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Imagine you have 48 square feet of grass to build a rectangular puppy pen, and one wall must be 8 feet long. How wide will the puppy's new play space be?

You can find missing geometric dimensions in a snap by turning the shape's formula into a simple one-step equation.

The **area** of a rectangle measures the square units that fit inside it, calculated by multiplying length times width ($A = l \cdot w$).

<!DOCTYPE html>
<html lang="en">
<head>
  <meta charset="UTF-8">
  <meta name="viewport" content="width=device-width, initial-scale=1.0">
  <meta name="aspect-ratio" content="1:1">
  <title>Solving One-Step Equations: Puppy Pen</title>
  <style>
    * {
      box-sizing: border-box;
      margin: 0;
      padding: 0;
    }
    body {
      font-family: system-ui, -apple-system, sans-serif;
      color: #1e2945;
      background: transparent;
      display: flex;
      flex-direction: column;
      align-items: center;
      justify-content: space-between;
      min-height: 100%;
      padding: 10px;
      user-select: none;
    }
    .diagram-wrap {
      width: 100%;
      max-width: 340px;
      display: flex;
      flex-direction: column;
      align-items: center;
      gap: 10px;
    }

    /* Top badge */
    .area-badge {
      font-size: 15px;
      font-weight: 700;
      background: #e0f2fe;
      color: #0369a1;
      padding: 4px 12px;
      border-radius: 20px;
      border: 1px solid #bae6fd;
      display: inline-flex;
      align-items: center;
      gap: 5px;
    }

    /* Pen visual structure */
    .geometry-container {
      display: flex;
      align-items: center;
      justify-content: center;
      position: relative;
      padding-top: 22px;
      padding-left: 48px;
      margin: 2px 0;
    }

    .top-dimension {
      position: absolute;
      top: 0;
      left: 48px;
      right: 0;
      display: flex;
      flex-direction: column;
      align-items: center;
      font-size: 14px;
      font-weight: 700;
      color: #1e2945;
    }
    .top-dimension .dim-line {
      width: 100%;
      height: 2px;
      background: #94a3b8;
      position: relative;
      margin-top: 2px;
    }
    .top-dimension .dim-line::before,
    .top-dimension .dim-line::after {
      content: '';
      position: absolute;
      top: -3px;
      width: 2px;
      height: 8px;
      background: #94a3b8;
    }
    .top-dimension .dim-line::before { left: 0; }
    .top-dimension .dim-line::after { right: 0; }

    .left-dimension {
      position: absolute;
      left: 0;
      top: 22px;
      bottom: 0;
      width: 44px;
      display: flex;
      align-items: center;
      justify-content: flex-end;
      gap: 4px;
      font-size: 14px;
      font-weight: 700;
      color: #1e2945;
      transition: color 0.3s ease;
    }
    .left-dimension .dim-line-v {
      width: 2px;
      height: 100%;
      background: #94a3b8;
      position: relative;
    }
    .left-dimension .dim-line-v::before,
    .left-dimension .dim-line-v::after {
      content: '';
      position: absolute;
      left: -3px;
      width: 8px;
      height: 2px;
      background: #94a3b8;
    }
    .left-dimension .dim-line-v::before { top: 0; }
    .left-dimension .dim-line-v::after { bottom: 0; }

    .grid-pen {
      display: grid;
      grid-template-columns: repeat(8, 1fr);
      grid-template-rows: repeat(6, 1fr);
      width: 216px;
      height: 156px;
      background: #e0f2fe;
      border: 2px solid #0284c7;
      border-radius: 6px;
      overflow: hidden;
      box-shadow: 0 2px 6px rgba(2, 132, 199, 0.15);
    }
    .grid-cell {
      border: 0.5px solid rgba(2, 132, 199, 0.25);
      transition: background-color 0.3s ease;
    }
    .col-highlight .grid-cell:nth-child(8n+1) {
      background-color: #bae6fd;
    }

    /* Equation Steps container */
    .equation-card {
      width: 100%;
      background: #ffffff;
      border: 1px solid #e6e6e6;
      border-radius: 12px;
      padding: 10px 14px;
      display: flex;
      flex-direction: column;
      align-items: center;
      gap: 6px;
      min-height: 86px;
      justify-content: center;
    }

    .step-display {
      display: none;
      flex-direction: column;
      align-items: center;
      justify-content: center;
      gap: 4px;
      width: 100%;
      text-align: center;
    }
    .step-display.active {
      display: flex;
    }

