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Tutoring abilities

Imagine you have 6 delicious cookies to share with your best friend. How can you make sure you both get the exact same amount?

When we split a group of objects into **two equal piles**, each pile is called **half** of the whole group.

<!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>Sharing into Two Equal Groups</title>
  <style>
    * {
      box-sizing: border-box;
      margin: 0;
      padding: 0;
      font-family: -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, sans-serif;
      user-select: none;
    }
    body {
      background: #f8f9fa;
      color: #1e2945;
      display: flex;
      flex-direction: column;
      align-items: center;
      justify-content: space-between;
      min-height: 100%;
      padding: 12px;
      gap: 10px;
    }
    .controls {
      display: flex;
      align-items: center;
      justify-content: center;
      gap: 8px;
      flex-wrap: wrap;
    }
    .btn-num {
      padding: 6px 14px;
      font-size: 15px;
      font-weight: 600;
      border-radius: 20px;
      border: 2px solid transparent;
      background: #ffffff;
      color: #1e2945;
      box-shadow: 0 1px 3px rgba(0,0,0,0.08);
      cursor: pointer;
      transition: background 0.2s, box-shadow 0.2s;
    }
    .btn-num.active {
      background: #22b7ff;
      color: #ffffff;
      box-shadow: 0 2px 6px rgba(34, 183, 255, 0.35);
    }
    .btn-action {
      padding: 6px 16px;
      font-size: 15px;
      font-weight: 600;
      border-radius: 20px;
      border: none;
      background: #1e2945;
      color: #ffffff;
      cursor: pointer;
      transition: opacity 0.2s;
    }
    .btn-action:hover {
      opacity: 0.9;
    }
    .stage {
      position: relative;
      width: 100%;
      max-width: 480px;
      height: 240px;
      background: #ffffff;
      border-radius: 16px;
      box-shadow: 0 2px 8px rgba(0,0,0,0.05);
      display: flex;
      flex-direction: column;
      justify-content: space-between;
      padding: 12px 16px;
      overflow: hidden;
    }
    .pool-zone {
      height: 50px;
      display: flex;
      align-items: center;
      justify-content: center;
      position: relative;
    }
    .groups-zone {
      display: flex;
      justify-content: space-between;
      gap: 12px;
      height: 120px;
    }
    .group-box {
      flex: 1;
      background: #f0f7ff;
      border: 2px dashed #93c5fd;
      border-radius: 12px;
      display: flex;
      flex-direction: column;
      align-items: center;
      justify-content: flex-end;
      padding: 8px;
      position: relative;
    }
    .group-label {
      position: absolute;
      top: 6px;
      font-size: 13px;
      font-weight: 700;
      color: #0284c7;
      text-transform: uppercase;
      letter-spacing: 0.5px;
    }
    .token-grid {
      display: flex;
      flex-wrap: wrap;
      justify-content: center;
      align-items: center;
      gap: 6px;
      width: 100%;
      height: 70px;
    }
    .item {
      width: 32px;
      height: 32px;
      border-radius: 50%;
      background: #ff595e;
      color: #fff;
      display: flex;
      align-items: center;
      justify-content: center;
      font-size: 18px;
      box-shadow: 0 2px 4px rgba(0,0,0,0.12);
      transition: all 0.45s cubic-bezier(0.4, 0, 0.2, 1);
    }
    .math-bar {
      font-size: 18px;
      font-weight: 700;
      color: #1e2945;
      text-align: center;
      min-height: 28px;
      display: flex;
      align-items: center;
      justify-content: center;
      gap: 6px;
    }
    .badge {
      background: #e0f2fe;
      color: #0369a1;
      padding: 2px 10px;
      border-radius: 8px;
    }
  </style>
</head>
<body>

  <div class="controls">
    <button class="btn-num" data-count="4">4</button>
    <button class="btn-num active" data-count="6">6</button>
    <button class="btn-num" data-count="8">8</button>
    <button class="btn-action" id="shareBtn">▶ Share</button>
  </div>

