<!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>Commutative Property of Multiplication</title>
  <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;
      display: flex;
      flex-direction: column;
      align-items: center;
      justify-content: center;
      min-height: 100%;
      padding: 12px;
      user-select: none;
      -webkit-user-select: none;
    }
    .wrapper {
      width: 100%;
      max-width: 480px;
      display: flex;
      flex-direction: column;
      align-items: center;
      gap: 12px;
    }
    .comparison {
      width: 100%;
      display: flex;
      align-items: center;
      justify-content: space-between;
      gap: 8px;
    }
    .panel {
      flex: 1;
      background: #f8fafc;
      border: 1px solid #e6e6e6;
      border-radius: 12px;
      padding: 12px 8px;
      display: flex;
      flex-direction: column;
      align-items: center;
      justify-content: center;
      gap: 10px;
      min-height: 190px;
      transition: border-color 0.3s ease, box-shadow 0.3s ease;
      cursor: pointer;
    }
    .panel.active {
      border-color: #0ea5e9;
      box-shadow: 0 0 0 2px rgba(14, 165, 233, 0.15);
    }
    .equation {
      font-size: 18px;
      font-weight: 700;
      letter-spacing: -0.2px;
    }
    .subtext {
      font-size: 13px;
      font-weight: 600;
      color: #64748b;
    }
    .grid-container {
      display: flex;
      flex-direction: column;
      align-items: center;
      justify-content: center;
      height: 110px;
    }
    .grid-2x5 {
      display: grid;
      grid-template-columns: repeat(5, 1fr);
      grid-template-rows: repeat(2, 1fr);
      gap: 8px;
    }
    .grid-5x2 {
      display: grid;
      grid-template-columns: repeat(2, 1fr);
      grid-template-rows: repeat(5, 1fr);
      gap: 8px;
    }
    .dot {
      width: 14px;
      height: 14px;
      border-radius: 50%;
      transition: transform 0.3s ease;
    }
    .dot.coral {
      background-color: #f43f5e;
      box-shadow: 0 1px 3px rgba(244, 63, 94, 0.3);
    }
    .dot.teal {
      background-color: #0ea5e9;
      box-shadow: 0 1px 3px rgba(14, 165, 233, 0.3);
    }
    .rotate-btn {
      background: #ffffff;
      border: 1px solid #e6e6e6;
      border-radius: 50%;
      width: 42px;
      height: 42px;
      display: flex;
      align-items: center;
      justify-content: center;
      font-size: 20px;
      color: #1e2945;
      cursor: pointer;
      box-shadow: 0 2px 5px rgba(0,0,0,0.06);
      transition: background-color 0.2s, transform 0.5s ease;
      flex-shrink: 0;
    }
    .rotate-btn:active {
      background-color: #f1f5f9;
    }
    .footer-badge {
      font-size: 14px;
      font-weight: 600;
      padding: 6px 16px;
      background: #f1f5f9;
      border-radius: 20px;
      border: 1px solid #e2e8f0;
      color: #1e2945;
    }
    .highlight {
      font-weight: 700;
      color: #0ea5e9;
    }
  </style>
</head>
<body>
  <div class="wrapper">
    <div class="comparison">
      
      <div class="panel" id="panelLeft">
        <div class="equation">2 × 5 = 10</div>
        <div class="grid-container">
          <div class="grid-2x5" id="gridLeft">
            
            <div class="dot coral"></div>
            <div class="dot coral"></div>
            <div class="dot coral"></div>
            <div class="dot coral"></div>
            <div class="dot coral"></div>
            
            <div class="dot teal"></div>
            <div class="dot teal"></div>
            <div class="dot teal"></div>
            <div class="dot teal"></div>
            <div class="dot teal"></div>
          </div>
        </div>
        <div class="subtext">2 rows of 5</div>
      </div>

      
      <button class="rotate-btn" id="rotateBtn" title="Rotate array" aria-label="Rotate array">↻</button>

