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What would you like to learn?

Override for the tutor's lesson content generation calls. Auto uses the system default (Claude Sonnet 5 for lesson text, Opus 5 for diagrams).

Lesson generation model

System default

i58 💰:18.8

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i25 💰:31.3

Tutoring abilities

Imagine you have 5 red apples and a friend gives you 1 more. Do you need paper and pencil to figure out your total, or can you do it in your head?

You can just think "5 plus 1 is 6" right inside your brain!

What happens when the numbers get bigger or the story has extra steps? Let's check our math toolbag.

You have three helpful math tools: **mental math** in your head, quick **jottings**, and **written drawings**.

<!DOCTYPE html>
<html lang="en">
<head>
  <meta charset="UTF-8">
  <meta name="viewport" content="width=device-width, initial-scale=1.0">
  <meta name="aspect-ratio" content="4:3">
  <style>
    * {
      box-sizing: border-box;
      margin: 0;
      padding: 0;
      font-family: system-ui, -apple-system, BlinkMacSystemFont, 'Segoe UI', Roboto, sans-serif;
      -webkit-tap-highlight-color: transparent;
    }
    body {
      background-color: #f8f9fa;
      color: #1e2945;
      padding: 12px;
      display: flex;
      flex-direction: column;
      align-items: center;
      justify-content: center;
      min-height: 100%;
    }
    .container {
      width: 100%;
      max-width: 540px;
      display: flex;
      flex-direction: column;
      gap: 12px;
    }
    .method-nav {
      display: grid;
      grid-template-columns: repeat(3, 1fr);
      gap: 8px;
    }
    .tab-btn {
      background: #ffffff;
      border: 1px solid #e6e6e6;
      border-radius: 10px;
      padding: 8px 4px;
      text-align: center;
      cursor: pointer;
      box-shadow: 0 1px 3px rgba(0,0,0,0.04);
      transition: all 0.2s ease;
      display: flex;
      flex-direction: column;
      align-items: center;
      gap: 2px;
    }
    .tab-btn:hover {
      background: #f1f7ff;
    }
    .tab-btn.active {
      background: #ffffff;
      box-shadow: 0 0 0 2px #22b7ff, 0 2px 6px rgba(34, 183, 255, 0.2);
    }
    .tab-icon {
      font-size: 20px;
    }
    .tab-label {
      font-size: 13px;
      font-weight: 700;
      color: #1e2945;
    }
    .tab-sub {
      font-size: 11px;
      color: #6b7280;
    }

    .display-area {
      position: relative;
      height: 230px;
      background: #ffffff;
      border-radius: 12px;
      border: 1px solid #e6e6e6;
      box-shadow: 0 2px 8px rgba(0,0,0,0.04);
      overflow: hidden;
    }
    .view-panel {
      position: absolute;
      inset: 0;
      padding: 16px;
      display: flex;
      flex-direction: column;
      align-items: center;
      justify-content: space-between;
      opacity: 0;
      pointer-events: none;
      transition: opacity 0.25s ease, transform 0.25s ease;
      transform: translateY(6px);
    }
    .view-panel.active {
      opacity: 1;
      pointer-events: auto;
      transform: translateY(0);
    }

    .math-problem {
      font-size: 24px;
      font-weight: 800;
      color: #1e2945;
      letter-spacing: 0.5px;
    }

    /* Mental Method Visual */
    .brain-track {
      display: flex;
      align-items: center;
      justify-content: center;
      gap: 12px;
      width: 100%;
      margin: auto 0;
    }
    .thought-bubble {
      background: #eff8ff;
      border: 2px dashed #22b7ff;
      border-radius: 20px;
      padding: 12px 20px;
      font-size: 18px;
      font-weight: 700;
      color: #0284c7;
      display: flex;
      align-items: center;
      gap: 8px;
    }
    .thought-bubble span {
      color: #1e2945;
    }

