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<!DOCTYPE html>
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  <title>Getting Started — Geometry Playground</title>
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      <a href="01.html" class="current"><span class="dd-num">01</span> Getting Started</a>
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      <a href="03.html"><span class="dd-num">03</span> Doing Stuff Again</a>
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      <div class="ch-label">Chapter 1 of 6</div>
      <h1>Getting Started</h1>
      <p class="lead">Learn to draw with code using the <code style="background:rgba(255,255,255,0.15);color:#F2B13E">Pen</code> API. You'll draw squares, triangles, stars and more — building your geometric intuition along the way.</p>
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         01 — INTRO TO PEN
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        <span class="section-tag tutorial">◆ Tutorial</span>
        <h1>Intro to Pen</h1>
        <p class="lead">Meet the <code>Pen</code> — your drawing tool. A pen starts at the origin (0, 0), faces right, and draws a line every time it moves forward.</p>
        <div class="img-wrap">
          <img src="images/00-intro-to-pen.png" alt="A single horizontal line drawn from the origin (0,0) using the Pen API in Geometry Playground">
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        <h2>The Pen API</h2>
        <p>In this playground, you draw shapes using a <strong>Pen</strong> object. Think of it like a turtle on a canvas — it has a position and a direction, and it moves forward when you tell it to.</p>

        <h3>Creating a Pen</h3>
        <div class="code-wrap">
          <div class="code-header"><span class="code-lang">Swift</span><button class="code-copy" onclick="copyCode(this)">Copy</button></div>
          <pre><span class="kw">var</span> <span class="vr">p</span> = <span class="tp">Pen</span>()          <span class="cm">// Create a new pen at (0, 0), facing right</span>
<span class="vr">p</span>.<span class="fn">addLine</span>(distance: <span class="num">100</span>)  <span class="cm">// Move forward 100 units, drawing as you go</span>
<span class="fn">addShape</span>(pen: <span class="vr">p</span>)          <span class="cm">// Render the shape on screen</span></pre>
        </div>

        <h3>Key Commands</h3>
        <div class="code-wrap">
          <div class="code-header"><span class="code-lang">Swift</span><button class="code-copy" onclick="copyCode(this)">Copy</button></div>
          <pre><span class="vr">p</span>.<span class="fn">addLine</span>(distance: <span class="num">100</span>)  <span class="cm">// Draw a line 100 units forward</span>
<span class="vr">p</span>.<span class="fn">turn</span>(degrees: <span class="num">90</span>)       <span class="cm">// Turn LEFT 90°</span>
<span class="vr">p</span>.<span class="fn">move</span>(distance: <span class="num">50</span>)      <span class="cm">// Move 50 units without drawing</span>
<span class="vr">p</span>.<span class="fn">penColor</span> = .<span class="fn">red</span>          <span class="cm">// Change line colour</span>
<span class="vr">p</span>.<span class="fn">lineWidth</span> = <span class="num">3</span>            <span class="cm">// Change line thickness</span></pre>
        </div>

        <h3>Coordinate System</h3>
        <p>The canvas uses a standard Cartesian coordinate system — <strong>x</strong> increases to the right, <strong>y</strong> increases upward. The pen starts at the origin <strong>(0, 0)</strong> and faces right (along the positive x-axis). <code>turn(degrees: 90)</code> rotates the pen <em>anti-clockwise</em> (left turn).</p>

        <div class="img-wrap">
          <img src="images/01-intro-to-pen.png" alt="A single horizontal line drawn from the origin (0,0) using the Pen API in Geometry Playground">
        </div>

        <div class="callout">
          <h3>💡 Think About It</h3>
          <ul>
            <li>What direction does the pen face at the start?</li>
            <li>What happens if you call <code>addLine</code> twice without turning?</li>
            <li>What coordinates does the pen reach after <code>addLine(distance: 100)</code>?</li>
          </ul>
        </div>

        <div class="im-table-wrap">
          <div class="im-table-header">IM1 Curriculum Connections</div>
          <table>
            <tr><th>IM1 Concept</th><th>Connection</th></tr>
            <tr><td>Coordinate geometry</td><td>The pen uses an (x, y) coordinate system — moving right increases x; the starting position is the <strong>origin (0, 0)</strong></td></tr>
            <tr><td>Directed distance</td><td><code>addLine(distance:)</code> moves the pen a <strong>directed</strong> amount — length and direction both matter</td></tr>
            <tr><td>Geometric definitions</td><td>A line segment has two endpoints; every call to <code>addLine</code> creates a segment between the current and new pen positions</td></tr>
          </table>
        </div>
      </div>
    </section>

    <!-- ═══════════════════════════════════════════════════════
         02 — TURNING CORNERS
    ═══════════════════════════════════════════════════════ -->
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        <span class="section-tag tutorial">◆ Tutorial</span>
        <h1>Turning Corners</h1>
        <p class="lead">Explore <code>turn(degrees:)</code> — and discover how exterior angles and interior angles relate in any polygon.</p>
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        <h2>Angles and Turning</h2>
        <p>The <code>turn</code> command rotates the pen in place. Positive degrees turn <strong>left</strong> (anti-clockwise); negative degrees turn <strong>right</strong> (clockwise).</p>
        <div class="img-wrap">
          <img src="images/02-turning-corners.png" alt="Demonstration of angles and turning in Geometry Playground">
        </div>
        <h3>Interior vs. Exterior Angles</h3>
        <p>When the pen draws a polygon, the angle you pass to <code>turn</code> is the <strong>exterior angle</strong> — the supplement of the interior angle.</p>
        <ul>
          <li><strong>Interior angle:</strong> the angle inside the polygon at each vertex</li>
          <li><strong>Exterior angle:</strong> the supplement — how much you turn to keep walking along the boundary</li>
          <li>For any convex polygon: <strong>interior + exterior = 180°</strong></li>
        </ul>

        <h3>Angle Classification</h3>
        <ul>
          <li><strong>Acute</strong> — less than 90°</li>
          <li><strong>Right</strong> — exactly 90°</li>
          <li><strong>Obtuse</strong> — between 90° and 180°</li>
          <li><strong>Straight</strong> — exactly 180°</li>
          <li><strong>Reflex</strong> — greater than 180°</li>
        </ul>