    .eq-label {
      font-size: 11px;
      font-weight: 700;
      text-transform: uppercase;
      letter-spacing: 0.5px;
      color: #64748b;
    }

    .eq-math {
      font-size: 19px;
      font-weight: 700;
      color: #1e2945;
      font-family: 'Cambria Math', 'Times New Roman', serif, system-ui;
      display: flex;
      align-items: center;
      justify-content: center;
      gap: 6px;
    }

    .highlight-blue {
      color: #0284c7;
      background: #e0f2fe;
      padding: 1px 6px;
      border-radius: 6px;
    }

    .highlight-green {
      color: #15803d;
      background: #dcfce7;
      padding: 1px 6px;
      border-radius: 6px;
    }

    .division-note {
      font-size: 12px;
      color: #0284c7;
      font-weight: 600;
      display: flex;
      align-items: center;
      gap: 4px;
    }

    /* Controls bar */
    .controls-row {
      display: flex;
      align-items: center;
      justify-content: center;
      gap: 8px;
      width: 100%;
    }

    .btn-step {
      background: #f1f5f9;
      border: 1px solid #cbd5e1;
      color: #475569;
      padding: 6px 12px;
      font-size: 13px;
      font-weight: 600;
      border-radius: 8px;
      cursor: pointer;
      display: inline-flex;
      align-items: center;
      gap: 4px;
      transition: all 0.2s ease;
    }
    .btn-step:hover {
      background: #e2e8f0;
    }
    .btn-step.active {
      background: #0284c7;
      color: #ffffff;
      border-color: #0284c7;
    }

    .btn-play {
      background: #f8fafc;
      border: 1px solid #cbd5e1;
      color: #1e2945;
      width: 32px;
      height: 32px;
      border-radius: 8px;
      cursor: pointer;
      display: flex;
      align-items: center;
      justify-content: center;
      font-size: 12px;
    }
    .btn-play:hover {
      background: #e2e8f0;
    }
  </style>
</head>
<body>

  <div class="diagram-wrap">
    
    <div class="area-badge">
      <span>🐶</span>
      <span>Area = 48 sq ft</span>
    </div>

    
    <div class="geometry-container">
      
      <div class="top-dimension">
        <span>8 ft</span>
        <div class="dim-line"></div>
      </div>

      
      <div class="left-dimension" id="leftDim">
        <span id="leftLabel">w = ?</span>
        <div class="dim-line-v"></div>
      </div>

      
      <div class="grid-pen" id="gridPen">
        
        <script>
          for (let i = 0; i < 48; i++) {
            document.write('<div class="grid-cell"></div>');
          }
        </script>
      </div>
    </div>

    
    <div class="equation-card">
      
      <div class="step-display active" id="step1">
        <div class="eq-label">Step 1: Set up equation</div>
        <div class="eq-math">
          <span>8 · w = 48</span>
        </div>
      </div>

      
      <div class="step-display" id="step2">
        <div class="eq-label">Step 2: Divide both sides by 8</div>
        <div class="eq-math">
          <span>(8 · w) <span class="highlight-blue">÷ 8</span> = 48 <span class="highlight-blue">÷ 8</span></span>
        </div>
      </div>

      
      <div class="step-display" id="step3">
        <div class="eq-label">Step 3: Solved width</div>
        <div class="eq-math">
          <span class="highlight-green">w = 6 ft</span>
        </div>
      </div>
    </div>

    
    <div class="controls-row">
      <button class="btn-step active" onclick="setStep(0)">Step 1</button>
      <button class="btn-step" onclick="setStep(1)">Step 2</button>
      <button class="btn-step" onclick="setStep(2)">Step 3</button>
      <button class="btn-play" id="playBtn" onclick="togglePlay()" title="Play / Pause">⏸</button>
    </div>
  </div>

  <script src="{{VENDOR_CDN}}/classace-diagram.js"></script>
  <script>
    let currentStep = 0;
    let isPlaying = true;
    let autoTimer = null;

    const leftLabel = document.getElementById('leftLabel');
    const leftDim = document.getElementById('leftDim');
    const gridPen = document.getElementById('gridPen');
    const stepEls = [
      document.getElementById('step1'),
      document.getElementById('step2'),
      document.getElementById('step3')
    ];
    const buttons = document.querySelectorAll('.btn-step');
    const playBtn = document.getElementById('playBtn');

    function updateView(step) {
      currentStep = step;