      
      <div class="panel" id="panelRight">
        <div class="equation">5 × 2 = 10</div>
        <div class="grid-container">
          <div class="grid-5x2" id="gridRight">
            
            <div class="dot coral"></div>
            <div class="dot teal"></div>
            <div class="dot coral"></div>
            <div class="dot teal"></div>
            <div class="dot coral"></div>
            <div class="dot teal"></div>
            <div class="dot coral"></div>
            <div class="dot teal"></div>
            <div class="dot coral"></div>
            <div class="dot teal"></div>
          </div>
        </div>
        <div class="subtext">5 rows of 2</div>
      </div>
    </div>

    <div class="footer-badge">
      <span>2 × 5</span> = <span>5 × 2</span> = <span class="highlight">10</span>
    </div>
  </div>

  <script>
    const rotateBtn = document.getElementById('rotateBtn');
    const panelLeft = document.getElementById('panelLeft');
    const panelRight = document.getElementById('panelRight');
    let rotationAngle = 0;
    let activeSide = 'left';

    function triggerRotation() {
      rotationAngle += 90;
      rotateBtn.style.transform = `rotate(${rotationAngle}deg)`;

      if (activeSide === 'left') {
        activeSide = 'right';
        panelRight.classList.add('active');
        panelLeft.classList.remove('active');
      } else {
        activeSide = 'left';
        panelLeft.classList.add('active');
        panelRight.classList.remove('active');
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      // Animate dots slightly
      const dots = document.querySelectorAll('.dot');
      dots.forEach(dot => {
        dot.style.transform = 'scale(1.15)';
        setTimeout(() => {
          dot.style.transform = 'scale(1)';
        }, 200);
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    }

    rotateBtn.addEventListener('click', triggerRotation);
    panelLeft.addEventListener('click', () => {
      if (activeSide !== 'left') triggerRotation();
    });
    panelRight.addEventListener('click', () => {
      if (activeSide !== 'right') triggerRotation();
    });

    // Initial state highlight
    panelLeft.classList.add('active');
  </script>
</body>
</html>

Multiplication Facts for 2, 5, and 10

<!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, sans-serif;
      color: #1e2945;
      background: transparent;
      padding: 10px;
      display: flex;
      flex-direction: column;
      align-items: center;
      justify-content: center;
      min-height: 100%;
    }
    .filter-tabs {
      display: flex;
      gap: 6px;
      margin-bottom: 12px;
      background: #f1f5f9;
      padding: 3px;
      border-radius: 20px;
    }
    .tab-btn {
      border: none;
      background: transparent;
      padding: 5px 14px;
      border-radius: 16px;
      font-size: 13px;
      font-weight: 700;
      color: #64748b;
      cursor: pointer;
      transition: all 0.2s ease;
    }
    .tab-btn.active {
      background: #ffffff;
      color: #1e2945;
      box-shadow: 0 1px 4px rgba(0,0,0,0.1);
    }
    .grid {
      display: grid;
      grid-template-columns: 1fr 1fr;
      gap: 10px;
      width: 100%;
      max-width: 420px;
    }
    .col-header {
      text-align: center;
      padding: 6px 4px;
      border-radius: 8px;
      font-size: 13px;
      font-weight: 800;
      letter-spacing: -0.2px;
      margin-bottom: 8px;
    }
    .odd-header {
      background: #fef3c7;
      color: #b45309;
      border: 1px solid #fde68a;
    }
    .even-header {
      background: #ccfbf1;
      color: #0f766e;
      border: 1px solid #99f6e4;
    }
    .card-list {
      display: flex;
      flex-direction: column;
      gap: 8px;
    }
    .fact-card {
      background: #f8fafc;
      border: 1.5px solid #e2e8f0;
      border-radius: 10px;
      padding: 8px 6px;
      display: flex;
      flex-direction: column;
      align-items: center;
      gap: 4px;
      transition: opacity 0.25s ease, border-color 0.25s ease, background-color 0.25s ease;
      cursor: pointer;
    }
    .fact-card:hover {
      border-color: #cbd5e1;
      background: #f1f5f9;
    }
    .fact-card.dimmed {
      opacity: 0.25;
    }
    .eq-row {
      display: flex;
      align-items: center;
      justify-content: center;
      gap: 4px;
      font-size: 15px;
      font-weight: 700;
    }
    .badge {
      display: inline-flex;
      align-items: center;
      justify-content: center;
      min-width: 28px;
      height: 24px;
      padding: 0 6px;
      border-radius: 6px;
      color: #ffffff;
      font-weight: 800;
      font-size: 15px;
    }
    .badge-odd {
      background: #f59e0b;
    }
    .badge-even {
      background: #10b981;
    }
    .last-digit {
      text-decoration: underline;
      text-underline-offset: 2px;
    }
    .hands-row {
      display: flex;
      flex-wrap: wrap;
      justify-content: center;
      align-items: center;
      gap: 1px;
      font-size: 14px;
      line-height: 1.2;
      min-height: 20px;
    }
    .hand-unit {
      filter: drop-shadow(0 1px 1px rgba(0,0,0,0.05));
    }
  </style>
</head>
<body>