  <div class="stage">
    <div class="pool-zone" id="poolZone"></div>
    <div class="groups-zone">
      <div class="group-box">
        <span class="group-label">Half</span>
        <div class="token-grid" id="leftGrid"></div>
      </div>
      <div class="group-box">
        <span class="group-label">Half</span>
        <div class="token-grid" id="rightGrid"></div>
      </div>
    </div>
  </div>

  <div class="math-bar" id="mathBar">
    Whole: <span class="badge">6</span>
  </div>

  <script>
    let total = 6;
    let shared = false;
    let timer = null;

    const poolZone = document.getElementById('poolZone');
    const leftGrid = document.getElementById('leftGrid');
    const rightGrid = document.getElementById('rightGrid');
    const mathBar = document.getElementById('mathBar');
    const shareBtn = document.getElementById('shareBtn');
    const numBtns = document.querySelectorAll('.btn-num');

    function createToken() {
      const el = document.createElement('div');
      el.className = 'item';
      el.textContent = '🍎';
      return el;
    }

    function resetStage() {
      if (timer) clearInterval(timer);
      poolZone.innerHTML = '';
      leftGrid.innerHTML = '';
      rightGrid.innerHTML = '';
      shared = false;
      shareBtn.textContent = '▶ Share';
      mathBar.innerHTML = `Whole: <span class="badge">${total}</span>`;

      for (let i = 0; i < total; i++) {
        poolZone.appendChild(createToken());
      }
    }

    function shareItems() {
      if (shared) {
        resetStage();
        return;
      }

      const items = Array.from(poolZone.children);
      if (!items.length) return;

      shareBtn.disabled = true;
      let i = 0;

      timer = setInterval(() => {
        if (i >= total) {
          clearInterval(timer);
          shared = true;
          shareBtn.disabled = false;
          shareBtn.textContent = '↺ Reset';
          const half = total / 2;
          mathBar.innerHTML = `Half of <span class="badge">${total}</span> is <span class="badge">${half}</span>`;
          return;
        }

        const item = items[i];
        if (i % 2 === 0) {
          leftGrid.appendChild(item);
        } else {
          rightGrid.appendChild(item);
        }
        i++;
      }, 400);
    }

    numBtns.forEach(btn => {
      btn.addEventListener('click', () => {
        numBtns.forEach(b => b.classList.remove('active'));
        btn.classList.add('active');
        total = parseInt(btn.getAttribute('data-count'), 10);
        resetStage();
      });
    });

    shareBtn.addEventListener('click', shareItems);

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

How can we find half of a bigger group without getting confused?

The easiest way to share fairly is to deal items out **one by one**, saying 'one for pile A, one for pile B' until everything is gone.

<!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>Sharing into Two Equal Groups</title>
<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: space-between;
    min-height: 100%;
    padding: 12px;
    user-select: none;
    -webkit-user-select: none;
  }

  /* Pool area */
  .pool-section {
    display: flex;
    flex-direction: column;
    align-items: center;
    gap: 6px;
    width: 100%;
    max-width: 420px;
  }
  .pool-label {
    font-size: 13px;
    font-weight: 700;
    text-transform: uppercase;
    letter-spacing: 0.5px;
    color: #6b7280;
  }
  .pool-tray {
    display: flex;
    justify-content: center;
    align-items: center;
    gap: 8px;
    min-height: 48px;
    padding: 6px 14px;
    background: #f1f5f9;
    border: 2px dashed #cbd5e1;
    border-radius: 12px;
    width: 100%;
  }

  /* Star styling */
  .star-item {
    font-size: 26px;
    line-height: 1;
    transition: transform 0.3s ease, opacity 0.3s ease;
    display: inline-block;
  }
  .star-item.empty {
    opacity: 0.15;
    filter: grayscale(1);
    transform: scale(0.85);
  }

