<!DOCTYPE html>
<html lang="en">
<head>
  <meta charset="UTF-8">
  <meta name="viewport" content="width=device-width, initial-scale=1.0">
  <title>Factor Pairs of 36</title>
  <style>
    * { box-sizing: border-box; margin: 0; padding: 0; }
    body {
      font-family: system-ui, -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, sans-serif;
      color: #0f172a;
      background: transparent;
      padding: 12px 8px;
      display: flex;
      flex-direction: column;
      align-items: center;
      justify-content: flex-start;
      gap: 10px;
      min-height: 100%;
      user-select: none;
    }

    .header-badge {
      font-size: 15px;
      font-weight: 700;
      color: #1e293b;
      background: #f1f5f9;
      border: 1px solid #e2e8f0;
      padding: 4px 14px;
      border-radius: 20px;
      text-align: center;
    }

    /* Rainbow Section */
    .rainbow-area {
      width: 100%;
      max-width: 480px;
      height: 115px;
      position: relative;
      display: flex;
      flex-direction: column;
      justify-content: flex-end;
      align-items: center;
    }

    .rainbow-svg {
      position: absolute;
      top: 0;
      left: 0;
      width: 100%;
      height: calc(100% - 14px);
      overflow: visible;
      pointer-events: none;
    }

    .rainbow-arc {
      fill: none;
      stroke-width: 3.5;
      stroke-linecap: round;
      opacity: 0;
      transition: stroke-dashoffset 0.65s cubic-bezier(0.4, 0, 0.2, 1), opacity 0.25s ease;
    }

    .rainbow-arc.active {
      opacity: 1;
    }

    .factor-axis {
      width: 100%;
      display: grid;
      grid-template-columns: repeat(9, 1fr);
      justify-items: center;
      align-items: center;
      z-index: 2;
    }

    .factor-pill {
      width: 28px;
      height: 28px;
      border-radius: 50%;
      background: #f8fafc;
      border: 1.5px solid #cbd5e1;
      color: #94a3b8;
      font-size: 12px;
      font-weight: 700;
      display: flex;
      align-items: center;
      justify-content: center;
      transition: background-color 0.3s ease, border-color 0.3s ease, color 0.3s ease;
    }

    .factor-pill.revealed {
      color: #ffffff;
      border-color: transparent;
    }

    .factor-pill.pill-p1.revealed { background: #ef4444; }
    .factor-pill.pill-p2.revealed { background: #f97316; }
    .factor-pill.pill-p3.revealed { background: #10b981; }
    .factor-pill.pill-p4.revealed { background: #0284c7; }
    .factor-pill.pill-p6.revealed { background: #7c3aed; }

    /* T-Chart Section */
    .tchart-box {
      width: 100%;
      max-width: 480px;
      background: #ffffff;
      border: 1px solid #cbd5e1;
      border-radius: 10px;
      overflow: hidden;
    }

    .tchart-head {
      display: grid;
      grid-template-columns: 68px 1fr;
      background: #f1f5f9;
      border-bottom: 1px solid #cbd5e1;
      font-weight: 700;
      font-size: 12px;
      color: #475569;
      text-transform: uppercase;
      letter-spacing: 0.5px;
      padding: 6px 10px;
    }

    .tchart-body {
      display: flex;
      flex-direction: column;
    }

    .tchart-row {
      display: none;
      grid-template-columns: 68px 1fr;
      align-items: center;
      padding: 6px 10px;
      border-bottom: 1px solid #f1f5f9;
      font-size: 13.5px;
      animation: rowFadeIn 0.25s ease forwards;
    }

    @keyframes rowFadeIn {
      from { opacity: 0; background-color: #f8fafc; }
      to { opacity: 1; }
    }

    .tchart-row:last-child {
      border-bottom: none;
    }

    .tchart-row.revealed-step {
      display: grid;
      background: #ffffff;
    }

    .tchart-row.current-step {
      background: #f0f7ff;
      border-left: 3px solid #2563eb;
      padding-left: 7px;
    }

    .test-cell {
      font-weight: 700;
      color: #334155;
      font-size: 13px;
    }

    .pair-cell {
      display: flex;
      align-items: center;
      flex-wrap: wrap;
      gap: 4px 6px;
      font-variant-numeric: tabular-nums;
    }

    .equation-text {
      white-space: nowrap;
      font-weight: 600;
      color: #0f172a;
    }

    .status-tag {
      display: inline-flex;
      align-items: center;
      justify-content: center;
      width: 18px;
      height: 18px;
      border-radius: 50%;
      font-size: 11px;
      font-weight: 800;
      flex-shrink: 0;
    }

    .tag-yes { background: #dcfce7; color: #15803d; }
    .tag-no { background: #fee2e2; color: #b91c1c; }

    .stop-badge {
      background: #ede9fe;
      color: #6d28d9;
      border: 1px solid #ddd6fe;
      font-size: 11px;
      font-weight: 700;
      padding: 2px 7px;
      border-radius: 8px;
      white-space: nowrap;
    }

    /* Controls */
    .controls {
      display: flex;
      align-items: center;
      justify-content: center;
      gap: 6px;
      margin-top: 2px;
    }

    .btn {
      background: #ffffff;
      border: 1px solid #cbd5e1;
      color: #334155;
      padding: 6px 14px;
      border-radius: 8px;
      font-size: 13px;
      font-weight: 600;
      cursor: pointer;
      display: flex;
      align-items: center;
      justify-content: center;
      min-width: 36px;
      height: 32px;
      transition: background-color 0.15s ease, border-color 0.15s ease;
    }

    .btn:active { background: #f1f5f9; }

    .step-dots {
      display: flex;
      gap: 4px;
    }

    .dot {
      width: 28px;
      height: 28px;
      border-radius: 6px;
      background: #f8fafc;
      border: 1px solid #cbd5e1;
      font-size: 12px;
      font-weight: 700;
      color: #475569;
      display: flex;
      align-items: center;
      justify-content: center;
      cursor: pointer;
      transition: background-color 0.2s, border-color 0.2s, color 0.2s;
    }

    .dot.active {
      background: #2563eb;
      border-color: #2563eb;
      color: #ffffff;
    }

    @media (max-width: 380px) {
      .factor-pill {
        width: 24px;
        height: 24px;
        font-size: 11px;
      }
      .tchart-head, .tchart-row {
        grid-template-columns: 58px 1fr;
        padding: 5px 8px;
      }
      .stop-badge {
        font-size: 10px;
        padding: 1px 5px;
      }
    }
  </style>
</head>
<body>

  <div class="header-badge">Factor Pairs & Rainbow for 36</div>

  
  <div class="rainbow-area">
    <svg class="rainbow-svg" viewBox="0 0 900 100" preserveAspectRatio="none">
      
      <path id="arc-1" class="rainbow-arc" d="M 50 98 A 400 86 0 0 1 850 98" stroke="#ef4444" />
      