        <h3>The Sum of Exterior Angles</h3>
        <p>For <em>any</em> convex polygon, the exterior angles add up to exactly <strong>360°</strong> — one full rotation. This is why, after drawing a closed shape, the pen always faces its original direction.</p>

        <div class="code-wrap">
          <div class="code-header"><span class="code-lang">Swift</span><button class="code-copy" onclick="copyCode(this)">Copy</button></div>
          <pre><span class="cm">// A right turn (clockwise): use a negative angle</span>
<span class="kw">var</span> <span class="vr">p</span> = <span class="tp">Pen</span>()
<span class="vr">p</span>.<span class="fn">addLine</span>(distance: <span class="num">100</span>)
<span class="vr">p</span>.<span class="fn">turn</span>(degrees: -<span class="num">90</span>)      <span class="cm">// Turn RIGHT 90°</span>
<span class="vr">p</span>.<span class="fn">addLine</span>(distance: <span class="num">100</span>)
<span class="fn">addShape</span>(pen: <span class="vr">p</span>)</pre>
          </div>

        <div class="im-table-wrap">
          <div class="im-table-header">IM1 Curriculum Connections</div>
          <table>
            <tr><th>IM1 Concept</th><th>Connection</th></tr>
            <tr><td>Angle classification</td><td>Turns of 90°, 120°, 144° etc. correspond to <strong>right</strong>, <strong>obtuse</strong>, and <strong>obtuse</strong> exterior angles</td></tr>
            <tr><td>Supplementary angles</td><td>Interior angle + exterior angle = <strong>180°</strong> — they are supplementary</td></tr>
            <tr><td>Sum of exterior angles</td><td>The pen always rotates a total of <strong>360°</strong> to return to its starting direction</td></tr>
          </table>
        </div>
      </div>
    </section>

    <!-- ═══════════════════════════════════════════════════════
         03 — SQUARES
    ═══════════════════════════════════════════════════════ -->
    <section id="squares">
      <div class="section-hero">
        <span class="section-tag exercise">◆ Exercise</span>
        <h1>Squares</h1>
        <p class="lead">Draw a square with side length 100. A square has 4 equal sides and 4 right angles — so each turn is <strong>90°</strong>.</p>
        <button class="complete-btn" data-id="squares" onclick="toggleComplete(this)">
          <span class="btn-icon">○</span> Mark as Complete
        </button>
      </div>
      <div class="article">
        <h2>Your Task</h2>
        <p>Draw a square with side length 100 using the Pen API. Remember: a square has 4 sides and turns of 90° at each corner.</p>
        <div class="code-wrap">
          <div class="code-header"><span class="code-lang">Swift</span><button class="code-copy" onclick="copyCode(this)">Copy</button></div>
          <pre><span class="kw">var</span> <span class="vr">p</span> = <span class="tp">Pen</span>()
<span class="cm">// Your code here — 4 lines, 4 turns</span>

<span class="fn">addShape</span>(pen: <span class="vr">p</span>)</pre>
        </div>

        <h2>Mathematical Concepts</h2>
        <h3>Properties of a Square</h3>
        <ul>
          <li>4 equal sides</li>
          <li>4 right angles (90° each)</li>
          <li>Perimeter = 4 × side length</li>
          <li>Area = side² = <strong>100² = 10,000 square units</strong></li>
          <li>Sum of exterior angles = 4 × 90° = 360° ✓</li>
        </ul>

        <h3>Quadrilateral Definition</h3>
        <p>A square is a special <strong>rectangle</strong> (all angles 90°), which is a special <strong>parallelogram</strong> (opposite sides parallel), which is a special <strong>quadrilateral</strong> (4-sided polygon).</p>

        <div class="img-wrap">
          <img src="images/03-squares.png" alt="A square is a special rectangle (all angles are 90 degrees)">
        </div>

        <button class="solution-toggle" onclick="toggleSolution(this,'sol-squares')">
          <svg width="12" height="7" viewBox="0 0 12 7" fill="none"><path d="M1 1l5 5 5-5" stroke="currentColor" stroke-width="1.8" stroke-linecap="round"/></svg>
          Show Solution
        </button>
        <div class="solution-body" id="sol-squares">
          <div class="code-wrap">
            <div class="code-header"><span class="code-lang">Swift</span><button class="code-copy" onclick="copyCode(this)">Copy</button></div>
            <pre><span class="kw">var</span> <span class="vr">p</span> = <span class="tp">Pen</span>()
<span class="vr">p</span>.<span class="fn">addLine</span>(distance: <span class="num">100</span>)
<span class="vr">p</span>.<span class="fn">turn</span>(degrees: <span class="num">90</span>)
<span class="vr">p</span>.<span class="fn">addLine</span>(distance: <span class="num">100</span>)
<span class="vr">p</span>.<span class="fn">turn</span>(degrees: <span class="num">90</span>)
<span class="vr">p</span>.<span class="fn">addLine</span>(distance: <span class="num">100</span>)
<span class="vr">p</span>.<span class="fn">turn</span>(degrees: <span class="num">90</span>)
<span class="vr">p</span>.<span class="fn">addLine</span>(distance: <span class="num">100</span>)
<span class="fn">addShape</span>(pen: <span class="vr">p</span>)
<span class="cm">// 4 × 90° = 360° — the pen faces its original direction again</span></pre>
          </div>
        </div>

        <div class="im-table-wrap">
          <div class="im-table-header">IM1 Curriculum Connections</div>
          <table>
            <tr><th>IM1 Concept</th><th>Connection</th></tr>
            <tr><td>Quadrilateral properties</td><td>A square is a <strong>regular quadrilateral</strong> — all sides equal, all angles 90°</td></tr>
            <tr><td>Perimeter &amp; area</td><td>P = 4s = 400; A = s² = 10,000 sq units</td></tr>
            <tr><td>Sum of exterior angles</td><td>4 × 90° = 360° — the pen makes one complete rotation</td></tr>
          </table>
        </div>
      </div>
    </section>