    /* Jottings Visual */
    .jotting-box {
      width: 100%;
      display: flex;
      flex-direction: column;
      align-items: center;
      justify-content: center;
      gap: 12px;
      margin: auto 0;
    }
    .number-line {
      position: relative;
      width: 90%;
      height: 4px;
      background: #cbd5e1;
      border-radius: 2px;
      margin: 28px 0 16px;
    }
    .jump {
      position: absolute;
      top: -24px;
      height: 24px;
      border: 2px solid #22b7ff;
      border-bottom: none;
      border-radius: 16px 16px 0 0;
      display: flex;
      justify-content: center;
      align-items: flex-start;
    }
    .jump-tag {
      font-size: 11px;
      font-weight: 700;
      color: #0284c7;
      background: #eff8ff;
      padding: 0 4px;
      border-radius: 4px;
      transform: translateY(-10px);
    }
    .line-point {
      position: absolute;
      top: 50%;
      transform: translate(-50%, -50%);
      width: 10px;
      height: 10px;
      background: #0284c7;
      border-radius: 50%;
    }
    .point-label {
      position: absolute;
      top: 14px;
      transform: translateX(-50%);
      font-size: 13px;
      font-weight: 700;
      color: #1e2945;
    }

    /* Column Visual */
    .column-box {
      margin: auto 0;
      font-family: monospace;
      font-size: 20px;
      font-weight: 700;
      line-height: 1.35;
      text-align: right;
      display: inline-block;
      padding: 6px 16px;
      background: #f8fafc;
      border-radius: 8px;
      border: 1px solid #e2e8f0;
    }
    .regroup {
      font-size: 12px;
      color: #0284c7;
      font-weight: 800;
    }
    .column-line {
      border-top: 2px solid #1e2945;
      margin-top: 2px;
      padding-top: 2px;
    }

    .badge-tag {
      font-size: 12px;
      font-weight: 700;
      padding: 4px 12px;
      border-radius: 12px;
      background: #e0f2fe;
      color: #0369a1;
    }
  </style>
</head>
<body>
  <div class="container">
    
    <div class="method-nav">
      <button class="tab-btn active" onclick="setMethod(0)">
        <span class="tab-icon">🧠</span>
        <span class="tab-label">Mental</span>
        <span class="tab-sub">In your head</span>
      </button>
      <button class="tab-btn" onclick="setMethod(1)">
        <span class="tab-icon">✏️</span>
        <span class="tab-label">Jottings</span>
        <span class="tab-sub">Quick notes</span>
      </button>
      <button class="tab-btn" onclick="setMethod(2)">
        <span class="tab-icon">📝</span>
        <span class="tab-label">Written</span>
        <span class="tab-sub">Column form</span>
      </button>
    </div>

    
    <div class="display-area">
      
      <div class="view-panel active" id="panel-0">
        <div class="math-problem">45 + 20 = 65</div>
        <div class="brain-track">
          <div class="thought-bubble">
            🧠 <span>45 → +2 tens → <b>65</b></span>
          </div>
        </div>
        <div class="badge-tag">No paper needed</div>
      </div>

      
      <div class="view-panel" id="panel-1">
        <div class="math-problem">48 + 25 = 73</div>
        <div class="jotting-box">
          <div class="number-line">
            
            <div class="jump" style="left: 10%; width: 50%;">
              <span class="jump-tag">+20</span>
            </div>
            
            <div class="jump" style="left: 60%; width: 15%;">
              <span class="jump-tag">+2</span>
            </div>
            
            <div class="jump" style="left: 75%; width: 15%;">
              <span class="jump-tag">+3</span>
            </div>

            
            <div class="line-point" style="left: 10%;"><span class="point-label">48</span></div>
            <div class="line-point" style="left: 60%;"><span class="point-label">68</span></div>
            <div class="line-point" style="left: 75%;"><span class="point-label">70</span></div>
            <div class="line-point" style="left: 90%;"><span class="point-label">73</span></div>
          </div>
        </div>
        <div class="badge-tag">Empty number line</div>
      </div>

      
      <div class="view-panel" id="panel-2">
        <div class="math-problem">368 + 257 = 625</div>
        <div class="column-box">
          <div class="regroup">&nbsp;¹ ¹ &nbsp;</div>
          <div>&nbsp;3 6 8</div>
          <div>+ 2 5 7</div>
          <div class="column-line"><b>&nbsp;6 2 5</b></div>
        </div>
        <div class="badge-tag">Step-by-step regrouping</div>
      </div>
    </div>
  </div>

  <script>
    const tabs = document.querySelectorAll('.tab-btn');
    const panels = document.querySelectorAll('.view-panel');

    function setMethod(index) {
      tabs.forEach((tab, i) => {
        tab.classList.toggle('active', i === index);
      });
      panels.forEach((panel, i) => {
        panel.classList.toggle('active', i === index);
      });
    }
  </script>
</body>
</html>

How do you know when your head is all you need?