  <div class="filter-tabs">
    <button class="tab-btn active" onclick="setFilter('all')">All</button>
    <button class="tab-btn" onclick="setFilter('odd')">Ends in 5</button>
    <button class="tab-btn" onclick="setFilter('even')">Ends in 0</button>
  </div>

  <div class="grid">
    
    <div>
      <div class="col-header odd-header">Odd Multipliers → 5</div>
      <div class="card-list">
        <div class="fact-card odd-item" onclick="setFilter('odd')">
          <div class="eq-row">
            <span>5 × 1 =</span>
            <span class="badge badge-odd"><span class="last-digit">5</span></span>
          </div>
          <div class="hands-row">
            <span class="hand-unit">🖐️</span>
          </div>
        </div>

        <div class="fact-card odd-item" onclick="setFilter('odd')">
          <div class="eq-row">
            <span>5 × 3 =</span>
            <span class="badge badge-odd">1<span class="last-digit">5</span></span>
          </div>
          <div class="hands-row">
            <span class="hand-unit">🖐️</span><span class="hand-unit">🖐️</span><span class="hand-unit">🖐️</span>
          </div>
        </div>

        <div class="fact-card odd-item" onclick="setFilter('odd')">
          <div class="eq-row">
            <span>5 × 5 =</span>
            <span class="badge badge-odd">2<span class="last-digit">5</span></span>
          </div>
          <div class="hands-row">
            <span class="hand-unit">🖐️</span><span class="hand-unit">🖐️</span><span class="hand-unit">🖐️</span><span class="hand-unit">🖐️</span><span class="hand-unit">🖐️</span>
          </div>
        </div>
      </div>
    </div>

    
    <div>
      <div class="col-header even-header">Even Multipliers → 0</div>
      <div class="card-list">
        <div class="fact-card even-item" onclick="setFilter('even')">
          <div class="eq-row">
            <span>5 × 2 =</span>
            <span class="badge badge-even">1<span class="last-digit">0</span></span>
          </div>
          <div class="hands-row">
            <span class="hand-unit">🖐️</span><span class="hand-unit">🖐️</span>
          </div>
        </div>

        <div class="fact-card even-item" onclick="setFilter('even')">
          <div class="eq-row">
            <span>5 × 4 =</span>
            <span class="badge badge-even">2<span class="last-digit">0</span></span>
          </div>
          <div class="hands-row">
            <span class="hand-unit">🖐️</span><span class="hand-unit">🖐️</span><span class="hand-unit">🖐️</span><span class="hand-unit">🖐️</span>
          </div>
        </div>

        <div class="fact-card even-item" onclick="setFilter('even')">
          <div class="eq-row">
            <span>5 × 6 =</span>
            <span class="badge badge-even">3<span class="last-digit">0</span></span>
          </div>
          <div class="hands-row">
            <span class="hand-unit">🖐️</span><span class="hand-unit">🖐️</span><span class="hand-unit">🖐️</span><span class="hand-unit">🖐️</span><span class="hand-unit">🖐️</span><span class="hand-unit">🖐️</span>
          </div>
        </div>
      </div>
    </div>
  </div>