  /* Dealing destination boxes */
  .groups-container {
    display: flex;
    gap: 12px;
    width: 100%;
    max-width: 420px;
    justify-content: center;
    margin: 8px 0;
  }
  .group-box {
    flex: 1;
    background: #ffffff;
    border: 2px solid #e2e8f0;
    border-radius: 12px;
    padding: 10px 8px;
    display: flex;
    flex-direction: column;
    align-items: center;
    box-shadow: 0 2px 6px rgba(0,0,0,0.04);
    transition: border-color 0.25s ease, box-shadow 0.25s ease;
  }
  .group-box.active-target {
    border-color: #22b7ff;
    box-shadow: 0 0 0 3px rgba(34, 183, 255, 0.2);
  }
  .group-header {
    display: flex;
    justify-content: space-between;
    align-items: center;
    width: 100%;
    padding: 0 4px 6px;
    border-bottom: 1px solid #f1f5f9;
    margin-bottom: 6px;
  }
  .group-title {
    font-size: 14px;
    font-weight: 700;
    color: #1e2945;
  }
  .group-count {
    font-size: 13px;
    font-weight: 700;
    background: #e0f2fe;
    color: #0284c7;
    padding: 2px 8px;
    border-radius: 10px;
    min-width: 24px;
    text-align: center;
  }
  .group-stars {
    display: grid;
    grid-template-columns: repeat(2, 1fr);
    gap: 6px;
    width: 100%;
    min-height: 84px;
    padding: 4px;
    place-items: center;
  }
  .star-slot {
    width: 36px;
    height: 36px;
    border-radius: 8px;
    background: #f8fafc;
    border: 1px dashed #e2e8f0;
    display: flex;
    align-items: center;
    justify-content: center;
    font-size: 22px;
  }
  .star-slot.filled {
    border-color: transparent;
    background: #fffbeb;
  }

  /* Result banner */
  .result-banner {
    min-height: 32px;
    display: flex;
    align-items: center;
    justify-content: center;
    font-size: 15px;
    font-weight: 700;
    color: #0f766e;
    background: #ccfbf1;
    border-radius: 8px;
    padding: 4px 16px;
    opacity: 0;
    transform: translateY(4px);
    transition: opacity 0.3s ease, transform 0.3s ease;
  }
  .result-banner.visible {
    opacity: 1;
    transform: translateY(0);
  }

  /* Controls */
  .controls {
    display: flex;
    align-items: center;
    gap: 8px;
    margin-top: 4px;
  }
  .btn {
    appearance: none;
    border: 1px solid #cbd5e1;
    background: #ffffff;
    color: #1e2945;
    font-size: 14px;
    font-weight: 600;
    padding: 8px 14px;
    border-radius: 8px;
    cursor: pointer;
    display: inline-flex;
    align-items: center;
    gap: 4px;
    transition: background 0.15s ease, border-color 0.15s ease;
  }
  .btn:active {
    background: #f1f5f9;
  }
  .btn-primary {
    background: #22b7ff;
    border-color: #22b7ff;
    color: #ffffff;
  }
  .btn-primary:active {
    background: #009de0;
    border-color: #009de0;
  }
  .btn:disabled {
    opacity: 0.4;
    cursor: not-allowed;
  }
</style>
</head>
<body>

  
  <div class="pool-section">
    <span class="pool-label" id="poolLabel">8 Stars</span>
    <div class="pool-tray" id="poolTray">
      <span class="star-item" id="p-0">⭐</span>
      <span class="star-item" id="p-1">⭐</span>
      <span class="star-item" id="p-2">⭐</span>
      <span class="star-item" id="p-3">⭐</span>
      <span class="star-item" id="p-4">⭐</span>
      <span class="star-item" id="p-5">⭐</span>
      <span class="star-item" id="p-6">⭐</span>
      <span class="star-item" id="p-7">⭐</span>
    </div>
  </div>

  
  <div class="groups-container">
    
    <div class="group-box" id="boxA">
      <div class="group-header">
        <span class="group-title">Group A</span>
        <span class="group-count" id="countA">0</span>
      </div>
      <div class="group-stars">
        <div class="star-slot" id="slotA-0"></div>
        <div class="star-slot" id="slotA-1"></div>
        <div class="star-slot" id="slotA-2"></div>
        <div class="star-slot" id="slotA-3"></div>
      </div>
    </div>

