{
 "model": "qwen/qwen3.8-27b",
 "provider": "Groq API (free tier)",
 "task": "math7-proportions",
 "prompt": "Create a 10-question quiz for 7th graders on ratios and proportional relationships, including unit rates, percent increase/decrease, and identifying the constant of proportionality from a table and an equation. Include an answer key with worked solutions.",
 "system": "You are helping a grade 3-8 teacher. Produce classroom-ready material.",
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 "ran_at": "2026-10-16T08:08:14-0700",
 "output": "# 7th Grade Math Quiz: Ratios & Proportional Relationships\n\n**Name:** ___________________________  \n**Date:** ___________________________  \n**Score:** ______ / 10  \n\n**Instructions:** Read each question carefully. Show all work for full credit. Use exact answers unless otherwise specified.\n\n---\n\n### **Part 1: Unit Rates**\n\n**1.** A car travels 240 miles in 4 hours. What is the unit rate in miles per hour?  \n   **Answer:** _______________\n\n**2.** A recipe calls for 3 cups of flour to make 12 cookies. What is the unit rate of cups of flour per cookie?  \n   **Answer:** _______________\n\n---\n\n### **Part 2: Constant of Proportionality**\n\n**3.** Look at the table below. Find the constant of proportionality ($k$).\n\n| $x$ | 2 | 4 | 6 | 8 |\n|-----|---|---|---|---|\n| $y$ | 10| 20| 30| 40|\n\n   **Answer:** $k =$ _______________\n\n**4.** The equation $y = 7.5x$ represents a proportional relationship. What is the constant of proportionality?  \n   **Answer:** $k =$ _______________\n\n**5.** A graph of a proportional relationship passes through the origin $(0,0)$ and the point $(5, 15)$. What is the constant of proportionality?  \n   **Answer:** $k =$ _______________\n\n---\n\n### **Part 3: Solving Proportions**\n\n**6.** If 5 pens cost \\$7.50, how much would 8 pens cost? Set up and solve a proportion.  \n   **Answer:** _______________\n\n**7.** A map scale is 1 inch = 50 miles. If two cities are 3.5 inches apart on the map, how many miles apart are they in real life?  \n   **Answer:** _______________\n\n---\n\n### **Part 4: Percent Increase and Decrease**\n\n**8.** A shirt originally costs \\$40. It is on sale for 25% off. What is the sale price?  \n   **Answer:** _______________\n\n**9.** The number of students in a club increased from 20 to 25. What is the percent increase?  \n   **Answer:** _______________\n\n**10.** A phone\u2019s price decreased from \\$500 to \\$450. What is the percent decrease?  \n    **Answer:** _______________\n\n---\n\n## **Answer Key & Worked Solutions**\n\n### **1. Unit Rate: Miles per Hour**\n*   **Problem:** 240 miles in 4 hours.\n*   **Solution:** Divide total miles by total hours.\n    $$240 \\div 4 = 60$$\n*   **Answer:** **60 miles per hour**\n\n### **2. Unit Rate: Cups per Cookie**\n*   **Problem:** 3 cups of flour for 12 cookies.\n*   **Solution:** Divide total cups by total cookies.\n    $$3 \\div 12 = \\frac{3}{12} = \\frac{1}{4}$$\n*   **Answer:** **$\\frac{1}{4}$ cup per cookie** (or 0.25 cup)\n\n### **3. Constant of Proportionality from Table**\n*   **Problem:** Table shows $(2,10), (4,20), (6,30), (8,40)$.\n*   **Solution:** Divide $y$ by $x$ for any pair.\n    $$10 \\div 2 = 5$$\n    $$20 \\div 4 = 5$$\n*   **Answer:** **$k = 5$**\n\n### **4. Constant of Proportionality from Equation**\n*   **Problem:** $y = 7.5x$\n*   **Solution:** In the form $y = kx$, $k$ is the coefficient of $x$.\n*   **Answer:** **$k = 7.5$**\n\n### **5. Constant of Proportionality from Graph/Point**\n*   **Problem:** Point $(5, 15)$ on a proportional line.\n*   **Solution:** $k = \\frac{y}{x} = \\frac{15}{5} = 3$\n*   **Answer:** **$k = 3$**\n\n### **6. Solving a Proportion (Cost of Pens)**\n*   **Problem:** 5 pens = \\$7.50. Find cost of 8 pens.\n*   **Solution:**\n    $$\\frac{7.50}{5} = \\frac{x}{8}$$\n    $$1.50 = \\frac{x}{8}$$\n    $$x = 1.50 \\times 8 = 12.00$$\n*   **Answer:** **\\$12.00**\n\n### **7. Solving a Proportion (Map Scale)**\n*   **Problem:** 1 inch = 50 miles. Map distance = 3.5 inches.\n*   **Solution:**\n    $$\\frac{50 \\text{ miles}}{1 \\text{ inch}} = \\frac{x \\text{ miles}}{3.5 \\text{ inches}}$$\n    $$x = 50 \\times 3.5 = 175$$\n*   **Answer:** **175 miles**\n\n### **8. Percent Decrease (Sale Price)**\n*   **Problem:** \\$40 shirt, 25% off.\n*   **Solution:**\n    *   Find 25% of 40: $0.25 \\times 40 = 10$\n    *   Subtract discount from original price: $40 - 10 = 30$\n    *   *Alternative:* $40 \\times (1 - 0.25) = 40 \\times 0.75 = 30$\n*   **Answer:** **\\$30.00**\n\n### **9. Percent Increase (Club Members)**\n*   **Problem:** From 20 to 25 students.\n*   **Solution:**\n    *   Find the amount of change: $25 - 20 = 5$\n    *   Divide change by original amount: $\\frac{5}{20} = 0.25$\n    *   Convert to percent: $0.25 \\times 100 = 25\\%$\n*   **Answer:** **25% increase**\n\n### **10. Percent Decrease (Phone Price)**\n*   **Problem:** From \\$500 to \\$450.\n*",
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 "retry_note": "ran with a 1,500-token budget: Groq's free tier now rejects Qwen3.8 27B requests whose expected output exceeds its 1,000 output-tokens-per-minute limit"
}