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<!DOCTYPE html>
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<title>Fancy Shapes — Geometry Playground</title>
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<span>◆</span>Geometry Playground
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Ch 2 — Fancy Shapes
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<a href="01.html"><span class="dd-num">01</span> Getting Started</a>
<a href="02.html" class="current"><span class="dd-num">02</span> Fancy Shapes</a>
<a href="03.html"><span class="dd-num">03</span> Doing Stuff Again</a>
<a href="04.html"><span class="dd-num">04</span> Testing & Classifying</a>
<a href="05.html"><span class="dd-num">05</span> Tell It How</a>
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<div class="nav-dropdown-heading">Sections — Chapter 2</div>
<a href="#adding-pens" onclick="closePills()"><span class="dd-num">01</span> Adding Pens</a>
<a href="#multiple-pens" onclick="closePills()"><span class="dd-num">02</span> Multiple Pens</a>
<a href="#turning-both-ways" onclick="closePills()"><span class="dd-num">03</span> Turning Both Ways</a>
<a href="#two-squares" onclick="closePills()"><span class="dd-num">04</span> Two Squares</a>
<a href="#thicker-lines" onclick="closePills()"><span class="dd-num">05</span> Thicker Lines</a>
<a href="#coloured-triangle" onclick="closePills()"><span class="dd-num">06</span> Coloured Triangle</a>
<a href="#diamond" onclick="closePills()"><span class="dd-num">07</span> Diamond</a>
<a href="#fill-it-in" onclick="closePills()"><span class="dd-num">08</span> Fill It In</a>
<a href="#coloured-squares" onclick="closePills()"><span class="dd-num">09</span> Coloured Squares</a>
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<a href="#variable-house" onclick="closePills()"><span class="dd-num">13</span> Variable House</a>
<a href="#red-cross" onclick="closePills()"><span class="dd-num">14</span> Red Cross</a>
<a href="#simple-snowflake" onclick="closePills()"><span class="dd-num">15</span> Simple Snowflake</a>
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<a href="#letter-z" onclick="closePills()"><span class="dd-num">17</span> Letter Z</a>
<a href="#rhombus" onclick="closePills()"><span class="dd-num">18</span> Rhombus</a>
<a href="#parallelogram" onclick="closePills()"><span class="dd-num">19</span> Parallelogram</a>
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<div class="sidebar-chapter">Chapter 2</div>
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<a href="#adding-pens" data-section="adding-pens"><span class="nav-num">01</span><span>Adding Pens<br><span class="nav-badge badge-tutorial">Tutorial</span></span><span class="nav-done">✓</span></a>
<a href="#multiple-pens" data-section="multiple-pens"><span class="nav-num">02</span><span>Multiple Pens<br><span class="nav-badge badge-exercise">Exercise</span></span><span class="nav-done">✓</span></a>
<a href="#turning-both-ways" data-section="turning-both-ways"><span class="nav-num">03</span><span>Turning Both Ways<br><span class="nav-badge badge-tutorial">Tutorial</span></span><span class="nav-done">✓</span></a>
<a href="#two-squares" data-section="two-squares"><span class="nav-num">04</span><span>Two Squares<br><span class="nav-badge badge-exercise">Exercise</span></span><span class="nav-done">✓</span></a>
<a href="#thicker-lines" data-section="thicker-lines"><span class="nav-num">05</span><span>Thicker Lines<br><span class="nav-badge badge-exercise">Exercise</span></span><span class="nav-done">✓</span></a>
<a href="#coloured-triangle" data-section="coloured-triangle"><span class="nav-num">06</span><span>Coloured Triangle<br><span class="nav-badge badge-exercise">Exercise</span></span><span class="nav-done">✓</span></a>
<a href="#diamond" data-section="diamond"><span class="nav-num">07</span><span>Diamond<br><span class="nav-badge badge-exercise">Exercise</span></span><span class="nav-done">✓</span></a>
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<a href="#coloured-squares" data-section="coloured-squares"><span class="nav-num">09</span><span>Coloured Squares<br><span class="nav-badge badge-exercise">Exercise</span></span><span class="nav-done">✓</span></a>
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<a href="#house" data-section="house"><span class="nav-num">11</span><span>House<br><span class="nav-badge badge-exercise">Exercise</span></span><span class="nav-done">✓</span></a>
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<a href="#simple-snowflake" data-section="simple-snowflake"><span class="nav-num">15</span><span>Simple Snowflake<br><span class="nav-badge badge-exercise">Exercise</span></span><span class="nav-done">✓</span></a>
<a href="#parallel-lines" data-section="parallel-lines"><span class="nav-num">16</span><span>Parallel Lines<br><span class="nav-badge badge-exercise">Exercise</span></span><span class="nav-done">✓</span></a>
<a href="#letter-z" data-section="letter-z"><span class="nav-num">17</span><span>Letter Z<br><span class="nav-badge badge-exercise">Exercise</span></span><span class="nav-done">✓</span></a>
<a href="#rhombus" data-section="rhombus"><span class="nav-num">18</span><span>Rhombus<br><span class="nav-badge badge-exercise">Exercise</span></span><span class="nav-done">✓</span></a>
<a href="#parallelogram" data-section="parallelogram"><span class="nav-num">19</span><span>Parallelogram<br><span class="nav-badge badge-exercise">Exercise</span></span><span class="nav-done">✓</span></a>
<a href="#polygon-explorer" data-section="polygon-explorer"><span class="nav-num">20</span><span>Polygon Explorer<br><span class="nav-badge badge-exercise">Exercise</span></span><span class="nav-done">✓</span></a>
<a href="#angle-classification" data-section="angle-classification"><span class="nav-num">21</span><span>Angle Classification<br><span class="nav-badge badge-exercise">Exercise</span></span><span class="nav-done">✓</span></a>
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<div class="ch-label">Chapter 2 of 6</div>
<h1>Fancy Shapes</h1>
<p class="lead">Work with multiple pens, colours, fill, and variables to create diamonds, crosses, snowflakes, and complex polygons — building a deeper understanding of geometry in the process.</p>
