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Imagine you have a box of 10 delicious donuts. You can see 7 glazed donuts, but the lid hides the rest — how many jelly donuts are inside?

We can solve this mystery using a **ten-frame**, which is a grid of 10 empty boxes that helps us picture numbers.

<!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>Ten-Frame Fact Family</title>
  <style>
    * {
      box-sizing: border-box;
      margin: 0;
      padding: 0;
      -webkit-tap-highlight-color: transparent;
      user-select: none;
    }

    body {
      font-family: system-ui, -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, sans-serif;
      background: #f8f9fa;
      color: #1e2945;
      display: flex;
      flex-direction: column;
      align-items: center;
      justify-content: space-between;
      min-height: 100%;
      padding: 12px 16px;
    }

    .main-wrap {
      width: 100%;
      max-width: 440px;
      display: flex;
      flex-direction: column;
      align-items: center;
      gap: 14px;
    }

    /* Ten-Frame */
    .ten-frame-container {
      width: 100%;
      display: flex;
      flex-direction: column;
      align-items: center;
      gap: 6px;
    }

    .ten-frame {
      display: grid;
      grid-template-columns: repeat(5, 1fr);
      grid-template-rows: repeat(2, 1fr);
      gap: 6px;
      width: 100%;
      background: #ffffff;
      padding: 8px;
      border-radius: 12px;
      box-shadow: 0 2px 6px rgba(0, 0, 0, 0.05);
      border: 2px solid #e2e8f0;
    }

    .slot {
      aspect-ratio: 1;
      border: 2px dashed #cbd5e1;
      border-radius: 10px;
      display: flex;
      align-items: center;
      justify-content: center;
      cursor: pointer;
      background: #f8fafc;
      transition: background-color 0.15s ease;
    }

    .slot:hover {
      background: #f1f5f9;
    }

    .counter {
      width: 78%;
      height: 78%;
      border-radius: 50%;
      transition: transform 0.25s ease, background-color 0.25s ease;
      box-shadow: 0 2px 4px rgba(0, 0, 0, 0.12);
    }

    .counter.blue {
      background-color: #22b7ff;
    }

    .counter.orange {
      background-color: #ff922b;
    }

    /* Controls */
    .controls {
      display: flex;
      align-items: center;
      justify-content: center;
      gap: 12px;
      width: 100%;
    }

    .btn-step {
      background: #ffffff;
      border: 1px solid #cbd5e1;
      color: #1e2945;
      font-size: 18px;
      font-weight: bold;
      width: 36px;
      height: 36px;
      border-radius: 50%;
      display: flex;
      align-items: center;
      justify-content: center;
      cursor: pointer;
      box-shadow: 0 1px 3px rgba(0,0,0,0.08);
      transition: background-color 0.15s ease;
    }

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

    .parts-indicator {
      display: flex;
      align-items: center;
      gap: 8px;
      font-size: 18px;
      font-weight: 700;
      background: #ffffff;
      padding: 6px 16px;
      border-radius: 20px;
      border: 1px solid #e2e8f0;
    }

    .num-tag {
      display: inline-flex;
      align-items: center;
      justify-content: center;
      min-width: 24px;
      border-radius: 6px;
      padding: 2px 6px;
      color: #ffffff;
    }

    .num-tag.blue {
      background: #22b7ff;
    }

    .num-tag.orange {
      background: #ff922b;
    }

    /* Fact Family Equations Grid */
    .facts-grid {
      display: grid;
      grid-template-columns: 1fr 1fr;
      gap: 8px;
      width: 100%;
    }

    .fact-card {
      background: #ffffff;
      border: 1px solid #e2e8f0;
      border-radius: 10px;
      padding: 10px;
      text-align: center;
      font-size: 18px;
      font-weight: 600;
      box-shadow: 0 1px 3px rgba(0, 0, 0, 0.04);
      display: flex;
      align-items: center;
      justify-content: center;
      gap: 4px;
    }

    .c-blue {
      color: #0284c7;
      font-weight: 700;
    }

    .c-orange {
      color: #ea580c;
      font-weight: 700;
    }

    .c-total {
      color: #1e2945;
      font-weight: 800;
    }
  </style>
</head>
<body>

  <div class="main-wrap">
    
    <div class="ten-frame-container">
      <div class="ten-frame" id="tenFrame"></div>
    </div>

    
    <div class="controls">
      <button class="btn-step" id="btnMinus" aria-label="Decrease Blue">−</button>
      <div class="parts-indicator">
        <span class="num-tag blue" id="labelA">7</span>
        <span>+</span>
        <span class="num-tag orange" id="labelB">3</span>
        <span>=</span>
        <span>10</span>
      </div>
      <button class="btn-step" id="btnPlus" aria-label="Increase Blue">+</button>
    </div>