**Mental math** means solving the problem silently in your head without writing anything down.

Use mental math for easy facts, like adding 0 or 1, known doubles like $4 + 4$, or **making ten** like $8 + 2$.

<!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>Mental Math Strategies</title>
  <link rel="stylesheet" href="https://cdn.jsdelivr.net/npm/katex@0.16.9/dist/katex.min.css">
  <script src="https://cdn.jsdelivr.net/npm/katex@0.16.9/dist/katex.min.js"></script>
  <style>
    * {
      box-sizing: border-box;
      margin: 0;
      padding: 0;
      font-family: -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, sans-serif;
      user-select: none;
      -webkit-user-select: none;
    }
    body {
      background: transparent;
      color: #1e2945;
      display: flex;
      flex-direction: column;
      align-items: center;
      justify-content: space-between;
      min-height: 100%;
      padding: 12px;
      gap: 12px;
    }
    .nav-tabs {
      display: flex;
      gap: 8px;
      width: 100%;
      max-width: 420px;
    }
    .tab-btn {
      flex: 1;
      border: 2px solid #e2e8f0;
      background: #ffffff;
      color: #64748b;
      padding: 8px 4px;
      border-radius: 10px;
      font-size: 14px;
      font-weight: 700;
      cursor: pointer;
      text-align: center;
      transition: all 0.25s ease;
    }
    .tab-btn.active {
      border-color: #22b7ff;
      background: #f0f9ff;
      color: #0284c7;
      box-shadow: 0 2px 8px rgba(34, 183, 255, 0.2);
    }
    .stage {
      position: relative;
      width: 100%;
      max-width: 420px;
      height: 240px;
      background: #ffffff;
      border-radius: 16px;
      border: 1px solid #e6e6e6;
      box-shadow: 0 4px 12px rgba(0, 0, 0, 0.03);
      overflow: hidden;
      display: flex;
      flex-direction: column;
      align-items: center;
      justify-content: space-between;
      padding: 18px 12px 14px;
    }
    .view-panel {
      position: absolute;
      top: 0;
      left: 0;
      width: 100%;
      height: 100%;
      display: flex;
      flex-direction: column;
      align-items: center;
      justify-content: space-between;
      padding: 16px 12px;
      opacity: 0;
      pointer-events: none;
      transition: opacity 0.3s ease;
    }
    .view-panel.active {
      opacity: 1;
      pointer-events: auto;
    }
    .math-title {
      font-size: 26px;
      font-weight: 800;
      color: #1e2945;
      min-height: 36px;
      display: flex;
      align-items: center;
      justify-content: center;
    }
    .visual-area {
      flex: 1;
      width: 100%;
      display: flex;
      align-items: center;
      justify-content: center;
      gap: 12px;
    }
    /* Frame & Dots */
    .ten-frame {
      display: grid;
      grid-template-columns: repeat(5, 36px);
      grid-template-rows: repeat(2, 36px);
      gap: 4px;
      background: #f8fafc;
      padding: 6px;
      border: 2px solid #cbd5e1;
      border-radius: 10px;
    }
    .cell {
      background: #ffffff;
      border-radius: 6px;
      border: 1px dashed #cbd5e1;
      display: flex;
      align-items: center;
      justify-content: center;
    }
    .dot {
      width: 26px;
      height: 26px;
      border-radius: 50%;
      transition: transform 0.3s ease;
    }
    .dot.blue {
      background: #22b7ff;
      box-shadow: inset 0 -2px 0 rgba(0,0,0,0.15);
    }
    .dot.orange {
      background: #f97316;
      box-shadow: inset 0 -2px 0 rgba(0,0,0,0.15);
    }
    .dot.green {
      background: #10b981;
      box-shadow: inset 0 -2px 0 rgba(0,0,0,0.15);
    }
    /* Number Track */
    .track {
      display: flex;
      gap: 6px;
    }
    .track-num {
      width: 44px;
      height: 48px;
      background: #f1f5f9;
      border: 2px solid #cbd5e1;
      border-radius: 10px;
      display: flex;
      flex-direction: column;
      align-items: center;
      justify-content: center;
      font-size: 18px;
      font-weight: 700;
      color: #64748b;
      position: relative;
    }
    .track-num.highlight {
      background: #e0f2fe;
      border-color: #22b7ff;
      color: #0284c7;
    }
    .track-num.target {
      background: #ecfdf5;
      border-color: #10b981;
      color: #059669;
    }
    .jump-arrow {
      position: absolute;
      top: -18px;
      font-size: 12px;
      font-weight: 800;
      color: #10b981;
    }
    /* Doubles layout */
    .doubles-container {
      display: flex;
      flex-direction: column;
      gap: 10px;
    }
    .doubles-row {
      display: flex;
      gap: 8px;
      align-items: center;
      background: #f8fafc;
      padding: 6px 10px;
      border-radius: 8px;
      border: 1px solid #e2e8f0;
    }
    .badge-pill {
      font-size: 13px;
      font-weight: 700;
      padding: 4px 12px;
      border-radius: 20px;
      background: #f1f5f9;
      color: #475569;
    }
    .controls {
      display: flex;
      align-items: center;
      justify-content: center;
      gap: 12px;
    }
    .play-btn {
      background: #f1f5f9;
      border: 1px solid #cbd5e1;
      border-radius: 20px;
      padding: 4px 14px;
      font-size: 12px;
      font-weight: 600;
      color: #475569;
      cursor: pointer;
      display: flex;
      align-items: center;
      gap: 6px;
    }
    .play-btn:active {
      background: #e2e8f0;
    }
  </style>
</head>
<body>