      <path id="arc-2" class="rainbow-arc" d="M 150 98 A 300 68 0 0 1 750 98" stroke="#f97316" />
      
      <path id="arc-3" class="rainbow-arc" d="M 250 98 A 200 50 0 0 1 650 98" stroke="#10b981" />
      
      <path id="arc-4" class="rainbow-arc" d="M 350 98 A 100 32 0 0 1 550 98" stroke="#0284c7" />
      
      <path id="arc-6" class="rainbow-arc" d="M 436 98 C 436 68 464 68 464 98" stroke="#7c3aed" />
    </svg>

    <div class="factor-axis">
      <div class="factor-pill pill-p1" id="pill-1">1</div>
      <div class="factor-pill pill-p2" id="pill-2">2</div>
      <div class="factor-pill pill-p3" id="pill-3">3</div>
      <div class="factor-pill pill-p4" id="pill-4">4</div>
      <div class="factor-pill pill-p6" id="pill-6">6</div>
      <div class="factor-pill pill-p4" id="pill-9">9</div>
      <div class="factor-pill pill-p3" id="pill-12">12</div>
      <div class="factor-pill pill-p2" id="pill-18">18</div>
      <div class="factor-pill pill-p1" id="pill-36">36</div>
    </div>
  </div>

  
  <div class="tchart-box">
    <div class="tchart-head">
      <div>Test</div>
      <div>Factor Pair Result</div>
    </div>
    <div class="tchart-body">
      <div class="tchart-row" id="row-1">
        <div class="test-cell">Test 1</div>
        <div class="pair-cell">
          <span class="status-tag tag-yes">✓</span>
          <span class="equation-text">1 × 36 = 36</span>
        </div>
      </div>
      <div class="tchart-row" id="row-2">
        <div class="test-cell">Test 2</div>
        <div class="pair-cell">
          <span class="status-tag tag-yes">✓</span>
          <span class="equation-text">2 × 18 = 36</span>
        </div>
      </div>
      <div class="tchart-row" id="row-3">
        <div class="test-cell">Test 3</div>
        <div class="pair-cell">
          <span class="status-tag tag-yes">✓</span>
          <span class="equation-text">3 × 12 = 36</span>
        </div>
      </div>
      <div class="tchart-row" id="row-4">
        <div class="test-cell">Test 4</div>
        <div class="pair-cell">
          <span class="status-tag tag-yes">✓</span>
          <span class="equation-text">4 × 9 = 36</span>
        </div>
      </div>
      <div class="tchart-row" id="row-5">
        <div class="test-cell">Test 5</div>
        <div class="pair-cell">
          <span class="status-tag tag-no">✕</span>
          <span class="equation-text" style="color: #475569;">36 ÷ 5 = 7 R 1</span>
        </div>
      </div>
      <div class="tchart-row" id="row-6">
        <div class="test-cell">Test 6</div>
        <div class="pair-cell">
          <span class="status-tag tag-yes">✓</span>
          <span class="equation-text">6 × 6 = 36</span>
          <span class="stop-badge">STOP: Factors met in the middle!</span>
        </div>
      </div>
    </div>
  </div>

  
  <div class="controls">
    <button class="btn" id="btnPrev" title="Previous Step">←</button>
    <div class="step-dots">
      <div class="dot active" data-step="1">1</div>
      <div class="dot" data-step="2">2</div>
      <div class="dot" data-step="3">3</div>
      <div class="dot" data-step="4">4</div>
      <div class="dot" data-step="5">5</div>
      <div class="dot" data-step="6">6</div>
    </div>
    <button class="btn" id="btnNext" title="Next Step">→</button>
    <button class="btn" id="btnPlay" title="Auto Play">▶</button>
  </div>

  <script>
    const stepData = [
      { step: 1, pills: ['pill-1', 'pill-36'], arc: 'arc-1' },
      { step: 2, pills: ['pill-2', 'pill-18'], arc: 'arc-2' },
      { step: 3, pills: ['pill-3', 'pill-12'], arc: 'arc-3' },
      { step: 4, pills: ['pill-4', 'pill-9'], arc: 'arc-4' },
      { step: 5, pills: [], arc: null },
      { step: 6, pills: ['pill-6'], arc: 'arc-6' }
    ];

    const arcLengths = {};
    document.querySelectorAll('.rainbow-arc').forEach(arc => {
      const len = arc.getTotalLength();
      arcLengths[arc.id] = len;
      arc.style.strokeDasharray = len;
      arc.style.strokeDashoffset = len;
    });

    let currentStep = 1;
    let timer = null;

    function render(step) {
      currentStep = step;

      // Update Step Dots
      document.querySelectorAll('.dot').forEach(d => {
        const s = parseInt(d.getAttribute('data-step'), 10);
        d.classList.toggle('active', s === step);
      });

      // Update T-Chart Rows (Hide future steps completely to prevent low-contrast defects)
      for (let i = 1; i <= 6; i++) {
        const row = document.getElementById(`row-${i}`);
        row.classList.toggle('revealed-step', i <= step);
        row.classList.toggle('current-step', i === step);
      }

      // Collect revealed factor pills and active arcs
      const activePills = new Set();
      const activeArcs = new Set();

      for (let i = 0; i < step; i++) {
        stepData[i].pills.forEach(p => activePills.add(p));
        if (stepData[i].arc) activeArcs.add(stepData[i].arc);
      }

      // Update Pills
      ['pill-1', 'pill-2', 'pill-3', 'pill-4', 'pill-6', 'pill-9', 'pill-12', 'pill-18', 'pill-36'].forEach(id => {
        document.getElementById(id).classList.toggle('revealed', activePills.has(id));
      });

      // Update Arcs with accurate dash offsets
      ['arc-1', 'arc-2', 'arc-3', 'arc-4', 'arc-6'].forEach(id => {
        const el = document.getElementById(id);
        const isActive = activeArcs.has(id);
        el.classList.toggle('active', isActive);
        el.style.strokeDashoffset = isActive ? '0' : arcLengths[id];
      });
    }

    function setStep(s) {
      if (s < 1) s = 1;
      if (s > 6) s = 6;
      render(s);
    }

    function togglePlay() {
      const btn = document.getElementById('btnPlay');
      if (timer) {
        clearInterval(timer);
        timer = null;
        btn.textContent = '▶';
      } else {
        btn.textContent = '⏸';
        if (currentStep >= 6) render(1);
        timer = setInterval(() => {
          if (currentStep < 6) {
            render(currentStep + 1);
          } else {
            clearInterval(timer);
            timer = null;
            btn.textContent = '▶';
          }
        }, 2000);
      }
    }

    document.getElementById('btnPrev').addEventListener('click', () => {
      if (timer) togglePlay();
      setStep(currentStep - 1);
    });

    document.getElementById('btnNext').addEventListener('click', () => {
      if (timer) togglePlay();
      setStep(currentStep + 1);
    });

    document.getElementById('btnPlay').addEventListener('click', togglePlay);

    document.querySelectorAll('.dot').forEach(d => {
      d.addEventListener('click', () => {
        if (timer) togglePlay();
        setStep(parseInt(d.getAttribute('data-step'), 10));
      });
    });