    <!-- ═══════════════════════════════════════════════════════
         04 — RECTANGLES
    ═══════════════════════════════════════════════════════ -->
    <section id="rectangles">
      <div class="section-hero">
        <span class="section-tag exercise">◆ Exercise</span>
        <h1>Rectangles</h1>
        <p class="lead">Draw a rectangle that is 100 units wide and 200 units tall. Rectangles have two pairs of equal sides — so the distances <em>alternate</em> between the width and height.</p>
        <button class="complete-btn" data-id="rectangles" onclick="toggleComplete(this)">
          <span class="btn-icon">○</span> Mark as Complete
        </button>
      </div>
      <div class="article">
        <h2>Your Task</h2>
        <p>Draw a 100 × 200 rectangle. The pen still turns 90° at each corner, but now the side lengths alternate.</p>
        <div class="code-wrap">
          <div class="code-header"><span class="code-lang">Swift</span><button class="code-copy" onclick="copyCode(this)">Copy</button></div>
          <pre><span class="kw">var</span> <span class="vr">p</span> = <span class="tp">Pen</span>()
<span class="cm">// 4 sides, alternating 100 and 200</span>

<span class="fn">addShape</span>(pen: <span class="vr">p</span>)</pre>
        </div>

        <h2>Mathematical Concepts</h2>
        <h3>Rectangle Properties</h3>
        <ul>
          <li>2 pairs of equal parallel sides</li>
          <li>4 right angles (90° each)</li>
          <li>Perimeter = 2(width + height) = 2(100 + 200) = <strong>600 units</strong></li>
          <li>Area = width × height = 100 × 200 = <strong>20,000 square units</strong></li>
        </ul>

        <div class="img-wrap">
          <img src="images/04-rectangles.png" alt="A rectangle">
        </div>

        <button class="solution-toggle" onclick="toggleSolution(this,'sol-rect')">
          <svg width="12" height="7" viewBox="0 0 12 7" fill="none"><path d="M1 1l5 5 5-5" stroke="currentColor" stroke-width="1.8" stroke-linecap="round"/></svg>
          Show Solution
        </button>
        <div class="solution-body" id="sol-rect">
          <div class="code-wrap">
            <div class="code-header"><span class="code-lang">Swift</span><button class="code-copy" onclick="copyCode(this)">Copy</button></div>
            <pre><span class="kw">var</span> <span class="vr">p</span> = <span class="tp">Pen</span>()
<span class="vr">p</span>.<span class="fn">addLine</span>(distance: <span class="num">100</span>)   <span class="cm">// bottom</span>
<span class="vr">p</span>.<span class="fn">turn</span>(degrees: <span class="num">90</span>)
<span class="vr">p</span>.<span class="fn">addLine</span>(distance: <span class="num">200</span>)   <span class="cm">// right side</span>
<span class="vr">p</span>.<span class="fn">turn</span>(degrees: <span class="num">90</span>)
<span class="vr">p</span>.<span class="fn">addLine</span>(distance: <span class="num">100</span>)   <span class="cm">// top</span>
<span class="vr">p</span>.<span class="fn">turn</span>(degrees: <span class="num">90</span>)
<span class="vr">p</span>.<span class="fn">addLine</span>(distance: <span class="num">200</span>)   <span class="cm">// left side</span>
<span class="fn">addShape</span>(pen: <span class="vr">p</span>)</pre>
          </div>
        </div>

        <div class="im-table-wrap">
          <div class="im-table-header">IM1 Curriculum Connections</div>
          <table>
            <tr><th>IM1 Concept</th><th>Connection</th></tr>
            <tr><td>Rectangle properties</td><td>Opposite sides are <strong>equal and parallel</strong>; all angles are 90°</td></tr>
            <tr><td>Perimeter formula</td><td>P = 2(w + h) = 2(100 + 200) = <strong>600</strong></td></tr>
            <tr><td>Area formula</td><td>A = w × h = <strong>20,000 sq units</strong></td></tr>
          </table>
        </div>
      </div>
    </section>

    <!-- ═══════════════════════════════════════════════════════
         05 — MORE SQUARES
    ═══════════════════════════════════════════════════════ -->
    <section id="more-squares">
      <div class="section-hero">
        <span class="section-tag exercise">◆ Exercise</span>
        <h1>More Squares</h1>
        <p class="lead">Draw three nested squares with side lengths 50, 100, and 150. They all share the same starting point — creating a nested, concentric pattern.</p>
        <button class="complete-btn" data-id="more-squares" onclick="toggleComplete(this)">
          <span class="btn-icon">○</span> Mark as Complete
        </button>
      </div>
      <div class="article">
        <h2>Your Task</h2>
        <p>Draw three squares: side lengths 50, 100, and 150. Each starts from the same origin point. Use a single Pen and draw them one after the other.</p>
        <div class="code-wrap">
          <div class="code-header"><span class="code-lang">Swift</span><button class="code-copy" onclick="copyCode(this)">Copy</button></div>
          <pre><span class="kw">var</span> <span class="vr">pen</span> = <span class="tp">Pen</span>()

<span class="cm">// Square 1: side 50</span>

<span class="cm">// Square 2: side 100</span>

<span class="cm">// Square 3: side 150</span>

<span class="fn">addShape</span>(pen: <span class="vr">pen</span>)</pre>
        </div>

        <h2>Mathematical Concepts</h2>
        <h3>Similar Figures</h3>
        <p>The three squares are <strong>similar figures</strong> — they have the same shape but different sizes. In similar figures:</p>
        <ul>
          <li>Corresponding angles are <strong>equal</strong></li>
          <li>Corresponding side lengths are in the same <strong>ratio</strong></li>
          <li>The scale factor from the 50-unit to the 100-unit square is <strong>2</strong>; from 50 to 150 is <strong>3</strong></li>
        </ul>
        <p>Any two squares are always similar — all squares have 90° angles and all sides are equal.</p>

        <div class="img-wrap">
          <img src="images/05-more-squares.png" alt="A rectangle">
        </div>

        <button class="solution-toggle" onclick="toggleSolution(this,'sol-more-sq')">
          <svg width="12" height="7" viewBox="0 0 12 7" fill="none"><path d="M1 1l5 5 5-5" stroke="currentColor" stroke-width="1.8" stroke-linecap="round"/></svg>
          Show Solution
        </button>
        <div class="solution-body" id="sol-more-sq">
          <div class="code-wrap">
            <div class="code-header"><span class="code-lang">Swift</span><button class="code-copy" onclick="copyCode(this)">Copy</button></div>
            <pre><span class="kw">var</span> <span class="vr">pen</span> = <span class="tp">Pen</span>()

