# EduVis Showcase: Negative Numbers - Full Lesson
# Pattern: confidence_ladder
# Demonstrates: hook -> explore -> explain -> guided -> starter -> routine -> challenge -> recall
# This lesson builds from concrete scenarios (temperature, money) through abstract rules

schema_version: "0.6"

curriculum:
  code: "SEC-math-2027"
  topic: "Chapter-2-Negative-Numbers"
  concept: "negative_numbers"
  learning_outcomes:
    - "Understand negative integers and represent them on a number line"
    - "Perform addition and subtraction involving negative numbers"
    - "Apply negative number operations to solve real-world problems"

lesson:
  title: "Negative Numbers - Understanding Values Below Zero"
  concepts:
    - "integers"
    - "negative_numbers"

progression:
  pattern: confidence_ladder
  pedagogy:
    confidence_first: true
    explain_why: true
    no_skipped_steps: true
  phases:
    - phase: hook
    - phase: explore
    - phase: explain
      purpose: conceptual_model
    - phase: explain
      purpose: procedure
    - phase: explain
      purpose: comparison
    - phase: guided_practice
      count: 1
    - phase: independent_practice
      difficulty: starter
      count: 3
    - phase: independent_practice
      difficulty: routine
      count: 2
    - phase: challenge
      count: 1
    - phase: recall
      count: 2

content:

  # --- HOOK ------------------------------------------------------------------
  # Concrete, real-world scenarios. Negative numbers not named yet.

  - id: hook_real_world
    type: fact_boxes
    placement:
      lesson_phase: hook
      layout_zone: center
      visual_weight: primary
      memory_role: example
    items:
      - text: "Temperature: Five degrees below zero (-5 deg C)"
        border_color: blue
      - text: "Finance: Owing ten dollars (-$10)"
        border_color: red

  # --- EXPLORE ---------------------------------------------------------------
  # Student observes: where do "below zero" and "owing" sit on a line?
  # Pattern discovery before the rule is stated.

  - id: explore_temperature_scale
    type: number_line
    placement:
      lesson_phase: explore
      layout_zone: center
      visual_weight: primary
      memory_role: example
      difficulty: starter
    actions:
      conceptual:
        - compare: [-5, 3]
    relationships:
      anchors:
        - hook_real_world
    range: [-5, 5]
    direction_labels:
      left: "Colder / Less"
      right: "Warmer / More"
    highlight:
      - value: -5
        label: "-5 deg C"
        color: blue
      - value: 3
        label: "3 deg C"
        color: green
      - value: 0
        label: "0 deg C"
        color: grey

  # --- EXPLAIN (conceptual model) ---------------------------------------------
  # Visual understanding: what does position mean?

  - id: explain_concept_negative
    type: number_line
    placement:
      lesson_phase: explain
      purpose: conceptual_model
      layout_zone: center
      visual_weight: primary
      memory_role: anchor
    actions:
      conceptual:
        - identify: direction
    relationships:
      reinforces:
        - explore_temperature_scale
      precedes:
        - explain_rule_negative
    range: [-5, 5]
    direction_labels:
      left: "Smaller values"
      right: "Larger values"
    highlight:
      - value: -3
        label: "-3\n(further left,\nsmaller value)"
        color: red
      - value: 0
        label: "0\n(reference zero)"
        color: grey
      - value: 3
        label: "3\n(further right,\nlarger value)"
        color: green

  # --- EXPLAIN (procedure) ---------------------------------------------------
  # State the rule explicitly — after intuition is built.

  - id: explain_rule_negative
    type: text_list
    placement:
      lesson_phase: explain
      purpose: procedure
      layout_zone: center
      visual_weight: primary
      memory_role: anchor
    relationships:
      reinforces:
        - explain_concept_negative
      precedes:
        - guided_example_negative
    items:
      - "Numbers less than zero are called NEGATIVE NUMBERS."
      - "On a number line, negative numbers sit to the LEFT of zero."
      - "The further left a number is, the smaller it is."
      - "Negative numbers are always smaller than zero and any positive number."

  # --- MISCONCEPTION IDENTIFICATION ------------------------------------------
  # Before practice: show the common error so students recognize and avoid it.

