How Can I Design A Word Problem That Effectively Assesses Students' Ability To Apply Percentage Increase And Decrease Concepts To Real-world Scenarios, Such As Sales Tax And Discounts, While Also Incorporating Ratios To Represent Proportional Relationships Between Quantities, And What Specific Linguistic And Mathematical Scaffolds Can I Use To Support English Language Learners And Students With Math Anxiety?

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Word Problem Design: Applying Percentages and Ratios in a Shopping Scenario

Context:
A local clothing store is offering a 20% discount on all shirts. Additionally, there's an 8% sales tax applied after the discount. The original price of a shirt is $50.

Problem:

  1. Calculate the Discounted Price:

    • Apply a 20% discount to the original price of the shirt. Show your calculations.

  2. Apply Sales Tax:

    • Add an 8% sales tax to the discounted price. Show your calculations.

  3. Determine the Ratio:

    • Find the ratio of the final price (after discount and tax) to the original price. Simplify the ratio.

Linguistic and Mathematical Scaffolds:

  • Visual Aid:
    Use a flowchart to illustrate the process from original price to discounted price, then to final price with tax.

  • Formula Reference Card:
    Provide formulas for percentage decrease and increase, and ratio definition.

  • Word Bank:
    Include terms like "discount," "sales tax," "ratio," and "proportional."

  • Sentence Frames:
    Offer prompts like "The discounted price is... because..." to aid articulation.

  • Step-by-Step Guide:
    Break down each calculation with examples, such as:

    • Discount: $50 * 20% = $10 off; New price = $50 - $10 = $40.
    • Sales Tax: $40 * 8% = $3.20; Final price = $40 + $3.20 = $43.20.
    • Ratio: $43.20 : $50 = 43.2 : 50 = 4.32 : 5 ≈ 4:5.

  • Reflection Question:
    Ask students to explain if the ratio makes sense given the percentage changes.

  • Peer Discussion:
    Encourage students to compare answers, fostering language practice and clarification.

Assessment:

  • Evaluate calculations for discount, tax, and ratio.
  • Assess understanding through the reflection question.

This structured approach ensures clarity, supports diverse learners, and engages students in applying mathematical concepts to real-world scenarios.