<span class="cm">// Square 1: side 50</span>
<span class="vr">pen</span>.<span class="fn">addLine</span>(distance: <span class="num">50</span>); <span class="vr">pen</span>.<span class="fn">turn</span>(degrees: <span class="num">90</span>)
<span class="vr">pen</span>.<span class="fn">addLine</span>(distance: <span class="num">50</span>); <span class="vr">pen</span>.<span class="fn">turn</span>(degrees: <span class="num">90</span>)
<span class="vr">pen</span>.<span class="fn">addLine</span>(distance: <span class="num">50</span>); <span class="vr">pen</span>.<span class="fn">turn</span>(degrees: <span class="num">90</span>)
<span class="vr">pen</span>.<span class="fn">addLine</span>(distance: <span class="num">50</span>); <span class="vr">pen</span>.<span class="fn">turn</span>(degrees: <span class="num">90</span>)

<span class="cm">// Square 2: side 100</span>
<span class="vr">pen</span>.<span class="fn">addLine</span>(distance: <span class="num">100</span>); <span class="vr">pen</span>.<span class="fn">turn</span>(degrees: <span class="num">90</span>)
<span class="vr">pen</span>.<span class="fn">addLine</span>(distance: <span class="num">100</span>); <span class="vr">pen</span>.<span class="fn">turn</span>(degrees: <span class="num">90</span>)
<span class="vr">pen</span>.<span class="fn">addLine</span>(distance: <span class="num">100</span>); <span class="vr">pen</span>.<span class="fn">turn</span>(degrees: <span class="num">90</span>)
<span class="vr">pen</span>.<span class="fn">addLine</span>(distance: <span class="num">100</span>); <span class="vr">pen</span>.<span class="fn">turn</span>(degrees: <span class="num">90</span>)

<span class="cm">// Square 3: side 150</span>
<span class="vr">pen</span>.<span class="fn">addLine</span>(distance: <span class="num">150</span>); <span class="vr">pen</span>.<span class="fn">turn</span>(degrees: <span class="num">90</span>)
<span class="vr">pen</span>.<span class="fn">addLine</span>(distance: <span class="num">150</span>); <span class="vr">pen</span>.<span class="fn">turn</span>(degrees: <span class="num">90</span>)
<span class="vr">pen</span>.<span class="fn">addLine</span>(distance: <span class="num">150</span>); <span class="vr">pen</span>.<span class="fn">turn</span>(degrees: <span class="num">90</span>)
<span class="vr">pen</span>.<span class="fn">addLine</span>(distance: <span class="num">150</span>); <span class="vr">pen</span>.<span class="fn">turn</span>(degrees: <span class="num">90</span>)

<span class="fn">addShape</span>(pen: <span class="vr">pen</span>)</pre>
          </div>
        </div>

        <div class="im-table-wrap">
          <div class="im-table-header">IM1 Curriculum Connections</div>
          <table>
            <tr><th>IM1 Concept</th><th>Connection</th></tr>
            <tr><td>Similar figures</td><td>All three squares are <strong>similar</strong> — same angles, proportional sides</td></tr>
            <tr><td>Scale factor</td><td>50→100 scale factor = <strong>2</strong>; 50→150 = <strong>3</strong></td></tr>
            <tr><td>Geometric patterns</td><td>Nesting similar figures at a common vertex reveals <strong>proportional growth</strong></td></tr>
          </table>
        </div>
      </div>
    </section>

    <!-- ═══════════════════════════════════════════════════════
         06 — TRIANGLE IN SQUARE
    ═══════════════════════════════════════════════════════ -->
    <section id="triangle-in-square">
      <div class="section-hero">
        <span class="section-tag exercise">◆ Exercise</span>
        <h1>Triangle in Square</h1>
        <p class="lead">Draw an equilateral triangle (side 100) and a square (side 100) sharing the same base. Discover how the turn angles differ between polygons.</p>
        <button class="complete-btn" data-id="triangle-in-square" onclick="toggleComplete(this)">
          <span class="btn-icon">○</span> Mark as Complete
        </button>
      </div>
      <div class="article">
        <h2>Your Task</h2>
        <p>Draw an equilateral triangle and a square, both with side length 100. You can share the first side, or draw them as separate shapes next to each other.</p>
        <div class="code-wrap">
          <div class="code-header"><span class="code-lang">Swift</span><button class="code-copy" onclick="copyCode(this)">Copy</button></div>
          <pre><span class="kw">var</span> <span class="vr">triangle</span> = <span class="tp">Pen</span>()
<span class="cm">// Equilateral triangle — 3 sides, 120° turns</span>

<span class="kw">var</span> <span class="vr">square</span> = <span class="tp">Pen</span>()
<span class="cm">// Square — 4 sides, 90° turns</span>

<span class="fn">addShape</span>(pen: <span class="vr">triangle</span>)
<span class="fn">addShape</span>(pen: <span class="vr">square</span>)</pre>
        </div>

        <h2>Mathematical Concepts</h2>
        <h3>Equilateral Triangle</h3>
        <ul>
          <li>3 equal sides, 3 equal angles</li>
          <li>Each interior angle = <strong>60°</strong></li>
          <li>Turn angle (exterior) = 180° − 60° = <strong>120°</strong></li>
          <li>3 × 120° = 360° ✓</li>
        </ul>

        <h3>Angle Sum Theorem</h3>
        <p>For any triangle, the interior angles sum to <strong>180°</strong>. For an equilateral triangle: 60° + 60° + 60° = 180°. For a square: 90° + 90° + 90° + 90° = 360°.</p>
        <blockquote>General formula: Sum of interior angles = (n − 2) × 180°, where n is the number of sides.</blockquote>

        <div class="img-wrap">
          <img src="images/06-triangle-in-square.png" alt="Triangle in a Square">
        </div>