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<div class="banner-stat"><span class="stat-num">21</span><span class="stat-label">Sections</span></div>
<div class="banner-stat"><span class="stat-num">3</span><span class="stat-label">Tutorials</span></div>
<div class="banner-stat"><span class="stat-num">18</span><span class="stat-label">Exercises</span></div>
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</section>
<!-- ═══════════════════ 01 — ADDING PENS ═══════════════════ -->
<section id="adding-pens">
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<span class="section-tag tutorial">◆ Tutorial</span>
<h1>Adding Pens</h1>
<p class="lead">Discover how to use the <code>addShape(pen:)</code> call and what happens when you create multiple independent pens on the same canvas.</p>
<button class="complete-btn" data-id="adding-pens" onclick="toggleComplete(this)"><span class="btn-icon">○</span> Mark as Complete</button>
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<h2>Rendering Shapes</h2>
<p>Each pen tracks its own path independently. To display a pen's path on the canvas you must call <code>addShape(pen:)</code>. You can call it once at the end, or after each pen individually.</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">p1</span> = <span class="tp">Pen</span>()
<span class="vr">p1</span>.<span class="fn">addLine</span>(distance: <span class="num">100</span>)
<span class="fn">addShape</span>(pen: <span class="vr">p1</span>) <span class="cm">// render p1's path</span>
<span class="kw">var</span> <span class="vr">p2</span> = <span class="tp">Pen</span>()
<span class="vr">p2</span>.<span class="fn">turn</span>(degrees: <span class="num">90</span>)
<span class="vr">p2</span>.<span class="fn">addLine</span>(distance: <span class="num">100</span>)
<span class="fn">addShape</span>(pen: <span class="vr">p2</span>) <span class="cm">// render p2's path</span></pre>
</div>
<div class="img-wrap">
<img src="images/02-01-adding-pens.png" alt="Two Lines">
</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>Each pen starts at the origin — independent paths share the same coordinate system</td></tr>
<tr><td>Line segments</td><td>Each <code>addLine</code> call produces a directed segment with defined start and end points</td></tr>
</table>
</div>
</div>
</section>
<!-- ═══════════════════ 02 — MULTIPLE PENS ═══════════════════ -->
<section id="multiple-pens">
<div class="section-hero">
<span class="section-tag exercise">◆ Exercise</span>
<h1>Multiple Pens</h1>
<p class="lead">Draw two separate squares side-by-side using two independent pens — one starting at the origin and the other offset to the right.</p>
<button class="complete-btn" data-id="multiple-pens" onclick="toggleComplete(this)"><span class="btn-icon">○</span> Mark as Complete</button>
</div>
<div class="article">
<h2>Your Task</h2>
<p>Create two pens. Draw a 100-unit square with <code>p1</code> starting at the origin. Then use <code>p2</code> — start it at (150, 0) using <code>move(distance:)</code> or by setting its position — and draw a second 100-unit square.</p>
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<pre><span class="kw">var</span> <span class="vr">p1</span> = <span class="tp">Pen</span>()
<span class="cm">// Draw first square with p1</span>
<span class="kw">var</span> <span class="vr">p2</span> = <span class="tp">Pen</span>()
<span class="cm">// Position p2 and draw second square</span>
<span class="fn">addShape</span>(pen: <span class="vr">p1</span>)
<span class="fn">addShape</span>(pen: <span class="vr">p2</span>)</pre>
</div>
<div class="img-wrap">
<img src="images/02-02-multiple-pens.png" alt="Two Lines">
</div>
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<svg width="14" height="14" viewBox="0 0 24 24" fill="none"><path d="M12 2L2 7l10 5 10-5-10-5zM2 17l10 5 10-5M2 12l10 5 10-5" stroke="currentColor" stroke-width="2" stroke-linecap="round"/></svg>
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<pre><span class="kw">var</span> <span class="vr">p1</span> = <span class="tp">Pen</span>()
<span class="vr">p1</span>.<span class="fn">addLine</span>(distance: <span class="num">100</span>); <span class="vr">p1</span>.<span class="fn">turn</span>(degrees: <span class="num">90</span>)
<span class="vr">p1</span>.<span class="fn">addLine</span>(distance: <span class="num">100</span>); <span class="vr">p1</span>.<span class="fn">turn</span>(degrees: <span class="num">90</span>)
<span class="vr">p1</span>.<span class="fn">addLine</span>(distance: <span class="num">100</span>); <span class="vr">p1</span>.<span class="fn">turn</span>(degrees: <span class="num">90</span>)
<span class="vr">p1</span>.<span class="fn">addLine</span>(distance: <span class="num">100</span>)
<span class="fn">addShape</span>(pen: <span class="vr">p1</span>)
<span class="kw">var</span> <span class="vr">p2</span> = <span class="tp">Pen</span>()
<span class="vr">p2</span>.<span class="fn">move</span>(distance: <span class="num">150</span>) <span class="cm">// move right without drawing</span>
<span class="vr">p2</span>.<span class="fn">addLine</span>(distance: <span class="num">100</span>); <span class="vr">p2</span>.<span class="fn">turn</span>(degrees: <span class="num">90</span>)
<span class="vr">p2</span>.<span class="fn">addLine</span>(distance: <span class="num">100</span>); <span class="vr">p2</span>.<span class="fn">turn</span>(degrees: <span class="num">90</span>)
<span class="vr">p2</span>.<span class="fn">addLine</span>(distance: <span class="num">100</span>); <span class="vr">p2</span>.<span class="fn">turn</span>(degrees: <span class="num">90</span>)
<span class="vr">p2</span>.<span class="fn">addLine</span>(distance: <span class="num">100</span>)
<span class="fn">addShape</span>(pen: <span class="vr">p2</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>Translations</td><td>Offsetting <code>p2</code> by 150 units is a <strong>translation</strong> — a rigid motion that shifts every point the same distance</td></tr>
<tr><td>Congruence</td><td>Both squares are <strong>congruent</strong> — same shape, same size, different position</td></tr>
</table>
</div>
</div>
</section>
