{
  "Id": "1fea98b4-8475-4d2a-9dc0-5fd434af5249",
  "Title": "Grade 6 Integers: Advanced Reasoning and Applications",
  "Subject": "Mathematics",
  "Topic": "Integers \u2014 number line, operations, opposites, and absolute value",
  "Instructions": "Read each question carefully and answer to the best of your ability. Show all working for word problems.",
  "EstimatedMinutes": 35,
  "StudentProfileId": "dd186faa-f489-46ee-84e4-26e2d01e2691",
  "SourceFileName": "manual-input",
  "SessionMaterialId": "438c5847-105a-4f9a-bc68-a03c5ff296cd",
  "GeneratedAt": "2026-07-25T12:35:15.330383Z",
  "Questions": [
    {
      "Id": 1,
      "Type": "word_problem",
      "Text": "A bank account is overdrawn by $85. It receives deposits of $140 and $35 on two successive days, then a withdrawal of $96 and a monthly fee of $12. What is the final balance?",
      "Options": [],
      "Answer": "Step 1: Start at \u221285.\nStep 2: Add 140 and 35: \u221285 \u002B 140 \u002B 35 = 90.\nStep 3: Subtract 96 and 12: 90 \u2212 96 \u2212 12 = \u221218.\nAnswer: \u2212$18",
      "Points": 3
    },
    {
      "Id": 2,
      "Type": "word_problem",
      "Text": "A city\u2019s temperature is \u22127\u00B0C at dawn. It warms by 9\u00B0C, cools by 4\u00B0C, drops another 5\u00B0C, and then rises by 6\u00B0C. What is the final temperature?",
      "Options": [],
      "Answer": "Step 1: \u22127 \u002B 9 = 2.\nStep 2: 2 \u2212 4 = \u22122.\nStep 3: \u22122 \u2212 5 = \u22127.\nStep 4: \u22127 \u002B 6 = \u22121.\nAnswer: \u22121\u00B0C",
      "Points": 3
    },
    {
      "Id": 3,
      "Type": "word_problem",
      "Text": "An elevator starts at level B3 (count this as \u22123). It rises 7 floors, then descends 11 floors, then rises 5 floors. Which floor does it stop on?",
      "Options": [],
      "Answer": "Step 1: \u22123 \u002B 7 = 4.\nStep 2: 4 \u2212 11 = \u22127.\nStep 3: \u22127 \u002B 5 = \u22122.\nAnswer: Level \u22122 (B2)",
      "Points": 3
    },
    {
      "Id": 4,
      "Type": "word_problem",
      "Text": "A submarine is at a depth of 120 m below sea level. It dives 65 m, ascends 150 m, then dives 48 m. What is its final depth relative to sea level?",
      "Options": [],
      "Answer": "Step 1: Start at \u2212120.\nStep 2: Dive 65: \u2212120 \u2212 65 = \u2212185.\nStep 3: Ascend 150: \u2212185 \u002B 150 = \u221235.\nStep 4: Dive 48: \u221235 \u2212 48 = \u221283.\nAnswer: \u221283 m",
      "Points": 3
    },
    {
      "Id": 5,
      "Type": "word_problem",
      "Text": "A hiker begins at 1,240 m above sea level, descends 180 m, climbs 360 m, then descends 95 m. What is the hiker\u2019s final altitude?",
      "Options": [],
      "Answer": "Step 1: 1240 \u2212 180 = 1060.\nStep 2: 1060 \u002B 360 = 1420.\nStep 3: 1420 \u2212 95 = 1325.\nAnswer: 1,325 m",
      "Points": 3
    },
    {
      "Id": 6,
      "Type": "word_problem",
      "Text": "Two integers x and y satisfy x \u002B y = \u221211 and x \u2212 y = 7. What is the smaller integer?",
      "Options": [],
      "Answer": "Step 1: Add equations: (x \u002B y) \u002B (x \u2212 y) = \u221211 \u002B 7 \u2192 2x = \u22124.\nStep 2: Solve for x: x = \u22122.\nStep 3: Use x \u2212 y = 7 \u2192 \u22122 \u2212 y = 7 \u2192 y = \u22129.\nAnswer: \u22129",
      "Points": 3
    },
    {
      "Id": 7,
      "Type": "word_problem",