        <button class="solution-toggle" onclick="toggleSolution(this,'sol-trisq')">
          <svg width="12" height="7" viewBox="0 0 12 7" fill="none"><path d="M1 1l5 5 5-5" stroke="currentColor" stroke-width="1.8" stroke-linecap="round"/></svg>
          Show Solution
        </button>
        <div class="solution-body" id="sol-trisq">
          <div class="code-wrap">
            <div class="code-header"><span class="code-lang">Swift</span><button class="code-copy" onclick="copyCode(this)">Copy</button></div>
            <pre><span class="kw">var</span> <span class="vr">triangle</span> = <span class="tp">Pen</span>()
<span class="vr">triangle</span>.<span class="fn">addLine</span>(distance: <span class="num">100</span>)
<span class="vr">triangle</span>.<span class="fn">turn</span>(degrees: <span class="num">120</span>)
<span class="vr">triangle</span>.<span class="fn">addLine</span>(distance: <span class="num">100</span>)
<span class="vr">triangle</span>.<span class="fn">turn</span>(degrees: <span class="num">120</span>)
<span class="vr">triangle</span>.<span class="fn">addLine</span>(distance: <span class="num">100</span>)

<span class="kw">var</span> <span class="vr">square</span> = <span class="tp">Pen</span>()
<span class="vr">square</span>.<span class="fn">addLine</span>(distance: <span class="num">100</span>)
<span class="vr">square</span>.<span class="fn">turn</span>(degrees: <span class="num">90</span>)
<span class="vr">square</span>.<span class="fn">addLine</span>(distance: <span class="num">100</span>)
<span class="vr">square</span>.<span class="fn">turn</span>(degrees: <span class="num">90</span>)
<span class="vr">square</span>.<span class="fn">addLine</span>(distance: <span class="num">100</span>)
<span class="vr">square</span>.<span class="fn">turn</span>(degrees: <span class="num">90</span>)
<span class="vr">square</span>.<span class="fn">addLine</span>(distance: <span class="num">100</span>)

<span class="fn">addShape</span>(pen: <span class="vr">triangle</span>)
<span class="fn">addShape</span>(pen: <span class="vr">square</span>)</pre>
          </div>
        </div>

        <div class="im-table-wrap">
          <div class="im-table-header">IM1 Curriculum Connections</div>
          <table>
            <tr><th>IM1 Concept</th><th>Connection</th></tr>
            <tr><td>Triangle angle sum</td><td>All triangles: angles sum to <strong>180°</strong>; equilateral = 3 × 60°</td></tr>
            <tr><td>Interior angle formula</td><td>(n−2) × 180° / n: triangle → 60°; square → 90°</td></tr>
            <tr><td>Polygon comparison</td><td>Different n-gons need different turn angles to close their paths</td></tr>
          </table>
        </div>
      </div>
    </section>

    <!-- ═══════════════════════════════════════════════════════
         07 — UP AND DOWN
    ═══════════════════════════════════════════════════════ -->
    <section id="up-and-down">
      <div class="section-hero">
        <span class="section-tag tutorial">◆ Tutorial</span>
        <h1>Up and Down</h1>
        <p class="lead">Meet <code>move(distance:)</code> — just like <code>addLine</code>, but without drawing. Use it to reposition the pen and draw shapes in separate locations.</p>
        <button class="complete-btn" data-id="up-and-down" onclick="toggleComplete(this)">
          <span class="btn-icon">○</span> Mark as Complete
        </button>
      </div>
      <div class="article">
        <h2>Moving Without Drawing</h2>

        <div class="code-wrap">
          <div class="code-header"><span class="code-lang">Swift</span><button class="code-copy" onclick="copyCode(this)">Copy</button></div>
          <pre><span class="vr">p</span>.<span class="fn">addLine</span>(distance: <span class="num">100</span>)  <span class="cm">// Moves forward AND draws a line</span>
<span class="vr">p</span>.<span class="fn">move</span>(distance: <span class="num">100</span>)     <span class="cm">// Moves forward — no line drawn</span></pre>
        </div>

        <p>The two commands behave identically in terms of changing the pen's position — the only difference is whether a line appears on screen.</p>

        <h3>Dashed Lines</h3>
        <p>Alternating <code>addLine</code> and <code>move</code> creates a <strong>dashed line</strong>:</p>
        <div class="code-wrap">
          <div class="code-header"><span class="code-lang">Swift</span><button class="code-copy" onclick="copyCode(this)">Copy</button></div>
          <pre><span class="kw">var</span> <span class="vr">p</span> = <span class="tp">Pen</span>()
<span class="vr">p</span>.<span class="fn">addLine</span>(distance: <span class="num">50</span>)   <span class="cm">// dash</span>
<span class="vr">p</span>.<span class="fn">move</span>(distance: <span class="num">20</span>)      <span class="cm">// gap</span>
<span class="vr">p</span>.<span class="fn">addLine</span>(distance: <span class="num">50</span>)   <span class="cm">// dash</span>
<span class="vr">p</span>.<span class="fn">move</span>(distance: <span class="num">20</span>)      <span class="cm">// gap</span>
<span class="vr">p</span>.<span class="fn">addLine</span>(distance: <span class="num">50</span>)   <span class="cm">// dash</span>
<span class="fn">addShape</span>(pen: <span class="vr">p</span>)</pre>
        </div>

        <h3>Exercise: Two Stacked Squares</h3>
        <p>Try drawing two separate squares — one above the other — using a single pen. Use <code>move</code> to jump from the first square to the second without connecting them.</p>

        <div class="img-wrap">
          <img src="images/07-up-and-down.png" alt="Two squares next to each other">
        </div>

        <button class="solution-toggle" onclick="toggleSolution(this,'sol-updown')">
          <svg width="12" height="7" viewBox="0 0 12 7" fill="none"><path d="M1 1l5 5 5-5" stroke="currentColor" stroke-width="1.8" stroke-linecap="round"/></svg>
          Show Solution
        </button>
        <div class="solution-body" id="sol-updown">
          <div class="code-wrap">
            <div class="code-header"><span class="code-lang">Swift</span><button class="code-copy" onclick="copyCode(this)">Copy</button></div>
            <pre><span class="kw">var</span> <span class="vr">p</span> = <span class="tp">Pen</span>()

<span class="cm">// First square</span>
<span class="vr">p</span>.<span class="fn">addLine</span>(distance: <span class="num">80</span>)
<span class="vr">p</span>.<span class="fn">turn</span>(degrees: <span class="num">90</span>)
<span class="vr">p</span>.<span class="fn">addLine</span>(distance: <span class="num">80</span>)
<span class="vr">p</span>.<span class="fn">turn</span>(degrees: <span class="num">90</span>)
<span class="vr">p</span>.<span class="fn">addLine</span>(distance: <span class="num">80</span>)
<span class="vr">p</span>.<span class="fn">turn</span>(degrees: <span class="num">90</span>)
<span class="vr">p</span>.<span class="fn">addLine</span>(distance: <span class="num">80</span>)
<span class="vr">p</span>.<span class="fn">turn</span>(degrees: <span class="num">90</span>)

