Integers

{
  "antigravity_content": "**Lesson Plan: Adding and Subtracting Positive and Negative Numbers**\n\n**Objective:**  \nStudents will learn how to add and subtract positive and negative integers using a number line and the concepts of \"balloons\" and \"weights.\"\n\n---\n\n### 1. **Can You Do This? Check-In**\nLet\u2019s begin with a quick check!  \n**Question:** What is \\(5 + (-3)\\)?  \nTry to solve this on your own. \n\n---\n\n### 2. **Introduction to Positive and Negative Numbers**\n- **Positive Numbers**: Represented by a \"+\" sign or no sign at all (e.g., \\(5\\) is the same as \\(+5\\)).\n- **Negative Numbers**: Represented by a \"\u2212\" sign (e.g., \\(-3\\)).\n\n**Visual Aid:** Show a number line. Explain that on a number line, positive numbers go right and negative numbers go left.\n\n---\n\n### 3. **Using the Balloon and Weight Analogy**\n- **Balloons (Positive Numbers)**: They lift up. \n- **Weights (Negative Numbers)**: They pull down.\n\n---\n\n### 4. **Adding Positive Numbers**\n**I Do:**  \nExample: \\(2 + 3\\)  \n- Positive \\(2\\) plus Positive \\(3\\) equals Positive \\(5\\).  \n- Written as \\((+2) + (+3) = (+5)\\).\n\n**We Do:**  \nLet\u2019s try one together: \\(4 + 2\\).   \nWhat do we get?\n\n**You Do:**  \nNow, try \\(7 + 1\\). What is your answer?\n\n---\n\n### 5. **Subtracting Positive Numbers**\n**I Do:**  \nExample: \\(6 - 3\\)  \n- Positive \\(6\\) minus Positive \\(3\\) equals Positive \\(3\\).  \n- Written as \\((+6) - (+3) = (+3)\\).\n\n**We Do:**  \nLet\u2019s solve \\(8 - 5\\) together. What do we get?\n\n**You Do:**  \nNow try \\(10 - 6\\). What is your answer?\n\n---\n\n### 6. **Adding a Negative Number**\n**I Do:**  \nExample: \\(6 + (-3)\\)  \n- Positive \\(6\\) plus Negative \\(3\\) equals Positive \\(3\\).  \n- Written as \\((+6) + (\u22123) = (+3)\\).\n\n**We Do:**  \nLet\u2019s solve \\(5 + (-2)\\) together. What do we get?\n\n**You Do:**  \nNow, try \\(7 + (-4)\\). What is your answer? \n\n---\n\n### 7. **Subtracting a Negative Number**\n**I Do:**  \nExample: \\(6 - (-3)\\)  \n- Positive \\(6\\) minus Negative \\(3\\) equals Positive \\(9\\).  \n- Written as \\((+6) - (\u22123) = (+9)\\).\n\n**We Do:**  \nLet\u2019s try \\(10 - (-2)\\) together. \n\n**You Do:**  \nWhat is \\(14 - (-4)\\)?\n\n---\n\n### 8. **Understanding the Rules**\n- **Like Signs**: \n  - \\((+)(+)\\) or \\((-)(-)\\) becomes Positive.\n- **Unlike Signs**: \n  - \\((+)(-)\\) or \\((-)(+)\\) becomes Negative.\n\n**We Do:**  \nLet\u2019s try \\(3 + (-2)\\) together. \n\n**You Do:**  \nNow, what about \\(25 - (-4)\\)?\n\n---\n\n### 9. **Starting with a Negative Number**\n**I Do:**  \nExample: \\(-3 + (+2)\\)  \n- Start at \\(-3\\) on the number line and move up \\(2\\) to \\(-1\\).\n\n**We Do:**  \nLet\u2019s solve \\(-5 + (+3)\\).\n\n**You Do:**  \nNow try \\(-4 + (-2)\\). \n\n---\n\n### 10. **Wrap-Up and Play!**\nYou\u2019ve done a great job learning about integers today! Remember, it\u2019s all about practicing these concepts. \n\n**Activity Suggestion:**  \nTry playing \"Casey Runner\" to practice your skills with positive and negative numbers.\n\n### 11. **Celebrate!**\nNo matter what answers you got, I celebrate your effort! You\u2019ve put in great work to learn how to add and subtract integers. Keep practicing, and you\u0027ll become even better at it! \n\n---\n\n**End of Lesson**",
  "meta": {
    "difficulty_distribution": {
      "1": 10,
      "2": 10,
      "3": 10,
      "4": 10
    },
    "total_questions": 40
  },
  "prompt_id": "zpd_adaptive",
  "prompt_name": "\ud83c\udfaf ZPD Adaptive Tutor (Research: Vygotsky 1978)",
  "questions": [
    {
      "correct_answer": "A",
      "difficulty": 1,
      "explanation": "When you add a negative number, you move left on the number line. So 5 - 3 = 2.",
      "id": 1,
      "options": [
        "A) 2",
        "B) 8",
        "C) 3",
        "D) 1"
      ],
      "question": "What is 5 + (-3)?"
