{"model": "claude-web", "provider": "Claude web app (claude.ai), signed in on a paid Max plan, Opus 5.5, default settings", "task": "math7-proportions", "ran_at": "2026-10-17T13:43:18-0700", "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.", "output": "Claude Opus 5.5\n\nI'll put this together as a printable doc: the quiz first, then a separate answer key with worked solutions.\n\nOutline's up; now writing the questions.\n\nWriting the 10 quiz questions now.\n\nQuestions are in; now writing the answer key.\n\nThe Ratios & Proportional Relationships Quiz is ready. You can read it over, edit it directly, or leave comments, and it exports to Word or PDF for printing.\n\n----- ARTIFACT CONTENT (Claude Docs: \"Ratios & Proportional Relationships Quiz (Grade 7)\") -----\n\nRatios & Proportional Relationships Quiz (Grade 7)\nOct 17, 2026 · @Leon\nQuiz\nName: ______________________ Date: ____________ Period: ______\nDirections: Answer all 10 questions. Show your work in the space provided. Round money to the nearest cent. Each question is worth 10 points.\n1. Unit rate. A 12-ounce box of cereal costs $3.60. What is the cost per ounce?\n2. Better buy. A 6-pack of juice boxes costs $4.50. An 8-pack costs $5.60. Which is the better buy? Justify your answer using unit prices.\n3. Unit rate with fractions. Maya walks 2/3 of a mile in 1/4 of an hour. At this rate, how many miles does she walk per hour?\n4. Percent increase. The price of a T-shirt went up from $20 to $25. What is the percent increase?\n5. Percent decrease. A school had 400 students last year and 340 students this year. What is the percent decrease in enrollment?\n6. Discount. A jacket regularly costs $80. It is on sale for 30% off. What is the sale price?\n7. Constant of proportionality from a table. The table shows a proportional relationship between x and y. What is the constant of proportionality, k? Write an equation for the relationship.\nx\n2\n5\n8\ny\n7\n17.5\n28\n8. Is it proportional? Which table shows a proportional relationship? Explain how you know.\nTable A\nx\n1\n2\n3\n4\ny\n4\n7\n10\n13\nTable B\nx\n2\n4\n6\n8\ny\n5\n10\n15\n20\n9. Constant of proportionality from an equation. The cost y (in dollars) of x pounds of bananas is given by y = (2/5)x.\n1. What is the constant of proportionality?\n2. What does it mean in this situation?\n3. How much do 20 pounds of bananas cost?\n10. Writing and using an equation. A cookie recipe uses 3 cups of flour for every 4 dozen cookies.\n1. Write an equation for f, the cups of flour needed for d dozen cookies.\n2. How many cups of flour are needed for 10 dozen cookies?\nAnswer Key\n#\nAnswer\n1\n$0.30 per ounce\n2\n8-pack ($0.70 each vs. $0.75 each)\n3\n2 2/3 miles per hour\n4\n25% increase\n5\n15% decrease\n6\n$56.00\n7\nk = 3.5; y = 3.5x\n8\nTable B\n9\nk = 2/5; $0.40 per pound; $8.00\n10\nf = (3/4)d; 7.5 cups\nWorked solutions\n1. Unit rate = total cost ÷ number of ounces = $3.60 ÷ 12 = $0.30 per ounce.\n2. Find the price per juice box for each pack.\n• 6-pack: $4.50 ÷ 6 = $0.75 per box\n• 8-pack: $5.60 ÷ 8 = $0.70 per box\nSince $0.70 < $0.75, the 8-pack is the better buy.\n3. Miles per hour = miles ÷ hours = (2/3) ÷ (1/4). Dividing by a fraction means multiplying by its reciprocal: (2/3) × (4/1) = 8/3 = 2 2/3 miles per hour (about 2.67 mph).\n4. Amount of change = $25 − $20 = $5. Percent change = change ÷ original = 5 ÷ 20 = 0.25 = 25% increase. Common mistake: dividing by the new price (5 ÷ 25 = 20%).\n5. Amount of change = 400 − 340 = 60 students. Percent change = 60 ÷ 400 = 0.15 = 15% decrease.\n6. Method 1: Discount = 30% of $80 = 0.30 × 80 = $24. Sale price = $80 − $24 = $56.00. Method 2: If 30% is taken off, you pay 70%: 0.70 × 80 = $56.00.\n7. In a proportional relationship, k = y ÷ x for every pair.\n• 7 ÷ 2 = 3.5\n• 17.5 ÷ 5 = 3.5\n• 28 ÷ 8 = 3.5\nThe constant of proportionality is k = 3.5, so the equation is y = 3.5x.\n8. Check y ÷ x for each pair.\n• Table A: 4 ÷ 1 = 4, but 7 ÷ 2 = 3.5. The ratios are not equal, so A is not proportional. (Its graph would also not pass through the origin: working backward, x = 0 gives y = 1.)\n• Table B: 5 ÷ 2 = 10 ÷ 4 = 15 ÷ 6 = 20 ÷ 8 = 2.5. Every ratio is the same, so Table B is proportional, with k = 2.5.\n9.\n1. An equation in the form y = kx has constant of proportionality k, so k = 2/5.\n2. 2/5 = 0.40, so bananas cost $0.40 per pound. The constant of proportionality is the unit rate.\n3. y = (2/5)(20) = 40/5 = $8.00.\n10.\n1. k = cups of flour ÷ dozens of cookies = 3 ÷ 4 = 3/4. So the equation is f = (3/4)d (or f = 0.75d).\n2. f = (3/4)(10) = 30/4 = 7.5 cups of flour. Check: 3 cups for 4 dozen and 7.5 cups for 10 dozen give the same ratio, 3/4 = 7.5/10 = 0.75.\n", "capture_note": "Claude's chat reply, then the Claude Docs document text as copied (tables copy as one cell per line; document links copy as plain text)"}