      // Update step cards
      stepEls.forEach((el, idx) => {
        el.classList.toggle('active', idx === step);
      });

      // Update buttons
      buttons.forEach((btn, idx) => {
        btn.classList.toggle('active', idx === step);
      });

      // Visual state updates
      if (step === 0) {
        leftLabel.textContent = 'w = ?';
        leftLabel.style.color = '#1e2945';
        gridPen.classList.remove('col-highlight');
      } else if (step === 1) {
        leftLabel.textContent = 'w = ?';
        leftLabel.style.color = '#0284c7';
        gridPen.classList.add('col-highlight');
      } else {
        leftLabel.textContent = 'w = 6 ft';
        leftLabel.style.color = '#15803d';
        gridPen.classList.add('col-highlight');
      }
    }

    function setStep(step) {
      updateView(step);
      resetAutoTimer();
    }

    function nextStep() {
      const next = (currentStep + 1) % 3;
      updateView(next);
    }

    function startTimer() {
      stopTimer();
      autoTimer = setInterval(nextStep, 3500);
    }

    function stopTimer() {
      if (autoTimer) {
        clearInterval(autoTimer);
        autoTimer = null;
      }
    }

    function resetAutoTimer() {
      if (isPlaying) {
        startTimer();
      }
    }

    function togglePlay() {
      isPlaying = !isPlaying;
      playBtn.textContent = isPlaying ? '⏸' : '▶';
      if (isPlaying) {
        startTimer();
      } else {
        stopTimer();
      }
    }

    // Initialize auto play
    startTimer();
  </script>
</body>
</html>

To solve $8w = 48$, we use the **inverse operation** of multiplication, which is division. Dividing both sides by 8 gives a width of $w = 6\text{ ft}$.

A common mistake is subtracting the side length from the total area ($48 - 8 = 40$). Remember: area is created by multiplication, so undoing it always requires division!

What if you need to find the boundary around the outside of a shape instead of the flat space inside?

The **perimeter** is the total distance around the outside edge of a closed shape, found by adding all its side lengths together.

<!DOCTYPE html>
<html lang="en">
<head>
  <meta charset="UTF-8">
  <meta name="viewport" content="width=device-width, initial-scale=1.0">
  <meta name="aspect-ratio" content="1:1">
  <style>
    * {
      box-sizing: border-box;
      margin: 0;
      padding: 0;
    }

    body {
      font-family: system-ui, -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, sans-serif;
      color: #1e2945;
      background: transparent;
      display: flex;
      flex-direction: column;
      align-items: center;
      justify-content: space-between;
      min-height: 100%;
      padding: 12px 8px;
    }

    .visual-area {
      width: 100%;
      max-width: 420px;
      display: flex;
      flex-direction: column;
      align-items: center;
      gap: 10px;
    }

    .svg-container {
      width: 100%;
      max-width: 280px;
      height: 160px;
      display: flex;
      justify-content: center;
      align-items: center;
    }

    svg {
      width: 100%;
      height: 100%;
      overflow: visible;
    }

    .side-label {
      font-size: 15px;
      font-weight: 700;
      fill: #1e2945;
      text-anchor: middle;
      dominant-baseline: central;
    }

    .unknown-label {
      fill: #ea580c;
      font-weight: 800;
      font-size: 16px;
    }

    .badge-perimeter {
      background-color: #fff7ed;
      border: 2px solid #f97316;
      color: #c2410c;
      font-size: 14px;
      font-weight: 700;
      padding: 6px 14px;
      border-radius: 20px;
      display: inline-flex;
      align-items: center;
      gap: 6px;
      box-shadow: 0 1px 3px rgba(249, 115, 22, 0.12);
    }

    /* Equation Steps Display */
    .steps-card {
      width: 100%;
      max-width: 400px;
      background: #f8fafc;
      border: 1px solid #e2e8f0;
      border-radius: 12px;
      padding: 12px 14px;
      display: flex;
      flex-direction: column;
      gap: 8px;
      min-height: 140px;
      justify-content: center;
    }

    .step-row {
      display: flex;
      align-items: center;
      justify-content: space-between;
      padding: 6px 10px;
      border-radius: 8px;
      font-size: 15px;
      font-weight: 600;
      color: #64748b;
      background: transparent;
      transition: all 0.25s ease;
      opacity: 0.45;
    }

