# EduVis Showcase: Geometry Triangles - Full Lesson
# Pattern: confidence_ladder
# Topic: Angle Sum of a Triangle (finding the unknown angle)
# Demonstrates: hook -> explore -> explain -> guided -> starter -> routine -> challenge -> recall

schema_version: "0.6"

curriculum:
  code: showcase
  topic: geometry-triangles

lesson:
  title: Angle Sum of a Triangle - Finding the Unknown Angle

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: guided_practice
      count: 1
    - phase: independent_practice
      difficulty: starter
      count: 2
    - phase: independent_practice
      difficulty: routine
      count: 2
    - phase: challenge
      count: 1
    - phase: recall
      count: 1

content:

  # --- HOOK ------------------------------------------------------------------
  # Real-world scenario to introduce triangles without math formulas yet.
  - id: hook_roof_truss
    type: fact_boxes
    placement:
      lesson_phase: hook
      layout_zone: center
      visual_weight: primary
      memory_role: example
    items:
      - text: "Roof Truss: Triangles distribute weight evenly and resist deformation."
        border_color: green
      - text: "Stability: A triangle's shape is rigid and cannot change without changing its side lengths."
        border_color: cyan

  # --- EXPLORE ---------------------------------------------------------------
  # Students observe a right-angled isosceles triangle.
  - id: explore_isosceles_triangle
    type: geometry_shape
    placement:
      lesson_phase: explore
      layout_zone: center
      visual_weight: primary
      memory_role: example
      difficulty: starter
    actions:
      conceptual:
        - compare: ["A", "C"]
    vertices: [[150, 350], [350, 150], [550, 350]]
    labels: ["A", "B", "C"]
    side_labels:
      - edge: "AB"
        label: "5 cm"
      - edge: "BC"
        label: "5 cm"
    angles:
      - vertex: "A"
        label: "45 deg"
      - vertex: "B"
        label: "90 deg"
        arc: "square"
      - vertex: "C"
        label: "45 deg"

  # --- EXPLAIN (conceptual model) ---------------------------------------------
  # Introduce the primary concept: Sum of angles equals 180 degrees.
  - id: explain_concept_angle_sum
    type: geometry_shape
    placement:
      lesson_phase: explain
      purpose: conceptual_model
      layout_zone: center
      visual_weight: primary
      memory_role: anchor
    actions:
      conceptual:
        - identify: pattern
    vertices: [[150, 320], [300, 120], [500, 320]]
    labels: ["P", "Q", "R"]
    angles:
      - vertex: "P"
        label: "53 deg"
      - vertex: "Q"
        label: "87 deg"
      - vertex: "R"
        label: "40 deg"

  # --- EXPLAIN (procedure) ---------------------------------------------------
  # State the formal rule and calculation steps.
  - id: explain_rule_angle_sum
    type: text_list
    placement:
      lesson_phase: explain
      purpose: procedure
      layout_zone: center
      visual_weight: primary
      memory_role: anchor
    items:
      - "The interior angles of any triangle always add up to exactly 180 deg."
      - "Formula: Angle A + Angle B + Angle C = 180 deg"
      - "To find an unknown angle, subtract the two known angles from 180 deg."
      - "Example: Unknown Angle = 180 deg - (Known Angle 1 + Known Angle 2)"

  # --- GUIDED PRACTICE -------------------------------------------------------
  # Walkthrough example with a clear procedure.
  - id: guided_example_triangle
    type: example_panel
    placement:
      lesson_phase: guided_practice
      layout_zone: center
      visual_weight: primary
      memory_role: example
    actions:
      procedural:
        - calculate: "x"
    items:
      - heading: "Question: Find the unknown angle 'x' in triangle ABC where Angle A = 60 deg and Angle B = 70 deg."
        body: |
          Step 1: Write down the angle sum equation:
                  60 deg + 70 deg + x = 180 deg
          Step 2: Add the two known angles:
                  130 deg + x = 180 deg
          Step 3: Subtract 130 deg from 180 deg to isolate x:
                  x = 180 deg - 130 deg
          Step 4: Solve for x:
                  x = 50 deg
          Answer: x = 50 deg

  # --- INDEPENDENT PRACTICE (STARTER) ----------------------------------------
  # Simple confidence-building questions.
  - id: practice_starter_triangle_1
    type: multiple_choice
    placement:
      lesson_phase: independent_practice
      difficulty: starter
      layout_zone: center
      visual_weight: primary
      memory_role: practice
    actions:
      conceptual:
        - apply: angle-sum-calculation
    question: "If a triangle has angles of 90 deg and 30 deg, what is the third angle?"
    options:
      A: "60 deg"
      B: "90 deg"
      C: "45 deg"
      D: "30 deg"
    answer: "A"

  - id: practice_starter_triangle_2
    type: multiple_choice
    placement:
      lesson_phase: independent_practice
      difficulty: starter
      layout_zone: center
      visual_weight: primary
      memory_role: practice
    actions:
      conceptual:
        - apply: angle-sum-calculation
    question: "If a triangle has three equal angles, what is the measure of each angle?"
    options:
      A: "60 deg"
      B: "90 deg"
      C: "45 deg"
      D: "180 deg"
    answer: "A"

  # --- INDEPENDENT PRACTICE (ROUTINE) ----------------------------------------
  # Regular, standard geometry problems.
  - id: practice_routine_triangle_1
    type: multiple_choice
    placement:
      lesson_phase: independent_practice
      difficulty: routine
      layout_zone: center
      visual_weight: primary
      memory_role: practice
    actions:
      conceptual:
        - apply: angle-sum-calculation
    question: "In triangle PQR, Angle P = 42 deg and Angle Q = 115 deg. Find the value of Angle R."
    options:
      A: "23 deg"
      B: "33 deg"
      C: "65 deg"
      D: "13 deg"
    answer: "A"

  - id: practice_routine_triangle_2
    type: multiple_choice
    placement:
      lesson_phase: independent_practice
      difficulty: routine
      layout_zone: center
      visual_weight: primary
      memory_role: practice
    actions:
      conceptual:
        - apply: angle-sum-calculation
    question: "An isosceles triangle has one vertex angle of 40 deg. What is the measure of each of the other two equal base angles?"
    options:
      A: "70 deg"
      B: "40 deg"
      C: "80 deg"
      D: "140 deg"
    answer: "A"

  # --- CHALLENGE -------------------------------------------------------------
  # Advanced algebraic angle sum problem.
  - id: challenge_triangle
    type: multiple_choice
    placement:
      lesson_phase: challenge
      difficulty: challenge
      layout_zone: center
      visual_weight: primary
      memory_role: practice
    actions:
      conceptual:
        - apply: algebraic-geometry
    question: |
      The angles of a triangle are x, 2x, and 3x.
      What is the value of the largest angle?
    options:
      A: "90 deg"
      B: "60 deg"
      C: "30 deg"
      D: "120 deg"
    answer: "A"

  # --- RECALL ----------------------------------------------------------------
  # Simple retrieval check.
  - id: recall_triangle_1
    type: multiple_choice
    placement:
      lesson_phase: recall
      layout_zone: center
      visual_weight: supporting
      memory_role: retrieval
    actions:
      conceptual:
        - retrieve: angle-sum-rule
    question: "WITHOUT LOOKING BACK - What do the interior angles of a triangle add up to?"
    options:
      A: "180 deg"
      B: "360 deg"
      C: "90 deg"
      D: "It depends on the triangle"
    answer: "A"