<!-- ═══════════════════ 03 — TURNING BOTH WAYS ═══════════════════ -->
<section id="turning-both-ways">
<div class="section-hero">
<span class="section-tag tutorial">◆ Tutorial</span>
<h1>Turning Both Ways</h1>
<p class="lead">Explore negative degree values — turning right (clockwise) instead of left — and understand how this unlocks a wider range of shapes.</p>
<button class="complete-btn" data-id="turning-both-ways" onclick="toggleComplete(this)"><span class="btn-icon">○</span> Mark as Complete</button>
</div>
<div class="article">
<h2>Positive vs Negative Turns</h2>
<p>A positive turn angle rotates the pen <strong>anti-clockwise</strong> (left). A negative angle rotates it <strong>clockwise</strong> (right). This matches standard mathematical convention.</p>
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<pre><span class="vr">p</span>.<span class="fn">turn</span>(degrees: <span class="num">90</span>) <span class="cm">// rotate LEFT 90° (anti-clockwise)</span>
<span class="vr">p</span>.<span class="fn">turn</span>(degrees: -<span class="num">90</span>) <span class="cm">// rotate RIGHT 90° (clockwise)</span></pre>
</div>
<div class="img-wrap">
<img src="images/02-03-turning-both-ways.png" alt="Two Lines">
</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>Directed angles</td><td>Positive = anti-clockwise, negative = clockwise — this is the convention used in trigonometry and coordinate geometry</td></tr>
<tr><td>Rotations</td><td>Turning the pen is equivalent to a <strong>rotation</strong> of the direction vector around the pen's current position</td></tr>
</table>
</div>
</div>
</section>
<!-- ═══════════════════ 04 — TWO SQUARES ═══════════════════ -->
<section id="two-squares">
<div class="section-hero">
<span class="section-tag exercise">◆ Exercise</span>
<h1>Two Squares</h1>
<p class="lead">Draw a large square (200 units) and a small square (100 units) that shares the same bottom-left corner — creating a nested effect.</p>
<button class="complete-btn" data-id="two-squares" onclick="toggleComplete(this)"><span class="btn-icon">○</span> Mark as Complete</button>
</div>
<div class="article">
<h2>Your Task</h2>
<p>Use a single pen to draw both squares without lifting it (use <code>move</code> to reposition if needed), or use two separate pens.</p>
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<pre><span class="kw">var</span> <span class="vr">p</span> = <span class="tp">Pen</span>()
<span class="cm">// Draw large square (200 units)</span>
<span class="cm">// Draw small square (100 units)</span>
<span class="fn">addShape</span>(pen: <span class="vr">p</span>)</pre>
</div>
<div class="img-placeholder">
<div class="img-icon">✏️</div>
<span class="img-name">02-04-two-squares.png</span>
<span class="img-hint">Screenshot: large and small square sharing the same bottom-left corner</span>
</div>
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<svg width="14" height="14" viewBox="0 0 24 24" fill="none"><path d="M12 2L2 7l10 5 10-5-10-5zM2 17l10 5 10-5M2 12l10 5 10-5" stroke="currentColor" stroke-width="2" stroke-linecap="round"/></svg>
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<pre><span class="kw">var</span> <span class="vr">p</span> = <span class="tp">Pen</span>()
<span class="cm">// Large square: 200 units</span>
<span class="vr">p</span>.<span class="fn">addLine</span>(distance: <span class="num">200</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="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="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="vr">p</span>.<span class="fn">turn</span>(degrees: <span class="num">90</span>)
<span class="cm">// Small square: 100 units</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>Similarity</td><td>The two squares are <strong>similar</strong> — same shape but different sizes, with a scale factor of 2:1</td></tr>
<tr><td>Perimeter</td><td>Perimeter of large square = 4 × 200 = 800; small = 4 × 100 = 400</td></tr>
</table>
</div>
</div>
</section>
<!-- ═══════════════════ 05 — THICKER LINES ═══════════════════ -->
<section id="thicker-lines">
<div class="section-hero">
<span class="section-tag exercise">◆ Exercise</span>
<h1>Thicker Lines</h1>
<p class="lead">Use the <code>lineWidth</code> property to draw a bold triangle — and explore how stroke width affects a shape's visual weight.</p>
<button class="complete-btn" data-id="thicker-lines" 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 (3 sides, turning 120° at each corner) with a <code>lineWidth</code> of 6.</p>
<div class="code-wrap">
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<pre><span class="kw">var</span> <span class="vr">p</span> = <span class="tp">Pen</span>()
<span class="vr">p</span>.<span class="fn">lineWidth</span> = <span class="num">6</span>
<span class="cm">// Draw equilateral triangle</span>
<span class="fn">addShape</span>(pen: <span class="vr">p</span>)</pre>
</div>
<div class="img-placeholder">
<div class="img-icon">✏️</div>
<span class="img-name">02-05-thicker-lines.png</span>
<span class="img-hint">Screenshot: equilateral triangle drawn with a thick stroke</span>
</div>
<button class="solution-toggle" onclick="toggleSolution(this,'sol-thicker-lines')">
<svg width="14" height="14" viewBox="0 0 24 24" fill="none"><path d="M12 2L2 7l10 5 10-5-10-5zM2 17l10 5 10-5M2 12l10 5 10-5" stroke="currentColor" stroke-width="2" stroke-linecap="round"/></svg>
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<div class="solution-body" id="sol-thicker-lines">
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<pre><span class="kw">var</span> <span class="vr">p</span> = <span class="tp">Pen</span>()
<span class="vr">p</span>.<span class="fn">lineWidth</span> = <span class="num">6</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">120</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">120</span>)
<span class="vr">p</span>.<span class="fn">addLine</span>(distance: <span class="num">150</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>Equilateral triangle</td><td>All three sides equal; all interior angles = 60°; exterior turn = 120°</td></tr>
<tr><td>Exterior angle theorem</td><td>360° ÷ 3 sides = 120° per turn; verifies sum of exterior angles = 360°</td></tr>