    .step-row.active {
      background: #ffffff;
      color: #1e2945;
      opacity: 1;
      box-shadow: 0 2px 6px rgba(0, 0, 0, 0.06);
      border-left: 4px solid #f97316;
    }

    .step-row.done {
      opacity: 0.85;
      color: #334155;
    }

    .step-tag {
      font-size: 12px;
      font-weight: 700;
      text-transform: uppercase;
      letter-spacing: 0.5px;
    }

    .step-math {
      font-family: "Cambria Math", "KaTeX_Math", "Times New Roman", serif;
      font-size: 17px;
      letter-spacing: 0.5px;
    }

    .highlight-sub {
      color: #ea580c;
      font-weight: 700;
    }

    .highlight-res {
      color: #16a34a;
      font-weight: 700;
    }

    /* Stepper Controls */
    .controls {
      display: flex;
      align-items: center;
      justify-content: center;
      gap: 6px;
      width: 100%;
      max-width: 400px;
      margin-top: 4px;
    }

    .step-btn {
      flex: 1;
      padding: 8px 4px;
      font-size: 13px;
      font-weight: 600;
      color: #475569;
      background: #f1f5f9;
      border: 1px solid #cbd5e1;
      border-radius: 8px;
      cursor: pointer;
      text-align: center;
      user-select: none;
      transition: background 0.2s, color 0.2s, box-shadow 0.2s;
    }

    .step-btn:hover {
      background: #e2e8f0;
    }

    .step-btn.active {
      background: #f97316;
      color: #ffffff;
      border-color: #f97316;
      box-shadow: 0 2px 4px rgba(249, 115, 22, 0.3);
    }

    .play-btn {
      flex: 0 0 38px;
      height: 34px;
      display: flex;
      align-items: center;
      justify-content: center;
      background: #1e2945;
      color: #ffffff;
      border: none;
      border-radius: 8px;
      cursor: pointer;
      font-size: 13px;
    }

    .play-btn:hover {
      background: #334155;
    }
  </style>
</head>
<body>

  <div class="visual-area">
    
    <div class="svg-container">
      <svg viewBox="0 0 260 140">
        
        <polygon points="130,20 25,120 235,120" 
                 fill="#fff7ed" 
                 stroke="#f97316" 
                 stroke-width="3" 
                 stroke-linejoin="round" />
        
        
        <text x="60" y="60" class="side-label">7 cm</text>
        
        
        <text x="200" y="60" class="side-label">9 cm</text>
        
        
        <rect id="baseBadge" x="98" y="106" width="64" height="26" rx="6" fill="#ffffff" stroke="#f97316" stroke-width="1.5" />
        <text id="baseLabel" x="130" y="120" class="side-label unknown-label">x cm</text>
      </svg>
    </div>

    
    <div class="badge-perimeter">
      <span>Total Perimeter = 24 cm</span>
    </div>
  </div>

  
  <div class="steps-card">
    <div class="step-row active" id="stepRow0">
      <span class="step-tag">Step 1</span>
      <span class="step-math">x + 7 + 9 = 24</span>
    </div>
    <div class="step-row" id="stepRow1">
      <span class="step-tag">Step 2</span>
      <span class="step-math">x + 16 = 24</span>
    </div>
    <div class="step-row" id="stepRow2">
      <span class="step-tag">Step 3</span>
      <span class="step-math">x + 16 <span class="highlight-sub">− 16</span> = 24 <span class="highlight-sub">− 16</span></span>
    </div>
    <div class="step-row" id="stepRow3">
      <span class="step-tag">Step 4</span>
      <span class="step-math"><span class="highlight-res">x = 8 cm</span></span>
    </div>
  </div>

  
  <div class="controls">
    <button class="play-btn" id="togglePlay" aria-label="Play/Pause">⏸</button>
    <button class="step-btn active" data-step="0">1</button>
    <button class="step-btn" data-step="1">2</button>
    <button class="step-btn" data-step="2">3</button>
    <button class="step-btn" data-step="3">4</button>
  </div>