<span class="cm">// Jump up to next position</span>
<span class="vr">p</span>.<span class="fn">turn</span>(degrees: <span class="num">90</span>)       <span class="cm">// Face upward</span>
<span class="vr">p</span>.<span class="fn">move</span>(distance: <span class="num">120</span>)     <span class="cm">// Move up 120 units</span>
<span class="vr">p</span>.<span class="fn">turn</span>(degrees: -<span class="num">90</span>)      <span class="cm">// Face right again</span>

<span class="cm">// Second square</span>
<span class="vr">p</span>.<span class="fn">addLine</span>(distance: <span class="num">80</span>)
<span class="vr">p</span>.<span class="fn">turn</span>(degrees: <span class="num">90</span>)
<span class="vr">p</span>.<span class="fn">addLine</span>(distance: <span class="num">80</span>)
<span class="vr">p</span>.<span class="fn">turn</span>(degrees: <span class="num">90</span>)
<span class="vr">p</span>.<span class="fn">addLine</span>(distance: <span class="num">80</span>)
<span class="vr">p</span>.<span class="fn">turn</span>(degrees: <span class="num">90</span>)
<span class="vr">p</span>.<span class="fn">addLine</span>(distance: <span class="num">80</span>)

<span class="fn">addShape</span>(pen: <span class="vr">p</span>)</pre>
          </div>
        </div>

        <div class="im-table-wrap">
          <div class="im-table-header">IM1 Curriculum Connections</div>
          <table>
            <tr><th>IM1 Concept</th><th>Connection</th></tr>
            <tr><td>Transformations — translations</td><td><code>move(distance:)</code> is a <strong>translation</strong> — the pen slides without rotating</td></tr>
            <tr><td>Congruence</td><td>Two squares drawn at different positions are <strong>congruent</strong> — identical in size, shape, and angles</td></tr>
            <tr><td>Coordinate geometry</td><td>Moving up increases y; moving right increases x</td></tr>
          </table>
        </div>
      </div>
    </section>

    <!-- ═══════════════════════════════════════════════════════
         08 — MULTIPLE SHAPES
    ═══════════════════════════════════════════════════════ -->
    <section id="multiple-shapes">
      <div class="section-hero">
        <span class="section-tag exercise">◆ Exercise</span>
        <h1>Multiple Shapes</h1>
        <p class="lead">Draw three shapes in a horizontal row: a square, a triangle, and another square — each with side length 100. Use <code>move</code> to leave a gap between them.</p>
        <button class="complete-btn" data-id="multiple-shapes" onclick="toggleComplete(this)">
          <span class="btn-icon">○</span> Mark as Complete
        </button>
      </div>
      <div class="article">
        <h2>Your Task</h2>
        <p>Using one or more pens, draw a square (100), an equilateral triangle (100), and another square (100) in a row with small gaps between each shape.</p>
        <div class="code-wrap">
          <div class="code-header"><span class="code-lang">Swift</span><button class="code-copy" onclick="copyCode(this)">Copy</button></div>
          <pre><span class="kw">var</span> <span class="vr">p</span> = <span class="tp">Pen</span>()
<span class="cm">// Square 1, then move, then Triangle, then move, then Square 2</span>
<span class="fn">addShape</span>(pen: <span class="vr">p</span>)</pre>
        </div>

        <h2>Mathematical Concepts</h2>
        <h3>Composing Shapes</h3>
        <p>Placing shapes side-by-side is an example of <strong>geometric composition</strong> — building complex figures from simple ones. The second square is a <strong>translation</strong> of the first — same shape, moved horizontally.</p>

        <div class="img-wrap">
          <img src="images/08-multiple-shapes.png" alt="Triangle with two squares either side">
        </div>

        <button class="solution-toggle" onclick="toggleSolution(this,'sol-multi')">
          <svg width="12" height="7" viewBox="0 0 12 7" fill="none"><path d="M1 1l5 5 5-5" stroke="currentColor" stroke-width="1.8" stroke-linecap="round"/></svg>
          Show Solution
        </button>
        <div class="solution-body" id="sol-multi">
          <div class="code-wrap">
            <div class="code-header"><span class="code-lang">Swift</span><button class="code-copy" onclick="copyCode(this)">Copy</button></div>
            <pre><span class="kw">var</span> <span class="vr">p</span> = <span class="tp">Pen</span>()

<span class="cm">// Square 1</span>
<span class="vr">p</span>.<span class="fn">addLine</span>(distance: <span class="num">100</span>); <span class="vr">p</span>.<span class="fn">turn</span>(degrees: <span class="num">90</span>)
<span class="vr">p</span>.<span class="fn">addLine</span>(distance: <span class="num">100</span>); <span class="vr">p</span>.<span class="fn">turn</span>(degrees: <span class="num">90</span>)
<span class="vr">p</span>.<span class="fn">addLine</span>(distance: <span class="num">100</span>); <span class="vr">p</span>.<span class="fn">turn</span>(degrees: <span class="num">90</span>)
<span class="vr">p</span>.<span class="fn">addLine</span>(distance: <span class="num">100</span>); <span class="vr">p</span>.<span class="fn">turn</span>(degrees: <span class="num">90</span>)

<span class="cm">// Gap to triangle</span>
<span class="vr">p</span>.<span class="fn">move</span>(distance: <span class="num">120</span>)

<span class="cm">// Triangle</span>
<span class="vr">p</span>.<span class="fn">addLine</span>(distance: <span class="num">100</span>); <span class="vr">p</span>.<span class="fn">turn</span>(degrees: <span class="num">120</span>)
<span class="vr">p</span>.<span class="fn">addLine</span>(distance: <span class="num">100</span>); <span class="vr">p</span>.<span class="fn">turn</span>(degrees: <span class="num">120</span>)
<span class="vr">p</span>.<span class="fn">addLine</span>(distance: <span class="num">100</span>); <span class="vr">p</span>.<span class="fn">turn</span>(degrees: <span class="num">120</span>)