    
    <div class="facts-grid">
      <div class="fact-card" id="fact1"></div>
      <div class="fact-card" id="fact2"></div>
      <div class="fact-card" id="fact3"></div>
      <div class="fact-card" id="fact4"></div>
    </div>
  </div>

  <script>
    const TOTAL = 10;
    let split = 7; // Number of blue counters (1 to 9)

    const frameEl = document.getElementById('tenFrame');
    const labelA = document.getElementById('labelA');
    const labelB = document.getElementById('labelB');
    const btnMinus = document.getElementById('btnMinus');
    const btnPlus = document.getElementById('btnPlus');

    const f1 = document.getElementById('fact1');
    const f2 = document.getElementById('fact2');
    const f3 = document.getElementById('fact3');
    const f4 = document.getElementById('fact4');

    // Build 10 slots
    for (let i = 0; i < TOTAL; i++) {
      const slot = document.createElement('div');
      slot.className = 'slot';
      slot.setAttribute('data-index', i + 1);

      const counter = document.createElement('div');
      counter.className = 'counter';
      slot.appendChild(counter);

      slot.addEventListener('click', () => {
        split = i + 1;
        render();
      });

      frameEl.appendChild(slot);
    }

    function render() {
      const b = TOTAL - split;

      labelA.textContent = split;
      labelB.textContent = b;

      // Update counters
      const counters = frameEl.querySelectorAll('.counter');
      counters.forEach((c, idx) => {
        if (idx < split) {
          c.className = 'counter blue';
        } else {
          c.className = 'counter orange';
        }
      });

      // Update Fact Family
      f1.innerHTML = `<span class="c-blue">${split}</span> + <span class="c-orange">${b}</span> = <span class="c-total">10</span>`;
      f2.innerHTML = `<span class="c-orange">${b}</span> + <span class="c-blue">${split}</span> = <span class="c-total">10</span>`;
      f3.innerHTML = `<span class="c-total">10</span> − <span class="c-blue">${split}</span> = <span class="c-orange">${b}</span>`;
      f4.innerHTML = `<span class="c-total">10</span> − <span class="c-orange">${b}</span> = <span class="c-blue">${split}</span>`;
    }

    btnMinus.addEventListener('click', () => {
      if (split > 1) {
        split--;
        render();
      }
    });

    btnPlus.addEventListener('click', () => {
      if (split < 9) {
        split++;
        render();
      }
    });

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

Three numbers that fit together like best friends make a **fact family**.

The numbers 7, 3, and 10 belong together because $7 + 3 = 10$, $3 + 7 = 10$, $10 - 3 = 7$, and $10 - 7 = 3$.

<!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>Ten-Frame Fact Families</title>
  <style>
    * {
      box-sizing: border-box;
      margin: 0;
      padding: 0;
      font-family: system-ui, -apple-system, BlinkMacSystemFont, 'Segoe UI', Roboto, sans-serif;
    }

    body {
      background: #f8f9fa;
      color: #1e2945;
      display: flex;
      flex-direction: column;
      align-items: center;
      justify-content: space-between;
      min-height: 100%;
      padding: 12px;
      gap: 10px;
    }

    /* Top: Number Bond */
    .bond-container {
      display: flex;
      flex-direction: column;
      align-items: center;
      position: relative;
      width: 140px;
      height: 70px;
    }

    .bond-svg {
      position: absolute;
      top: 0;
      left: 0;
      width: 100%;
      height: 100%;
      pointer-events: none;
    }

    .bond-node {
      position: absolute;
      width: 32px;
      height: 32px;
      border-radius: 50%;
      display: flex;
      align-items: center;
      justify-content: center;
      font-weight: 700;
      font-size: 16px;
      background: #ffffff;
      box-shadow: 0 2px 6px rgba(0, 0, 0, 0.08);
      border: 2px solid #e6e6e6;
      z-index: 1;
      transition: box-shadow 0.3s ease, border-color 0.3s ease;
    }

    .node-total {
      top: 0;
      left: 54px;
      color: #1e2945;
      border-color: #1e2945;
    }

    .node-part-a {
      bottom: 0;
      left: 14px;
      color: #e11d48;
      border-color: #e11d48;
    }

    .node-part-b {
      bottom: 0;
      right: 14px;
      color: #2563eb;
      border-color: #2563eb;
    }

    /* Middle: Equation Display */
    .equation-card {
      background: #ffffff;
      padding: 6px 18px;
      border-radius: 12px;
      box-shadow: 0 2px 8px rgba(0, 0, 0, 0.04);
      border: 1px solid #e6e6e6;
      font-size: 26px;
      font-weight: 800;
      display: flex;
      align-items: center;
      gap: 8px;
      min-height: 46px;
    }