    },
    {
      "correct_answer": "A",
      "difficulty": 1,
      "explanation": "Subtracting 2 from 7 gives you 5.",
      "id": 2,
      "options": [
        "A) 5",
        "B) 4",
        "C) 6",
        "D) 3"
      ],
      "question": "What is 7 - 2?"
    },
    {
      "correct_answer": "A",
      "difficulty": 1,
      "explanation": "Adding 3 and 4 results in 7.",
      "id": 3,
      "options": [
        "A) 7",
        "B) 6",
        "C) 5",
        "D) 8"
      ],
      "question": "What is 3 + 4?"
    },
    {
      "correct_answer": "A",
      "difficulty": 1,
      "explanation": "When you subtract 6 from 10, you get 4.",
      "id": 4,
      "options": [
        "A) 4",
        "B) 3",
        "C) 5",
        "D) 2"
      ],
      "question": "What is 10 - 6?"
    },
    {
      "correct_answer": "A",
      "difficulty": 1,
      "explanation": "Adding zero does not change the number, so 6 + 0 = 6.",
      "id": 5,
      "options": [
        "A) 6",
        "B) 0",
        "C) 1",
        "D) 5"
      ],
      "question": "What is 6 + 0?"
    },
    {
      "correct_answer": "A",
      "difficulty": 1,
      "explanation": "Starting at -5 and moving 2 up gives you -3.",
      "id": 6,
      "options": [
        "A) -3",
        "B) -7",
        "C) -4",
        "D) -2"
      ],
      "question": "What is (-5) + 2?"
    },
    {
      "correct_answer": "A",
      "difficulty": 1,
      "explanation": "Subtracting 5 from 12 results in 7.",
      "id": 7,
      "options": [
        "A) 7",
        "B) 8",
        "C) 6",
        "D) 5"
      ],
      "question": "What is 12 - 5?"
    },
    {
      "correct_answer": "A",
      "difficulty": 1,
      "explanation": "Adding two negative numbers results in a more negative number: -3 - 2 = -5.",
      "id": 8,
      "options": [
        "A) -5",
        "B) -4",
        "C) -6",
        "D) -1"
      ],
      "question": "What is (-3) + (-2)?"
    },
    {
      "correct_answer": "A",
      "difficulty": 1,
      "explanation": "Adding a negative number means going down, so 4 - 1 = 3.",
      "id": 9,
      "options": [
        "A) 3",
        "B) 5",
        "C) 4",
        "D) 2"
      ],
      "question": "What is 4 + (-1)?"
    },
    {
      "correct_answer": "A",
      "difficulty": 1,
      "explanation": "8 minus 2 equals 6.",
      "id": 10,
      "options": [
        "A) 6",
        "B) 7",
        "C) 5",
        "D) 8"
      ],
      "question": "What is 8 - 2?"