  <script>
    const rows = [
      document.getElementById('stepRow0'),
      document.getElementById('stepRow1'),
      document.getElementById('stepRow2'),
      document.getElementById('stepRow3')
    ];
    const btns = document.querySelectorAll('.step-btn');
    const playBtn = document.getElementById('togglePlay');
    const baseLabel = document.getElementById('baseLabel');

    let currentStep = 0;
    let isPlaying = true;
    let timer = null;

    function render(step) {
      currentStep = step;
      rows.forEach((row, i) => {
        row.classList.remove('active', 'done');
        if (i === step) {
          row.classList.add('active');
        } else if (i < step) {
          row.classList.add('done');
        }
      });

      btns.forEach((btn, i) => {
        btn.classList.toggle('active', i === step);
      });

      if (step === 3) {
        baseLabel.textContent = 'x = 8 cm';
        baseLabel.style.fill = '#16a34a';
      } else {
        baseLabel.textContent = 'x cm';
        baseLabel.style.fill = '#ea580c';
      }
    }

    function nextStep() {
      const next = (currentStep + 1) % 4;
      render(next);
    }

    function startTimer() {
      stopTimer();
      timer = setInterval(nextStep, 3500);
      isPlaying = true;
      playBtn.textContent = '⏸';
    }

    function stopTimer() {
      if (timer) {
        clearInterval(timer);
        timer = null;
      }
      isPlaying = false;
      playBtn.textContent = '▶';
    }

    btns.forEach(btn => {
      btn.addEventListener('click', () => {
        const step = parseInt(btn.getAttribute('data-step'), 10);
        render(step);
        stopTimer();
      });
    });

    playBtn.addEventListener('click', () => {
      if (isPlaying) {
        stopTimer();
      } else {
        startTimer();
      }
    });

    // Initialize
    render(0);
    startTimer();
  </script>
</body>
</html>

First combine the known sides: $7 + 9 = 16\text{ cm}$. Then subtract 16 from both sides of $x + 16 = 24$ to isolate the unknown side, giving $x = 8\text{ cm}$.

Side lengths aren't the only parts of a shape that follow fixed rules. What happens when an angle is missing?

Two angles that form a straight line are called **supplementary angles**, and their measures always add up to exactly $180^\circ$.

<!DOCTYPE html>
<html lang="en">
<head>
  <meta charset="UTF-8">
  <meta name="viewport" content="width=device-width, initial-scale=1.0">
  <style>
    * { box-sizing: border-box; margin: 0; padding: 0; }
    body {
      font-family: system-ui, -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, sans-serif;
      color: #1e2945;
      background: #ffffff;
      padding: 16px;
      display: flex;
      flex-direction: column;
      align-items: center;
      justify-content: flex-start;
      min-height: 100%;
    }
    .diagram-wrap {
      width: 100%;
      max-width: 480px;
      display: flex;
      flex-direction: column;
      align-items: center;
      gap: 12px;
    }
    .svg-container {
      width: 100%;
      display: flex;
      justify-content: center;
      align-items: center;
    }
    svg {
      width: 100%;
      height: auto;
      max-height: 170px;
      display: block;
    }
    .steps-container {
      width: 100%;
      min-height: 84px;
      display: flex;
      justify-content: center;
      align-items: center;
      text-align: center;
    }
    .step-panel {
      display: none;
      width: 100%;
      flex-direction: column;
      align-items: center;
      justify-content: center;
      gap: 6px;
    }
    .step-panel.active {
      display: flex;
      animation: fadeIn 0.25s ease-out;
    }
    @keyframes fadeIn {
      from { opacity: 0; transform: translateY(3px); }
      to { opacity: 1; transform: translateY(0); }
    }
    .step-tag {
      font-size: 11px;
      font-weight: 700;
      text-transform: uppercase;
      letter-spacing: 0.5px;
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      font-weight: 600;
      display: flex;
      align-items: center;
      justify-content: center;
      gap: 6px;
      flex-wrap: wrap;
      line-height: 1.3;
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      font-size: 13px;
      color: #64748b;
      line-height: 1.4;
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      display: flex;
      align-items: center;
      justify-content: center;
      gap: 8px;
      width: 100%;
      margin-top: 4px;
    }
    .btn-step {
      background: #f1f5f9;
      border: 1px solid #cbd5e1;
      color: #475569;
      font-size: 13px;
      font-weight: 600;
      padding: 6px 14px;
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      cursor: pointer;
      transition: background-color 0.2s ease, border-color 0.2s ease, color 0.2s ease;
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    .btn-step:hover {
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      background: #6366f1;
      border-color: #6366f1;
      color: #ffffff;
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      background: #ffffff;
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      gap: 5px;
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    .btn-play:hover {
      background: #f8fafc;
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</head>
<body>
  <div class="diagram-wrap">
    <div class="svg-container">
      <svg viewBox="0 0 360 170" aria-label="Supplementary angles on a straight line">
        <defs>
          <marker id="arrow" viewBox="0 0 10 10" refX="6" refY="5" markerWidth="6" markerHeight="6" orient="auto-start-reverse">
            <path d="M 0 1.5 L 8 5 L 0 8.5 z" fill="#1e2945" />
          </marker>
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            <path d="M 0 1.5 L 8 5 L 0 8.5 z" fill="#1e2945" />
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        <path d="M 135 130 A 45 45 0 0 1 216.7 103.1" fill="none" stroke="#6366f1" stroke-width="2.5" />
        <rect x="110" y="74" width="46" height="24" rx="4" fill="#eef2ff" stroke="#c7d2fe" stroke-width="1" />
        <text x="133" y="90.5" fill="#4338ca" font-size="14" font-weight="700" text-anchor="middle">125°</text>

