{"model": "copilot-web", "provider": "Microsoft Copilot web app (copilot.microsoft.com), signed-in personal account, Auto mode, default settings; plan not verified", "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.", "ran_at": "2026-10-17T17:17:49-0700", "output": "Microsoft Copilot\n\nHere's your interactive quiz:\n\nQuiz (10 questions, transcribed by stepping through the widget; first option picked to advance; answer and explanation as shown after each selection)\n\n1. A recipe uses 2 cups of flour for 3 batches of muffins. What is the ratio of cups of flour to batches?\n   A. 2:3\n   B. 3:2\n   C. 2:5\n   D. 5:2\n   Correct answer: 2:3\n   Explanation: The ratio of flour to batches is 2 cups to 3 batches, written as 2:3.\n\n2. A car travels 180 miles in 3 hours. What is the unit rate in miles per hour?\n   A. 50 mph\n   B. 60 mph\n   C. 70 mph\n   D. 90 mph\n   Correct answer: 60 mph\n   Explanation: Unit rate = 180 ÷ 3 = 60 miles per hour.\n\n3. Which pair of ratios is proportional?\n   A. 2/3 and 4/5\n   B. 3/4 and 6/8\n   C. 5/6 and 10/11\n   D. 4/7 and 8/15\n   Correct answer: 3/4 and 6/8\n   Explanation: 3/4 = 0.75 and 6/8 = 0.75, so they are equivalent ratios and therefore proportional.\n\n4. A shirt costs $20 and is increased by 25%. What is the new price?\n   A. $22\n   B. $24\n   C. $25\n   D. $30\n   Correct answer: $25\n   Explanation: 25% of $20 is 0.25 × 20 = $5. Add the increase: $20 + $5 = $25.\n\n5. A video game costs $40 and is discounted by 15%. What is the sale price?\n   A. $34\n   B. $35\n   C. $46\n   D. $25\n   Correct answer: $34\n   Explanation: 15% of $40 is 0.15 × 40 = $6. Subtract the decrease: $40 − $6 = $34.\n\n6. Find the constant of proportionality from the equation y = 7x.\n   A. 1/7\n   B. 7\n   C. x\n   D. y\n   Correct answer: 7\n   Explanation: In an equation of the form y = kx, k is the constant of proportionality. Here k = 7.\n\n7. The table shows x: 2, 4, 6 and y: 10, 20, 30. What is the constant of proportionality?\n   A. 2\n   B. 5\n   C. 10\n   D. 15\n   Correct answer: 5\n   Explanation: Compute y/x: 10/2 = 5, 20/4 = 5, and 30/6 = 5. The constant of proportionality is 5.\n\n8. If 5 notebooks cost $12.50, what is the unit price per notebook?\n   A. $2.00\n   B. $2.25\n   C. $2.50\n   D. $3.00\n   Correct answer: $2.50\n   Explanation: Unit price = $12.50 ÷ 5 = $2.50 per notebook.\n\n9. A proportional relationship is represented by y = 4x. What is y when x = 9?\n   A. 13\n   B. 32\n   C. 36\n   D. 45\n   Correct answer: 36\n   Explanation: Substitute x = 9 into y = 4x: y = 4 × 9 = 36.\n\n10. A population of fish grows from 80 to 100. What is the percent increase?\n   A. 20%\n   B. 25%\n   C. 30%\n   D. 80%\n   Correct answer: 25%\n   Explanation: Increase = 100 − 80 = 20. Percent increase = 20 ÷ 80 = 0.25 = 25%.\n\nThe quiz includes: Ratios; Unit rates; Proportional relationships; Percent increase; Percent decrease; Constant of proportionality from equations and tables.\n\nEach question includes a worked solution and explanation in the answer key. Enjoy practicing!\n", "bytes": 2721, "plan_note": "Personal account, Auto mode", "capture_note": "Interactive quiz widget; questions and choices transcribed by stepping through it (first choice picked to advance), answer key copied with Copilot's copy button."}