  <script>
    function setFilter(type) {
      const tabs = document.querySelectorAll('.tab-btn');
      tabs.forEach((tab, i) => {
        const matches = (type === 'all' && i === 0) || (type === 'odd' && i === 1) || (type === 'even' && i === 2);
        tab.classList.toggle('active', matches);
      });

      const oddCards = document.querySelectorAll('.odd-item');
      const evenCards = document.querySelectorAll('.even-item');

      oddCards.forEach(c => {
        c.classList.toggle('dimmed', type === 'even');
      });

      evenCards.forEach(c => {
        c.classList.toggle('dimmed', type === 'odd');
      });
    }
  </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; }
    body {
      font-family: system-ui, -apple-system, sans-serif;
      color: #1e2945;
      background: #ffffff;
      padding: 10px;
      display: flex;
      flex-direction: column;
      align-items: center;
      justify-content: center;
      min-height: 100%;
    }

    .main-grid {
      display: grid;
      grid-template-columns: 1fr 130px;
      gap: 12px;
      width: 100%;
      max-width: 500px;
    }

    @media (max-width: 380px) {
      .main-grid {
        grid-template-columns: 1fr;
      }
    }

    /* Interactive Stepper Tabs */
    .nav-tabs {
      display: flex;
      gap: 6px;
      margin-bottom: 10px;
      width: 100%;
      max-width: 500px;
    }

    .tab-btn {
      flex: 1;
      border: 1px solid #cbd5e1;
      background: #f8fafc;
      color: #64748b;
      font-size: 14px;
      font-weight: 700;
      padding: 8px 12px;
      border-radius: 8px;
      cursor: pointer;
      display: flex;
      align-items: center;
      justify-content: center;
      gap: 6px;
      transition: all 0.25s ease;
    }

    .tab-btn.active {
      background: #0284c7;
      color: #ffffff;
      border-color: #0284c7;
      box-shadow: 0 2px 8px rgba(2, 132, 199, 0.25);
    }

    /* Left Stage Area */
    .stage-card {
      background: #f8fafc;
      border: 1px solid #e2e8f0;
      border-radius: 12px;
      padding: 12px;
      display: flex;
      flex-direction: column;
      align-items: center;
      gap: 12px;
    }

    .visual-viewport {
      height: 140px;
      width: 100%;
      display: flex;
      align-items: center;
      justify-content: center;
      background: #ffffff;
      border-radius: 8px;
      border: 1px dashed #cbd5e1;
      position: relative;
    }

    /* Base Ten Blocks */
    .units-group {
      display: flex;
      gap: 8px;
      align-items: center;
      transition: opacity 0.3s ease;
    }

    .unit-cube {
      width: 22px;
      height: 22px;
      background: #fef08a;
      border: 1.5px solid #ca8a04;
      border-radius: 3px;
      box-shadow: 0 1px 3px rgba(0,0,0,0.06);
    }

    .rods-group {
      display: flex;
      gap: 8px;
      align-items: center;
      transition: opacity 0.3s ease;
    }

    .ten-rod {
      width: 15px;
      height: 120px;
      background: #bae6fd;
      border: 1.5px solid #0284c7;
      border-radius: 3px;
      display: flex;
      flex-direction: column;
      box-shadow: 0 1px 3px rgba(0,0,0,0.06);
      overflow: hidden;
    }

    .rod-segment {
      flex: 1;
      border-bottom: 1px solid #7dd3fc;
    }
    .rod-segment:last-child {
      border-bottom: none;
    }

    /* Place Value Table */
    .pv-table {
      width: 100%;
      border-collapse: collapse;
      background: #ffffff;
      border-radius: 8px;
      overflow: hidden;
      border: 1px solid #cbd5e1;
    }