    // Initial render
    render(1);
  </script>
</body>
</html>

Finding All Factor Pairs of Numbers to 100

<!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="4:3">
  <style>
    * { box-sizing: border-box; margin: 0; padding: 0; }
    body {
      font-family: system-ui, -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, sans-serif;
      background: #faf8f5;
      color: #3e2723;
      display: flex;
      flex-direction: column;
      align-items: center;
      justify-content: space-between;
      min-height: 100%;
      padding: 12px;
      user-select: none;
    }

    /* Tabs */
    .tabs {
      display: flex;
      flex-wrap: wrap;
      gap: 6px;
      justify-content: center;
      width: 100%;
      max-width: 480px;
    }
    .tab-btn {
      flex: 1 1 calc(25% - 6px);
      min-width: 72px;
      padding: 8px 4px;
      font-size: 14px;
      font-weight: 700;
      color: #6d4c41;
      background: #efebe9;
      border: 2px solid transparent;
      border-radius: 8px;
      cursor: pointer;
      text-align: center;
      transition: all 0.2s ease;
    }
    .tab-btn.active {
      background: #fff;
      color: #3e2723;
      border-color: #d97706;
      box-shadow: 0 2px 6px rgba(217, 119, 6, 0.2);
    }

    /* Equation Display */
    .equation-badge {
      font-size: 22px;
      font-weight: 800;
      color: #451a03;
      background: #fef3c7;
      border: 1px solid #fde68a;
      border-radius: 20px;
      padding: 4px 18px;
      display: flex;
      align-items: center;
      gap: 8px;
      box-shadow: 0 1px 3px rgba(0,0,0,0.05);
    }
    .equation-badge span.total {
      color: #b45309;
    }

    /* Grid Stage Container */
    .stage {
      position: relative;
      width: 100%;
      max-width: 460px;
      height: 230px;
      display: flex;
      align-items: center;
      justify-content: center;
      background: #ffffff;
      border-radius: 12px;
      border: 1px solid #e7e5e4;
      box-shadow: inset 0 2px 4px rgba(0,0,0,0.02);
    }

    .grid-wrapper {
      position: relative;
      display: inline-flex;
      align-items: center;
      justify-content: center;
    }

    /* Dimension Labels */
    .dim-top {
      position: absolute;
      top: -24px;
      left: 0;
      right: 0;
      text-align: center;
      font-size: 13px;
      font-weight: 700;
      color: #b45309;
      display: flex;
      align-items: center;
      justify-content: center;
      gap: 4px;
    }
    .dim-top::before, .dim-top::after {
      content: '';
      flex: 1;
      height: 1px;
      background: #f59e0b;
      max-width: 40px;
    }

    .dim-left {
      position: absolute;
      left: -28px;
      top: 0;
      bottom: 0;
      display: flex;
      flex-direction: column;
      align-items: center;
      justify-content: center;
      font-size: 13px;
      font-weight: 700;
      color: #b45309;
      gap: 4px;
    }
    .dim-left::before, .dim-left::after {
      content: '';
      flex: 1;
      width: 1px;
      background: #f59e0b;
      max-height: 30px;
    }

    /* Brownie Grid */
    .brownie-grid {
      display: grid;
      gap: 2px;
      background: #3e2723;
      padding: 4px;
      border-radius: 6px;
      box-shadow: 0 4px 10px rgba(62, 39, 35, 0.25);
      transition: all 0.3s ease;
    }

    .brownie-tile {
      background: linear-gradient(135deg, #6d4c41 0%, #4e342e 100%);
      border-radius: 2px;
      box-shadow: inset 1px 1px 1px rgba(255, 255, 255, 0.15), inset -1px -1px 1px rgba(0, 0, 0, 0.3);
      position: relative;
    }
    .brownie-tile::after {
      content: '';
      position: absolute;
      top: 25%;
      left: 25%;
      width: 50%;
      height: 50%;
      background: radial-gradient(circle, rgba(217, 119, 6, 0.3) 0%, transparent 70%);
      pointer-events: none;
    }
  </style>
</head>
<body>

  <div class="tabs">
    <button class="tab-btn active" onclick="setGrid(0)">1 × 24</button>
    <button class="tab-btn" onclick="setGrid(1)">2 × 12</button>
    <button class="tab-btn" onclick="setGrid(2)">3 × 8</button>
    <button class="tab-btn" onclick="setGrid(3)">4 × 6</button>
  </div>

  <div class="equation-badge" id="equation">
    1 × 24 = <span class="total">24</span>
  </div>

  <div class="stage">
    <div class="grid-wrapper">
      <div class="dim-top" id="labelCols">24</div>
      <div class="dim-left" id="labelRows">1</div>
      <div class="brownie-grid" id="grid"></div>
    </div>
  </div>

  <script>
    const configs = [
      { r: 1, c: 24, size: 11, gap: 1.5 },
      { r: 2, c: 12, size: 22, gap: 2 },
      { r: 3, c: 8,  size: 30, gap: 2.5 },
      { r: 4, c: 6,  size: 36, gap: 3 }
    ];

    let currentIndex = 0;

    function setGrid(index) {
      currentIndex = index;
      const config = configs[index];
      
      // Update Tabs
      const btns = document.querySelectorAll('.tab-btn');
      btns.forEach((btn, i) => {
        btn.classList.toggle('active', i === index);
      });

      // Update Equation & Dimension labels
      document.getElementById('equation').innerHTML = `${config.r} × ${config.c} = <span class="total">24</span>`;
      document.getElementById('labelRows').textContent = config.r;
      document.getElementById('labelCols').textContent = config.c;

      // Render Grid
      const grid = document.getElementById('grid');
      grid.style.gridTemplateRows = `repeat(${config.r}, ${config.size}px)`;
      grid.style.gridTemplateColumns = `repeat(${config.c}, ${config.size}px)`;
      grid.style.gap = `${config.gap}px`;
      
      grid.innerHTML = '';
      for (let i = 0; i < 24; i++) {
        const tile = document.createElement('div');
        tile.className = 'brownie-tile';
        tile.style.width = `${config.size}px`;
        tile.style.height = `${config.size}px`;
        grid.appendChild(tile);
      }
    }

    // Initialize with 4x6 as default appetizing square view
    setGrid(3);
  </script>
</body>
</html>

<!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="4:3">
  <title>Factor Rainbow of 24</title>
  <style>
    * {
      box-sizing: border-box;
      margin: 0;
      padding: 0;
      user-select: none;
      -webkit-user-select: none;
    }

    body {
      font-family: system-ui, -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, sans-serif;
      background: #ffffff;
      color: #1e2945;
      display: flex;
      flex-direction: column;
      align-items: center;
      justify-content: space-between;
      width: 100%;
      min-height: 100%;
      padding: 12px 16px;
    }

    header {
      text-align: center;
      margin-bottom: 4px;
    }

    h1 {
      font-size: 19px;
      font-weight: 800;
      color: #1e2945;
      letter-spacing: -0.01em;
    }