    .num-red { color: #e11d48; }
    .num-blue { color: #2563eb; }
    .num-total { color: #1e2945; }
    .op-symbol { color: #94a3b8; font-weight: 600; }

    /* Ten-Frame Visual */
    .frame-wrapper {
      background: #ffffff;
      padding: 10px;
      border-radius: 14px;
      box-shadow: 0 3px 12px rgba(0, 0, 0, 0.05);
      border: 1px solid #e2e8f0;
    }

    .ten-frame {
      display: grid;
      grid-template-columns: repeat(5, 46px);
      grid-template-rows: repeat(2, 46px);
      gap: 4px;
      background: #cbd5e1;
      padding: 4px;
      border-radius: 8px;
    }

    .cell {
      background: #ffffff;
      border-radius: 6px;
      display: flex;
      align-items: center;
      justify-content: center;
      position: relative;
    }

    .counter {
      width: 34px;
      height: 34px;
      border-radius: 50%;
      transition: opacity 0.4s ease, transform 0.3s ease, filter 0.4s ease;
    }

    .counter-red {
      background: radial-gradient(circle at 35% 35%, #fb7185, #e11d48);
      box-shadow: 0 2px 4px rgba(225, 29, 72, 0.3);
    }

    .counter-blue {
      background: radial-gradient(circle at 35% 35%, #60a5fa, #2563eb);
      box-shadow: 0 2px 4px rgba(37, 99, 235, 0.3);
    }

    /* Counter States */
    .dimmed {
      opacity: 0.18;
      filter: grayscale(80%);
      transform: scale(0.85);
    }

    .takeaway-badge {
      position: absolute;
      font-size: 18px;
      font-weight: 900;
      color: #64748b;
      opacity: 0;
      transition: opacity 0.3s ease;
      pointer-events: none;
    }

    .dimmed + .takeaway-badge {
      opacity: 0.7;
    }

    /* Bottom: Stepper / Controls */
    .controls {
      display: flex;
      flex-direction: column;
      align-items: center;
      gap: 8px;
      width: 100%;
      max-width: 440px;
    }

    .fact-buttons {
      display: grid;
      grid-template-columns: 1fr 1fr;
      gap: 6px;
      width: 100%;
    }

    .fact-btn {
      background: #ffffff;
      border: 1.5px solid #e2e8f0;
      padding: 8px 10px;
      border-radius: 8px;
      font-size: 15px;
      font-weight: 700;
      color: #64748b;
      cursor: pointer;
      display: flex;
      justify-content: center;
      align-items: center;
      gap: 4px;
      transition: background 0.2s, border-color 0.2s, box-shadow 0.2s;
    }

    .fact-btn.active {
      border-color: #22b7ff;
      background: #f0f9ff;
      color: #0369a1;
      box-shadow: 0 0 0 2px rgba(34, 183, 255, 0.2);
    }

    .playback-bar {
      display: flex;
      align-items: center;
      justify-content: center;
      gap: 8px;
    }

    .play-btn {
      background: #ffffff;
      border: 1px solid #cbd5e1;
      width: 32px;
      height: 32px;
      border-radius: 50%;
      font-size: 13px;
      color: #475569;
      cursor: pointer;
      display: flex;
      align-items: center;
      justify-content: center;
    }

    @media (max-width: 340px) {
      .ten-frame {
        grid-template-columns: repeat(5, 38px);
        grid-template-rows: repeat(2, 38px);
      }
      .counter {
        width: 28px;
        height: 28px;
      }
      .equation-card {
        font-size: 22px;
      }
    }
  </style>
</head>
<body>

  
  <div class="bond-container">
    <svg class="bond-svg" viewBox="0 0 140 70">
      <line x1="70" y1="20" x2="30" y2="50" stroke="#cbd5e1" stroke-width="2.5" stroke-linecap="round" />
      <line x1="70" y1="20" x2="110" y2="50" stroke="#cbd5e1" stroke-width="2.5" stroke-linecap="round" />
    </svg>
    <div class="bond-node node-total" id="nodeTotal">10</div>
    <div class="bond-node node-part-a" id="nodeA">7</div>
    <div class="bond-node node-part-b" id="nodeB">3</div>
  </div>

  
  <div class="equation-card" id="equationDisplay">
    <span class="num-red">7</span>
    <span class="op-symbol">+</span>
    <span class="num-blue">3</span>
    <span class="op-symbol">=</span>
    <span class="num-total">10</span>
  </div>