</table>
</div>
</div>
</section>
<!-- ═══════════════════ 06 — COLOURED TRIANGLE ═══════════════════ -->
<section id="coloured-triangle">
<div class="section-hero">
<span class="section-tag exercise">◆ Exercise</span>
<h1>Coloured Triangle</h1>
<p class="lead">Draw a triangle where each side is a different colour — green, red, and blue — by changing <code>penColor</code> between sides.</p>
<button class="complete-btn" data-id="coloured-triangle" onclick="toggleComplete(this)"><span class="btn-icon">○</span> Mark as Complete</button>
</div>
<div class="article">
<h2>Your Task</h2>
<p>Use three pens (or change the colour on one pen before each side) to produce a triangle with sides in three different colours.</p>
<div class="code-wrap">
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<pre><span class="kw">var</span> <span class="vr">p</span> = <span class="tp">Pen</span>()
<span class="vr">p</span>.<span class="fn">penColor</span> = .<span class="fn">green</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">120</span>)
<span class="cm">// Continue for red and blue sides…</span>
<span class="fn">addShape</span>(pen: <span class="vr">p</span>)</pre>
</div>
<div class="img-placeholder">
<div class="img-icon">✏️</div>
<span class="img-name">02-06-coloured-triangle.png</span>
<span class="img-hint">Screenshot: equilateral triangle with green, red, and blue sides</span>
</div>
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<svg width="14" height="14" viewBox="0 0 24 24" fill="none"><path d="M12 2L2 7l10 5 10-5-10-5zM2 17l10 5 10-5M2 12l10 5 10-5" stroke="currentColor" stroke-width="2" stroke-linecap="round"/></svg>
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<div class="solution-body" id="sol-coloured-triangle">
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<pre><span class="kw">var</span> <span class="vr">p</span> = <span class="tp">Pen</span>()
<span class="vr">p</span>.<span class="fn">penColor</span> = .<span class="fn">green</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">120</span>)
<span class="vr">p</span>.<span class="fn">penColor</span> = .<span class="fn">red</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">120</span>)
<span class="vr">p</span>.<span class="fn">penColor</span> = .<span class="fn">blue</span>
<span class="vr">p</span>.<span class="fn">addLine</span>(distance: <span class="num">150</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>Triangle classification</td><td>Equilateral — three sides equal, three angles equal (60° each)</td></tr>
<tr><td>Angle sum</td><td>Interior angles of any triangle sum to 180°</td></tr>
</table>
</div>
</div>
</section>
<!-- ═══════════════════ 07 — DIAMOND ═══════════════════ -->
<section id="diamond">
<div class="section-hero">
<span class="section-tag exercise">◆ Exercise</span>
<h1>Diamond</h1>
<p class="lead">Draw a diamond (rhombus) with equal sides but non-right angles — using turn angles less than and greater than 90°.</p>
<button class="complete-btn" data-id="diamond" onclick="toggleComplete(this)"><span class="btn-icon">○</span> Mark as Complete</button>
</div>
<div class="article">
<h2>Your Task</h2>
<p>Draw a diamond with side length 150 and interior angles of 60° and 120°. Hint: the exterior turns will be 120° and 60° alternating.</p>
<div class="code-wrap">
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<pre><span class="kw">var</span> <span class="vr">p</span> = <span class="tp">Pen</span>()
<span class="cm">// 4 equal sides, alternating turns</span>
<span class="fn">addShape</span>(pen: <span class="vr">p</span>)</pre>
</div>
<div class="img-placeholder">
<div class="img-icon">✏️</div>
<span class="img-name">02-07-diamond.png</span>
<span class="img-hint">Screenshot: diamond shape with 60° and 120° interior angles</span>
</div>
<button class="solution-toggle" onclick="toggleSolution(this,'sol-diamond')">
<svg width="14" height="14" viewBox="0 0 24 24" fill="none"><path d="M12 2L2 7l10 5 10-5-10-5zM2 17l10 5 10-5M2 12l10 5 10-5" stroke="currentColor" stroke-width="2" stroke-linecap="round"/></svg>
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<div class="solution-body" id="sol-diamond">
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<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">60</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">120</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">60</span>)
<span class="vr">p</span>.<span class="fn">addLine</span>(distance: <span class="num">150</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>Rhombus properties</td><td>4 equal sides; opposite angles equal; diagonals bisect each other at right angles</td></tr>
<tr><td>Supplementary angles</td><td>Adjacent interior angles sum to 180°: 60° + 120° = 180°</td></tr>
</table>
</div>
</div>
</section>
<!-- ═══════════════════ 08 — FILL IT IN ═══════════════════ -->
<section id="fill-it-in">
<div class="section-hero">
<span class="section-tag tutorial">◆ Tutorial</span>
<h1>Fill It In</h1>
<p class="lead">Learn about the <code>fillColor</code> property to colour the interior of closed shapes.</p>
<button class="complete-btn" data-id="fill-it-in" onclick="toggleComplete(this)"><span class="btn-icon">○</span> Mark as Complete</button>
</div>
<div class="article">
<h2>Adding Fill</h2>
<p>Setting <code>fillColor</code> on a pen before drawing will colour the enclosed area of a closed shape. The path must be closed (return to its starting point) for fill to work correctly.</p>
<div class="code-wrap">
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<pre><span class="kw">var</span> <span class="vr">p</span> = <span class="tp">Pen</span>()
<span class="vr">p</span>.<span class="fn">fillColor</span> = .<span class="fn">yellow</span>
<span class="vr">p</span>.<span class="fn">penColor</span> = .<span class="fn">orange</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 class="img-placeholder">
<div class="img-icon">🟨</div>
<span class="img-name">02-08-fill-it-in.png</span>
<span class="img-hint">Screenshot: yellow-filled square with orange border</span>
</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>Area vs perimeter</td><td>Fill occupies the interior (area); the pen line defines the boundary (perimeter)</td></tr>