<span class="cm">// Gap to square 2  (pen already faces right after 3 × 120° = 360°)</span>
<span class="vr">p</span>.<span class="fn">move</span>(distance: <span class="num">120</span>)

<span class="cm">// Square 2</span>
<span class="vr">p</span>.<span class="fn">addLine</span>(distance: <span class="num">100</span>); <span class="vr">p</span>.<span class="fn">turn</span>(degrees: <span class="num">90</span>)
<span class="vr">p</span>.<span class="fn">addLine</span>(distance: <span class="num">100</span>); <span class="vr">p</span>.<span class="fn">turn</span>(degrees: <span class="num">90</span>)
<span class="vr">p</span>.<span class="fn">addLine</span>(distance: <span class="num">100</span>); <span class="vr">p</span>.<span class="fn">turn</span>(degrees: <span class="num">90</span>)
<span class="vr">p</span>.<span class="fn">addLine</span>(distance: <span class="num">100</span>)

<span class="fn">addShape</span>(pen: <span class="vr">p</span>)</pre>
          </div>
        </div>

        <div class="im-table-wrap">
          <div class="im-table-header">IM1 Curriculum Connections</div>
          <table>
            <tr><th>IM1 Concept</th><th>Connection</th></tr>
            <tr><td>Transformations — translations</td><td>Moving between shapes is a <strong>translation</strong>; the second square is the first translated</td></tr>
            <tr><td>Congruence</td><td>The two squares are <strong>congruent</strong> — identical shape, size, and angles</td></tr>
            <tr><td>Geometric modeling</td><td>Composing multiple shapes into one figure is a fundamental geometric skill</td></tr>
          </table>
        </div>
      </div>
    </section>

    <!-- ═══════════════════════════════════════════════════════
         09 — FIVE-POINT STAR
    ═══════════════════════════════════════════════════════ -->
    <section id="five-point-star">
      <div class="section-hero">
        <span class="section-tag exercise">◆ Exercise</span>
        <h1>Five-Point Star</h1>
        <p class="lead">Draw a five-pointed star (pentagram) in a single continuous path. The secret lies in the turn angle: <strong>144°</strong>.</p>
        <button class="complete-btn" data-id="five-point-star" onclick="toggleComplete(this)">
          <span class="btn-icon">○</span> Mark as Complete
        </button>
      </div>
      <div class="article">
        <h2>Your Task</h2>
        <p>Draw a five-pointed star. All arms should be the same length (150 units). The pen draws the whole star in one continuous stroke without lifting.</p>
        <div class="code-wrap">
          <div class="code-header"><span class="code-lang">Swift</span><button class="code-copy" onclick="copyCode(this)">Copy</button></div>
          <pre><span class="kw">var</span> <span class="vr">p</span> = <span class="tp">Pen</span>()
<span class="cm">// 5 lines, 5 turns — what's the turn angle?</span>
<span class="fn">addShape</span>(pen: <span class="vr">p</span>)</pre>
        </div>

        <h2>Mathematical Concepts</h2>
        <h3>The Turn Angle for a Pentagram</h3>
        <p>For a regular polygon, the exterior angle = 360° / n. But for a <strong>star polygon</strong>, the path winds around the centre more than once.</p>
        <ul>
          <li>A pentagram winds around the centre <strong>twice</strong></li>
          <li>Total rotation = 2 × 360° = <strong>720°</strong></li>
          <li>Each of the 5 turns = 720° ÷ 5 = <strong>144°</strong></li>
        </ul>

        <blockquote><strong>Why 720°?</strong> A regular polygon path winds once (360°). A star polygon {5/2} winds twice — the path overlaps itself, completing two loops before returning to the start.</blockquote>

        <h3>Star Polygon Notation</h3>
        <p>Mathematicians write this as <strong>{5/2}</strong> — a 5-point star connecting every 2nd vertex. The general turn angle for {n/k} is: 180° − 180°(n−2k)/n.</p>

        <div class="img-wrap">
          <img src="images/09-five-point-star.png" alt="Five point star">
        </div>

        <button class="solution-toggle" onclick="toggleSolution(this,'sol-star5')">
          <svg width="12" height="7" viewBox="0 0 12 7" fill="none"><path d="M1 1l5 5 5-5" stroke="currentColor" stroke-width="1.8" stroke-linecap="round"/></svg>
          Show Solution
        </button>
        <div class="solution-body" id="sol-star5">
          <div class="code-wrap">
            <div class="code-header"><span class="code-lang">Swift</span><button class="code-copy" onclick="copyCode(this)">Copy</button></div>
            <pre><span class="kw">var</span> <span class="vr">p</span> = <span class="tp">Pen</span>()
<span class="vr">p</span>.<span class="fn">addLine</span>(distance: <span class="num">150</span>); <span class="vr">p</span>.<span class="fn">turn</span>(degrees: <span class="num">144</span>)
<span class="vr">p</span>.<span class="fn">addLine</span>(distance: <span class="num">150</span>); <span class="vr">p</span>.<span class="fn">turn</span>(degrees: <span class="num">144</span>)
<span class="vr">p</span>.<span class="fn">addLine</span>(distance: <span class="num">150</span>); <span class="vr">p</span>.<span class="fn">turn</span>(degrees: <span class="num">144</span>)
<span class="vr">p</span>.<span class="fn">addLine</span>(distance: <span class="num">150</span>); <span class="vr">p</span>.<span class="fn">turn</span>(degrees: <span class="num">144</span>)
<span class="vr">p</span>.<span class="fn">addLine</span>(distance: <span class="num">150</span>); <span class="vr">p</span>.<span class="fn">turn</span>(degrees: <span class="num">144</span>)
<span class="fn">addShape</span>(pen: <span class="vr">p</span>)
<span class="cm">// 5 × 144° = 720° = 2 × 360° ✓</span></pre>
          </div>
        </div>

        <div class="im-table-wrap">
          <div class="im-table-header">IM1 Curriculum Connections</div>
          <table>
            <tr><th>IM1 Concept</th><th>Connection</th></tr>
            <tr><td>Angle relationships</td><td>Each star point is an <strong>acute</strong> angle (36°); the turn angle (144°) is obtuse</td></tr>
            <tr><td>Sum of exterior angles</td><td>5 × 144° = 720° = 2 × 360° — the path winds <strong>twice</strong> around the centre</td></tr>
            <tr><td>Star polygon {5/2}</td><td>A generalisation of the regular polygon concept — connecting every k-th vertex</td></tr>
          </table>
        </div>
      </div>
    </section>