    .svg-container {
      width: 100%;
      max-width: 580px;
      flex-grow: 1;
      display: flex;
      align-items: center;
      justify-content: center;
    }

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

    /* Pair groups transition */
    .pair-group {
      cursor: pointer;
      transition: opacity 0.25s ease, filter 0.25s ease;
    }

    .pair-arch {
      fill: none;
      stroke-linecap: round;
      transition: stroke-width 0.25s ease;
    }

    /* Touch-friendly invisible stroke for easier tapping */
    .hit-area {
      fill: none;
      stroke: transparent;
      stroke-width: 24px;
      cursor: pointer;
    }

    .equation-pill {
      rx: 11;
      ry: 11;
      stroke-width: 1.5;
    }

    .equation-text {
      font-size: 11.5px;
      font-weight: 700;
      text-anchor: middle;
      dominant-baseline: central;
      pointer-events: none;
    }

    .factor-circle {
      stroke-width: 2.5;
      transition: stroke-width 0.25s ease;
    }

    .factor-text {
      font-size: 14px;
      font-weight: 800;
      text-anchor: middle;
      dominant-baseline: central;
      pointer-events: none;
    }

    /* Dimmed / Active states */
    .dimmed {
      opacity: 0.16;
      filter: grayscale(40%);
    }

    .active .pair-arch {
      stroke-width: 7px;
    }

    .active .factor-circle {
      stroke-width: 3.5px;
    }

    /* Controls Bar */
    .controls {
      display: flex;
      flex-wrap: wrap;
      justify-content: center;
      gap: 6px;
      margin-top: 4px;
      width: 100%;
      max-width: 580px;
    }

    .btn {
      appearance: none;
      background: #f8fafc;
      border: 1.5px solid #e2e8f0;
      border-radius: 20px;
      padding: 6px 12px;
      font-size: 13px;
      font-weight: 700;
      color: #475569;
      cursor: pointer;
      transition: all 0.2s ease;
    }

    .btn:active {
      opacity: 0.8;
    }

    .btn.active-all {
      background: #1e2945;
      color: #ffffff;
      border-color: #1e2945;
    }

    .btn.active-p0 {
      background: #ffe4e6;
      color: #e11d48;
      border-color: #e11d48;
    }

    .btn.active-p1 {
      background: #ffedd5;
      color: #ea580c;
      border-color: #ea580c;
    }

    .btn.active-p2 {
      background: #dcfce7;
      color: #16a34a;
      border-color: #16a34a;
    }

    .btn.active-p3 {
      background: #dbeafe;
      color: #2563eb;
      border-color: #2563eb;
    }
  </style>
</head>
<body>

  <header>
    <h1>Factor Rainbow: 24</h1>
  </header>

  <div class="svg-container">
    <svg viewBox="0 0 600 300" aria-label="Factor Rainbow of 24 diagram">
      
      <g class="pair-group" data-pair="0" id="pair0">
        <path class="hit-area" d="M 50 252 A 250 196 0 0 1 550 252" />
        <path class="pair-arch" d="M 50 252 A 250 196 0 0 1 550 252" stroke="#e11d48" stroke-width="4.5" />
        
        
        <rect class="equation-pill" x="256" y="44" width="88" height="24" fill="#fff1f2" stroke="#e11d48" />
        <text class="equation-text" x="300" y="56" fill="#e11d48">1 × 24 = 24</text>
        
        
        <circle class="factor-circle" cx="50" cy="270" r="17" fill="#fff1f2" stroke="#e11d48" />
        <text class="factor-text" x="50" y="270" fill="#e11d48">1</text>
        
        
        <circle class="factor-circle" cx="550" cy="270" r="17" fill="#fff1f2" stroke="#e11d48" />
        <text class="factor-text" x="550" y="270" fill="#e11d48">24</text>
      </g>

      
      <g class="pair-group" data-pair="1" id="pair1">
        <path class="hit-area" d="M 118 252 A 182 144 0 0 1 482 252" />
        <path class="pair-arch" d="M 118 252 A 182 144 0 0 1 482 252" stroke="#ea580c" stroke-width="4.5" />
        
        
        <rect class="equation-pill" x="256" y="96" width="88" height="24" fill="#fff7ed" stroke="#ea580c" />
        <text class="equation-text" x="300" y="108" fill="#ea580c">2 × 12 = 24</text>
        
        
        <circle class="factor-circle" cx="118" cy="270" r="17" fill="#fff7ed" stroke="#ea580c" />
        <text class="factor-text" x="118" y="270" fill="#ea580c">2</text>
        
        
        <circle class="factor-circle" cx="482" cy="270" r="17" fill="#fff7ed" stroke="#ea580c" />
        <text class="factor-text" x="482" y="270" fill="#ea580c">12</text>
      </g>

      
      <g class="pair-group" data-pair="2" id="pair2">
        <path class="hit-area" d="M 186 252 A 114 92 0 0 1 414 252" />
        <path class="pair-arch" d="M 186 252 A 114 92 0 0 1 414 252" stroke="#16a34a" stroke-width="4.5" />
        
        
        <rect class="equation-pill" x="260" y="148" width="80" height="24" fill="#f0fdf4" stroke="#16a34a" />
        <text class="equation-text" x="300" y="160" fill="#16a34a">3 × 8 = 24</text>
        
        
        <circle class="factor-circle" cx="186" cy="270" r="17" fill="#f0fdf4" stroke="#16a34a" />
        <text class="factor-text" x="186" y="270" fill="#16a34a">3</text>
        
        
        <circle class="factor-circle" cx="414" cy="270" r="17" fill="#f0fdf4" stroke="#16a34a" />
        <text class="factor-text" x="414" y="270" fill="#16a34a">8</text>
      </g>

      
      <g class="pair-group" data-pair="3" id="pair3">
        <path class="hit-area" d="M 254 252 A 46 40 0 0 1 346 252" />
        <path class="pair-arch" d="M 254 252 A 46 40 0 0 1 346 252" stroke="#2563eb" stroke-width="4.5" />
        
        
        <rect class="equation-pill" x="260" y="200" width="80" height="24" fill="#eff6ff" stroke="#2563eb" />
        <text class="equation-text" x="300" y="212" fill="#2563eb">4 × 6 = 24</text>
        
        
        <circle class="factor-circle" cx="254" cy="270" r="17" fill="#eff6ff" stroke="#2563eb" />
        <text class="factor-text" x="254" y="270" fill="#2563eb">4</text>
        
        
        <circle class="factor-circle" cx="346" cy="270" r="17" fill="#eff6ff" stroke="#2563eb" />
        <text class="factor-text" x="346" y="270" fill="#2563eb">6</text>
      </g>
    </svg>
  </div>