    .pv-table th {
      background: #e2e8f0;
      font-size: 13px;
      font-weight: 700;
      padding: 6px;
      text-align: center;
      width: 50%;
      color: #334155;
    }

    .pv-table td {
      font-size: 26px;
      font-weight: 800;
      text-align: center;
      padding: 6px;
      height: 44px;
      color: #1e2945;
    }

    .pv-table .shifted {
      color: #0284c7;
      background: #f0f9ff;
    }

    .pv-table .zero-digit {
      color: #059669;
      background: #ecfdf5;
    }

    /* Comparison Badge Panel */
    .badge-card {
      background: #f8fafc;
      border: 1px solid #e2e8f0;
      border-radius: 12px;
      padding: 12px 10px;
      display: flex;
      flex-direction: column;
      justify-content: space-between;
      gap: 8px;
    }

    .fact-pill {
      background: #ffffff;
      border: 1px solid #cbd5e1;
      border-radius: 8px;
      padding: 8px 6px;
      text-align: center;
    }

    .fact-pill.highlight {
      border-color: #0284c7;
      background: #f0f9ff;
    }

    .fact-math {
      font-size: 15px;
      font-weight: 800;
      color: #1e2945;
    }

    .double-tag {
      display: flex;
      align-items: center;
      justify-content: center;
      gap: 4px;
      font-size: 12px;
      font-weight: 700;
      color: #d97706;
      background: #fef3c7;
      padding: 5px 6px;
      border-radius: 6px;
      text-align: center;
    }
  </style>
</head>
<body>

  
  <div class="nav-tabs">
    <button id="btn1" class="tab-btn active" onclick="setStep(1)">
      <span>4 × 1</span>
    </button>
    <button id="btn2" class="tab-btn" onclick="setStep(2)">
      <span>4 × 10</span>
    </button>
  </div>

  
  <div class="main-grid">
    
    <div class="stage-card">
      <div class="visual-viewport" id="viewport">
        
      </div>

      <table class="pv-table">
        <thead>
          <tr>
            <th>Tens</th>
            <th>Ones</th>
          </tr>
        </thead>
        <tbody>
          <tr>
            <td id="td-tens">—</td>
            <td id="td-ones" class="shifted">4</td>
          </tr>
        </tbody>
      </table>
    </div>

    
    <div class="badge-card">
      <div class="fact-pill highlight">
        <div class="fact-math">10 × 4 = 40</div>
      </div>

      <div class="double-tag">
        <span>↕ 10 = 2 × 5</span>
      </div>

      <div class="fact-pill">
        <div class="fact-math">5 × 8 = 40</div>
      </div>
    </div>
  </div>

  <script>
    function createUnits() {
      return `
        <div class="units-group">
          <div class="unit-cube"></div>
          <div class="unit-cube"></div>
          <div class="unit-cube"></div>
          <div class="unit-cube"></div>
        </div>
      `;
    }

    function createRods() {
      const rod = `
        <div class="ten-rod">
          ${'<div class="rod-segment"></div>'.repeat(10)}
        </div>
      `;
      return `
        <div class="rods-group">
          ${rod.repeat(4)}
        </div>
      `;
    }

    function setStep(step) {
      const btn1 = document.getElementById('btn1');
      const btn2 = document.getElementById('btn2');
      const viewport = document.getElementById('viewport');
      const tdTens = document.getElementById('td-tens');
      const tdOnes = document.getElementById('td-ones');

      if (step === 1) {
        btn1.classList.add('active');
        btn2.classList.remove('active');
        viewport.innerHTML = createUnits();
        tdTens.textContent = '—';
        tdTens.className = '';
        tdOnes.textContent = '4';
        tdOnes.className = 'shifted';
      } else {
        btn2.classList.add('active');
        btn1.classList.remove('active');
        viewport.innerHTML = createRods();
        tdTens.textContent = '4';
        tdTens.className = 'shifted';
        tdOnes.textContent = '0';
        tdOnes.className = 'zero-digit';
      }
    }

    // Initialize with Step 1
    setStep(1);