      "Text": "The sum of three consecutive integers is \u221230. What is the greatest of the three?",
      "Options": [],
      "Answer": "Step 1: Let the integers be n \u2212 1, n, n \u002B 1 \u2192 sum = 3n.\nStep 2: 3n = \u221230 \u2192 n = \u221210.\nStep 3: Greatest is n \u002B 1 = \u22129.\nAnswer: \u22129",
      "Points": 3
    },
    {
      "Id": 8,
      "Type": "word_problem",
      "Text": "A robot on a number line starts at \u221212. It moves right 15 units, then left 19 units, then right 8 units. Where does it end?",
      "Options": [],
      "Answer": "Step 1: \u221212 \u002B 15 = 3.\nStep 2: 3 \u2212 19 = \u221216.\nStep 3: \u221216 \u002B 8 = \u22128.\nAnswer: \u22128",
      "Points": 3
    },
    {
      "Id": 9,
      "Type": "word_problem",
      "Text": "A helicopter is at 1,250 m altitude, and a submarine is at \u2212380 m. The helicopter descends 420 m while the submarine ascends 95 m. After these changes, what is the vertical distance between them?",
      "Options": [],
      "Answer": "Step 1: Helicopter: 1250 \u2212 420 = 830 m.\nStep 2: Submarine: \u2212380 \u002B 95 = \u2212285 m.\nStep 3: Separation: 830 \u2212 (\u2212285) = 1115.\nAnswer: 1,115 m",
      "Points": 3
    },
    {
      "Id": 10,
      "Type": "word_problem",
      "Text": "An integer n satisfies |n| \u002B 5 = 2n \u2212 3. Find n.",
      "Options": [],
      "Answer": "Step 1: Consider n \u2265 0: |n| = n \u2192 n \u002B 5 = 2n \u2212 3 \u2192 n = 8.\nStep 2: Consider n \u003C 0: |n| = \u2212n \u2192 \u2212n \u002B 5 = 2n \u2212 3 \u2192 3n = 8 (not integer).\nAnswer: 8",
      "Points": 3
    },
    {
      "Id": 11,
      "Type": "word_problem",
      "Text": "A team\u2019s score changes by \u002B7, \u221212, \u002B9, \u22125, and \u002B4 over five rounds. Starting from 0, what is the final score?",
      "Options": [],
      "Answer": "Step 1: 0 \u002B 7 \u2212 12 = \u22125.\nStep 2: \u22125 \u002B 9 \u2212 5 = \u22121.\nStep 3: \u22121 \u002B 4 = 3.\nAnswer: 3",
      "Points": 3
    },
    {
      "Id": 12,
      "Type": "word_problem",
      "Text": "A day starts at 6\u00B0C. Over four intervals, the temperature changes by \u221211\u00B0C, \u002B4\u00B0C, \u22129\u00B0C, and \u002B7\u00B0C. What is the final temperature?",
      "Options": [],
      "Answer": "Step 1: 6 \u2212 11 = \u22125.\nStep 2: \u22125 \u002B 4 = \u22121.\nStep 3: \u22121 \u2212 9 = \u221210.\nStep 4: \u221210 \u002B 7 = \u22123.\nAnswer: \u22123\u00B0C",
      "Points": 3
    },
    {
      "Id": 13,
      "Type": "word_problem",
      "Text": "Solve for the integer k: \u22124 \u002B k \u2212 7 \u002B 3k = 9.",
      "Options": [],
      "Answer": "Step 1: Combine like terms: (k \u002B 3k) \u002B (\u22124 \u2212 7) = 4k \u2212 11.\nStep 2: 4k \u2212 11 = 9 \u2192 4k = 20.\nStep 3: k = 20 \u00F7 4 = 5.\nAnswer: 5",
      "Points": 3
    },
    {
      "Id": 14,
      "Type": "word_problem",
      "Text": "In a parking structure, ground is 0. A car starts at level \u22122, goes up 5 levels, then down 3, then up 4. Which level is the car on?",
      "Options": [],
      "Answer": "Step 1: \u22122 \u002B 5 = 3.\nStep 2: 3 \u2212 3 = 0.\nStep 3: 0 \u002B 4 = 4.\nAnswer: Level 4",
      "Points": 3
    },
    {
      "Id": 15,
      "Type": "word_problem",