  <div class="controls">
    <button class="btn active-all" id="btn-all" onclick="selectPair(null)">All Pairs</button>
    <button class="btn" id="btn-0" onclick="selectPair(0)">1 × 24</button>
    <button class="btn" id="btn-1" onclick="selectPair(1)">2 × 12</button>
    <button class="btn" id="btn-2" onclick="selectPair(2)">3 × 8</button>
    <button class="btn" id="btn-3" onclick="selectPair(3)">4 × 6</button>
  </div>

  <script>
    let selectedPair = null;
    const pairGroups = document.querySelectorAll('.pair-group');
    const buttons = [
      document.getElementById('btn-0'),
      document.getElementById('btn-1'),
      document.getElementById('btn-2'),
      document.getElementById('btn-3')
    ];
    const btnAll = document.getElementById('btn-all');

    function selectPair(idx) {
      if (selectedPair === idx) {
        selectedPair = null;
      } else {
        selectedPair = idx;
      }
      updateView();
    }

    function updateView() {
      // Update SVG elements
      pairGroups.forEach((group, index) => {
        if (selectedPair === null) {
          group.classList.remove('dimmed', 'active');
        } else if (index === selectedPair) {
          group.classList.remove('dimmed');
          group.classList.add('active');
        } else {
          group.classList.add('dimmed');
          group.classList.remove('active');
        }
      });

      // Update buttons
      btnAll.className = selectedPair === null ? 'btn active-all' : 'btn';
      buttons.forEach((btn, index) => {
        btn.className = 'btn';
        if (selectedPair === index) {
          btn.classList.add('active-p' + index);
        }
      });
    }

    // Attach click listeners to SVG groups
    pairGroups.forEach((group) => {
      const pairIndex = parseInt(group.getAttribute('data-pair'), 10);
      group.addEventListener('click', () => selectPair(pairIndex));
    });
  </script>
</body>
</html>

<!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="4:3">
  <style>
    * {
      box-sizing: border-box;
      margin: 0;
      padding: 0;
      font-family: system-ui, -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, sans-serif;
    }

    body {
      width: 100%;
      background: transparent;
      color: #1e2945;
      display: flex;
      flex-direction: column;
      align-items: center;
      justify-content: center;
      padding: 8px 12px;
    }

    .svg-container {
      width: 100%;
      max-width: 580px;
      height: auto;
      display: block;
    }

    /* Branch lines */
    .branch {
      stroke: #cbd5e1;
      stroke-width: 2.5;
      stroke-linecap: round;
    }

    /* Composite Number Node */
    .node-comp {
      fill: #f1f5f9;
      stroke: #94a3b8;
      stroke-width: 2;
    }

    .node-comp-root {
      fill: #e0f2fe;
      stroke: #0284c7;
      stroke-width: 2;
    }

    /* Prime Number Node (End of branch) */
    .node-prime {
      fill: #16a34a;
      stroke: #15803d;
      stroke-width: 2;
      filter: drop-shadow(0 2px 4px rgba(22, 163, 74, 0.25));
      transition: transform 0.2s ease, filter 0.2s ease;
      cursor: pointer;
    }

    .node-prime:hover {
      filter: drop-shadow(0 0 8px #22c55e);
    }

    /* Typography */
    .text-num {
      font-size: 15px;
      font-weight: 700;
      text-anchor: middle;
      dominant-baseline: central;
      pointer-events: none;
    }

    .text-comp {
      fill: #1e2945;
    }

    .text-prime {
      fill: #ffffff;
    }

    .tree-title {
      font-size: 13px;
      font-weight: 700;
      fill: #64748b;
      text-anchor: middle;
      letter-spacing: 0.5px;
    }

    /* Bottom summary box */
    .summary-card {
      fill: #f0fdf4;
      stroke: #86efac;
      stroke-width: 1.5;
      rx: 10px;
    }

    .summary-text {
      font-size: 15px;
      font-weight: 700;
      fill: #15803d;
      text-anchor: middle;
      dominant-baseline: central;
    }

    .prime-pill {
      fill: #16a34a;
      rx: 6px;
    }

    .pill-text {
      font-size: 14px;
      font-weight: 800;
      fill: #ffffff;
      text-anchor: middle;
      dominant-baseline: central;
    }

    .mult-sym {
      font-size: 16px;
      font-weight: 700;
      fill: #15803d;
      text-anchor: middle;
      dominant-baseline: central;
    }
  </style>
</head>
<body>

  <svg class="svg-container" viewBox="0 0 540 370" xmlns="http://www.w3.org/2000/svg">
    
    <text x="135" y="20" class="tree-title">START: 2 × 12</text>

    
    <text x="405" y="20" class="tree-title">START: 3 × 8</text>

    
    <line x1="270" y1="15" x2="270" y2="280" stroke="#e2e8f0" stroke-width="1.5" stroke-dasharray="4 4" />

    
    
    <line x1="135" y1="45" x2="80" y2="100" class="branch" />
    <line x1="135" y1="45" x2="190" y2="100" class="branch" />

    <line x1="190" y1="100" x2="145" y2="160" class="branch" />
    <line x1="190" y1="100" x2="235" y2="160" class="branch" />

    <line x1="235" y1="160" x2="195" y2="225" class="branch" />
    <line x1="235" y1="160" x2="255" y2="225" class="branch" />

    
    
    <circle cx="135" cy="45" r="17" class="node-comp-root" />
    <text x="135" y="45" class="text-num text-comp">24</text>

    
    <circle cx="80" cy="100" r="16" class="node-prime" />
    <text x="80" y="100" class="text-num text-prime">2</text>

    <circle cx="190" cy="100" r="16" class="node-comp" />
    <text x="190" y="100" class="text-num text-comp">12</text>

    
    <circle cx="145" cy="160" r="16" class="node-prime" />
    <text x="145" y="160" class="text-num text-prime">2</text>

    <circle cx="235" cy="160" r="16" class="node-comp" />
    <text x="235" y="160" class="text-num text-comp">6</text>

    
    <circle cx="195" cy="225" r="16" class="node-prime" />
    <text x="195" y="225" class="text-num text-prime">2</text>

    <circle cx="255" cy="225" r="16" class="node-prime" />
    <text x="255" y="225" class="text-num text-prime">3</text>


    
    
    <line x1="405" y1="45" x2="350" y2="100" class="branch" />
    <line x1="405" y1="45" x2="460" y2="100" class="branch" />

    <line x1="460" y1="100" x2="415" y2="160" class="branch" />
    <line x1="460" y1="100" x2="505" y2="160" class="branch" />

    <line x1="505" y1="160" x2="475" y2="225" class="branch" />
    <line x1="505" y1="160" x2="525" y2="225" class="branch" />

    
    
    <circle cx="405" cy="45" r="17" class="node-comp-root" />
    <text x="405" y="45" class="text-num text-comp">24</text>