  
  <div class="frame-wrapper">
    <div class="ten-frame">
      
      <div class="cell"><div class="counter counter-red" data-group="red"></div><span class="takeaway-badge">✕</span></div>
      <div class="cell"><div class="counter counter-red" data-group="red"></div><span class="takeaway-badge">✕</span></div>
      <div class="cell"><div class="counter counter-red" data-group="red"></div><span class="takeaway-badge">✕</span></div>
      <div class="cell"><div class="counter counter-red" data-group="red"></div><span class="takeaway-badge">✕</span></div>
      <div class="cell"><div class="counter counter-red" data-group="red"></div><span class="takeaway-badge">✕</span></div>
      <div class="cell"><div class="counter counter-red" data-group="red"></div><span class="takeaway-badge">✕</span></div>
      <div class="cell"><div class="counter counter-red" data-group="red"></div><span class="takeaway-badge">✕</span></div>
      
      <div class="cell"><div class="counter counter-blue" data-group="blue"></div><span class="takeaway-badge">✕</span></div>
      <div class="cell"><div class="counter counter-blue" data-group="blue"></div><span class="takeaway-badge">✕</span></div>
      <div class="cell"><div class="counter counter-blue" data-group="blue"></div><span class="takeaway-badge">✕</span></div>
    </div>
  </div>

  
  <div class="controls">
    <div class="fact-buttons">
      <button class="fact-btn active" data-step="0">
        <span class="num-red">7</span> + <span class="num-blue">3</span> = 10
      </button>
      <button class="fact-btn" data-step="1">
        <span class="num-blue">3</span> + <span class="num-red">7</span> = 10
      </button>
      <button class="fact-btn" data-step="2">
        10 - <span class="num-blue">3</span> = <span class="num-red">7</span>
      </button>
      <button class="fact-btn" data-step="3">
        10 - <span class="num-red">7</span> = <span class="num-blue">3</span>
      </button>
    </div>

    <div class="playback-bar">
      <button class="play-btn" id="playBtn" aria-label="Play or Pause">⏸</button>
    </div>
  </div>

  <script src="{{VENDOR_CDN}}/classace-diagram.js"></script>
  <script>
    const facts = [
      {
        html: '<span class="num-red">7</span><span class="op-symbol">+</span><span class="num-blue">3</span><span class="op-symbol">=</span><span class="num-total">10</span>',
        dimRed: false,
        dimBlue: false,
        activeNode: 'all'
      },
      {
        html: '<span class="num-blue">3</span><span class="op-symbol">+</span><span class="num-red">7</span><span class="op-symbol">=</span><span class="num-total">10</span>',
        dimRed: false,
        dimBlue: false,
        activeNode: 'all'
      },
      {
        html: '<span class="num-total">10</span><span class="op-symbol">-</span><span class="num-blue">3</span><span class="op-symbol">=</span><span class="num-red">7</span>',
        dimRed: false,
        dimBlue: true,
        activeNode: 'red'
      },
      {
        html: '<span class="num-total">10</span><span class="op-symbol">-</span><span class="num-red">7</span><span class="op-symbol">=</span><span class="num-blue">3</span>',
        dimRed: true,
        dimBlue: false,
        activeNode: 'blue'
      }
    ];

    const eqEl = document.getElementById('equationDisplay');
    const redCounters = document.querySelectorAll('.counter[data-group="red"]');
    const blueCounters = document.querySelectorAll('.counter[data-group="blue"]');
    const factButtons = document.querySelectorAll('.fact-btn');
    const playBtn = document.getElementById('playBtn');

    function applyFact(index) {
      const f = facts[index];
      eqEl.innerHTML = f.html;

      redCounters.forEach(c => c.classList.toggle('dimmed', f.dimRed));
      blueCounters.forEach(c => c.classList.toggle('dimmed', f.dimBlue));

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

    // Step player setup (3.5s per fact family member)
    const player = new StepPlayer('.fact-btn', {
      interval: 3500,
      onChange: (idx) => {
        applyFact(idx);
      }
    });

    player.start();

    factButtons.forEach((btn, idx) => {
      onTap(btn, () => {
        player.goTo(idx);
      });
    });

    onTap(playBtn, () => {
      player.toggle();
      playBtn.textContent = player.playing ? '⏸' : '▶';
    });
  </script>
</body>
</html>

What happens when one of those numbers is hidden behind a mystery box? Let's find out!

Look at this missing number puzzle: $8 + \Box = 10$.

You start with 8 dots in your ten-frame. To reach 10, you only need to count the empty spaces left over.

