{
    "title": "Linear Equations Mastery Check",
    "questions": [
        {
            "type": "short_answer",
            "prompt": "Solve for x: 7x - 12 = 3x + 8",
            "answer": "x = 5",
            "explanation": "Subtract 3x from both sides to get 4x - 12 = 8. Add 12 to both sides to get 4x = 20. Divide by 4 to get x = 5."
        },
        {
            "type": "short_answer",
            "prompt": "Solve for y: 2(y + 5) = 4y - 6",
            "answer": "y = 8",
            "explanation": "Distribute 2: 2y + 10 = 4y - 6. Subtract 2y from both sides: 10 = 2y - 6. Add 6 to both sides: 16 = 2y. Divide by 2: y = 8."
        },
        {
            "type": "short_answer",
            "prompt": "Solve for z: 5z - 1 = 5z + 3",
            "answer": "No solution",
            "explanation": "Subtract 5z from both sides: -1 = 3. This is a false statement, so there is no solution."
        },
        {
            "type": "short_answer",
            "prompt": "Solve for m: 3(m - 2) = 3m - 6",
            "answer": "Infinitely many solutions",
            "explanation": "Distribute 3: 3m - 6 = 3m - 6. Subtract 3m from both sides: -6 = -6. This is a true statement, so there are infinitely many solutions."
        },
        {
            "type": "short_answer",
            "prompt": "Find the value of 'a' that makes the equation true: 4a + 7 = 2a + 15",
            "answer": "a = 4",
            "explanation": "Subtract 2a from both sides: 2a + 7 = 15. Subtract 7 from both sides: 2a = 8. Divide by 2: a = 4."
        },
        {
            "type": "short_answer",
            "prompt": "Solve: 6 - 2x = 3x + 16",
            "answer": "x = -2",
            "explanation": "Add 2x to both sides: 6 = 5x + 16. Subtract 16 from both sides: -10 = 5x. Divide by 5: x = -2."
        },
        {
            "type": "short_answer",
            "prompt": "What is the solution to 1\/2(4p + 8) = p + 10?",
            "answer": "p = 6",
            "explanation": "Distribute 1\/2: 2p + 4 = p + 10. Subtract p from both sides: p + 4 = 10. Subtract 4 from both sides: p = 6."
        },
        {
            "type": "short_answer",
            "prompt": "Determine if the equation 9k - 4 = 9k + 2 has one, no, or infinitely many solutions.",
            "answer": "No solution",
            "explanation": "Subtract 9k from both sides: -4 = 2. This is a false statement, indicating no solution."
        }
    ],
    "rubric": [
        {
            "criteria": "Variable Isolation",
            "excellent": "Consistently and accurately isolates the variable term using correct inverse operations.",
            "developing": "Attempts to isolate the variable but makes errors in applying inverse operations or combining terms."
        },
        {
            "criteria": "Simplification",
            "excellent": "Correctly combines like terms and applies the distributive property without errors.",
            "developing": "Shows some understanding of combining like terms or distribution but makes occasional errors."
        },
        {
            "criteria": "Solution Accuracy",
            "excellent": "Provides the correct numerical solution or identifies special cases (no\/infinite solutions) with 100% accuracy.",
            "developing": "Arrives at an incorrect numerical solution due to calculation errors, or misidentifies special cases."
        },
        {
            "criteria": "Procedural Steps",
            "excellent": "Demonstrates a clear, logical, and complete sequence of steps to solve the equation.",
            "developing": "Steps are partially complete or lack logical flow, making it difficult to follow the solution process."
        },
        {
            "criteria": "Special Cases Understanding",
            "excellent": "Accurately identifies and explains 'no solution' and 'infinitely many solutions' scenarios.",
            "developing": "Struggles to identify or correctly explain 'no solution' or 'infinitely many solutions' cases."
        }
    ]
}