    
    <circle cx="350" cy="100" r="16" class="node-prime" />
    <text x="350" y="100" class="text-num text-prime">3</text>

    <circle cx="460" cy="100" r="16" class="node-comp" />
    <text x="460" y="100" class="text-num text-comp">8</text>

    
    <circle cx="415" cy="160" r="16" class="node-prime" />
    <text x="415" y="160" class="text-num text-prime">2</text>

    <circle cx="505" cy="160" r="16" class="node-comp" />
    <text x="505" y="160" class="text-num text-comp">4</text>

    
    <circle cx="475" cy="225" r="16" class="node-prime" />
    <text x="475" y="225" class="text-num text-prime">2</text>

    <circle cx="525" cy="225" r="16" class="node-prime" />
    <text x="525" y="225" class="text-num text-prime">2</text>


    
    <rect x="70" y="295" width="400" height="58" class="summary-card" />

    
    <g transform="translate(140, 324)">
      
      <rect x="0" y="-12" width="24" height="24" class="prime-pill" />
      <text x="12" y="0" class="pill-text">2</text>

      <text x="35" y="0" class="mult-sym">×</text>

      
      <rect x="46" y="-12" width="24" height="24" class="prime-pill" />
      <text x="58" y="0" class="pill-text">2</text>

      <text x="81" y="0" class="mult-sym">×</text>

      
      <rect x="92" y="-12" width="24" height="24" class="prime-pill" />
      <text x="104" y="0" class="pill-text">2</text>

      <text x="127" y="0" class="mult-sym">×</text>

      
      <rect x="138" y="-12" width="24" height="24" class="prime-pill" />
      <text x="150" y="0" class="pill-text">3</text>

      <text x="180" y="0" class="mult-sym">=</text>
      <text x="212" y="0" class="summary-text" style="font-size: 18px;">24</text>
    </g>
  </svg>

</body>
</html>

Breaking Down Numbers with Factor Trees

<!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;
      background: #ffffff;
      color: #1e2945;
      display: flex;
      flex-direction: column;
      align-items: center;
      justify-content: space-between;
      padding: 12px;
      min-height: 100%;
      user-select: none;
    }

    .controls-top {
      display: flex;
      align-items: center;
      justify-content: space-between;
      width: 100%;
      max-width: 440px;
      gap: 8px;
    }

    .step-pills {
      display: flex;
      gap: 6px;
    }

    .pill {
      font-size: 12px;
      font-weight: 700;
      padding: 4px 10px;
      border-radius: 999px;
      background: #f1f5f9;
      color: #64748b;
      cursor: pointer;
      border: 1px solid transparent;
      transition: all 0.2s ease;
    }

    .pill.active {
      background: #e0f2fe;
      color: #0284c7;
      border-color: #38bdf8;
    }

    .toggle-group {
      display: flex;
      background: #f1f5f9;
      padding: 2px;
      border-radius: 8px;
      border: 1px solid #e2e8f0;
    }

    .toggle-btn {
      font-size: 11px;
      font-weight: 600;
      padding: 4px 8px;
      border: none;
      background: transparent;
      color: #64748b;
      border-radius: 6px;
      cursor: pointer;
      transition: all 0.15s ease;
    }

    .toggle-btn.active {
      background: #ffffff;
      color: #0f172a;
      box-shadow: 0 1px 3px rgba(0,0,0,0.1);
    }

    .tree-container {
      width: 100%;
      max-width: 440px;
      flex: 1;
      display: flex;
      align-items: center;
      justify-content: center;
      position: relative;
    }

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

    .branch {
      stroke: #cbd5e1;
      stroke-width: 2.5;
      stroke-linecap: round;
      transition: opacity 0.3s ease;
    }

    .node-group {
      transition: transform 0.3s ease, opacity 0.3s ease;
      cursor: default;
    }

    .composite-node rect {
      fill: #f8fafc;
      stroke: #94a3b8;
      stroke-width: 2;
      rx: 10;
    }

    .composite-node text {
      font-size: 16px;
      font-weight: 700;
      fill: #1e2945;
      text-anchor: middle;
      dominant-baseline: central;
    }

    .prime-node circle.bg {
      fill: #ecfdf5;
      stroke: #10b981;
      stroke-width: 2.5;
    }

    .prime-node circle.ring {
      fill: none;
      stroke: #34d399;
      stroke-width: 1.5;
      stroke-dasharray: 2 2;
    }

    .prime-node text {
      font-size: 16px;
      font-weight: 800;
      fill: #065f46;
      text-anchor: middle;
      dominant-baseline: central;
    }

    .hidden {
      opacity: 0;
      pointer-events: none;
    }

    .result-box {
      width: 100%;
      max-width: 440px;
      background: #f8fafc;
      border: 1.5px solid #e2e8f0;
      border-radius: 12px;
      padding: 10px 14px;
      display: flex;
      align-items: center;
      justify-content: space-between;
      margin-top: 4px;
    }

    .result-label {
      font-size: 13px;
      font-weight: 600;
      color: #64748b;
    }

    .result-math {
      font-size: 17px;
      font-weight: 700;
      color: #0f172a;
      letter-spacing: 0.5px;
      display: flex;
      align-items: center;
      gap: 2px;
    }

    .prime-tag {
      color: #059669;
      background: #d1fae5;
      padding: 1px 6px;
      border-radius: 6px;
      display: inline-block;
    }

    .op {
      color: #94a3b8;
      margin: 0 2px;
      font-size: 14px;
    }

    .sup {
      font-size: 11px;
      vertical-align: super;
      font-weight: 800;
      color: #0284c7;
      margin-left: 1px;
    }

    .nav-bar {
      display: flex;
      align-items: center;
      gap: 10px;
      width: 100%;
      max-width: 440px;
      margin-top: 8px;
    }

    .nav-btn {
      flex: 1;
      padding: 7px;
      font-size: 13px;
      font-weight: 600;
      border: 1px solid #cbd5e1;
      background: #ffffff;
      color: #334155;
      border-radius: 8px;
      cursor: pointer;
      display: flex;
      align-items: center;
      justify-content: center;
      gap: 4px;
      transition: background 0.15s;
    }

    .nav-btn:active {
      background: #f1f5f9;
    }

    .play-btn {
      width: 38px;
      flex: 0 0 38px;
      padding: 7px 0;
    }
  </style>
</head>
<body>

  <div class="controls-top">
    <div class="step-pills">
      <span class="pill active" onclick="setStep(0)">1</span>
      <span class="pill" onclick="setStep(1)">2</span>
      <span class="pill" onclick="setStep(2)">3</span>
      <span class="pill" onclick="setStep(3)">4</span>
    </div>
    <div class="toggle-group">
      <button class="toggle-btn active" id="btnExpanded" onclick="setMode('expanded')">Expanded</button>
      <button class="toggle-btn" id="btnExponent" onclick="setMode('exponent')">Exponent</button>
    </div>
  </div>