<tr><td>Closed figures</td><td>A shape must be topologically closed for fill to render — a key property in geometry</td></tr>
</table>
</div>
</div>
</section>
<!-- ═══════════════════ 09 — COLOURED SQUARES ═══════════════════ -->
<section id="coloured-squares">
<div class="section-hero">
<span class="section-tag exercise">◆ Exercise</span>
<h1>Coloured Squares</h1>
<p class="lead">Draw three filled squares in a row — red, green, and blue — each 80 units wide with a 20-unit gap between them.</p>
<button class="complete-btn" data-id="coloured-squares" onclick="toggleComplete(this)"><span class="btn-icon">○</span> Mark as Complete</button>
</div>
<div class="article">
<h2>Your Task</h2>
<p>Use three separate pens positioned at different x-coordinates. Give each pen a different <code>fillColor</code>.</p>
<div class="code-wrap">
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<pre><span class="cm">// Three pens at x = 0, 100, 200</span>
<span class="cm">// Each draws an 80×80 filled square</span></pre>
</div>
<div class="img-placeholder">
<div class="img-icon">✏️</div>
<span class="img-name">02-09-coloured-squares.png</span>
<span class="img-hint">Screenshot: three filled squares in red, green, and blue side by side</span>
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<pre><span class="kw">var</span> <span class="vr">p1</span> = <span class="tp">Pen</span>()
<span class="vr">p1</span>.<span class="fn">fillColor</span> = .<span class="fn">red</span>
<span class="vr">p1</span>.<span class="fn">addLine</span>(distance: <span class="num">80</span>); <span class="vr">p1</span>.<span class="fn">turn</span>(degrees: <span class="num">90</span>)
<span class="vr">p1</span>.<span class="fn">addLine</span>(distance: <span class="num">80</span>); <span class="vr">p1</span>.<span class="fn">turn</span>(degrees: <span class="num">90</span>)
<span class="vr">p1</span>.<span class="fn">addLine</span>(distance: <span class="num">80</span>); <span class="vr">p1</span>.<span class="fn">turn</span>(degrees: <span class="num">90</span>)
<span class="vr">p1</span>.<span class="fn">addLine</span>(distance: <span class="num">80</span>)
<span class="fn">addShape</span>(pen: <span class="vr">p1</span>)
<span class="kw">var</span> <span class="vr">p2</span> = <span class="tp">Pen</span>()
<span class="vr">p2</span>.<span class="fn">move</span>(distance: <span class="num">100</span>)
<span class="vr">p2</span>.<span class="fn">fillColor</span> = .<span class="fn">green</span>
<span class="vr">p2</span>.<span class="fn">addLine</span>(distance: <span class="num">80</span>); <span class="vr">p2</span>.<span class="fn">turn</span>(degrees: <span class="num">90</span>)
<span class="vr">p2</span>.<span class="fn">addLine</span>(distance: <span class="num">80</span>); <span class="vr">p2</span>.<span class="fn">turn</span>(degrees: <span class="num">90</span>)
<span class="vr">p2</span>.<span class="fn">addLine</span>(distance: <span class="num">80</span>); <span class="vr">p2</span>.<span class="fn">turn</span>(degrees: <span class="num">90</span>)
<span class="vr">p2</span>.<span class="fn">addLine</span>(distance: <span class="num">80</span>)
<span class="fn">addShape</span>(pen: <span class="vr">p2</span>)
<span class="kw">var</span> <span class="vr">p3</span> = <span class="tp">Pen</span>()
<span class="vr">p3</span>.<span class="fn">move</span>(distance: <span class="num">200</span>)
<span class="vr">p3</span>.<span class="fn">fillColor</span> = .<span class="fn">blue</span>
<span class="vr">p3</span>.<span class="fn">addLine</span>(distance: <span class="num">80</span>); <span class="vr">p3</span>.<span class="fn">turn</span>(degrees: <span class="num">90</span>)
<span class="vr">p3</span>.<span class="fn">addLine</span>(distance: <span class="num">80</span>); <span class="vr">p3</span>.<span class="fn">turn</span>(degrees: <span class="num">90</span>)
<span class="vr">p3</span>.<span class="fn">addLine</span>(distance: <span class="num">80</span>); <span class="vr">p3</span>.<span class="fn">turn</span>(degrees: <span class="num">90</span>)
<span class="vr">p3</span>.<span class="fn">addLine</span>(distance: <span class="num">80</span>)
<span class="fn">addShape</span>(pen: <span class="vr">p3</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>Area</td><td>Each square: area = 80² = 6400 square units; total area = 3 × 6400 = 19,200</td></tr>
<tr><td>Translations</td><td>Each square is a translated copy — same shape, size, and orientation at a different position</td></tr>
</table>
</div>
</div>
</section>
<!-- ═══════════════════ 10 — VARIABLES ═══════════════════ -->
<section id="variables">
<div class="section-hero">
<span class="section-tag tutorial">◆ Tutorial</span>
<h1>Variables</h1>
<p class="lead">Store sizes in variables so you can change your shape's dimensions in one place and have the whole drawing update automatically.</p>
<button class="complete-btn" data-id="variables" onclick="toggleComplete(this)"><span class="btn-icon">○</span> Mark as Complete</button>
</div>
<div class="article">
<h2>Using Variables for Dimensions</h2>
<p>A <strong>variable</strong> is a named container for a value. By storing a side length in a variable, changing it once updates the entire drawing.</p>
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<pre><span class="kw">let</span> <span class="vr">side</span> = <span class="num">120.0</span> <span class="cm">// change this one value to resize everything</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="vr">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="vr">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="vr">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="vr">side</span>)
<span class="fn">addShape</span>(pen: <span class="vr">p</span>)</pre>
</div>
<h2>Variables vs Constants</h2>
<p>You may have noticed two different keywords in Swift: <code>var</code> and <code>let</code>. They both name a value — but behave differently.</p>
<table>
<tr><th>Keyword</th><th>Name</th><th>Can it change?</th><th>Use it for…</th></tr>
<tr><td><code>var</code></td><td>Variable</td><td>Yes</td><td>Things that change over time — like a <code>Pen</code> as it moves and turns</td></tr>