    },
    {
      "correct_answer": "C",
      "difficulty": 2,
      "explanation": "First add, 5 + 6 = 11, then subtract 3, so 11 - 3 = 8.",
      "id": 11,
      "options": [
        "A) 8",
        "B) 10",
        "C) 9",
        "D) 7"
      ],
      "question": "What is 5 + 6 - 3?"
    },
    {
      "correct_answer": "C",
      "difficulty": 2,
      "explanation": "First solve the parentheses: 5 - 2 = 3, then 10 - 3 = 7.",
      "id": 12,
      "options": [
        "A) 7",
        "B) 6",
        "C) 8",
        "D) 5"
      ],
      "question": "What is 10 - (5 - 2)?"
    },
    {
      "correct_answer": "A",
      "difficulty": 2,
      "explanation": "3 - 5 = -2, then add 4: -2 + 4 = 2.",
      "id": 13,
      "options": [
        "A) 1",
        "B) 0",
        "C) 2",
        "D) -1"
      ],
      "question": "What is 3 + (-5) + 4?"
    },
    {
      "correct_answer": "A",
      "difficulty": 2,
      "explanation": "Combine: -2 - 6 = -8, then add 4: -8 + 4 = -4.",
      "id": 14,
      "options": [
        "A) -4",
        "B) -6",
        "C) -8",
        "D) -2"
      ],
      "question": "What is (-2) + (-6) + 4?"
    },
    {
      "correct_answer": "C",
      "difficulty": 2,
      "explanation": "Solve inside parentheses first: 3 + 2 = 5, then 9 - 5 = 4.",
      "id": 15,
      "options": [
        "A) 3",
        "B) 4",
        "C) 5",
        "D) 2"
      ],
      "question": "What is 9 - (3 + 2)?"
    },
    {
      "correct_answer": "B",
      "difficulty": 2,
      "explanation": "8 - 3 = 5, then subtract 2: 5 - 2 = 3.",
      "id": 16,
      "options": [
        "A) 3",
        "B) 4",
        "C) 5",
        "D) 6"
      ],
      "question": "What is 8 + (-3) - 2?"
    },
    {
      "correct_answer": "A",
      "difficulty": 2,
      "explanation": "14 - 7 = 7, then 7 - 2 = 5.",
      "id": 17,
      "options": [
        "A) 5",
        "B) 6",
        "C) 7",
        "D) 8"
      ],
      "question": "What is 14 - 7 + (-2)?"
    },
    {
      "correct_answer": "A",
      "difficulty": 2,
      "explanation": "First: -1 + 5 = 4, then 4 - 4 = 0.",
      "id": 18,
      "options": [
        "A) 0",
        "B) 1",
        "C) 2",
        "D) 3"
      ],
      "question": "What is (-1) + 5 - 4?"
    },
    {
      "correct_answer": "A",
      "difficulty": 2,
      "explanation": "Combine: -3 + 4 = 1, then 1 + 2 = 3.",
      "id": 19,
      "options": [
        "A) 3",
        "B) 2",
        "C) 4",
        "D) 1"
      ],
      "question": "What is (-3) + 4 + 2?"
    },
    {
      "correct_answer": "B",
      "difficulty": 2,
      "explanation": "6 - 3 = 3, then 3 - 1 = 2.",
      "id": 20,
      "options": [
        "A) 5",
        "B) 4",
        "C) 3",
        "D) 2"
      ],
      "question": "What is 6 + (-3) + (-1)?"
    },
    {
      "correct_answer": "C",
      "difficulty": 3,
      "explanation": "10 - 5 = 5, then 5 + 3 = 8, and finally 8 - 2 = 6.",
      "id": 21,
      "options": [
        "A) 6",
        "B) 7",
        "C) 8",
        "D) 9"
      ],
      "question": "What is 10 + (-5) + 3 - 2?"