<!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>Ten-Frame Missing Value</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: #f8f9fa;
      display: flex;
      flex-direction: column;
      align-items: center;
      justify-content: center;
      min-height: 100%;
      padding: 16px;
      gap: 14px;
    }

    /* Equation Display */
    .equation-card {
      background: #ffffff;
      padding: 10px 20px;
      border-radius: 12px;
      box-shadow: 0 2px 8px rgba(0, 0, 0, 0.05);
      display: flex;
      align-items: center;
      gap: 8px;
      font-size: 24px;
      font-weight: 700;
    }

    .num-start {
      color: #16a34a;
    }

    .num-missing {
      background: #fef08a;
      color: #854d0e;
      border: 2px dashed #eab308;
      border-radius: 8px;
      padding: 2px 10px;
      min-width: 38px;
      text-align: center;
      transition: all 0.3s ease;
    }

    .num-missing.solved {
      background: #fef08a;
      border: 2px solid #eab308;
    }

    .num-missing.error {
      background: #fee2e2;
      color: #b91c1c;
      border: 2px solid #ef4444;
    }

    .num-total {
      color: #1e2945;
    }

    /* Ten-Frame Container */
    .frame-container {
      position: relative;
      background: #ffffff;
      padding: 12px;
      border-radius: 12px;
      box-shadow: 0 2px 8px rgba(0, 0, 0, 0.05);
      display: flex;
      flex-direction: column;
      align-items: center;
      gap: 10px;
      width: 100%;
      max-width: 380px;
    }

    .ten-frame {
      display: grid;
      grid-template-columns: repeat(5, 1fr);
      grid-template-rows: repeat(2, 1fr);
      gap: 6px;
      width: 100%;
      aspect-ratio: 5 / 2;
    }

    .cell {
      background: #f1f5f9;
      border: 2px solid #cbd5e1;
      border-radius: 8px;
      display: flex;
      align-items: center;
      justify-content: center;
      position: relative;
    }

    .cell.missing-slot {
      border: 2px dashed #eab308;
      background: #fefce8;
    }

    .dot {
      width: 68%;
      height: 68%;
      border-radius: 50%;
      transition: all 0.3s ease;
      opacity: 0;
      transform: scale(0.3);
    }

    .dot.green {
      background: #16a34a;
      opacity: 1;
      transform: scale(1);
    }

    .dot.yellow {
      background: #eab308;
      opacity: 1;
      transform: scale(1);
    }

    .dot-question {
      font-size: 20px;
      font-weight: 800;
      color: #ca8a04;
      opacity: 0;
      transform: scale(0.3);
      transition: all 0.3s ease;
    }

    .dot-question.show {
      opacity: 1;
      transform: scale(1);
    }

    /* Overflow Indicator */
    .overflow-box {
      width: 100%;
      display: flex;
      align-items: center;
      justify-content: space-between;
      padding: 6px 12px;
      border-radius: 8px;
      font-size: 14px;
      font-weight: 600;
      background: #f8fafc;
      color: #64748b;
      min-height: 34px;
    }

    .overflow-box.alert {
      background: #fee2e2;
      color: #b91c1c;
    }

    /* Step / Tab Controls */
    .controls {
      display: flex;
      flex-wrap: wrap;
      gap: 8px;
      justify-content: center;
      width: 100%;
      max-width: 380px;
    }

    .btn {
      padding: 8px 14px;
      font-size: 14px;
      font-weight: 600;
      border-radius: 8px;
      border: 1px solid #cbd5e1;
      background: #ffffff;
      color: #1e2945;
      cursor: pointer;
      box-shadow: 0 1px 2px rgba(0, 0, 0, 0.05);
      transition: all 0.2s ease;
    }

    .btn:active {
      transform: scale(0.97);
    }

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

    .btn-warn.active {
      background: #ef4444;
      border-color: #ef4444;
      color: #ffffff;
    }
  </style>
</head>
<body>

  
  <div class="equation-card">
    <span class="num-start">8</span>
    <span>+</span>
    <span class="num-missing" id="missingBox">?</span>
    <span>=</span>
    <span class="num-total" id="totalBox">10</span>
  </div>

  
  <div class="frame-container">
    <div class="ten-frame" id="tenFrame">
      
    </div>
    <div class="overflow-box" id="statusLabel">
      <span>Frame capacity: 10</span>
      <span id="countTag">8 / 10 filled</span>
    </div>
  </div>

  
  <div class="controls">
    <button class="btn active" id="btn1" onclick="setStep(1)">1. Start (8)</button>
    <button class="btn" id="btn2" onclick="setStep(2)">2. Find Empty (?)</button>
    <button class="btn" id="btn3" onclick="setStep(3)">3. Complete (10)</button>
    <button class="btn btn-warn" id="btn4" onclick="setStep(4)">⚠️ 8 + 10 = 18</button>
  </div>