      "Text": "A walker starts at 0 on a number line and makes moves of \u002B8, \u221213, \u002B7, \u22124, and \u002B10. What is the final position?",
      "Options": [],
      "Answer": "Step 1: 0 \u002B 8 \u2212 13 = \u22125.\nStep 2: \u22125 \u002B 7 \u2212 4 = \u22122.\nStep 3: \u22122 \u002B 10 = 8.\nAnswer: 8",
      "Points": 3
    },
    {
      "Id": 16,
      "Type": "word_problem",
      "Text": "You start at \u221220 on a number line, add an integer x, then subtract 9, and arrive at \u221212. Find x.",
      "Options": [],
      "Answer": "Step 1: Equation: \u221220 \u002B x \u2212 9 = \u221212.\nStep 2: Combine constants: x \u2212 29 = \u221212.\nStep 3: x = \u221212 \u002B 29 = 17.\nAnswer: 17",
      "Points": 3
    },
    {
      "Id": 17,
      "Type": "word_problem",
      "Text": "Path A moves \u002B18, \u221225, \u002B14 from 0. Path B moves \u22129, \u002B22, \u22125 from 0. What is the absolute difference between their final positions?",
      "Options": [],
      "Answer": "Step 1: Path A: 0 \u002B 18 \u2212 25 \u002B 14 = 7.\nStep 2: Path B: 0 \u2212 9 \u002B 22 \u2212 5 = 8.\nStep 3: Difference: |7 \u2212 8| = 1.\nAnswer: 1",
      "Points": 3
    },
    {
      "Id": 18,
      "Type": "word_problem",
      "Text": "An integer is such that its opposite is 6 more than the integer itself. What is the integer?",
      "Options": [],
      "Answer": "Step 1: Let the integer be n; then \u2212n = n \u002B 6.\nStep 2: 2n = \u22126 \u2192 n = \u22123.\nAnswer: \u22123",
      "Points": 3
    },
    {
      "Id": 19,
      "Type": "word_problem",
      "Text": "Starting at \u22122\u00B0C, the temperature changes every hour by \u22123\u00B0C, then \u002B5\u00B0C, then \u22124\u00B0C, repeating this three-step cycle twice. What is the final temperature?",
      "Options": [],
      "Answer": "Step 1: One cycle change: \u22123 \u002B 5 \u2212 4 = \u22122.\nStep 2: Two cycles: \u22122 \u00D7 2 = \u22124.\nStep 3: Start at \u22122: \u22122 \u002B (\u22124) = \u22126.\nAnswer: \u22126\u00B0C",
      "Points": 3
    },
    {
      "Id": 20,
      "Type": "word_problem",
      "Text": "Start with the integer 9. First take its opposite, then add \u22127, then subtract the opposite of \u22124. What integer do you get?",
      "Options": [],
      "Answer": "Step 1: Opposite of 9 is \u22129.\nStep 2: Add \u22127: \u22129 \u002B (\u22127) = \u221216.\nStep 3: Opposite of \u22124 is 4; subtract it: \u221216 \u2212 4 = \u221220.\nAnswer: \u221220",
      "Points": 3
    },
    {
      "Id": 21,
      "Type": "fill_blank",
      "Text": "If integers x and y satisfy x \u002B y = \u221217 and x \u2212 y = 3, the smaller integer is _____",
      "Options": [],
      "Answer": "-10",
      "Points": 3
    },
    {
      "Id": 22,
      "Type": "fill_blank",
      "Text": "Evaluate: 4 \u2212 { \u22123 \u2212 [2 \u2212 (\u22125)] } = _____",
      "Options": [],
      "Answer": "14",
      "Points": 3
    },
    {
      "Id": 23,
      "Type": "fill_blank",
      "Text": "If |m \u2212 6| = 11 and m is an integer, the smaller solution is _____",
      "Options": [],
      "Answer": "-5",
      "Points": 3
    },
    {
      "Id": 24,
      "Type": "fill_blank",
      "Text": "The distance between \u221217 and 8 on the number line is _____",
      "Options": [],
      "Answer": "25",
      "Points": 3
    },
