6.

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QWhat grade level and standards does this worksheet align with?

This worksheet is designed specifically for Algebra I Math students. It aligns with educational standard A-REI connections (course-model dependent) (Primary standard selected for prompt fields in this prompt cell: CCSS A-REI connections (course-model dependent). Skill statement in this prompt cell: Select the statement that correctly interprets absolute value as distance from zero and as magnitude of change; Select the option that shows how to use distance interpretations to set up simple equations and inequalities. Associated standards listed with this skill in the curriculum source: CCSS: A-REI connections (course-model dependent); TEKS: §111.39(c)(2)(B) (inequalities) and local curricula; VA SOL: A.EI.1 (method reasoning); FL B.E.S.T.: MA.912.AR.4.1; NY-NGLS: AI-F.IF.7b connections; CA CCSSM: F-IF.7b; MA 2017: HS.F-IF.7b; DoDEA CCRSM; NAEP: Algebra—equations; NCTM P2A: Practices 1, 3. Use this prompt-provided wording as the supporting standard description for this workflow.).

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