    
    <div class="group-box" id="boxB">
      <div class="group-header">
        <span class="group-title">Group B</span>
        <span class="group-count" id="countB">0</span>
      </div>
      <div class="group-stars">
        <div class="star-slot" id="slotB-0"></div>
        <div class="star-slot" id="slotB-1"></div>
        <div class="star-slot" id="slotB-2"></div>
        <div class="star-slot" id="slotB-3"></div>
      </div>
    </div>
  </div>

  
  <div class="result-banner" id="resultBanner">
    Half of 8 is 4
  </div>

  
  <div class="controls">
    <button class="btn" id="resetBtn" title="Reset">↺ Reset</button>
    <button class="btn btn-primary" id="dealBtn">Deal ⭐</button>
    <button class="btn" id="playBtn">▶ Auto</button>
  </div>

  <script>
    const TOTAL = 8;
    let dealt = 0;
    let autoTimer = null;

    const poolLabel = document.getElementById('poolLabel');
    const boxA = document.getElementById('boxA');
    const boxB = document.getElementById('boxB');
    const countA = document.getElementById('countA');
    const countB = document.getElementById('countB');
    const resultBanner = document.getElementById('resultBanner');
    const dealBtn = document.getElementById('dealBtn');
    const playBtn = document.getElementById('playBtn');
    const resetBtn = document.getElementById('resetBtn');

    function render() {
      // Remaining pool
      const remaining = TOTAL - dealt;
      poolLabel.textContent = remaining > 0 ? `${remaining} Remaining` : 'All Shared';

      for (let i = 0; i < TOTAL; i++) {
        const star = document.getElementById(`p-${i}`);
        if (i < remaining) {
          star.className = 'star-item';
        } else {
          star.className = 'star-item empty';
        }
      }

      // Group A items (indices 0, 2, 4, 6 dealt -> slot 0, 1, 2, 3)
      const numA = Math.ceil(dealt / 2);
      countA.textContent = numA;
      for (let i = 0; i < 4; i++) {
        const slot = document.getElementById(`slotA-${i}`);
        if (i < numA) {
          slot.textContent = '⭐';
          slot.className = 'star-slot filled';
        } else {
          slot.textContent = '';
          slot.className = 'star-slot';
        }
      }

      // Group B items (indices 1, 3, 5, 7 dealt -> slot 0, 1, 2, 3)
      const numB = Math.floor(dealt / 2);
      countB.textContent = numB;
      for (let i = 0; i < 4; i++) {
        const slot = document.getElementById(`slotB-${i}`);
        if (i < numB) {
          slot.textContent = '⭐';
          slot.className = 'star-slot filled';
        } else {
          slot.textContent = '';
          slot.className = 'star-slot';
        }
      }

      // Box highlights
      boxA.classList.toggle('active-target', dealt > 0 && dealt % 2 === 1);
      boxB.classList.toggle('active-target', dealt > 0 && dealt % 2 === 0 && dealt < TOTAL);

      // Result banner
      if (dealt === TOTAL) {
        resultBanner.classList.add('visible');
        dealBtn.disabled = true;
        boxA.classList.remove('active-target');
        boxB.classList.remove('active-target');
      } else {
        resultBanner.classList.remove('visible');
        dealBtn.disabled = false;
      }
    }

    function dealNext() {
      if (dealt < TOTAL) {
        dealt++;
        render();
      }
      if (dealt === TOTAL) {
        stopAuto();
      }
    }

    function reset() {
      stopAuto();
      dealt = 0;
      render();
    }

    function stopAuto() {
      if (autoTimer) {
        clearInterval(autoTimer);
        autoTimer = null;
        playBtn.textContent = '▶ Auto';
      }
    }

    function toggleAuto() {
      if (autoTimer) {
        stopAuto();
      } else {
        if (dealt === TOTAL) {
          dealt = 0;
          render();
        }
        playBtn.textContent = '⏸ Pause';
        autoTimer = setInterval(() => {
          if (dealt < TOTAL) {
            dealNext();
          } else {
            stopAuto();
          }
        }, 1000);
      }
    }

    dealBtn.addEventListener('click', () => {
      stopAuto();
      dealNext();
    });

    resetBtn.addEventListener('click', reset);
    playBtn.addEventListener('click', toggleAuto);

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

Since both boxes ended up with 4 stars, **half of 8 is 4**.