    {
      "Id": 25,
      "Type": "fill_blank",
      "Text": "The opposite of the sum (\u221212) \u002B 7 \u002B (\u22125) is _____",
      "Options": [],
      "Answer": "10",
      "Points": 3
    },
    {
      "Id": 26,
      "Type": "fill_blank",
      "Text": "Compute: (\u22126) \u00D7 [ (\u22123) \u002B 5 ] \u2212 { (\u22124) \u00D7 [ 2 \u2212 (\u22121) ] } = _____",
      "Options": [],
      "Answer": "0",
      "Points": 3
    },
    {
      "Id": 27,
      "Type": "fill_blank",
      "Text": "If the sum of three consecutive integers is \u221221, the middle integer is _____",
      "Options": [],
      "Answer": "-7",
      "Points": 3
    },
    {
      "Id": 28,
      "Type": "fill_blank",
      "Text": "Solve for n: \u22123 \u002B 2n = 11 \u2192 n = _____",
      "Options": [],
      "Answer": "7",
      "Points": 3
    },
    {
      "Id": 29,
      "Type": "fill_blank",
      "Text": "Starting at \u221214, moving 6 units right and then 9 units left lands at _____",
      "Options": [],
      "Answer": "-17",
      "Points": 3
    },
    {
      "Id": 30,
      "Type": "fill_blank",
      "Text": "The sum of all integers from \u221212 to 5 inclusive is _____",
      "Options": [],
      "Answer": "-63",
      "Points": 3
    },
    {
      "Id": 31,
      "Type": "fill_blank",
      "Text": "Evaluate: |\u221218| \u2212 |5 \u2212 (\u22129)| = _____",
      "Options": [],
      "Answer": "4",
      "Points": 3
    },
    {
      "Id": 32,
      "Type": "fill_blank",
      "Text": "The integer closest to zero among { \u221217, 9 \u2212 12, (\u22123) \u00D7 2 } is _____",
      "Options": [],
      "Answer": "-3",
      "Points": 3
    },
    {
      "Id": 33,
      "Type": "fill_blank",
      "Text": "If 4 \u002B [\u22122 \u2212 (q)] = \u22125, then q = _____",
      "Options": [],
      "Answer": "7",
      "Points": 3
    },
    {
      "Id": 34,
      "Type": "fill_blank",
      "Text": "Compute: 50 \u2212 (\u221240) \u2212 (\u22122) \u2212 7 = _____",
      "Options": [],
      "Answer": "85",
      "Points": 3
    },
    {
      "Id": 35,
      "Type": "fill_blank",
      "Text": "If |r| \u002B |r \u2212 4| = 10 and r \u2264 4, then r = _____",
      "Options": [],
      "Answer": "-3",
      "Points": 3
    },
    {
      "Id": 36,
      "Type": "fill_blank",
      "Text": "The number of integers strictly between \u221213 and 6 is _____",
      "Options": [],
      "Answer": "18",
      "Points": 3
    },
    {
      "Id": 37,
      "Type": "fill_blank",
      "Text": "Evaluate: (\u22122) \u00D7 (\u22127) \u002B (\u22123) \u00D7 5 \u2212 [\u22124 \u00D7 (\u22122)] = _____",
      "Options": [],
      "Answer": "-9",
      "Points": 3
    },
    {
      "Id": 38,
      "Type": "fill_blank",
      "Text": "The smaller integer n satisfying |n \u002B 5| = 14 is _____",
      "Options": [],
      "Answer": "-19",
      "Points": 3
    },
    {
      "Id": 39,
      "Type": "fill_blank",
      "Text": "Subtracting the opposite of \u221227 from \u22128 gives _____",
      "Options": [],
      "Answer": "-35",
      "Points": 3
    },
    {
      "Id": 40,
      "Type": "fill_blank",
      "Text": "Solve for t: t \u2212 [\u2212(t \u2212 9)] = \u22123 \u2192 t = _____",
      "Options": [],
      "Answer": "3",
      "Points": 3
    }
  ],
  "TotalPoints": 120
}