    },
    {
      "correct_answer": "A",
      "difficulty": 3,
      "explanation": "First, solve inside parentheses: 6 - 2 = 4, then 15 - 4 = 11, and 11 - 3 = 8.",
      "id": 22,
      "options": [
        "A) 10",
        "B) 12",
        "C) 8",
        "D) 6"
      ],
      "question": "What is 15 - (6 - 2) + (-3)?"
    },
    {
      "correct_answer": "A",
      "difficulty": 3,
      "explanation": "Combine: -4 + 5 = 1, then 1 - 2 = -1, and finally -1 + 3 = 2.",
      "id": 23,
      "options": [
        "A) 2",
        "B) 1",
        "C) 0",
        "D) 3"
      ],
      "question": "What is (-4) + 5 + (-2) + 3?"
    },
    {
      "correct_answer": "A",
      "difficulty": 3,
      "explanation": "First, calculate inside the parentheses: 3 + 4 = 7, then 12 - 7 = 5, and finally 5 + 5 = 10.",
      "id": 24,
      "options": [
        "A) 10",
        "B) 9",
        "C) 8",
        "D) 7"
      ],
      "question": "What is 12 - (3 + 4) + 5?"
    },
    {
      "correct_answer": "A",
      "difficulty": 3,
      "explanation": "First, calculate: 20 - 8 = 12, then 12 - 4 = 8, and finally 8 + 1 = 9.",
      "id": 25,
      "options": [
        "A) 9",
        "B) 10",
        "C) 11",
        "D) 12"
      ],
      "question": "What is 20 + (-8) - 4 + 1?"
    },
    {
      "correct_answer": "A",
      "difficulty": 3,
      "explanation": "First, 6 - 3 = 3, then 3 + 2 = 5, and finally 5 - 5 = 0.",
      "id": 26,
      "options": [
        "A) 0",
        "B) 1",
        "C) -1",
        "D) 2"
      ],
      "question": "What is 6 + (-3) + 2 - 5?"
    },
    {
      "correct_answer": "A",
      "difficulty": 3,
      "explanation": "First, calculate: 18 - 12 = 6, then 6 - 3 = 3, and finally 3 + 9 = 12.",
      "id": 27,
      "options": [
        "A) 12",
        "B) 9",
        "C) 6",
        "D) 3"
      ],
      "question": "What is 18 - 12 + (-3) + 9?"
    },
    {
      "correct_answer": "A",
      "difficulty": 3,
      "explanation": "First, solve inside parentheses: 4 - 6 = -2, then -2 - 2 = -4, and finally -4 + 5 = 1.",
      "id": 28,
      "options": [
        "A) 7",
        "B) 6",
        "C) 5",
        "D) 4"
      ],
      "question": "What is (-2) + (4 - 6) + 5?"
    },
    {
      "correct_answer": "A",
      "difficulty": 3,
      "explanation": "First, calculate: 10 - 3 = 7, then 7 - 4 = 3, and finally 3 + 1 = 4.",
      "id": 29,
      "options": [
        "A) 4",
        "B) 5",
        "C) 6",
        "D) 7"
      ],
      "question": "What is 10 + (-3) - 4 + 1?"
    },
    {
      "correct_answer": "A",
      "difficulty": 3,
      "explanation": "Adding a negative number means moving left: 5 + 2 = 7, then 7 + 3 = 10, and finally 10 - 4 = 6.",
      "id": 30,
      "options": [
        "A) 6",
        "B) 5",
        "C) 4",
        "D) 3"
      ],
      "question": "What is 5 - (-2) + 3 - 4?"
    },
    {
      "correct_answer": "A",
      "difficulty": 4,
      "explanation": "5 - 7 = -2, then -2 - 4 = -6, and finally -6 + 2 = -4.",
      "id": 31,
      "options": [
        "A) -4",
        "B) -5",
        "C) -3",
        "D) 0"
      ],
      "question": "What is 5 + (-7) - 4 + 2?"