<tr><td><code>let</code></td><td>Constant</td><td>No</td><td>Fixed values that should stay the same — like a side length you set once</td></tr>
</table>
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<pre><span class="kw">let</span> <span class="vr">side</span> = <span class="num">100.0</span> <span class="cm">// constant — the value is fixed</span>
<span class="kw">var</span> <span class="vr">p</span> = <span class="tp">Pen</span>() <span class="cm">// variable — p changes as we call methods on it</span></pre>
</div>
<p>Use <code>let</code> when a value should never change after you set it — Swift will warn you if you accidentally try to modify it. Use <code>var</code> when the value needs to change (or when Swift requires it, as with <code>Pen</code>).</p>
<div class="img-placeholder">
<div class="img-icon">✏️</div>
<span class="img-name">02-10-variables.png</span>
<span class="img-hint">Screenshot: square drawn using a variable side length</span>
</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>Variables & expressions</td><td>Side length <em>s</em> is a variable; perimeter = 4s and area = s² are expressions derived from it</td></tr>
<tr><td>Generalisation</td><td>Writing a formula in terms of a variable generalises from specific numbers to all cases</td></tr>
</table>
</div>
</div>
</section>
<!-- ═══ Sections 11–21: Exercise stubs ═══ -->
<!-- 11 — HOUSE -->
<section id="house">
<div class="section-hero">
<span class="section-tag exercise">◆ Exercise</span>
<h1>House</h1>
<p class="lead">Combine a square base and a triangular roof to draw a simple house shape using two pens or careful repositioning.</p>
<button class="complete-btn" data-id="house" onclick="toggleComplete(this)"><span class="btn-icon">○</span> Mark as Complete</button>
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<div class="article">
<h2>Your Task</h2>
<p>Draw a square (100 units) for the walls, then continue from the top-left corner to draw an isosceles triangle roof. The roof peak should be centred above the square.</p>
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<pre><span class="kw">var</span> <span class="vr">p</span> = <span class="tp">Pen</span>()
<span class="cm">// Square body + triangular roof</span>
<span class="fn">addShape</span>(pen: <span class="vr">p</span>)</pre>
</div>
<div class="img-placeholder">
<div class="img-icon">✏️</div>
<span class="img-name">02-11-house.png</span>
<span class="img-hint">Screenshot: square base with triangular roof forming a house outline</span>
</div>
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<pre><span class="kw">var</span> <span class="vr">p</span> = <span class="tp">Pen</span>()
<span class="cm">// Square base</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">// Move to top-left of square</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">move</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">// Roof: two sides at 30° from horizontal, meeting at apex</span>
<span class="vr">p</span>.<span class="fn">turn</span>(degrees: <span class="num">30</span>)
<span class="vr">p</span>.<span class="fn">addLine</span>(distance: <span class="num">57.74</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">57.74</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>Composite figures</td><td>Total area = area of square + area of triangle — composites are decomposed into simpler shapes</td></tr>
<tr><td>Isosceles triangle</td><td>Roof triangle has two equal sides and two equal base angles</td></tr>
</table>
</div>
</div>
</section>
<!-- 12 — CALCULATE -->
<section id="calculate">
<div class="section-hero">
<span class="section-tag exercise">◆ Exercise</span>
<h1>Calculate</h1>
<p class="lead">Use Swift arithmetic to compute side lengths and angles — let the code do the maths rather than calculating by hand.</p>
<button class="complete-btn" data-id="calculate" onclick="toggleComplete(this)"><span class="btn-icon">○</span> Mark as Complete</button>
</div>
<div class="article">
<h2>Your Task</h2>
<p>Draw a regular hexagon. Instead of calculating the turn angle yourself, store the number of sides in a constant and use <code>360.0 / 6</code> to let Swift compute it. Then write one <code>addLine</code> and one <code>turn</code> for each of the six sides.</p>
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<pre><span class="kw">let</span> <span class="vr">sides</span> = <span class="num">6</span>
<span class="kw">let</span> <span class="vr">turn</span> = <span class="num">360.0</span> / <span class="tp">Double</span>(<span class="vr">sides</span>)
<span class="kw">var</span> <span class="vr">p</span> = <span class="tp">Pen</span>()
<span class="cm">// Draw each of the 6 sides using 'turn'</span>
<span class="fn">addShape</span>(pen: <span class="vr">p</span>)</pre>
</div>
<div class="img-placeholder">
<div class="img-icon">✏️</div>
<span class="img-name">02-12-calculate.png</span>
<span class="img-hint">Screenshot: regular hexagon drawn using a calculated turn angle</span>
</div>
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<pre><span class="kw">let</span> <span class="vr">sides</span> = <span class="num">6</span>
<span class="kw">let</span> <span class="vr">turn</span> = <span class="num">360.0</span> / <span class="tp">Double</span>(<span class="vr">sides</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="vr">turn</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="vr">turn</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="vr">turn</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="vr">turn</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="vr">turn</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="vr">turn</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>Regular polygons</td><td>Exterior angle = 360° ÷ n; interior angle = 180° − (360° ÷ n)</td></tr>
<tr><td>Algebraic reasoning</td><td>Expressing the angle as 360/n generalises the formula for all regular polygons</td></tr>
</table>
</div>
</div>
</section>
<!-- 13 — VARIABLE HOUSE -->
<section id="variable-house">
<div class="section-hero">
<span class="section-tag exercise">◆ Exercise</span>
<h1>Variable House</h1>