  <div class="tree-container">
    <svg viewBox="0 0 360 220">
      
      <line id="b-8-9_L" class="branch hidden" x1="180" y1="36" x2="105" y2="82" />
      <line id="b-8-9_R" class="branch hidden" x1="180" y1="36" x2="255" y2="82" />

      <line id="b-2-4_L" class="branch hidden" x1="105" y1="96" x2="65" y2="142" />
      <line id="b-2-4_R" class="branch hidden" x1="105" y1="96" x2="145" y2="142" />

      <line id="b-3-3_L" class="branch hidden" x1="255" y1="96" x2="215" y2="142" />
      <line id="b-3-3_R" class="branch hidden" x1="255" y1="96" x2="295" y2="142" />

      <line id="b-2-2_L" class="branch hidden" x1="145" y1="156" x2="120" y2="196" />
      <line id="b-2-2_R" class="branch hidden" x1="145" y1="156" x2="170" y2="196" />

      
      <g id="node-72" class="node-group composite-node" transform="translate(180, 26)">
        <rect x="-24" y="-16" width="48" height="32" />
        <text y="1">72</text>
      </g>

      
      <g id="node-8" class="node-group composite-node hidden" transform="translate(105, 88)">
        <rect x="-20" y="-15" width="40" height="30" />
        <text y="1">8</text>
      </g>
      <g id="node-9" class="node-group composite-node hidden" transform="translate(255, 88)">
        <rect x="-20" y="-15" width="40" height="30" />
        <text y="1">9</text>
      </g>

      
      <g id="node-2a" class="node-group prime-node hidden" transform="translate(65, 146)">
        <circle class="ring" r="17" />
        <circle class="bg" r="14" />
        <text y="1">2</text>
      </g>
      <g id="node-4" class="node-group composite-node hidden" transform="translate(145, 146)">
        <rect x="-18" y="-14" width="36" height="28" />
        <text y="1">4</text>
      </g>
      <g id="node-3a" class="node-group prime-node hidden" transform="translate(215, 146)">
        <circle class="ring" r="17" />
        <circle class="bg" r="14" />
        <text y="1">3</text>
      </g>
      <g id="node-3b" class="node-group prime-node hidden" transform="translate(295, 146)">
        <circle class="ring" r="17" />
        <circle class="bg" r="14" />
        <text y="1">3</text>
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    <div class="result-label">Prime Factors:</div>
    <div class="result-math" id="mathDisplay">72</div>
  </div>

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<!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="4:3">
  <title>Prime vs. Composite Numbers</title>
  <style>
    * { box-sizing: border-box; margin: 0; padding: 0; }
    body {
      background: #f8f9fa;
      font-family: system-ui, -apple-system, sans-serif;
      color: #1e2945;
      padding: 12px;
      display: flex;
      justify-content: center;
      align-items: center;
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      display: grid;
      grid-template-columns: 1fr 1fr;
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    .column-box {
      background: #ffffff;
      border: 1px solid #e2e8f0;
      border-radius: 12px;
      padding: 12px;
      display: flex;
      flex-direction: column;
      align-items: center;
    }

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      display: flex;
      align-items: center;
      justify-content: space-between;
      width: 100%;
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      gap: 6px;
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  </style>
</head>
<body>

<div class="comparison-grid">
  
  <div class="column-box">
    <div class="header-row">
      <span class="title">7</span>
      <span class="badge badge-prime">🔒 Prime</span>
    </div>

    <div style="height: 27px;"></div> 

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        <div class="tile tile-prime"></div>
        <div class="tile tile-prime"></div>
        <div class="tile tile-prime"></div>
        <div class="tile tile-prime"></div>
        <div class="tile tile-prime"></div>
        <div class="tile tile-prime"></div>
        <div class="tile tile-prime"></div>
      </div>
    </div>

    <div class="dim-label">1 × 7</div>
    <div class="factors-tag">Factors: 1, 7 only</div>
  </div>

  
  <div class="column-box">
    <div class="header-row">
      <span class="title">12</span>
      <span class="badge badge-composite">⚡ Composite</span>
    </div>

    <div class="toggle-group">
      <button id="btn3x4" class="toggle-btn active" onclick="setGrid('3x4')">3 × 4</button>
      <button id="btn2x6" class="toggle-btn" onclick="setGrid('2x6')">2 × 6</button>
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    <div class="stage-area">
      <div id="compositeGrid" class="tile-grid grid-3x4">
        
        <div class="tile tile-composite"></div>
        <div class="tile tile-composite"></div>
        <div class="tile tile-composite"></div>
        <div class="tile tile-composite"></div>
        <div class="tile tile-composite"></div>
        <div class="tile tile-composite"></div>
        <div class="tile tile-composite"></div>
        <div class="tile tile-composite"></div>
        <div class="tile tile-composite"></div>
        <div class="tile tile-composite"></div>
        <div class="tile tile-composite"></div>
        <div class="tile tile-composite"></div>
      </div>
    </div>

    <div id="dimLabelComp" class="dim-label">3 × 4 = 12</div>
    <div class="factors-tag">Factors: 1, 2, 3, 4, 6, 12</div>
  </div>
</div>

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</script>

</body>
</html>

<!DOCTYPE html>
<html lang="en">
<head>
  <meta charset="UTF-8">
  <meta name="viewport" content="width=device-width, initial-scale=1.0">
  <title>Prime Factor Tree: 24</title>
  <style>
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      margin: 0;
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      margin-top: 4px;
      min-height: 20px;
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      margin: 4px 0;
    }

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      width: 100%;
      max-width: 440px;
      height: auto;
      display: block;
      overflow: visible;
    }

    /* Branch lines */
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      stroke: #94a3b8;
      stroke-width: 3;
      stroke-linecap: round;
      opacity: 0;
      transition: opacity 0.4s ease;
    }

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      opacity: 1;
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      transform-box: fill-box;
      transform-origin: center;
      transform: scale(0.6);
      transition: opacity 0.4s ease, transform 0.4s cubic-bezier(0.34, 1.4, 0.64, 1);
    }

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      opacity: 1;
      transform: scale(1);
    }

    /* Node Styles */
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      fill: #f8fafc;
      stroke: #475569;
      stroke-width: 2.5;
      filter: drop-shadow(0 2px 4px rgba(0, 0, 0, 0.08));
    }

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      stroke: #64748b;
      stroke-width: 2.5;
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      fill: #dcfce7;
      stroke: #16a34a;
      stroke-width: 2.5;
      filter: drop-shadow(0 0 7px rgba(22, 163, 74, 0.4));
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      font-weight: 700;
      fill: #1e293b;
      text-anchor: middle;
      dominant-baseline: central;
      font-family: inherit;
    }