    },
    {
      "correct_answer": "A",
      "difficulty": 4,
      "explanation": "First, solve inside parentheses: 2 + 6 = 8, then 3 + 5 = 8, and finally 8 - 8 + 4 = 6.",
      "id": 32,
      "options": [
        "A) 6",
        "B) 5",
        "C) 4",
        "D) 3"
      ],
      "question": "What is 3 + 5 - (2 + 6) + 4?"
    },
    {
      "correct_answer": "A",
      "difficulty": 4,
      "explanation": "First calculate: 10 - 3 = 7, then 7 + 2 = 9, and finally 9 + 4 = 13.",
      "id": 33,
      "options": [
        "A) 15",
        "B) 14",
        "C) 13",
        "D) 12"
      ],
      "question": "What is 10 - 3 + 2 - (-4)?"
    },
    {
      "correct_answer": "A",
      "difficulty": 4,
      "explanation": "First, solve inside parentheses: 3 + 5 = 8, then 20 - 8 = 12, and finally 12 + 2 - 6 = 8.",
      "id": 34,
      "options": [
        "A) 6",
        "B) 7",
        "C) 8",
        "D) 9"
      ],
      "question": "What is 20 - (3 + 5) + 2 - 6?"
    },
    {
      "correct_answer": "A",
      "difficulty": 4,
      "explanation": "First, solve inside parentheses: 5 - 2 = 3, then -10 + 3 = -7, and finally -7 + 8 = 1.",
      "id": 35,
      "options": [
        "A) 1",
        "B) 0",
        "C) -1",
        "D) -2"
      ],
      "question": "What is (-10) + (5 - 2) + 8?"
    },
    {
      "correct_answer": "A",
      "difficulty": 4,
      "explanation": "First calculate: 15 - 5 = 10, then 10 - 3 = 7, and finally 7 - 4 = 3.",
      "id": 36,
      "options": [
        "A) 3",
        "B) 4",
        "C) 5",
        "D) 6"
      ],
      "question": "What is (15 - 5) + (-3) - 4?"
    },
    {
      "correct_answer": "A",
      "difficulty": 4,
      "explanation": "First solve inside parentheses: 6 - 4 = 2, then 8 - 2 = 6, and finally 6 - 2 = 4.",
      "id": 37,
      "options": [
        "A) 6",
        "B) 5",
        "C) 4",
        "D) 3"
      ],
      "question": "What is 8 - (6 - 4) - 2?"
    },
    {
      "correct_answer": "A",
      "difficulty": 4,
      "explanation": "First, calculate: 25 - 10 = 15, then 15 - 5 = 10, and finally 10 + 2 = 12.",
      "id": 38,
      "options": [
        "A) 9",
        "B) 11",
        "C) 10",
        "D) 12"
      ],
      "question": "What is 25 - 10 + (-5) + 2?"
    },
    {
      "correct_answer": "A",
      "difficulty": 4,
      "explanation": "First solve: 10 - 3 = 7, then 1 + 2 = 3, finally 7 - 3 = 4.",
      "id": 39,
      "options": [
        "A) 4",
        "B) 5",
        "C) 6",
        "D) 3"
      ],
      "question": "What is (10 + (-3)) - (1 + 2)?"
    },
    {
      "correct_answer": "A",
      "difficulty": 4,
      "explanation": "First solve inside parentheses: 2 + 3 = 5, then 18 - 6 = 12, and finally 12 - 5 = 7.",
      "id": 40,
      "options": [
        "A) 7",
        "B) 8",
        "C) 9",
        "D) 6"
      ],
      "question": "What is 18 + (-6) - (2 + 3)?"
    }
  ],
  "source_ixl_skills": [
    "Understanding integers",
    "Integers on number lines",
    "Graph integers on horizontal and vertical number lines",
    "Absolute value and opposite integers",
    "Compare and order integers",
    "Add and subtract integers using counters",
    "Add and subtract integers",
    "Complete addition and subtraction sentences with integers",
    "Add and subtract integers: word problems",
    "Multiply and divide integers"
  ],
  "topic": "Integers"
}