    // Auto-advance loop every 3.5s if untouched
    let currentStep = 1;
    let autoTimer = setInterval(() => {
      currentStep = currentStep === 1 ? 2 : 1;
      setStep(currentStep);
    }, 3500);

    // Pause auto-rotation on user click
    document.querySelectorAll('.tab-btn').forEach(btn => {
      btn.addEventListener('click', () => clearInterval(autoTimer));
    });
  </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="1:1">
  <title>Skip-Counting by 2s</title>
  <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;
      display: flex;
      flex-direction: column;
      align-items: center;
      justify-content: space-between;
      min-height: 100%;
      padding: 12px;
      user-select: none;
    }
    .top-controls {
      display: flex;
      flex-wrap: wrap;
      align-items: center;
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    .number-line-container {
      width: 100%;
      max-width: 520px;
      margin: 4px 0;
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    svg {
      width: 100%;
      height: auto;
      display: block;
      overflow: visible;
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    .info-card {
      width: 100%;
      max-width: 500px;
      background: #f8fafc;
      border: 1px solid #e6e6e6;
      border-radius: 12px;
      padding: 10px 12px;
      display: flex;
      flex-direction: column;
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      display: flex;
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      gap: 6px;
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    .pair-group {
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      border-radius: 8px;
      padding: 4px 6px;
      display: flex;
      align-items: center;
      gap: 3px;
      font-size: 16px;
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    .pair-group.current-pair {
      border-color: #22b7ff;
      background: #e0f2fe;
    }
    .pair-dot {
      width: 12px;
      height: 12px;
      border-radius: 50%;
      background: #22b7ff;
    }

    @keyframes fadeIn {
      from { opacity: 0; transform: translateY(4px); }
      to { opacity: 1; transform: translateY(0); }
    }
  </style>
</head>
<body>

  <div class="top-controls">
    <button class="btn" id="playBtn" onclick="togglePlay()">⏸ Pause</button>
    <button class="btn" onclick="prevStep()">◀ Back</button>
    <button class="btn" onclick="nextStep()">Next ▶</button>
  </div>

  <div class="step-pill-group" id="pillGroup"></div>

  <div class="number-line-container">
    <svg viewBox="0 0 540 125" id="nlSvg">
      <defs>
        <marker id="arrow" viewBox="0 0 10 10" refX="6" refY="5" markerWidth="5" markerHeight="5" orient="auto-start-reverse">
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  <div class="info-card">
    <div class="equation-badge" id="equationText">2 × 7 = 14</div>
    <div class="pairs-grid" id="pairsVisual"></div>
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  <script>
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      // Highlight circular badges
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        const isCurrent = i === currentStep;
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          <div class="pair-group ${isCurrent ? 'current-pair' : ''}" title="Pair ${i}">
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        playInterval = setInterval(() => {
          nextStep();
        }, 2800);
      }
    }

    // Initialize diagram
    initStaticElements();
    updateView();
  </script>
</body>
</html>

Multiplying by 0 and 1: Zero and Identity Properties

Multiplying by 2: Connecting to Doubles

Multiplying by 3: Using Known Facts

Multiplying by 4: Double-Double Strategy

Multiplying by 5 Using Skip-Counting

Multiplying by 6: Patterns and Strategies

Multiplying by 7: Patterns and Strategies

Multiplying by 8: Patterns and Strategies

Multiplying by 9: Patterns and Strategies

Multiplying by 10 Using Place Value

math

Building Multiplication Fact Fluency: Factors 0–10

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

Multiplying by 11 and 12: Extending Fact Fluency

Mixed Multiplication Facts Practice (0–10)