  <script>
    const frame = document.getElementById('tenFrame');
    const missingBox = document.getElementById('missingBox');
    const totalBox = document.getElementById('totalBox');
    const statusLabel = document.getElementById('statusLabel');
    const countTag = document.getElementById('countTag');

    // Create 10 cells
    for (let i = 0; i < 10; i++) {
      const cell = document.createElement('div');
      cell.className = 'cell';
      cell.id = `cell-${i}`;
      
      const dot = document.createElement('div');
      dot.className = 'dot';
      dot.id = `dot-${i}`;
      
      const q = document.createElement('span');
      q.className = 'dot-question';
      q.id = `q-${i}`;
      q.textContent = '?';

      cell.appendChild(dot);
      cell.appendChild(q);
      frame.appendChild(cell);
    }

    function setStep(step) {
      // Update buttons
      for (let i = 1; i <= 4; i++) {
        const btn = document.getElementById(`btn${i}`);
        btn.classList.toggle('active', i === step);
      }

      // Reset cells
      for (let i = 0; i < 10; i++) {
        const cell = document.getElementById(`cell-${i}`);
        const dot = document.getElementById(`dot-${i}`);
        const q = document.getElementById(`q-${i}`);
        
        cell.className = 'cell';
        dot.className = 'dot';
        q.className = 'dot-question';

        if (i < 8) {
          dot.classList.add('green');
        }
      }

      statusLabel.className = 'overflow-box';

      if (step === 1) {
        missingBox.className = 'num-missing';
        missingBox.textContent = '?';
        totalBox.textContent = '10';
        statusLabel.children[0].textContent = 'Start dots: 8';
        countTag.textContent = '2 spaces empty';
      } 
      else if (step === 2) {
        missingBox.className = 'num-missing';
        missingBox.textContent = '?';
        totalBox.textContent = '10';
        
        // Highlight 2 empty spaces
        for (let i = 8; i < 10; i++) {
          document.getElementById(`cell-${i}`).classList.add('missing-slot');
          document.getElementById(`q-${i}`).classList.add('show');
        }
        statusLabel.children[0].textContent = 'Count empty spaces:';
        countTag.textContent = '2 missing';
      } 
      else if (step === 3) {
        missingBox.className = 'num-missing solved';
        missingBox.textContent = '2';
        totalBox.textContent = '10';

        // Fill with yellow dots
        for (let i = 8; i < 10; i++) {
          document.getElementById(`dot-${i}`).classList.add('yellow');
        }
        statusLabel.children[0].textContent = 'Fact: 8 + 2 = 10';
        countTag.textContent = '10 / 10 full ✓';
      } 
      else if (step === 4) {
        missingBox.className = 'num-missing error';
        missingBox.textContent = '10';
        totalBox.textContent = '18';

        // Fill all ten frame and show overflow alert
        for (let i = 8; i < 10; i++) {
          document.getElementById(`dot-${i}`).classList.add('yellow');
        }
        statusLabel.classList.add('alert');
        statusLabel.children[0].textContent = '⚠️ 18 is too big!';
        countTag.textContent = '+8 overflow';
      }
    }

    // Initialize at step 1
    setStep(1);
  </script>
</body>
</html>

Be careful not to add the big total to your start number! If you did $8 + 10 = 18$, the answer would be too big to fit inside our 10-frame.

What if our mystery number puzzle goes all the way up to 20? Let's use two ten-frames together!

When we work with numbers larger than 10, a **double ten-frame** gives us 20 boxes to fill.

First, place 9 purple dots in the top frame. Then add orange dots until you have 15 in all: 1 to make 10, and 5 more in the bottom frame.

<!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>Ten-Frame Fact Family</title>
<link rel="stylesheet" href="https://cdn.jsdelivr.net/npm/katex@0.16.8/dist/katex.min.css">
<script defer src="https://cdn.jsdelivr.net/npm/katex@0.16.8/dist/katex.min.js"></script>
<script src="https://cdn.jsdelivr.net/npm/classace-diagram@latest/dist/classace-diagram.js"></script>
<style>
  * { box-sizing: border-box; margin: 0; padding: 0; }
  body {
    font-family: -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, Helvetica, Arial, sans-serif;
    background: transparent;
    color: #1e2945;
    display: flex;
    flex-direction: column;
    align-items: center;
    justify-content: center;
    padding: 12px;
    gap: 12px;
    min-height: 100%;
  }