What happens if one pile has more items than the other?

To be a true **half**, both piles must have the **exact same number** of items. If one friend gets 5 and the other gets 3, the piles are unequal, so it is not half!

<!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: -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, sans-serif;
    color: #1e2945;
    background: transparent;
    padding: 12px;
    display: flex;
    flex-direction: column;
    align-items: center;
    justify-content: center;
    min-height: 100%;
    user-select: none;
  }
  .controls {
    display: flex;
    gap: 8px;
    margin-bottom: 14px;
    flex-wrap: wrap;
    justify-content: center;
  }
  .btn-tab {
    padding: 8px 14px;
    font-size: 14px;
    font-weight: 600;
    border-radius: 20px;
    border: 1px solid #d1d5db;
    background: #ffffff;
    color: #4b5563;
    cursor: pointer;
    transition: background 0.2s, color 0.2s, box-shadow 0.2s;
  }
  .btn-tab.active {
    background: #22b7ff;
    color: #ffffff;
    border-color: #22b7ff;
    box-shadow: 0 2px 8px rgba(34, 183, 255, 0.35);
  }
  .board {
    width: 100%;
    max-width: 480px;
    display: flex;
    flex-direction: column;
    gap: 12px;
  }
  .piles {
    display: grid;
    grid-template-columns: 1fr 1fr;
    gap: 12px;
    width: 100%;
  }
  .pile {
    background: #ffffff;
    border: 2px solid #e5e7eb;
    border-radius: 16px;
    padding: 12px;
    display: flex;
    flex-direction: column;
    align-items: center;
    min-height: 140px;
    transition: border-color 0.3s;
  }
  .pile.equal {
    border-color: #22b7ff;
  }
  .pile.unequal {
    border-color: #f59e0b;
  }
  .pile-title {
    font-size: 14px;
    font-weight: 700;
    color: #6b7280;
    margin-bottom: 8px;
  }
  .items-grid {
    display: grid;
    grid-template-columns: repeat(3, 1fr);
    gap: 8px;
    width: 100%;
    min-height: 72px;
    align-content: start;
    justify-items: center;
  }
  .block {
    width: 32px;
    height: 32px;
    border-radius: 8px;
    background: #22b7ff;
    color: #ffffff;
    display: flex;
    align-items: center;
    justify-content: center;
    font-size: 14px;
    font-weight: 700;
    box-shadow: 0 2px 4px rgba(34, 183, 255, 0.25);
    transition: transform 0.25s ease, opacity 0.25s ease;
  }
  .block.pile2 {
    background: #0284c7;
  }
  .status-card {
    background: #ffffff;
    border: 1px solid #e5e7eb;
    border-radius: 12px;
    padding: 10px 16px;
    display: flex;
    align-items: center;
    justify-content: space-between;
    font-size: 15px;
    font-weight: 700;
  }
  .tag {
    padding: 4px 10px;
    border-radius: 8px;
    font-size: 13px;
  }
  .tag-equal {
    background: #e0f2fe;
    color: #0284c7;
  }
  .tag-unequal {
    background: #fef3c7;
    color: #d97706;
  }
</style>
</head>
<body>

<div class="controls">
  <button class="btn-tab active" id="btnEqual">Equal Halves</button>
  <button class="btn-tab" id="btnUnequal">Unequal</button>
  <button class="btn-tab" id="btnStep">Deal 1 by 1 ▶</button>
</div>