  
  <div class="nav-tabs">
    <button class="tab-btn active" onclick="setStrategy(0)">+0 / +1</button>
    <button class="tab-btn" onclick="setStrategy(1)">Doubles</button>
    <button class="tab-btn" onclick="setStrategy(2)">Make 10</button>
  </div>

  
  <div class="stage">

    
    <div class="view-panel active" id="panel-0">
      <div class="math-title" id="math-0"></div>
      <div class="visual-area">
        <div class="track">
          <div class="track-num">4</div>
          <div class="track-num highlight">
            5
            <span class="jump-arrow">+1 →</span>
          </div>
          <div class="track-num target">6</div>
          <div class="track-num">7</div>
        </div>
      </div>
      <div class="badge-pill">Count On 1</div>
    </div>

    
    <div class="view-panel" id="panel-1">
      <div class="math-title" id="math-1"></div>
      <div class="visual-area">
        <div class="doubles-container">
          <div class="doubles-row">
            <div class="dot blue"></div>
            <div class="dot blue"></div>
            <div class="dot blue"></div>
            <div class="dot blue"></div>
          </div>
          <div class="doubles-row">
            <div class="dot blue"></div>
            <div class="dot blue"></div>
            <div class="dot blue"></div>
            <div class="dot blue"></div>
          </div>
        </div>
      </div>
      <div class="badge-pill">Known Pairs</div>
    </div>

    
    <div class="view-panel" id="panel-2">
      <div class="math-title" id="math-2"></div>
      <div class="visual-area">
        <div class="ten-frame">
          <div class="cell"><div class="dot blue"></div></div>
          <div class="cell"><div class="dot blue"></div></div>
          <div class="cell"><div class="dot blue"></div></div>
          <div class="cell"><div class="dot blue"></div></div>
          <div class="cell"><div class="dot blue"></div></div>
          <div class="cell"><div class="dot blue"></div></div>
          <div class="cell"><div class="dot blue"></div></div>
          <div class="cell"><div class="dot blue"></div></div>
          <div class="cell"><div class="dot orange"></div></div>
          <div class="cell"><div class="dot orange"></div></div>
        </div>
      </div>
      <div class="badge-pill">Full Ten Frame</div>
    </div>

  </div>

  
  <div class="controls">
    <button class="play-btn" id="togglePlay" onclick="toggleAuto()">
      <span id="playIcon">⏸</span> Auto-cycle
    </button>
  </div>

  <script>
    const equations = [
      "5 + 1 = 6",
      "4 + 4 = 8",
      "8 + 2 = 10"
    ];

    equations.forEach((eq, idx) => {
      const el = document.getElementById(`math-${idx}`);
      if (window.katex) {
        katex.render(eq, el, { throwOnError: false });
      } else {
        el.textContent = eq;
      }
    });