        
        <path d="M 232 130 A 52 52 0 0 0 209.8 87.4" fill="none" stroke="#0284c7" stroke-width="2.5" />
        <rect x="236" y="92" width="34" height="24" rx="4" fill="#e0f2fe" stroke="#bae6fd" stroke-width="1" />
        <text x="253" y="108.5" fill="#0369a1" font-size="14" font-weight="700" text-anchor="middle">a°</text>

        
        <path d="M 55 138 Q 180 158 305 138" fill="none" stroke="#94a3b8" stroke-width="1.5" stroke-dasharray="3 3" />
        <text x="180" y="160" fill="#64748b" font-size="11" font-weight="600" text-anchor="middle">Straight Angle = 180°</text>
      </svg>
    </div>

    
    <div class="steps-container">
      <div class="step-panel active" id="step-1">
        <span class="step-tag tag-1">Step 1: Set Up</span>
        <div class="math-row">
          <span class="c-blue">a</span> + <span class="c-indigo">125°</span> = 180°
        </div>
        <div class="math-sub">Supplementary angles sum to 180°</div>
      </div>

      <div class="step-panel" id="step-2">
        <span class="step-tag tag-2">Step 2: Isolate a</span>
        <div class="math-row">
          <span class="c-blue">a</span> + 125° <span class="c-red">− 125°</span> = 180° <span class="c-red">− 125°</span>
        </div>
        <div class="math-sub">Subtract 125° from both sides</div>
      </div>

      <div class="step-panel" id="step-3">
        <span class="step-tag tag-3">Step 3: Solution</span>
        <div class="math-row">
          <span class="c-blue">a</span> = <span class="c-green">55°</span>
        </div>
        <div class="math-sub">Check: 55° + 125° = 180° ✓</div>
      </div>
    </div>

    
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      <button class="btn-step active" onclick="goToStep(0)">1</button>
      <button class="btn-step" onclick="goToStep(1)">2</button>
      <button class="btn-step" onclick="goToStep(2)">3</button>
      <button class="btn-play" id="playBtn" onclick="togglePlay()">
        <span id="playIcon">⏸</span> Pause
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  </div>

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      playBtn.lastChild.textContent = ' Pause';
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</body>
</html>

You can always verify your solution by plugging your answer back into the diagram: $55^\circ + 125^\circ = 180^\circ$, confirming the straight line is complete.

math

Solving One-Step Equations in Geometric Contexts. Model and solve one-step equations that represent geometric problems like finding missing dimensions

Finding a Missing Side Length When Given Area

6th Grade Unit: Area, Surface Area, and Equations

Area and Perimeter: Find the Missing Side Length

Teaching one-step equations within geometric contexts bridges algebraic reasoning with spatial intuition (TEKS 6.10A / 6.1A). Employ a Concrete-Representational-Abstract (CRA) instructional progression: begin by using unit tiles and tape diagrams to represent total area or perimeter, transition to labeled 2D/3D geometric sketches, and finally formulate formal algebraic equations ($ax = b$ or $x + a = b$). Emphasize that isolating the variable via inverse operations mathematically answers the question 'what dimension multiplied by or added to the known measure gives the whole figure?' Ensure students consistently append correct linear units to their final answers and perform verification checks.

Solving One-Step Equations in Geometric Contexts

Area of Rectangles

Perimeter and Missing Sides