Rates and Percentages Review

Grade: 6th

Duration: 35 minutes

Class size: 20 students

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Standards Alignment

Pennsylvania Department of Education (PDE) & Common Core State Standards (CCSS)

• CCSS.MATH.CONTENT.6.RP.A.3: Use ratio and rate reasoning to solve real-world and mathematical problems, including finding unit rates and using proportional relationships.
• CCSS.MATH.CONTENT.6.RP.A.3.C: Find a percent of a quantity as a rate per 100; solve problems involving finding the whole, given a part and the percent.
• CCSS.MATH.CONTENT.6.RP.A.3.D: Use ratio reasoning to convert measurement units and solve multi-step ratio problems.
• PA Standard - 2.1.6.A3: Use mathematical reasonings to solve problems including proportions and percentages.

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Learning Objectives

By the end of this lesson, students will be able to:

• Calculate unit rates from real-world shopping scenarios.
• Find percentages, discounts, and the corresponding parts and wholes of quantities.
• Set up and solve proportions involving parts, wholes, and percents.
• Apply these skills in hands-on, real-life contexts through a simulated shopping activity.

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Materials Needed

• Shopping cards/posters with item prices, discounts, and sale signs (4 distinct sets for rotation)
• Clipboards with worksheets for recording answers
• Calculators (optional)
• Pencils and erasers
• Large chart paper or whiteboard for debrief

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Lesson Outline

1. Introduction & Review (5 minutes)

• Briefly review key concepts from the rates and percentages unit:
  • Definition and examples of unit rates
  • How to find percentage discounts and parts of a whole
  • Setting up proportions with percentages (e.g., part/whole = percent/100)
• Use quick oral questioning or flashcards to activate prior knowledge.

2. Instructions for Shopping Rotation Activity (3 minutes)

• Explain the activity: students will rotate through 4 stations, each with different “store shelves” containing items with prices and discounts.
• Their job is to:
  • Find the unit rate (if applicable)
  • Calculate the discount amount in dollars
  • Find the sale price (part) and original price (whole)
  • Set up and solve proportions to verify percents or find missing values
• Emphasize recording calculations on their worksheet.

3. Rotation Activity: Hands-on Shopping (20 minutes)

• Divide students into 4 groups (5 students each).
• Groups start at different stations and rotate every 5 minutes so all groups visit each station.

Station Examples:

• Station 1: Grocery prices with bulk discounts (e.g., 3 cans for $6, find unit rate per can)
• Station 2: Clothing sale with percent discounts (e.g., 30% off a $40 shirt)
• Station 3: Electronics with markup and markdowns (find sale price after 15% discount, set up proportions)
• Station 4: Mixed items with missing parts in ratio problems (e.g., “If 25% corresponds to 15 apples, find total apples”)

4. Group Debrief and Review (7 minutes)

• Bring class back together; randomly pick examples from each station to solve on the board together.
• Discuss different strategies to find unit rates, solve proportions, and calculate percentages or discounts.
• Address misconceptions and highlight common errors.
• Reinforce connections to real-world math.

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Assessment & Evaluation

• Collect worksheets for formative assessment to check students’ accuracy and methodology.
• Observation notes on student participation and problem-solving approaches during rotations.
• Use exit ticket question: “Explain how you would find the sale price on an item if you know the original price and the discount percentage.”

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Differentiation Strategies

• Support students needing extra help with step-by-step guidance and calculators.
• Offer challenge tasks for advanced learners by increasing complexity at certain stations (e.g., multi-step discounts or combining percentages).

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Teacher Reflection (Post-Lesson)

• Reflect on student engagement during rotations and understanding of proportional reasoning with percents.
• Consider modifications to station scenarios for clarity or challenge next iteration.
• Evaluate if hands-on approach improved mastery before the unit test.

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This interactive, standards-aligned culminating activity ensures students apply rates, percentages, and proportion skills in a practical, memorable way—preparing them confidently for assessments and real-life math applications.