{"model": "openai/gpt-oss-20b", "provider": "Groq API (free tier)", "task": "construction-estimate", "prompt": "Create a worked example and practice problem for high school construction students: estimate materials for framing one 12-foot-long, 8-foot-tall interior wall with 2x4 studs at 16 inches on center (single bottom plate, double top plate). Show the math step by step, include a waste factor, and give a second practice wall with the answer.", "system": "You are helping a high school career and technical education (CTE) teacher. Produce classroom-ready material.", "temperature": 0.3, "max_tokens": 6000, "retry_note": "re-run with 6000-token budget after first attempt returned empty/incomplete output or hit rate limit", "ran_at": "2026-10-16T05:33:56-0700", "output": "# Classroom Hand\u2011Out  \n**Estimating Framing Materials for an Interior Wall**  \n*(High\u2011School Construction / CTE \u2013 2\u00d74 Framing)*  \n\n---\n\n## 1.  Worked Example  \n**Wall dimensions:** 12\u202fft long \u00d7 8\u202fft tall  \n**Stud spacing:** 16\u202fin. on\u2011center (OC)  \n**Bottom plate:** single 2\u00d74  \n**Top plate:** double 2\u00d74  \n\n> **Goal:**  Determine how many 8\u2011ft 2\u00d74 boards you need, including a 5\u202f% waste factor.\n\n---\n\n### Step 1 \u2013 Convert wall length to inches  \n12\u202fft \u00d7 12\u202fin/ft = **144\u202fin**  \n\n### Step 2 \u2013 Find the number of studs  \nFormula:  \n\\[\n\\text{Studs} = \\frac{\\text{Length (in)}}{\\text{OC (in)}} + 1\n\\]\n\n\\[\n\\text{Studs} = \\frac{144}{16} + 1 = 9 + 1 = \\boxed{10\\ \\text{studs}}\n\\]\n\n*(You place a stud at each end and one every 16\u202fin.)*\n\n### Step 3 \u2013 Calculate total stud length  \nEach stud is 8\u202fft tall (the nominal size of a 2\u00d74).  \n\n\\[\n10\\ \\text{studs} \\times 8\\ \\text{ft} = 80\\ \\text{ft}\n\\]\n\n### Step 4 \u2013 Bottom plate length  \nOne continuous plate = 12\u202fft  \n\n### Step 5 \u2013 Top plates (double)  \n2 plates \u00d7 12\u202fft = 24\u202fft  \n\n### Step 6 \u2013 Sum raw lumber length  \n\\[\n80\\ \\text{ft (studs)} + 12\\ \\text{ft (bottom)} + 24\\ \\text{ft (top)} = \\boxed{116\\ \\text{ft}}\n\\]\n\n### Step 7 \u2013 Add waste factor  \nTypical waste factor for framing: **5\u202f%**  \n\n\\[\n116\\ \\text{ft} \\times 1.05 = 121.8\\ \\text{ft}\n\\]\n\n### Step 8 \u2013 Convert to 8\u2011ft boards  \n\\[\n\\frac{121.8\\ \\text{ft}}{8\\ \\text{ft/board}} = 15.225\\ \\text{boards}\n\\]\n\nRound up to the next whole board: **16 boards**  \n\n> **Answer:** 16 pieces of 8\u2011ft 2\u00d74 lumber (10 studs, 1 bottom plate, 2 top plates, plus 5\u202f% waste).\n\n---\n\n## 2.  Quick Reference Formulae  \n\n| Item | Formula | Example (12\u202fft wall) |\n|------|---------|----------------------|\n| Studs | \\(\\frac{L}{OC} + 1\\) | \\(\\frac{144}{16}+1 = 10\\) |\n| Total stud length | \\(\\text{Studs} \\times \\text{Stud height}\\) | \\(10 \\times 8 = 80\\) ft |\n| Bottom plate | 1 \u00d7 wall length | 12 ft |\n| Top plates | 2 \u00d7 wall length | 24 ft |\n| Raw lumber | Sum of above | 116 ft |\n| With waste | Raw \u00d7 (1 + waste\u202f%) | 116 \u00d7 1.05 = 121.8 ft |\n| Boards needed | Raw\u202fft \u00f7 8 ft/board | 121.8 \u00f7 8 = 15.225 \u2192 16 |\n\n---\n\n## 3.  Practice Problem  \n\n**Wall dimensions:** 10\u202fft long \u00d7 9\u202fft tall  \n**Stud spacing:** 24\u202fin. on\u2011center  \n**Bottom plate:** single 2\u00d74  \n**Top plate:** double 2\u00d74  \n**Waste factor:** 5\u202f%  \n\n> **Question:** How many 8\u2011ft 2\u00d74 boards are required?\n\n---\n\n### Solution (for the teacher\u2019s reference)\n\n1. **Wall length in inches**: 10\u202fft \u00d7 12\u202fin/ft = 120\u202fin  \n2. **Studs**: \\(120/24 + 1 = 5 + 1 = 6\\) studs  \n3. **Stud length**: 6 studs \u00d7 9\u202fft = 54\u202fft  \n4. **Bottom plate**: 10\u202fft  \n5. **Top plates**: 2 \u00d7 10\u202fft = 20\u202fft  \n6. **Raw lumber**: 54 + 10 + 20 = 84\u202fft  \n7. **With waste**: 84 \u00d7 1.05 = 88.2\u202fft  \n8. **Boards needed**: 88.2 \u00f7 8 = 11.025 \u2192 **12 boards**\n\n---\n\n### Answer for students\n\n> **You need 12 pieces of 8\u2011ft 2\u00d74 lumber** (6 studs, 1 bottom plate, 2 top plates, plus a 5\u202f% waste allowance).\n\n---\n\n### How to use this hand\u2011out\n\n1. **Show the worked example** to the class, explaining each step.  \n2. **Give the practice problem** on a worksheet or as a quick quiz.  \n3. **Discuss common pitfalls** (e.g., forgetting the +1 stud, mis\u2011applying waste, using the wrong board length).  \n4. **Encourage students** to double\u2011check their calculations and to think about how waste can vary with different wall heights, plate lengths, or lumber sizes.\n\nHappy framing!", "finish_reason": "stop", "usage": {"queue_time": 0.030909038, "prompt_tokens": 168, "prompt_time": 0.00806582, "completion_tokens": 3639, "completion_time": 4.123863483, "total_tokens": 3807, "total_time": 4.131929303, "completion_tokens_details": {"reasoning_tokens": 2439}}}