  - id: misconception_comparing_negatives
    type: example_panel
    placement:
      lesson_phase: explain
      purpose: comparison
      layout_zone: center
      visual_weight: supporting
      memory_role: misconception_fix
    actions:
      conceptual:
        - identify: misconception
    relationships:
      contradicts:
        - explain_rule_negative
    items:
      - heading: "Common Mistake"
        body: |
          Some students think: "-10 is LARGER than -2 because 10 is bigger than 2."
          WHY THIS IS WRONG: The digit size does NOT determine negative number size.
          On the number line, -10 is further LEFT than -2, so -10 is SMALLER.
      - heading: "Correct Thinking"
        body: |
          -10 < -2 (negative ten is less than negative two)
          Because -10 is further left on the number line, it is smaller.

  # --- GUIDED PRACTICE -------------------------------------------------------
  # Instructor walks through a worked example. Student follows each step.

  - id: guided_example_negative
    type: example_panel
    placement:
      lesson_phase: guided_practice
      layout_zone: center
      visual_weight: primary
      memory_role: example
    actions:
      conceptual:
        - compare: [-5, -1]
    relationships:
      reinforces:
        - explain_concept_negative
      precedes:
        - check_negative_ordering
    items:
      - heading: "Question: Which is colder, -5 deg C or -1 deg C?"
        body: |
          Step 1: Locate both numbers on a number line.
          Step 2: -5 is to the LEFT of -1.
          Step 3: The number further left is smaller.
          Step 4: Therefore, -5 deg C is colder (smaller) than -1 deg C.
          Answer: -5 < -1

  # --- INDEPENDENT PRACTICE (STARTER) ----------------------------------------
  # Intentionally easy. Builds confidence before routine difficulty.

  - id: check_negative_ordering
    type: multiple_choice
    concepts:
      - "negative_numbers"
      - "integers"
    skills:
      - "order_integers"
    placement:
      lesson_phase: independent_practice
      difficulty: starter
      layout_zone: center
      memory_role: practice
      assessment_objective: conceptual_understanding
    question: "Which of the following statements is correct?"
    options:
      A: "−10 is larger than −2 because 10 is larger than 2"
      B: "−2 is larger than −10 because −2 is further to the right on a number line"
      C: "−10 and −2 represent the same value"
      D: "Cannot be compared"
    answer: "B"
    misconceptions:
      A: "digit_size_magnitude_error"
    solution_steps:
      - "Draw a number line with −10 and −2."
      - "−10 is located to the left of −2."
      - "Values increase as you move right."
      - "Therefore, −2 is larger than −10 (written as −2 > −10)."

  - id: check_negative_addition
    type: multiple_choice
    concepts:
      - "negative_numbers"
    skills:
      - "add_negative_numbers"
    placement:
      lesson_phase: independent_practice
      difficulty: starter
      layout_zone: center
      memory_role: practice
      assessment_objective: conceptual_understanding
    question: "Evaluate the expression: −3 + (−4)"
    options:
      A: "−1 (difference between 4 and 3)"
      B: "−7 (moving left on the number line)"
      C: "7 (overgeneralizing two negatives make a positive)"
      D: "1 (incorrect signs combination)"
    answer: "B"
    misconceptions:
      A: "difference_confusion"
      C: "double_negative_addition_confusion"
    solution_steps:
      - "Start at −3 on the number line."
      - "Adding a negative number (−4) means moving 4 units to the left."
      - "Moving 4 units left of −3 lands on −7."
      - "Therefore, −3 + (−4) = −7."

  - id: check_negative_subtraction
    type: multiple_choice
    concepts:
      - "negative_numbers"
    skills:
      - "subtract_negative_numbers"
    placement:
      lesson_phase: independent_practice
      difficulty: starter
      layout_zone: center
      memory_role: practice
      assessment_objective: conceptual_understanding
    question: "Evaluate the expression: −5 − (−3)"
    options:
      A: "−8 (incorrectly adding absolute values)"
      B: "−2 (correct, converting to −5 + 3)"
      C: "−15 (incorrectly multiplying)"
      D: "2 (incorrect sign)"
    answer: "B"
    misconceptions:
      A: "subtract_negative_minus_negative"
    solution_steps:
      - "Rewrite subtraction of a negative number as addition: −5 − (−3) = −5 + 3."
      - "Start at −5 and move 3 units to the right."
      - "You land on −2."
      - "Therefore, −5 − (−3) = −2."