  /* Step Controls */
  .controls {
    display: flex;
    align-items: center;
    justify-content: center;
    gap: 6px;
    flex-wrap: wrap;
    width: 100%;
    max-width: 480px;
  }
  .step-btn {
    border: 1px solid #e2e8f0;
    background: #ffffff;
    color: #64748b;
    font-size: 13px;
    font-weight: 600;
    padding: 5px 10px;
    border-radius: 16px;
    cursor: pointer;
    transition: all 0.2s ease;
    box-shadow: 0 1px 2px rgba(0,0,0,0.04);
  }
  .step-btn.active {
    background: #22b7ff;
    color: #ffffff;
    border-color: #22b7ff;
  }
  .play-btn {
    border: 1px solid #e2e8f0;
    background: #ffffff;
    color: #1e2945;
    font-size: 13px;
    font-weight: 600;
    padding: 5px 10px;
    border-radius: 16px;
    cursor: pointer;
    min-width: 34px;
    display: flex;
    align-items: center;
    justify-content: center;
  }

  /* Frames Container */
  .frames-wrapper {
    display: flex;
    flex-direction: column;
    gap: 10px;
    align-items: center;
    width: 100%;
    max-width: 380px;
  }

  .ten-frame-box {
    background: #ffffff;
    border: 2px solid #cbd5e1;
    border-radius: 10px;
    padding: 5px;
    width: 100%;
    box-shadow: 0 2px 4px rgba(0,0,0,0.03);
  }

  .ten-frame {
    display: grid;
    grid-template-columns: repeat(5, 1fr);
    grid-template-rows: repeat(2, 1fr);
    gap: 4px;
    width: 100%;
    aspect-ratio: 5 / 2;
  }

  .cell {
    background: #f8fafc;
    border: 1.5px dashed #cbd5e1;
    border-radius: 6px;
    display: flex;
    align-items: center;
    justify-content: center;
    position: relative;
  }

  /* Counters */
  .dot {
    width: 72%;
    height: 72%;
    border-radius: 50%;
    opacity: 0;
    transform: scale(0.4);
    transition: opacity 0.35s ease, transform 0.35s ease, box-shadow 0.35s ease;
  }
  .dot.purple {
    background: #9333ea;
  }
  .dot.orange {
    background: #f97316;
  }
  .dot.visible {
    opacity: 1;
    transform: scale(1);
  }
  .dot.highlight {
    box-shadow: 0 0 0 3px #fed7aa, 0 0 8px #f97316;
  }

  /* Equation display card */
  .math-bar {
    background: #ffffff;
    border: 1px solid #e2e8f0;
    border-radius: 12px;
    padding: 8px 16px;
    display: flex;
    align-items: center;
    justify-content: center;
    gap: 16px;
    width: 100%;
    max-width: 380px;
    min-height: 48px;
    box-shadow: 0 2px 5px rgba(0,0,0,0.04);
  }

  .badge {
    display: inline-flex;
    align-items: center;
    gap: 5px;
    font-size: 13px;
    font-weight: 700;
    padding: 3px 8px;
    border-radius: 6px;
  }
  .badge-purple { background: #f3e8ff; color: #7e22ce; }
  .badge-orange { background: #ffedd5; color: #c2410c; }
  .badge-total { background: #e0f2fe; color: #0369a1; }

  .equation {
    font-size: 18px;
    font-weight: 700;
    color: #1e2945;
  }
  .katex { font-size: 1.1em; }
</style>
</head>
<body>

  <div class="controls">
    <button class="step-btn active" data-step="0">1. Start (9)</button>
    <button class="step-btn" data-step="1">2. Make 10 (+1)</button>
    <button class="step-btn" data-step="2">3. Reach 15 (+5)</button>
    <button class="step-btn" data-step="3">4. Fact Family</button>
    <button class="play-btn" id="playToggle" title="Play/Pause">⏸</button>
  </div>

  <div class="frames-wrapper">
    
    <div class="ten-frame-box">
      <div class="ten-frame" id="frame1">
        <div class="cell"><div class="dot purple"></div></div>
        <div class="cell"><div class="dot purple"></div></div>
        <div class="cell"><div class="dot purple"></div></div>
        <div class="cell"><div class="dot purple"></div></div>
        <div class="cell"><div class="dot purple"></div></div>
        <div class="cell"><div class="dot purple"></div></div>
        <div class="cell"><div class="dot purple"></div></div>
        <div class="cell"><div class="dot purple"></div></div>
        <div class="cell"><div class="dot purple"></div></div>
        <div class="cell"><div class="dot orange" id="dot10"></div></div>
      </div>
    </div>

