Free Printable WorksheetMathAlgebra IMath CurriculumModeling (★) across A-CED, F-IF, F-LE, S-ID

ALG1.136 Integrated Modeling Problems Worksheet

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Worksheet Overview & Skills Covered

Core academic competencies and curriculum alignment

This Algebra I Math worksheet provides structured practice on ALG1.136 Integrated Modeling Problems. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

ALG1.136 Integrated Modeling Problems - Select the correct solution to multi-step modeling problems that require choosing among linear, quadratic, and exponential models; Select the statement that correctly interprets solutions, including units, constraints, and limitations. (CCSS: Modeling (★) across A-CED, F-IF, F-LE, S-ID; TEKS: §111.39(b)(3) (modeling and technology woven throughout); VA SOL: modeling emphasis across A.EI, A.F, A.ST; FL B.E.S.T.: modeling embedded in MA.912.AR.* and MA.912.F.*; NY-NGLS: ★ standards flagged across Algebra I; CA CCSSM: Modeling emphasis (Framework); MA 2017: Modeling throughout Model Algebra I; DoDEA CCRSM; NAEP: Algebra—applications; NCTM P2A: Practices 1–8.)

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 ALG1.136 Integrated Modeling Problems skill assessments:

Problem 1Difficulty: Mastery
A drone battery percentage is modeled by B(t) = 100(0.88)t, where t is minutes of flight. Which statement correctly finds the first whole minute below 50% and gives a limitation?
AAt 6 minutes, because B(5) is about 52.8% and B(6) is about 46.4%; the model should not be extended beyond realistic battery behavior
BAt 12 minutes, because the battery loses 12 percentage points per minute linearly
CAt 4 minutes, because 0.88(4) is less than 0.50
DAt 5 minutes, because B(5) is about 52.8%; the model is exact forever
Solution & Explanation:Check whole minutes: B(5) = 100(0.88)5 ≈ 52.8%, still above 50%. B(6) ≈ 46.4%, so the first whole minute below 50% is 6. Real batteries may not follow the same factor for all times.
Problem 2Difficulty: Mastery
A table shows x: 0, 1, 2, 3, 4 and y: 4, 7, 12, 19, 28. A student chooses exponential growth because the first differences increase. Which response is best?
AThe student is correct; the next value is 56
BThe data are linear because the first value is 4; the next value is 32
CNo model can be selected because the outputs increase
DThe data are quadratic because the second differences are constant; the next value is 39
Solution & Explanation:The first differences are 3, 5, 7, 9, and the second differences are 2, 2, 2. That supports a quadratic model, so the next difference is 11 and the next value is 28 + 11 = 39.
Problem 3Difficulty: Mastery
Solar panel output is shown in a table: time 8, 10, 12, 14, 16 hours; output 0, 300, 400, 300, 0 watts. Which model is most appropriate for this daylight interval?
AQuadratic, because the output rises to a maximum and then falls in a symmetric pattern
BConstant, because the first and last outputs are the same
CLinear, because time increases by equal amounts
DExponential, because watts are multiplied by a constant ratio
Solution & Explanation:The output increases to a maximum at midday and then decreases symmetrically, which is a parabolic pattern. A quadratic model is appropriate for this limited interval.

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Frequently Asked Questions

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QIs this ALG1.136 Integrated Modeling Problems worksheet free for teachers and homeschoolers?

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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 Modeling (★) across A-CED, F-IF, F-LE, S-ID (Primary standard selected for prompt fields in this prompt cell: CCSS Modeling (★) across A-CED, F-IF, F-LE, S-ID. Skill statement in this prompt cell: Select the correct solution to multi-step modeling problems that require choosing among linear, quadratic, and exponential models; Select the statement that correctly interprets solutions, including units, constraints, and limitations. Associated standards listed with this skill in the curriculum source: CCSS: Modeling (★) across A-CED, F-IF, F-LE, S-ID; TEKS: §111.39(b)(3) (modeling and technology woven throughout); VA SOL: modeling emphasis across A.EI, A.F, A.ST; FL B.E.S.T.: modeling embedded in MA.912.AR.* and MA.912.F.*; NY-NGLS: ★ standards flagged across Algebra I; CA CCSSM: Modeling emphasis (Framework); MA 2017: Modeling throughout Model Algebra I; DoDEA CCRSM; NAEP: Algebra—applications; NCTM P2A: Practices 1–8. Use this prompt-provided wording as the supporting standard description for this workflow.).

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