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

    function setStrategy(index) {
      current = index;
      document.querySelectorAll('.tab-btn').forEach((btn, i) => {
        btn.classList.toggle('active', i === index);
      });
      document.querySelectorAll('.view-panel').forEach((panel, i) => {
        panel.classList.toggle('active', i === index);
      });
    }

    function nextStrategy() {
      current = (current + 1) % 3;
      setStrategy(current);
    }

    function startTimer() {
      if (timer) clearInterval(timer);
      timer = setInterval(nextStrategy, 3200);
    }

    function toggleAuto() {
      isPlaying = !isPlaying;
      document.getElementById('playIcon').textContent = isPlaying ? '⏸' : '▶';
      if (isPlaying) {
        startTimer();
      } else {
        clearInterval(timer);
      }
    }

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

What if you need to add numbers that don't easily fit in your head?

A **jotting** is a quick sketch, like a few dots or hops, that holds numbers on paper so your brain doesn't forget.

To solve $7 + 5$, you hold 7 in your head, draw 5 quick dots, and count on: "7... 8, 9, 10, 11, 12!"

<!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>Counting On: 7 + 5</title>
  <style>
    * {
      box-sizing: border-box;
      margin: 0;
      padding: 0;
      font-family: -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, sans-serif;
      user-select: none;
      -webkit-user-select: none;
    }
    body {
      background: #f8f9fa;
      color: #1e2945;
      display: flex;
      flex-direction: column;
      align-items: center;
      justify-content: center;
      min-height: 100vh;
      padding: 16px;
    }
    .main-stage {
      width: 100%;
      max-width: 480px;
      display: flex;
      flex-direction: column;
      align-items: center;
      gap: 20px;
    }
    .math-row {
      display: flex;
      align-items: center;
      justify-content: center;
      gap: 12px;
      width: 100%;
      flex-wrap: wrap;
    }
    .head-card {
      background: #ffffff;
      border: 2px solid #22b7ff;
      border-radius: 16px;
      padding: 12px 18px;
      display: flex;
      flex-direction: column;
      align-items: center;
      box-shadow: 0 4px 12px rgba(34, 183, 255, 0.15);
      position: relative;
    }
    .head-icon {
      font-size: 24px;
      margin-bottom: 2px;
    }
    .head-num {
      font-size: 36px;
      font-weight: 800;
      color: #1e2945;
      line-height: 1;
    }
    .tag {
      font-size: 11px;
      font-weight: 700;
      text-transform: uppercase;
      letter-spacing: 0.5px;
      color: #22b7ff;
      margin-top: 4px;
    }
    .plus-symbol {
      font-size: 28px;
      font-weight: 700;
      color: #94a3b8;
    }
    .dots-container {
      display: flex;
      align-items: center;
      gap: 8px;
    }
    .count-dot {
      width: 44px;
      height: 44px;
      border-radius: 50%;
      background: #ffffff;
      border: 2px dashed #cbd5e1;
      display: flex;
      align-items: center;
      justify-content: center;
      font-size: 16px;
      font-weight: 800;
      color: #94a3b8;
      cursor: pointer;
      transition: all 0.25s ease;
      box-shadow: 0 2px 4px rgba(0, 0, 0, 0.04);
    }
    .count-dot.active {
      background: #22b7ff;
      border: 2px solid #22b7ff;
      border-style: solid;
      color: #ffffff;
      transform: translateY(-2px);
      box-shadow: 0 4px 10px rgba(34, 183, 255, 0.35);
    }
    .count-dot.final {
      background: #10b981;
      border-color: #10b981;
      color: #ffffff;
      box-shadow: 0 4px 10px rgba(16, 185, 129, 0.35);
    }
    .total-box {
      background: #ffffff;
      border-radius: 12px;
      padding: 12px 24px;
      font-size: 26px;
      font-weight: 800;
      color: #1e2945;
      display: flex;
      align-items: center;
      gap: 8px;
      box-shadow: 0 2px 8px rgba(0, 0, 0, 0.05);
    }
    .total-highlight {
      color: #10b981;
      transition: transform 0.25s ease;
    }
    .total-highlight.bump {
      transform: scale(1.15);
    }
    .controls {
      display: flex;
      align-items: center;
      gap: 12px;
    }
    .btn {
      background: #ffffff;
      border: 2px solid #e2e8f0;
      padding: 8px 16px;
      border-radius: 8px;
      font-size: 14px;
      font-weight: 700;
      color: #1e2945;
      cursor: pointer;
      display: flex;
      align-items: center;
      gap: 6px;
      transition: background 0.2s, border-color 0.2s;
    }
    .btn:active {
      background: #f1f5f9;
    }
    .btn-primary {
      background: #22b7ff;
      border-color: #22b7ff;
      color: #ffffff;
    }
    .btn-primary:active {
      background: #009be3;
    }
  </style>
</head>
<body>
  <div class="main-stage">
    <div class="math-row">
      <div class="head-card">
        <span class="head-icon">🧠</span>
        <span class="head-num">7</span>
        <span class="tag">In Head</span>
      </div>