<p class="lead">Refactor the House exercise using a variable for the house width, so you can resize the whole building by changing one number.</p>
<button class="complete-btn" data-id="variable-house" onclick="toggleComplete(this)"><span class="btn-icon">○</span> Mark as Complete</button>
</div>
<div class="article">
<h2>Your Task</h2>
<p>Store the house width in a variable <code>w</code>. The roof height and angles should be derived from <code>w</code> using arithmetic, so the shape scales correctly.</p>
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<pre><span class="kw">let</span> <span class="vr">w</span> = <span class="num">120.0</span> <span class="cm">// change this to resize the house</span>
<span class="kw">var</span> <span class="vr">p</span> = <span class="tp">Pen</span>()
<span class="cm">// Use w throughout</span>
<span class="fn">addShape</span>(pen: <span class="vr">p</span>)</pre>
</div>
<div class="img-placeholder">
<div class="img-icon">✏️</div>
<span class="img-name">02-13-variable-house.png</span>
<span class="img-hint">Screenshot: house shape drawn using a variable width</span>
</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>Proportional reasoning</td><td>Scaling all dimensions by the same factor produces a <strong>similar</strong> figure</td></tr>
<tr><td>Variables in geometry</td><td>Writing perimeter/area formulas in terms of <em>w</em> models geometric relationships algebraically</td></tr>
</table>
</div>
</div>
</section>
<!-- 14 — RED CROSS -->
<section id="red-cross">
<div class="section-hero">
<span class="section-tag exercise">◆ Exercise</span>
<h1>Red Cross</h1>
<p class="lead">Draw a filled red cross (plus sign) shape — a composite figure made from rectangles.</p>
<button class="complete-btn" data-id="red-cross" onclick="toggleComplete(this)"><span class="btn-icon">○</span> Mark as Complete</button>
</div>
<div class="article">
<h2>Your Task</h2>
<p>A cross can be drawn as a 12-sided polygon. Start at the bottom-left of the lower arm and work around the perimeter, alternating between long (100) and short (40) sides.</p>
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<pre><span class="kw">var</span> <span class="vr">p</span> = <span class="tp">Pen</span>()
<span class="vr">p</span>.<span class="fn">fillColor</span> = .<span class="fn">red</span>
<span class="vr">p</span>.<span class="fn">penColor</span> = .<span class="fn">red</span>
<span class="cm">// 12 sides, 4 outer corners (90°), 8 inner corners (-90°)</span>
<span class="fn">addShape</span>(pen: <span class="vr">p</span>)</pre>
</div>
<div class="img-placeholder">
<div class="img-icon">✏️</div>
<span class="img-name">02-14-red-cross.png</span>
<span class="img-hint">Screenshot: filled red cross (plus sign) shape</span>
</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>Area of composite figures</td><td>Cross area = 3 rectangles overlapping; use inclusion-exclusion: 3(100×40) − 2(40×40)</td></tr>
<tr><td>Perimeter of irregular shapes</td><td>Count each boundary segment: 4 long sides + 8 short sides</td></tr>
</table>
</div>
</div>
</section>
<!-- 15 — SIMPLE SNOWFLAKE -->
<section id="simple-snowflake">
<div class="section-hero">
<span class="section-tag exercise">◆ Exercise</span>
<h1>Simple Snowflake</h1>
<p class="lead">Draw 6 arms radiating from the centre — each arm a straight line — to create a basic snowflake with 6-fold symmetry.</p>
<button class="complete-btn" data-id="simple-snowflake" onclick="toggleComplete(this)"><span class="btn-icon">○</span> Mark as Complete</button>
</div>
<div class="article">
<h2>Your Task</h2>
<p>Draw 6 arms of equal length, each rotated 60° from the last. After each arm, return to the centre.</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">// Arm 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">move</span>(distance: -<span class="num">100</span>); <span class="vr">p</span>.<span class="fn">turn</span>(degrees: <span class="num">60</span>)
<span class="cm">// Arm 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">move</span>(distance: -<span class="num">100</span>); <span class="vr">p</span>.<span class="fn">turn</span>(degrees: <span class="num">60</span>)
<span class="cm">// Arm 3</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">move</span>(distance: -<span class="num">100</span>); <span class="vr">p</span>.<span class="fn">turn</span>(degrees: <span class="num">60</span>)
<span class="cm">// Arm 4</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">move</span>(distance: -<span class="num">100</span>); <span class="vr">p</span>.<span class="fn">turn</span>(degrees: <span class="num">60</span>)
<span class="cm">// Arm 5</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">move</span>(distance: -<span class="num">100</span>); <span class="vr">p</span>.<span class="fn">turn</span>(degrees: <span class="num">60</span>)
<span class="cm">// Arm 6</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="img-placeholder">
<div class="img-icon">✏️</div>
<span class="img-name">02-15-simple-snowflake.png</span>
<span class="img-hint">Screenshot: 6-arm snowflake radiating from the centre</span>
</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>Rotational symmetry</td><td>A 6-arm snowflake has order-6 rotational symmetry — it maps onto itself after 60° rotations</td></tr>
<tr><td>Angles at a point</td><td>6 arms × 60° = 360° — the angles around the centre sum to one full rotation</td></tr>
</table>
</div>
</div>
</section>
<!-- 16 — PARALLEL LINES -->
<section id="parallel-lines">
<div class="section-hero">
<span class="section-tag exercise">◆ Exercise</span>
<h1>Parallel Lines</h1>
<p class="lead">Draw four horizontal parallel lines — equally spaced — demonstrating lines that never meet.</p>
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</div>
<div class="article">
<h2>Your Task</h2>
<p>Draw 4 horizontal lines, each 200 units long, spaced 40 units apart vertically. Use 4 pens — start each one at a different height using <code>turn</code> and <code>move</code>.</p>
<div class="code-wrap">
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<pre><span class="cm">// Line 1 — at y = 0</span>
<span class="kw">var</span> <span class="vr">p1</span> = <span class="tp">Pen</span>()