    <!-- ═══════════════════════════════════════════════════════
         10 — STAR OF DAVID
    ═══════════════════════════════════════════════════════ -->
    <section id="star-of-david">
      <div class="section-hero">
        <span class="section-tag exercise">◆ Exercise</span>
        <h1>Star of David</h1>
        <p class="lead">Draw a Star of David (hexagram) using two overlapping equilateral triangles — one pointing up, one pointing down.</p>
        <button class="complete-btn" data-id="star-of-david" onclick="toggleComplete(this)">
          <span class="btn-icon">○</span> Mark as Complete
        </button>
      </div>
      <div class="article">
        <h2>Your Task</h2>
        <p>Draw a Star of David using two equilateral triangles of side length 150. The triangles should overlap to form a six-pointed star.</p>
        <div class="code-wrap">
          <div class="code-header"><span class="code-lang">Swift</span><button class="code-copy" onclick="copyCode(this)">Copy</button></div>
          <pre><span class="kw">var</span> <span class="vr">up</span> = <span class="tp">Pen</span>()
<span class="cm">// Draw upward triangle</span>

<span class="kw">var</span> <span class="vr">down</span> = <span class="tp">Pen</span>()
<span class="cm">// Draw downward triangle</span>

<span class="fn">addShape</span>(pen: <span class="vr">up</span>)
<span class="fn">addShape</span>(pen: <span class="vr">down</span>)</pre>
        </div>

        <h2>Mathematical Concepts</h2>
        <h3>The Hexagram</h3>
        <p>Unlike the five-pointed star (drawn in one continuous path), a hexagram is formed from <strong>two separate triangles</strong>. The downward triangle is a <strong>rotation</strong> of the upward triangle by 60° around the centre.</p>

        <h3>Rotational Symmetry</h3>
        <p>A shape has <strong>rotational symmetry</strong> if it can be rotated by less than 360° and look identical. The Star of David has <strong>order-6</strong> rotational symmetry — it looks the same after rotations of 60°, 120°, 180°, 240°, or 300°.</p>
        <ul>
          <li>Square → order-4 symmetry (looks same after 90°, 180°, 270°)</li>
          <li>Equilateral triangle → order-3 symmetry (looks same after 120°, 240°)</li>
          <li>Star of David → <strong>order-6</strong> symmetry</li>
        </ul>

        <div class="img-wrap">
          <img src="images/10-star-of-david.png" alt="Star of David">
        </div>

        <button class="solution-toggle" onclick="toggleSolution(this,'sol-david')">
          <svg width="12" height="7" viewBox="0 0 12 7" fill="none"><path d="M1 1l5 5 5-5" stroke="currentColor" stroke-width="1.8" stroke-linecap="round"/></svg>
          Show Solution
        </button>
        <div class="solution-body" id="sol-david">
          <div class="code-wrap">
            <div class="code-header"><span class="code-lang">Swift</span><button class="code-copy" onclick="copyCode(this)">Copy</button></div>
            <pre><span class="kw">var</span> <span class="vr">david</span> = <span class="tp">Pen</span>()

<span class="cm">// Triangle 1</span>
<span class="vr">david</span>.<span class="fn">addLine</span>(distance: <span class="num">150</span>)
<span class="vr">david</span>.<span class="fn">turn</span>(degrees: <span class="num">120</span>)
<span class="vr">david</span>.<span class="fn">addLine</span>(distance: <span class="num">150</span>)
<span class="vr">david</span>.<span class="fn">turn</span>(degrees: <span class="num">120</span>)
<span class="vr">david</span>.<span class="fn">addLine</span>(distance: <span class="num">150</span>)
<span class="vr">david</span>.<span class="fn">turn</span>(degrees: <span class="num">120</span>)

<span class="cm">// New start point</span>
<span class="vr">david</span>.<span class="fn">move</span>(distance: <span class="num">150</span>)
<span class="vr">david</span>.<span class="fn">turn</span>(degrees: <span class="num">90</span>)
<span class="vr">david</span>.<span class="fn">move</span>(distance: <span class="num">90</span>)
<span class="vr">david</span>.<span class="fn">turn</span>(degrees: <span class="num">90</span>)

<span class="cm">// Triangle 2</span>
<span class="vr">david</span>.<span class="fn">addLine</span>(distance: <span class="num">150</span>)
<span class="vr">david</span>.<span class="fn">turn</span>(degrees: <span class="num">120</span>)
<span class="vr">david</span>.<span class="fn">addLine</span>(distance: <span class="num">150</span>)
<span class="vr">david</span>.<span class="fn">turn</span>(degrees: <span class="num">120</span>)
<span class="vr">david</span>.<span class="fn">addLine</span>(distance: <span class="num">150</span>)
<span class="vr">david</span>.<span class="fn">turn</span>(degrees: <span class="num">120</span>)

<span class="fn">addShape</span>(pen: <span class="vr">david</span>)</pre>
          </div>
        </div>

        <div class="callout">
          <h3>💡 Think About It</h3>
          <ul>
            <li>How does the Star of David differ from the five-pointed star?</li>
            <li>Can you see the regular hexagon hidden in the middle?</li>
            <li>What other shapes can be constructed by overlapping simpler shapes?</li>
          </ul>
        </div>

        <div class="im-table-wrap">
          <div class="im-table-header">IM1 Curriculum Connections</div>
          <table>
            <tr><th>IM1 Concept</th><th>Connection</th></tr>
            <tr><td>Transformations — rotations</td><td>The downward triangle is a <strong>rotation</strong> of the upward triangle by 60° around the centre</td></tr>
            <tr><td>Congruence</td><td>The two triangles are <strong>congruent</strong> — same size, same angles; one is a rigid transformation of the other</td></tr>
            <tr><td>Rotational symmetry</td><td>The hexagram has <strong>order-6</strong> rotational symmetry</td></tr>
            <tr><td>Triangle properties</td><td>Both triangles are equilateral: 3 equal sides, 3 × 60° interior angles</td></tr>
          </table>
        </div>
      </div>
    </section>

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