      <span class="plus-symbol">+</span>

      <div class="dots-container" id="dotsContainer">
        <div class="count-dot" data-step="1">8</div>
        <div class="count-dot" data-step="2">9</div>
        <div class="count-dot" data-step="3">10</div>
        <div class="count-dot" data-step="4">11</div>
        <div class="count-dot" data-step="5">12</div>
      </div>
    </div>

    <div class="total-box">
      <span>7 + 5 =</span>
      <span class="total-highlight" id="totalNum">?</span>
    </div>

    <div class="controls">
      <button class="btn" id="prevBtn" title="Step Back">←</button>
      <button class="btn btn-primary" id="nextBtn">Count On ➔</button>
      <button class="btn" id="resetBtn" title="Reset">↻</button>
    </div>
  </div>

  <script>
    let step = 0;
    const maxSteps = 5;
    const dots = document.querySelectorAll('.count-dot');
    const totalNum = document.getElementById('totalNum');
    const nextBtn = document.getElementById('nextBtn');
    const prevBtn = document.getElementById('prevBtn');
    const resetBtn = document.getElementById('resetBtn');

    function update() {
      dots.forEach((dot, idx) => {
        const dotStep = idx + 1;
        dot.classList.remove('active', 'final');
        if (dotStep <= step) {
          if (dotStep === 5 && step === 5) {
            dot.classList.add('final');
          } else {
            dot.classList.add('active');
          }
        }
      });

      if (step === 0) {
        totalNum.textContent = '?';
        totalNum.style.color = '#94a3b8';
      } else {
        const currentVal = 7 + step;
        totalNum.textContent = currentVal;
        totalNum.style.color = (step === 5) ? '#10b981' : '#22b7ff';
      }

      totalNum.classList.add('bump');
      setTimeout(() => totalNum.classList.remove('bump'), 200);

      nextBtn.textContent = (step === maxSteps) ? 'Done ✓' : 'Count On ➔';
    }

    nextBtn.addEventListener('click', () => {
      if (step < maxSteps) {
        step++;
      } else {
        step = 0;
      }
      update();
    });

    prevBtn.addEventListener('click', () => {
      if (step > 0) {
        step--;
        update();
      }
    });

    resetBtn.addEventListener('click', () => {
      step = 0;
      update();
    });

    dots.forEach((dot, idx) => {
      dot.addEventListener('click', () => {
        step = idx + 1;
        update();
      });
    });

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

What if you are adding two bigger numbers, like $12 + 15$?

A **written drawing** uses base-ten blocks (tall rods for tens and small cubes for ones) to organize larger amounts clearly.

To solve $12 + 15$, draw 1 ten-rod and 2 ones for 12, then draw 1 ten-rod and 5 ones for 15.

<!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>Base 10 Model: 12 + 15</title>
<link rel="stylesheet" href="https://cdn.classace.io/assets/katex.min.css">
<script src="https://cdn.classace.io/assets/katex.min.js"></script>
<script src="https://cdn.classace.io/assets/classace-diagram.js"></script>
<style>
  * { box-sizing: border-box; margin: 0; padding: 0; }
  body {
    font-family: -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, sans-serif;
    color: #1e2945;
    background: transparent;
    display: flex;
    flex-direction: column;
    align-items: center;
    justify-content: center;
    min-height: 100%;
    padding: 12px;
    user-select: none;
    -webkit-user-select: none;
  }

  .stage-card {
    width: 100%;
    max-width: 440px;
    background: #ffffff;
    border: 1px solid #e2e8f0;
    border-radius: 16px;
    padding: 16px 14px;
    box-shadow: 0 4px 12px rgba(0,0,0,0.03);
    display: flex;
    flex-direction: column;
    align-items: center;
    gap: 12px;
  }