<div class="board">
  <div class="piles">
    <div class="pile equal" id="pileLeft">
      <div class="pile-title" id="titleLeft">Pile A: 4</div>
      <div class="items-grid" id="gridLeft"></div>
    </div>
    <div class="pile equal" id="pileRight">
      <div class="pile-title" id="titleRight">Pile B: 4</div>
      <div class="items-grid" id="gridRight"></div>
    </div>
  </div>

  <div class="status-card">
    <span id="mathLabel">4 = 4</span>
    <span class="tag tag-equal" id="statusTag">✓ Half</span>
  </div>
</div>

<script>
  const total = 8;
  const gridL = document.getElementById('gridLeft');
  const gridR = document.getElementById('gridRight');
  const titleL = document.getElementById('titleLeft');
  const titleR = document.getElementById('titleRight');
  const pileL = document.getElementById('pileLeft');
  const pileR = document.getElementById('pileRight');
  const mathLabel = document.getElementById('mathLabel');
  const statusTag = document.getElementById('statusTag');

  const btnEqual = document.getElementById('btnEqual');
  const btnUnequal = document.getElementById('btnUnequal');
  const btnStep = document.getElementById('btnStep');

  let dealTimer = null;

  function render(countL, countR, isEqual) {
    gridL.innerHTML = '';
    gridR.innerHTML = '';

    for (let i = 0; i < countL; i++) {
      const el = document.createElement('div');
      el.className = 'block';
      el.textContent = '1';
      gridL.appendChild(el);
    }
    for (let i = 0; i < countR; i++) {
      const el = document.createElement('div');
      el.className = 'block pile2';
      el.textContent = '1';
      gridR.appendChild(el);
    }

    titleL.textContent = `Pile A: ${countL}`;
    titleR.textContent = `Pile B: ${countR}`;

    pileL.className = `pile ${isEqual ? 'equal' : 'unequal'}`;
    pileR.className = `pile ${isEqual ? 'equal' : 'unequal'}`;

    if (isEqual) {
      mathLabel.textContent = `${countL} = ${countR}`;
      statusTag.className = 'tag tag-equal';
      statusTag.textContent = '✓ Half';
    } else {
      mathLabel.textContent = `${countL} ≠ ${countR}`;
      statusTag.className = 'tag tag-unequal';
      statusTag.textContent = '✗ Not Half';
    }
  }

  function setActive(btn) {
    clearInterval(dealTimer);
    btnEqual.classList.remove('active');
    btnUnequal.classList.remove('active');
    btnStep.classList.remove('active');
    btn.classList.add('active');
  }

  btnEqual.addEventListener('click', () => {
    setActive(btnEqual);
    render(4, 4, true);
  });

  btnUnequal.addEventListener('click', () => {
    setActive(btnUnequal);
    render(5, 3, false);
  });

  btnStep.addEventListener('click', () => {
    setActive(btnStep);
    let step = 0;
    render(0, 0, true);

    dealTimer = setInterval(() => {
      step++;
      const cL = Math.ceil(step / 2);
      const cR = Math.floor(step / 2);
      render(cL, cR, cL === cR);

      if (step >= total) {
        clearInterval(dealTimer);
      }
    }, 450);
  });

  render(4, 4, true);
</script>

</body>
</html>

Try grabbing 10 toy blocks and sharing them one by one into two piles to find your fair half.

math

Sharing a Set into Two Equal Groups to Find Half. Find half of an even group of discrete objects by sharing them into two equal piles.

First Level Maths: Sharing Equally and Finding Halves

Finding Half of a Number / Quantity Within 10

Fair Feast: Early Years & KS1 Equal Sharing and Halving

At Early Level (P1), instruction should follow the Concrete-Pictorial-Abstract (CPA) approach. Begin with physical manipulatives (cubes, counters, plastic food) and authentic contexts (sharing snacks between two friends). Emphasise the 'one for you, one for me' rhythm to build systematic distribution habits. Use stem sentences such as: 'The whole is ___. We shared it into ___ equal groups. One half is ___' to reinforce academic language and foundational division concepts (MNU 1-07b).

Sharing a Set into Two Equal Groups to Find Half

The One-by-One Strategy

Checking for Fair Shares