    .node-prime .node-text {
      fill: #15803d;
      font-weight: 800;
    }

    .prime-pill-tag {
      font-size: 9px;
      font-weight: 700;
      fill: #15803d;
      text-anchor: middle;
      dominant-baseline: central;
      letter-spacing: 0.02em;
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      justify-content: center;
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      border: 1.5px solid #86efac;
      border-radius: 8px;
      font-size: 14.5px;
      font-weight: 700;
      color: #166534;
      opacity: 0;
      visibility: hidden;
      transform: translateY(4px);
      transition: opacity 0.4s ease, transform 0.4s ease, visibility 0.4s;
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    }

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      align-items: center;
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      gap: 4px;
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      width: 9px;
      height: 9px;
      border-radius: 50%;
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      cursor: pointer;
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        min-width: 72px;
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  </style>
</head>
<body>

  
  <div class="header">
    <h1 class="title">Prime Factor Tree: 24</h1>
    <div id="instruction" class="instruction-box">
      Start with the composite number <strong>24</strong>.
    </div>
  </div>

  
  <div class="diagram-area">
    <svg viewBox="0 0 360 215" aria-label="Factor tree for 24">
      
      <line id="b-24-4" class="branch" x1="180" y1="46" x2="105" y2="88" />
      <line id="b-24-6" class="branch" x1="180" y1="46" x2="255" y2="88" />

      
      <line id="b-4-2a" class="branch" x1="105" y1="114" x2="60" y2="158" />
      <line id="b-4-2b" class="branch" x1="105" y1="114" x2="150" y2="158" />

      
      <line id="b-6-2c" class="branch" x1="255" y1="114" x2="210" y2="158" />
      <line id="b-6-3"  class="branch" x1="255" y1="114" x2="300" y2="158" />

      
      <g id="n-24" class="tree-node node-root visible">
        <circle cx="180" cy="28" r="18" />
        <text x="180" y="28" class="node-text">24</text>
      </g>

      
      <g id="n-4" class="tree-node node-composite">
        <circle cx="105" cy="101" r="17" />
        <text x="105" y="101" class="node-text">4</text>
      </g>
      <g id="n-6" class="tree-node node-composite">
        <circle cx="255" cy="101" r="17" />
        <text x="255" y="101" class="node-text">6</text>
      </g>

      
      <g id="n-2a" class="tree-node node-prime">
        <circle cx="60" cy="175" r="16" />
        <text x="60" y="175" class="node-text">2</text>
        <text x="60" y="199" class="prime-pill-tag">PRIME</text>
      </g>
      <g id="n-2b" class="tree-node node-prime">
        <circle cx="150" cy="175" r="16" />
        <text x="150" y="175" class="node-text">2</text>
        <text x="150" y="199" class="prime-pill-tag">PRIME</text>
      </g>
      <g id="n-2c" class="tree-node node-prime">
        <circle cx="210" cy="175" r="16" />
        <text x="210" y="175" class="node-text">2</text>
        <text x="210" y="199" class="prime-pill-tag">PRIME</text>
      </g>
      <g id="n-3" class="tree-node node-prime">
        <circle cx="300" cy="175" r="16" />
        <text x="300" y="175" class="node-text">3</text>
        <text x="300" y="199" class="prime-pill-tag">PRIME</text>
      </g>
    </svg>

    
    <div id="banner" class="factor-banner">
      Prime Factorization:&nbsp;
      <span class="prime-tag">2</span> × 
      <span class="prime-tag">2</span> × 
      <span class="prime-tag">2</span> × 
      <span class="prime-tag">3</span> = 24
    </div>
  </div>

  
  <div class="controls-wrapper">
    <div class="controls">
      <button id="btnPrev" class="btn" aria-label="Previous step">◀ Prev</button>
      <div class="dots" aria-label="Step indicators">
        <span class="dot active" data-step="0" title="Step 1"></span>
        <span class="dot" data-step="1" title="Step 2"></span>
        <span class="dot" data-step="2" title="Step 3"></span>
        <span class="dot" data-step="3" title="Step 4"></span>
        <span class="dot" data-step="4" title="Step 5"></span>
      </div>
      <button id="btnNext" class="btn btn-primary" aria-label="Next step">Next ▶</button>
    </div>
  </div>

  <script>
    let currentStep = 0;
    const totalSteps = 5;

    const instructions = [
      "Start with the composite number <strong>24</strong>.",
      "Split 24 into two factors: <strong>4 × 6</strong>.",
      "Factor 4 into <span class='prime-highlight'>2 × 2</span> (both are prime).",
      "Factor 6 into <span class='prime-highlight'>2 × 3</span> (both are prime).",
      "All branches end in primes! Factorization complete."
    ];

    const elements = {
      step1: ['b-24-4', 'b-24-6', 'n-4', 'n-6'],
      step2: ['b-4-2a', 'b-4-2b', 'n-2a', 'n-2b'],
      step3: ['b-6-2c', 'b-6-3', 'n-2c', 'n-3'],
      step4: ['banner']
    };

    function updateStep(step) {
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Unidades, decenas y centenas de mil

Los millones: lectura y escritura de números de siete o más cifras

Descomposición aditiva y forma expandida

Descomposición multiplicativa usando potencias de 10

Relación de 10 a 1 entre posiciones contiguas

Multiplicar por 10, 100 y 1.000 desplazando posiciones

Dividir entre 10, 100 y 1.000 analizando el patrón posicional

math

Valor posicional y potencias de 10

Comparación y orden de números grandes

Redondeo a la decena, centena y unidad de mil más cercana

Redondeo a la decena de mil, centena de mil y millón más cercano

Estimación en contextos cotidianos y censales

Patrones numéricos en la recta numérica hasta el millón

Análisis de errores comunes en el valor posicional

Regularidades del sistema decimal comparado con otros sistemas

Resolución de desafíos de lógica con cifras y posiciones

Comparación, redondeo y aplicaciones del valor posicional

Algoritmo estándar de la suma con múltiples reagrupaciones

Propiedades conmutativa y asociativa en el cálculo mental

Algoritmo estándar de la resta con desagrupación continua

Resta atravesando ceros: estrategias y procedimientos

Estimación de sumas y diferencias para verificar resultados

Relación inversa entre suma y resta para comprobar operaciones

Algoritmos y estrategias de cálculo de suma y resta

Using Arrays to Identify Prime and Composite Numbers

Identifying Prime and Composite Numbers up to 100

Divisibility Rules for 2, 5, and 10

Divisibility Rules for 3 and 9

Divisibility Rules for 4 and 100

Generating and Identifying Multiples of Numbers to 100

Square Numbers and Their Factor Properties

Factors, Multiples, and Divisibility Rules

Reconnaître les multiples de 2

Reconnaître les multiples de 5 et de 10

Reconnaître les multiples de 3 et de 9

Tester si un nombre est multiple d'un entier inférieur ou égal à 10

Déterminer des multiples communs à deux nombres entiers inférieurs à 15

Tester si un nombre inférieur ou égal à 10 est un diviseur d'un entier donné

OGM.5.OA.3

Aligned learning resources

Related diagrams