  .header-math {
    font-size: 22px;
    font-weight: 700;
    color: #1e2945;
    min-height: 32px;
    display: flex;
    align-items: center;
    justify-content: center;
  }

  .board {
    width: 100%;
    height: 190px;
    background: #f8fafc;
    border: 1px solid #edf2f7;
    border-radius: 12px;
    display: flex;
    position: relative;
    overflow: hidden;
  }

  .col-side {
    flex: 1;
    display: flex;
    flex-direction: column;
    align-items: center;
    padding: 8px 4px;
    position: relative;
  }

  .col-side:first-child {
    border-right: 1px dashed #cbd5e1;
  }

  .col-label {
    font-size: 13px;
    font-weight: 700;
    color: #64748b;
    text-transform: uppercase;
    letter-spacing: 0.5px;
    margin-bottom: 6px;
  }

  .items-container {
    flex: 1;
    width: 100%;
    display: flex;
    justify-content: center;
    align-items: flex-end;
    gap: 12px;
    padding-bottom: 8px;
  }

  /* Base-10 Rod (Ten) */
  .ten-group {
    display: flex;
    gap: 10px;
    align-items: flex-end;
  }

  .ten-rod {
    width: 18px;
    height: 120px;
    background: #e0f2fe;
    border: 1.5px solid #0284c7;
    border-radius: 4px;
    display: flex;
    flex-direction: column;
    justify-content: space-between;
    padding: 1px 0;
    transition: opacity 0.35s ease, transform 0.35s ease;
  }

  .ten-rod span {
    display: block;
    width: 100%;
    height: 1px;
    background: #38bdf8;
  }

  /* Base-10 Unit (One) */
  .ones-group {
    display: flex;
    flex-wrap: wrap-reverse;
    gap: 5px;
    width: 50px;
    align-content: flex-start;
    justify-content: center;
  }

  .unit-cube {
    width: 12px;
    height: 12px;
    background: #fed7aa;
    border: 1.5px solid #ea580c;
    border-radius: 2px;
    transition: opacity 0.35s ease, transform 0.35s ease;
  }

  .group-box {
    display: flex;
    flex-direction: column;
    align-items: center;
    gap: 4px;
    transition: opacity 0.35s ease;
  }

  .tag {
    font-size: 11px;
    font-weight: 600;
    padding: 2px 6px;
    border-radius: 4px;
  }
  .tag-12 { background: #e0f2fe; color: #0369a1; }
  .tag-15 { background: #ffedd5; color: #c2410c; }

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

  .step-btn {
    flex: 1;
    max-width: 105px;
    padding: 8px 4px;
    border: 1.5px solid #e2e8f0;
    background: #ffffff;
    border-radius: 8px;
    font-size: 13px;
    font-weight: 600;
    color: #475569;
    cursor: pointer;
    text-align: center;
    transition: all 0.2s ease;
  }

  .step-btn.active {
    border-color: #0284c7;
    background: #f0f9ff;
    color: #0369a1;
    box-shadow: 0 0 0 2px rgba(2, 132, 199, 0.15);
  }

  .ghost {
    opacity: 0.12;
    transform: scale(0.92);
  }
  .hidden {
    display: none !important;
  }
</style>
</head>
<body>

<div class="stage-card">
  <div class="header-math" id="mathExpr"></div>

  <div class="board">
    
    <div class="col-side">
      <div class="col-label" id="tensCount">Tens</div>
      <div class="items-container">
        <div class="group-box" id="rod12Box">
          <div class="ten-rod">
            <span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span>
          </div>
          <span class="tag tag-12">10</span>
        </div>
        <div class="group-box" id="rod15Box">
          <div class="ten-rod">
            <span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span>
          </div>
          <span class="tag tag-15">10</span>
        </div>
      </div>
    </div>

    
    <div class="col-side">
      <div class="col-label" id="onesCount">Ones</div>
      <div class="items-container">
        <div class="group-box" id="ones12Box">
          <div class="ones-group">
            <div class="unit-cube"></div>
            <div class="unit-cube"></div>
          </div>
          <span class="tag tag-12">2</span>
        </div>
        <div class="group-box" id="ones15Box">
          <div class="ones-group">
            <div class="unit-cube"></div>
            <div class="unit-cube"></div>
            <div class="unit-cube"></div>
            <div class="unit-cube"></div>
            <div class="unit-cube"></div>
          </div>
          <span class="tag tag-15">5</span>
        </div>
      </div>
    </div>
  </div>