Multiplication Facts Speed Practice

Using Multiplication Facts to Solve Problems

Extending and Applying Multiplication Fact Fluency

Division Facts for 2, 5, and 10

Multiplication Facts for 3, 4, and 8

Division Facts for 3, 4, and 8

Multiplication Facts for 6, 7, and 9

Division Facts for 6, 7, and 9

Multiplication and Division Fact Families to 100

Identifying Even and Odd Numbers Using Divisibility by 2

Rules of Parity in Multiplication and Division

Multiplication and Division Facts Fluency

Properties of Operations: Commutative and Associative

Using the Commutative Property to Multiply

Using the Associative Property to Multiply

Distributive Property with Area Models

Breaking Apart Numbers Using the Distributive Property

Multiplying by Multiples of Ten

Multiplication Properties and Place Value Patterns

Situaciones aditivas de composición parte-todo

Situaciones aditivas de transformación: aumento y disminución

Situaciones aditivas de comparación: cuánto más y cuánto menos

Situaciones aditivas de igualación: compensar cantidades

Resolución de problemas aditivos de dos y tres pasos

Uso de diagramas de barras para modelar problemas aditivos

Estrategias de compensación y descomposición mental

Ecuaciones aditivas simples: hallar el término desconocido

Formulación de problemas aditivos a partir de datos reales

Resolución de problemas aditivos: modelación y aplicaciones

Fluidez en las tablas de multiplicar hasta el 12

Propiedad distributiva de la multiplicación sobre la suma

Modelo de áreas rectangulares para la multiplicación

Multiplicación de un número de varias cifras por una cifra

Multiplicación por múltiplos de 10, 100 y 1.000

Multiplicación de dos cifras por dos cifras: productos parciales

Algoritmo estándar de la multiplicación de dos y tres cifras

Algoritmo de la multiplicación de números naturales

Building the 3 Times Table with Equal Groups

Recalling Multiplication and Division Facts for 3

Building the 4 Times Table by Doubling Twos

Recalling Multiplication and Division Facts for 4

Building the 8 Times Table by Doubling Fours

Recalling Multiplication and Division Facts for 8

Connecting the 2, 4 and 8 Times Tables

Using Inverse Operations to Check Multiplication

Finding Missing Numbers in Multiplication and Division Facts

Solving Word Problems with 3, 4 and 8 Times Tables

Times Tables Fluency Challenge: 3, 4 and 8

Times Tables Mastery: 3, 4, and 8

Propiedades asociativa y conmutativa de la multiplicación

Multiplicación de tres o más factores

Estimación de productos mediante redondeo

Problemas multiplicativos de grupos iguales y arreglos

Problemas multiplicativos de comparación: tantas veces más

Problemas multiplicativos de combinatoria y cartesiano

Duplicar y partir a la mitad como estrategia mental

Detección y corrección de errores en la multiplicación

Problemas multiplicativos de dos pasos con dinero y cantidades

Cálculo mental y problemas multiplicativos

Multiplying Multiples of Ten by Single Digits

Multiplying Two-Digit Numbers by Partitioning (Without Regrouping)

Multiplying Two-Digit Numbers by Partitioning (With Regrouping)

Using the Grid Method to Multiply Two-Digit Numbers

Expanded Short Multiplication (Two Digits by One Digit)