<span class="vr">p1</span>.<span class="fn">addLine</span>(distance: <span class="num">200</span>)
<span class="fn">addShape</span>(pen: <span class="vr">p1</span>)
<span class="cm">// Line 2 — at y = 40</span>
<span class="kw">var</span> <span class="vr">p2</span> = <span class="tp">Pen</span>()
<span class="cm">// Move p2 up 40 units, then face right again</span>
<span class="cm">// Line 3 and 4 — continue the pattern</span></pre>
</div>
<div class="img-placeholder">
<div class="img-icon">✏️</div>
<span class="img-name">02-16-parallel-lines.png</span>
<span class="img-hint">Screenshot: four equally-spaced horizontal parallel lines</span>
</div>
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<div class="solution-body" id="sol-parallel-lines">
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<pre><span class="cm">// Line 1 — at y = 0</span>
<span class="kw">var</span> <span class="vr">p1</span> = <span class="tp">Pen</span>()
<span class="vr">p1</span>.<span class="fn">addLine</span>(distance: <span class="num">200</span>)
<span class="fn">addShape</span>(pen: <span class="vr">p1</span>)
<span class="cm">// Line 2 — at y = 40</span>
<span class="kw">var</span> <span class="vr">p2</span> = <span class="tp">Pen</span>()
<span class="vr">p2</span>.<span class="fn">turn</span>(degrees: <span class="num">90</span>); <span class="vr">p2</span>.<span class="fn">move</span>(distance: <span class="num">40</span>); <span class="vr">p2</span>.<span class="fn">turn</span>(degrees: -<span class="num">90</span>)
<span class="vr">p2</span>.<span class="fn">addLine</span>(distance: <span class="num">200</span>)
<span class="fn">addShape</span>(pen: <span class="vr">p2</span>)
<span class="cm">// Line 3 — at y = 80</span>
<span class="kw">var</span> <span class="vr">p3</span> = <span class="tp">Pen</span>()
<span class="vr">p3</span>.<span class="fn">turn</span>(degrees: <span class="num">90</span>); <span class="vr">p3</span>.<span class="fn">move</span>(distance: <span class="num">80</span>); <span class="vr">p3</span>.<span class="fn">turn</span>(degrees: -<span class="num">90</span>)
<span class="vr">p3</span>.<span class="fn">addLine</span>(distance: <span class="num">200</span>)
<span class="fn">addShape</span>(pen: <span class="vr">p3</span>)
<span class="cm">// Line 4 — at y = 120</span>
<span class="kw">var</span> <span class="vr">p4</span> = <span class="tp">Pen</span>()
<span class="vr">p4</span>.<span class="fn">turn</span>(degrees: <span class="num">90</span>); <span class="vr">p4</span>.<span class="fn">move</span>(distance: <span class="num">120</span>); <span class="vr">p4</span>.<span class="fn">turn</span>(degrees: -<span class="num">90</span>)
<span class="vr">p4</span>.<span class="fn">addLine</span>(distance: <span class="num">200</span>)
<span class="fn">addShape</span>(pen: <span class="vr">p4</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>Parallel lines</td><td>Lines in the same direction that never intersect; have equal gradient (slope)</td></tr>
<tr><td>Coordinate geometry</td><td>Offsetting the y-start corresponds to a vertical translation</td></tr>
</table>
</div>
</div>
</section>
<!-- 17 — LETTER Z -->
<section id="letter-z">
<div class="section-hero">
<span class="section-tag exercise">◆ Exercise</span>
<h1>Letter Z</h1>
<p class="lead">Draw the letter Z using three line segments — a top horizontal, a diagonal, and a bottom horizontal — observing how the Z-angles relate to parallel lines.</p>
<button class="complete-btn" data-id="letter-z" onclick="toggleComplete(this)"><span class="btn-icon">○</span> Mark as Complete</button>
</div>
<div class="article">
<h2>Your Task</h2>
<p>Draw: a horizontal line right 100, then turn down-left to draw the diagonal, then turn to draw the bottom horizontal. The diagonal creates <strong>Z-angles</strong> (alternate interior angles) with the horizontal lines.</p>
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<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">// top line</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">115.5</span>) <span class="cm">// diagonal</span>
<span class="vr">p</span>.<span class="fn">turn</span>(degrees: -<span class="num">60</span>)
<span class="vr">p</span>.<span class="fn">addLine</span>(distance: <span class="num">100</span>) <span class="cm">// bottom line</span>
<span class="fn">addShape</span>(pen: <span class="vr">p</span>)</pre>
</div>
<div class="img-placeholder">
<div class="img-icon">✏️</div>
<span class="img-name">02-17-letter-z.png</span>
<span class="img-hint">Screenshot: letter Z shape showing Z-angles between parallel lines</span>
</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>Alternate interior angles</td><td>The Z-shape shows alternate angles — equal when lines are parallel — visually embedded in the letter</td></tr>
<tr><td>Transversal</td><td>The diagonal is a transversal crossing two parallel (horizontal) lines</td></tr>
</table>
</div>
</div>
</section>
<!-- 18 — RHOMBUS -->
<section id="rhombus">
<div class="section-hero">
<span class="section-tag exercise">◆ Exercise</span>
<h1>Rhombus</h1>
<p class="lead">Draw a filled rhombus with side length 120 and interior angles of 70° and 110°. Explore how opposite angles in a parallelogram are equal.</p>
<button class="complete-btn" data-id="rhombus" onclick="toggleComplete(this)"><span class="btn-icon">○</span> Mark as Complete</button>
</div>
<div class="article">
<h2>Your Task</h2>
<p>A rhombus has 4 equal sides. Opposite angles are equal; adjacent angles are supplementary (sum to 180°).</p>
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<pre><span class="kw">let</span> <span class="vr">interiorAngle</span> = <span class="num">70.0</span>
<span class="kw">let</span> <span class="vr">exterior</span> = <span class="num">180.0</span> - <span class="vr">interiorAngle</span>
<span class="kw">var</span> <span class="vr">p</span> = <span class="tp">Pen</span>()
<span class="vr">p</span>.<span class="fn">fillColor</span> = .<span class="fn">purple</span>
<span class="cm">// Use interior/exterior angles to draw rhombus</span>
<span class="fn">addShape</span>(pen: <span class="vr">p</span>)</pre>