  <div class="controls">
    <button class="step-btn active" id="btn0">12</button>
    <button class="step-btn" id="btn1">+ 15</button>
    <button class="step-btn" id="btn2">= 27</button>
  </div>
</div>

<script>
  const mathExpr = document.getElementById('mathExpr');
  const tensCount = document.getElementById('tensCount');
  const onesCount = document.getElementById('onesCount');

  const rod12Box = document.getElementById('rod12Box');
  const rod15Box = document.getElementById('rod15Box');
  const ones12Box = document.getElementById('ones12Box');
  const ones15Box = document.getElementById('ones15Box');

  const btns = [
    document.getElementById('btn0'),
    document.getElementById('btn1'),
    document.getElementById('btn2')
  ];

  let currentStep = 0;
  let timer = null;

  function renderMath(step) {
    if (typeof katex !== 'undefined') {
      if (step === 0) katex.render('12', mathExpr);
      if (step === 1) katex.render('12 + 15', mathExpr);
      if (step === 2) katex.render('12 + 15 = 27', mathExpr);
    } else {
      if (step === 0) mathExpr.textContent = '12';
      if (step === 1) mathExpr.textContent = '12 + 15';
      if (step === 2) mathExpr.textContent = '12 + 15 = 27';
    }
  }

  function applyStep(step) {
    currentStep = step;
    btns.forEach((btn, idx) => {
      btn.classList.toggle('active', idx === step);
    });

    renderMath(step);

    if (step === 0) {
      rod12Box.classList.remove('ghost');
      ones12Box.classList.remove('ghost');
      rod15Box.classList.add('ghost');
      ones15Box.classList.add('ghost');
      tensCount.textContent = '1 Ten';
      onesCount.textContent = '2 Ones';
    } else if (step === 1) {
      rod12Box.classList.remove('ghost');
      ones12Box.classList.remove('ghost');
      rod15Box.classList.remove('ghost');
      ones15Box.classList.remove('ghost');
      tensCount.textContent = '1 + 1 Tens';
      onesCount.textContent = '2 + 5 Ones';
    } else if (step === 2) {
      rod12Box.classList.remove('ghost');
      ones12Box.classList.remove('ghost');
      rod15Box.classList.remove('ghost');
      ones15Box.classList.remove('ghost');
      tensCount.textContent = '2 Tens (20)';
      onesCount.textContent = '7 Ones (7)';
    }
  }

  function startAutoPlay() {
    stopAutoPlay();
    timer = setInterval(() => {
      const next = (currentStep + 1) % 3;
      applyStep(next);
    }, 3200);
  }

  function stopAutoPlay() {
    if (timer) {
      clearInterval(timer);
      timer = null;
    }
  }

  btns.forEach((btn, idx) => {
    btn.addEventListener('click', () => {
      stopAutoPlay();
      applyStep(idx);
    });
  });

  // Init
  applyStep(0);
  startAutoPlay();
</script>
</body>
</html>

Before you begin any math problem, ask yourself: "Can I do this in my head, should I make a quick jotting, or should I draw it out?"

math

Choosing Between Mental and Written Calculation Methods. Evaluate a problem to decide whether mental calculation, jottings, or formal written algorithms are most efficient.

Developing Problem Solving and Calculation Selection Strategies in Early Mathematics

Early and First Level Numeracy: Mental Agility, Number Bonds, and Problem Solving

Progression in Calculation: Balancing Mental Fluency, Jottings, and Written Recording

At Early Level (P1) within Scotland's Curriculum for Excellence, the emphasis is on concrete-pictorial-abstract (CPA) progression and metacognitive decision-making. Teachers should use 'Think Aloud' protocols and 'Strategy Sorting' activities where learners physically sort arithmetic prompt cards into 'Head Only' (instant recall/subitising), 'Quick Dots/Drawings' (jottings), and 'Pen & Paper Record' (written number stories). This builds foundational algebraic and numerical reasoning (MNU 3-03a/b progression), preventing over-reliance on rote counting or redundant written procedures.

Choosing Between Mental and Written Calculation Methods

Your Math Toolbag

When to Use Mental Math

Quick Jottings