    
    <div class="ten-frame-box">
      <div class="ten-frame" id="frame2">
        <div class="cell"><div class="dot orange b-dot"></div></div>
        <div class="cell"><div class="dot orange b-dot"></div></div>
        <div class="cell"><div class="dot orange b-dot"></div></div>
        <div class="cell"><div class="dot orange b-dot"></div></div>
        <div class="cell"><div class="dot orange b-dot"></div></div>
        <div class="cell"><div class="dot"></div></div>
        <div class="cell"><div class="dot"></div></div>
        <div class="cell"><div class="dot"></div></div>
        <div class="cell"><div class="dot"></div></div>
        <div class="cell"><div class="dot"></div></div>
      </div>
    </div>
  </div>

  
  <div class="math-bar">
    <div id="mathDisplay" class="equation"></div>
  </div>

<script>
  const purpleDots = document.querySelectorAll('.dot.purple');
  const dot10 = document.getElementById('dot10');
  const bottomOrangeDots = document.querySelectorAll('.b-dot');
  const stepBtns = document.querySelectorAll('.step-btn');
  const playToggle = document.getElementById('playToggle');
  const mathDisplay = document.getElementById('mathDisplay');

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

  const mathFormulas = [
    "9 + \\Box = 15",
    "9 + \\color{#ea580c}{\\mathbf{1}} = 10",
    "10 + \\color{#ea580c}{\\mathbf{5}} = 15",
    "15 - 9 = \\color{#ea580c}{\\mathbf{6}}"
  ];

  function renderMath(step) {
    if (window.katex) {
      katex.render(mathFormulas[step], mathDisplay, { throwOnError: false });
    } else {
      const fallbacks = [
        "9 + ? = 15",
        "9 + 1 = 10",
        "10 + 5 = 15",
        "15 - 9 = 6"
      ];
      mathDisplay.textContent = fallbacks[step];
    }
  }

  function setStep(step) {
    currentStep = step;

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

    // Reset highlights
    dot10.classList.remove('highlight');
    bottomOrangeDots.forEach(d => d.classList.remove('highlight'));

    if (step === 0) {
      purpleDots.forEach(d => d.classList.add('visible'));
      dot10.classList.remove('visible');
      bottomOrangeDots.forEach(d => d.classList.remove('visible'));
    } else if (step === 1) {
      purpleDots.forEach(d => d.classList.add('visible'));
      dot10.classList.add('visible');
      dot10.classList.add('highlight');
      bottomOrangeDots.forEach(d => d.classList.remove('visible'));
    } else if (step === 2) {
      purpleDots.forEach(d => d.classList.add('visible'));
      dot10.classList.add('visible');
      bottomOrangeDots.forEach(d => {
        d.classList.add('visible');
        d.classList.add('highlight');
      });
    } else if (step === 3) {
      purpleDots.forEach(d => d.classList.add('visible'));
      dot10.classList.add('visible');
      dot10.classList.add('highlight');
      bottomOrangeDots.forEach(d => {
        d.classList.add('visible');
        d.classList.add('highlight');
      });
    }

    renderMath(step);
  }

  function nextStep() {
    setStep((currentStep + 1) % 4);
  }

  function startTimer() {
    clearInterval(timer);
    timer = setInterval(nextStep, 3400);
  }

  function pauseTimer() {
    clearInterval(timer);
  }

  playToggle.addEventListener('click', () => {
    isPlaying = !isPlaying;
    playToggle.textContent = isPlaying ? '⏸' : '▶';
    if (isPlaying) {
      nextStep();
      startTimer();
    } else {
      pauseTimer();
    }
  });

  stepBtns.forEach((btn, idx) => {
    btn.addEventListener('click', () => {
      setStep(idx);
      if (isPlaying) {
        startTimer();
      }
    });
  });

  // Initial render
  window.addEventListener('load', () => {
    setStep(0);
    startTimer();
  });
</script>
</body>
</html>

Because our fact family tells us $15 - 9 = 6$, our mystery box $\Box$ must be 6.

Whenever you see a mystery equation like $14 - \Box = 8$, remember you can use your ten-frames to find the missing partner every single time!

math

Using Ten-Frame Fact Families to Find Missing Values. Use addition and subtraction fact family connections to solve missing symbol equations within 20.

Number Fact Families: Addition and Subtraction Connections

Developing Early Number Sense and Ten-Frame Structures

Complete the Fact Family: Missing Numbers and Unknowns within 20

Adheres to the Scottish Curriculum for Excellence benchmark for MTH 1-15b via the Concrete-Pictorial-Abstract (CPA) approach. Young learners begin by physically placing dual-colour counters on double ten-frames, bridge to pictorial part-whole cherry diagrams and balance models, and finally connect these structures to abstract algebraic equations with missing symbols within 20.

Using Ten-Frame Fact Families to Find Missing Values

Finding the Missing Box