Free Printable WorksheetMathGrade 7Math Curriculum7.20

7.20 Multi step proportional reasoning and scaling Worksheet

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Worksheet Overview & Skills Covered

Core academic competencies and curriculum alignment

This Grade 7 Math worksheet provides structured practice on 7.20 Multi step proportional reasoning and scaling. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

7.20 Multi-step proportional reasoning and scaling - In multiple-choice items, students select the correct multi-step proportional solution and the intermediate step that correctly sets up the scaling. (CCSS 7.RP.A.3; CA 7.RP.3; MA 7.RP.3; NY 7.RP.3; FL MA.7.AR.4.5; TX 7.4(D); VA 7.CE.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 7.20 Multi step proportional reasoning and scaling skill assessments:

Problem 1Difficulty: Mastery

In a lab, a solution is made by dissolving 25 g of sugar in 300 mL of water. Dylan wants to make 2.4 L of the same solution, then adds 250 mL of water to dilute it. Which option shows a correct Step 1 (scaling up the amount of sugar) AND the final concentration in grams per 100 mL?

AStep 1: scale factor = 300 ÷ 2400 = 0.125; sugar needed = 25 × that; Concentration = divide by 250 only

BStep 1: sugar needed = 25 + (2400 − 300); Final concentration = 200 ÷ 250 × 100

CStep 1: scale factor = 2400 ÷ 300 = 8; sugar needed = 200 g; Final concentration = 200 g ÷ 2400 mL × 100 = 8.333

DStep 1: scale factor = 2400 ÷ 300 = 8; sugar needed = 25 × 8 = 200 g; Final concentration = 200 g ÷ 2650 mL × 100 = 7.547 g per 100 mL

Solution & Explanation:Step 1: scale factor = 2400 ÷ 300 = 8; sugar needed = 25 × 8 = 200 g; Final concentration = 200 g ÷ 2650 mL × 100 = 7.547 g per 100 mL

Problem 2Difficulty: Mastery

Dylan orders 3 graphic novel set(s) priced at €42 each. The exchange rate is $ 1.08 per €1, and the card charges a 4% conversion fee. Which option shows a correct Step 1 (scaling to the USD subtotal before the fee) AND the final total charge?

AStep 1: USD subtotal = €42 × 3 × $1.08 = $136.08; Total = $136.08 × 1.04 = $141.523

BStep 1: USD subtotal = €42 ÷ 3 ÷ $1.08; Total = add fee

CStep 1: USD subtotal = €42 × 3 × $1.08 = $136.08; Total = $136.08 + 4 = $140.08

DStep 1: USD subtotal = €42 × 3 × $1.08 = $136.08; Total = $136.08 × 0.04 = $5.443

Solution & Explanation:Step 1: USD subtotal = €42 × 3 × $1.08 = $136.08; Total = $136.08 × 1.04 = $141.523

Problem 3Difficulty: Mastery

A nature loop map uses the scale 1 cm = 0.6 km. The full route measures 14.2 cm on the map. Rowan runs only 60% of the route at a pace of 6 minutes per km. Which option shows a correct Step 1 (scaling cm to km) AND the total running time in minutes?

AStep 1: full distance = 0.6 ÷ 14.2 = 0.042 km; Time = multiply by pace

BStep 1: full distance = 14.2 + 0.6 = 14.8 km; Run distance = take 60%; Time = multiply by pace

CStep 1: full distance = 14.2 × 0.6 = 8.52 km; Run distance = 8.52 × 0.6 = 5.112 km; Time = 5.112 × 6 = 30.672 min

DStep 1: full distance = 14.2 × 0.6 = 8.52 km; Run distance = 8.52 ÷ 0.6 = 14.2 km; Time = multiply by pace

Solution & Explanation:Step 1: full distance = 14.2 × 0.6 = 8.52 km; Run distance = 8.52 × 0.6 = 5.112 km; Time = 5.112 × 6 = 30.672 min

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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 7 Math students. It aligns with educational standard 7.20 (Practice and review Grade 7 math skill 7.20: Multi-Step Proportional Reasoning and Scaling.).