  # --- INDEPENDENT PRACTICE (ROUTINE) ----------------------------------------
  # Exam-style problems. Typical difficulty for assessment.

  - id: practice_routine_negative_1
    type: multiple_choice
    placement:
      lesson_phase: independent_practice
      difficulty: routine
      layout_zone: center
      visual_weight: primary
      memory_role: practice
    actions:
      conceptual:
        - apply: signed-number-ordering
    question: "The temperature in City A is -8 deg C. City B is -3 deg C. Which city is colder?"
    options:
      A: "City A"
      B: "City B"
      C: "Both the same"
      D: "Cannot tell"
    answer: "A"

  - id: practice_routine_negative_2
    type: multiple_choice
    placement:
      lesson_phase: independent_practice
      difficulty: routine
      layout_zone: center
      visual_weight: primary
      memory_role: practice
    actions:
      conceptual:
        - apply: signed-number-ordering
    question: "A submarine is at -40 m. A fish is at -15 m. Which is deeper?"
    options:
      A: "The submarine (deeper)"
      B: "The fish (deeper)"
      C: "Same depth"
      D: "Cannot tell"
    answer: "A"

  - id: simplify_expression
    type: short_answer
    concepts:
      - "negative_numbers"
    skills:
      - "simplify_expressions"
    placement:
      lesson_phase: independent_practice
      difficulty: routine
      layout_zone: center
      memory_role: practice
      assessment_objective: procedural_fluency
    question: "Simplify the algebraic expression: 3x + 5 + 2x - 3"
    answer: "5x + 2"
    evaluation_mode: "algebraic"
    solution_steps:
      - "Group like terms together: (3x + 2x) + (5 - 3)."
      - "Combine variable terms: 3x + 2x = 5x."
      - "Combine constant terms: 5 - 3 = 2."
      - "Combine into the simplified form: 5x + 2."
    marking_scheme:
      - step: 0
        pattern: "(3x + 2x) + (5 - 3)"
        mark_type: "M"
        weight: 1
        description: "Grouped like terms: (3x + 2x) + (5 - 3)"
      - step: 1
        pattern: "5x + 2"
        mark_type: "A"
        weight: 1
        depends_on: 0
        description: "Simplified final expression: 5x + 2"

  # --- CHALLENGE -------------------------------------------------------------
  # Stretch question. Extends beyond routine application.

  - id: challenge_negative
    type: multiple_choice
    placement:
      lesson_phase: challenge
      difficulty: challenge
      layout_zone: center
      visual_weight: primary
      memory_role: practice
    actions:
      conceptual:
        - apply: signed-number-ordering
        - identify: misconception
    question: |
      Amir says: "-20 is BIGGER than -3 because 20 is bigger than 3."
      What is wrong with Amir's reasoning?
    options:
      A: "On the number line, -20 is further LEFT than -3, so -20 is SMALLER, not bigger"
      B: "He is correct — -20 > -3"
      C: "The digit size does not matter for negative numbers"
      D: "Both A and C"
    answer: "D"

  # --- RECALL ----------------------------------------------------------------
  # Retrieval without re-reading. Builds long-term memory.

  - id: recall_negative_1
    type: multiple_choice
    placement:
      lesson_phase: recall
      layout_zone: center
      visual_weight: supporting
      memory_role: retrieval
    actions:
      conceptual:
        - retrieve: signed-number-ordering
    question: "WITHOUT LOOKING BACK — Which is larger: -7 or -2?"
    options:
      A: "-7"
      B: "-2"
      C: "They are equal"
      D: "Cannot tell"
    answer: "B"

  - id: recall_negative_2
    type: multiple_choice
    placement:
      lesson_phase: recall
      layout_zone: center
      visual_weight: supporting
      memory_role: retrieval
    actions:
      conceptual:
        - retrieve: signed-number-ordering
    question: "WITHOUT LOOKING BACK — Arrange from smallest to largest: -3, 1, -8, 0"
    options:
      A: "-8, -3, 0, 1"
      B: "-3, -8, 0, 1"
      C: "1, 0, -3, -8"
      D: "0, 1, -3, -8"
    answer: "A"