Dividing Multiples of Ten by Single Digits

Dividing Two-Digit Numbers by Partitioning into Tens and Ones

Dividing Two-Digit Numbers with Remainders

Using Inverse Operations to Check Written Calculations

Solving Multiplication and Division Calculation Word Problems

Multiplication and Division: Two Digits by One Digit

Dodawanie trzech i więcej liczb

Obliczenia typu 250 + 50, 180 – 30

Własności dodawania – przemienność i łączność

Sprawdzanie dodawania odejmowaniem

Sprawdzanie odejmowania dodawaniem

Szacowanie sum i różnic

Równania z okienkiem – dodawanie i odejmowanie

Zadania tekstowe – dodawanie i odejmowanie

Sprawdzenie – dodawanie i odejmowanie

Sprawność w dodawaniu i odejmowaniu – zastosowania

What Is Division? Sharing Equally

Division as Equal Grouping

Using Arrays to Understand Division

Using Area Models to Understand Division

Relating Division to Multiplication

Building Division Fact Families

Understanding Division Concepts

Significados de la división: reparto equitativo y agrupamiento

Términos de la división y prueba de la división exacta e inexacta

División de números de varias cifras entre un dígito sin residuo

División entre un dígito con residuo y ceros en el cociente

Estimación del cociente usando múltiplos del divisor

División entre dos cifras: método de cocientes parciales

Algoritmo estándar de la división por dos cifras

Ajuste del cociente estimado cuando se pasa o queda corto

Interpretación del residuo: redondear al alza o descartar

Problemas de empaquetado, transporte y reparto con residuo

División de números naturales: algoritmos y aplicaciones

Division Facts for 3, 4, and 6

Division Facts for 7, 8, and 9

Even and Odd Numbers with Divisibility Rules

Finding Unknown Factors in Multiplication

Mixed Division Facts Practice (0–10)

Balancing Multiplication and Division Equations

Division Facts and Fluency

Generating and Extending Arithmetic Patterns

Generating and Extending Geometric Patterns

Exploring Patterns in Multiplication Tables

Input-Output Tables with Multiplication Rules

Input-Output Tables with Division Rules

Input-Output Tables with Two-Step Rules

Representing Patterns as Ordered Number Pairs

Formulating Verbal Rules and Step-by-Step Algorithms

Number Patterns and Input-Output Rules

Mnożenie jako dodawanie tych samych składników

Tabliczka mnożenia przez 2 i 3

Tabliczka mnożenia przez 4 i 5

Tabliczka mnożenia przez 6 i 7

Tabliczka mnożenia przez 8 i 9

Mnożenie przez 0, 1 i 10

Przemienność mnożenia

Łączność mnożenia – trzy czynniki

Rozdzielność mnożenia względem dodawania

Tabliczka mnożenia i jej właściwości

Mnożenie przez 10 liczb mniejszych od 20

Mnożenie liczb dwucyfrowych przez 2

Mnożenie liczb dwucyfrowych przez 3, 4 i 5

Mnożenie liczb dwucyfrowych przez 6–9

Mnożenie liczb z zerami na końcu

Mnożenie pisemne przez liczbę jednocyfrową

Mnożenie pisemne przez liczbę dwucyfrową – wprowadzenie

Mnożenie pisemne przez liczbę dwucyfrową – ćwiczenia

Mnożenie w pamięci i pisemne

Propiedad de invarianza del cociente al multiplicar o dividir ambos términos

Jerarquía de las operaciones sin signos de agrupación

Uso de paréntesis y corchetes en expresiones combinadas

Traducción entre lenguaje verbal y expresiones numéricas

Problemas verbales combinados con las cuatro operaciones

Propiedades de la división y operaciones combinadas

Concepto de múltiplo y secuencias multiplicativas

Concepto de divisor y pares de factores

Criterios de divisibilidad por 2, 5 y 10

Criterios de divisibilidad por 3, 4, 6 y 9

Números primos y compuestos: la criba de Eratóstenes

Descomposición en factores primos: árboles de factores

Descomposición en factores primos por divisiones sucesivas

Múltiplos, divisores, divisibilidad y números primos

Szacowanie iloczynów

Równania z okienkiem – mnożenie

Równania z okienkiem – dzielenie

Zadania tekstowe – mnożenie

Wiązki między mnożeniem a dodawaniem

Sprawdzenie – mnożenie

Zastosowanie mnożenia w zadaniach

Dzielenie jako podział na równe części

Dzielenie jako wielokrotne odejmowanie

Tabliczka dzielenia przez 2 i 3

Tabliczka dzielenia przez 4 i 5

Tabliczka dzielenia przez 6, 7, 8 i 9

Dzielenie przez 10

Dzielenie z resztą – wprowadzenie

Dzielenie z resztą – ćwiczenia

Sprawdzanie dzielenia mnożeniem

Dzielenie w pamięci i z resztą

Mínimo común múltiplo (m.c.m.): concepto y listas de múltiplos

Cálculo del m.c.m. por descomposición simultánea

m.c.m., m.c.d. y resolución de problemas

OGM.4.OA.3

Aligned learning resources

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