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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

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Tutoring abilities

Imagine a frog hopping across lily pads numbered **2**, **4**, and **6**.

A **number pattern** is a list of numbers that follows a secret jumping rule.

<!DOCTYPE html>
<html lang="en">
<head>
<meta charset="UTF-8">
<meta name="viewport" content="width=device-width, initial-scale=1.0">
<meta name="aspect-ratio" content="4:3">
<style>
  * { box-sizing: border-box; margin: 0; padding: 0; }
  body {
    font-family: system-ui, -apple-system, BlinkMacSystemFont, 'Segoe UI', Roboto, sans-serif;
    background: #f8f9fa;
    color: #1e2945;
    display: flex;
    flex-direction: column;
    align-items: center;
    justify-content: center;
    min-height: 100vh;
    padding: 12px;
    user-select: none;
  }

  .nav-tabs {
    display: flex;
    gap: 8px;
    margin-bottom: 24px;
    background: #e9ecef;
    padding: 4px;
    border-radius: 12px;
  }

  .tab-btn {
    border: none;
    background: transparent;
    padding: 8px 16px;
    font-size: 14px;
    font-weight: 600;
    color: #6b7280;
    border-radius: 8px;
    cursor: pointer;
    transition: all 0.2s ease;
  }

  .tab-btn.active {
    background: #ffffff;
    color: #22b7ff;
    box-shadow: 0 2px 6px rgba(0,0,0,0.06);
  }

  .stage {
    position: relative;
    width: 100%;
    max-width: 560px;
    background: #ffffff;
    border-radius: 16px;
    padding: 32px 16px 24px;
    box-shadow: 0 4px 16px rgba(0,0,0,0.04);
    display: flex;
    flex-direction: column;
    align-items: center;
  }

  .sequence-container {
    position: relative;
    width: 100%;
    height: 130px;
  }

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

  .arc {
    fill: none;
    stroke-width: 3;
    stroke-linecap: round;
    stroke-dasharray: 200;
    stroke-dashoffset: 200;
    transition: stroke-dashoffset 0.5s ease, opacity 0.3s ease;
  }

  .arc.add { stroke: #22b7ff; }
  .arc.sub { stroke: #f97316; }

  .nodes-row {
    position: absolute;
    bottom: 4px;
    left: 0;
    width: 100%;
    display: flex;
    justify-content: space-between;
    padding: 0 4%;
  }

  .node {
    width: 52px;
    height: 52px;
    background: #ffffff;
    border: 2.5px solid #e5e7eb;
    border-radius: 50%;
    display: flex;
    align-items: center;
    justify-content: center;
    font-size: 19px;
    font-weight: 700;
    color: #1e2945;
    transition: all 0.3s ease;
    z-index: 2;
  }

  .node.active {
    border-color: #22b7ff;
    background: #e0f2fe;
    color: #0284c7;
    transform: translateY(-2px);
    box-shadow: 0 4px 10px rgba(34, 183, 255, 0.25);
  }

  .node.mystery {
    border-style: dashed;
    border-color: #9ca3af;
    background: #f3f4f6;
    color: #6b7280;
    cursor: pointer;
  }

  .node.mystery.revealed {
    border-style: solid;
    border-color: #10b981;
    background: #d1fae5;
    color: #047857;
  }

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

  .rule-badge {
    position: absolute;
    top: 8px;
    transform: translateX(-50%);
    padding: 3px 8px;
    border-radius: 12px;
    font-size: 13px;
    font-weight: 700;
    opacity: 0;
    transition: opacity 0.4s ease;
    z-index: 3;
  }

  .rule-badge.add { background: #e0f2fe; color: #0284c7; }
  .rule-badge.sub { background: #ffedd5; color: #c2410c; }
  .rule-badge.show { opacity: 1; }

  .rule-banner {
    margin-top: 20px;
    font-size: 16px;
    font-weight: 700;
    color: #374151;
    display: flex;
    align-items: center;
    gap: 8px;
  }

  .tag {
    padding: 4px 10px;
    border-radius: 6px;
    font-weight: 800;
  }
  .tag.add { background: #e0f2fe; color: #0284c7; }
  .tag.sub { background: #ffedd5; color: #c2410c; }

  .controls {
    margin-top: 18px;
    display: flex;
    gap: 12px;
  }

  .ctrl-btn {
    border: none;
    background: #f1f5f9;
    color: #334155;
    font-size: 14px;
    font-weight: 600;
    padding: 8px 18px;
    border-radius: 8px;
    cursor: pointer;
    display: flex;
    align-items: center;
    gap: 6px;
    transition: all 0.2s ease;
  }

  .ctrl-btn:hover { background: #e2e8f0; }
  .ctrl-btn.primary { background: #22b7ff; color: #ffffff; }
  .ctrl-btn.primary:hover { background: #009be5; }

  @media (max-width: 420px) {
    .node { width: 44px; height: 44px; font-size: 16px; }
    .stage { padding: 24px 10px 18px; }
  }
</style>
</head>
<body>

<div class="nav-tabs">
  <button class="tab-btn active" id="tab0" onclick="setMode(0)">+3 Rule</button>
  <button class="tab-btn" id="tab1" onclick="setMode(1)">-5 Rule</button>
  <button class="tab-btn" id="tab2" onclick="setMode(2)">Find Rule</button>
</div>

<div class="stage">
  <div class="sequence-container" id="seqBox">
    <svg class="svg-layer" id="svgArcs" viewBox="0 0 500 130">
      <defs>
        <marker id="arrowAdd" viewBox="0 0 10 10" refX="6" refY="5" markerWidth="6" markerHeight="6" orient="auto-start-reverse">
          <path d="M 0 1 L 10 5 L 0 9 z" fill="#22b7ff" />
        </marker>
        <marker id="arrowSub" viewBox="0 0 10 10" refX="6" refY="5" markerWidth="6" markerHeight="6" orient="auto-start-reverse">
          <path d="M 0 1 L 10 5 L 0 9 z" fill="#f97316" />
        </marker>
      </defs>
      <path id="arc0" class="arc" d="M 50 82 Q 100 0 150 82" />
      <path id="arc1" class="arc" d="M 150 82 Q 200 0 250 82" />
      <path id="arc2" class="arc" d="M 250 82 Q 300 0 350 82" />
      <path id="arc3" class="arc" d="M 350 82 Q 400 0 450 82" />
    </svg>

    <div class="badge-layer">
      <div id="badge0" class="rule-badge" style="left: 20%;">+3</div>
      <div id="badge1" class="rule-badge" style="left: 40%;">+3</div>
      <div id="badge2" class="rule-badge" style="left: 60%;">+3</div>
      <div id="badge3" class="rule-badge" style="left: 80%;">+3</div>
    </div>

    <div class="nodes-row">
      <div class="node" id="n0">4</div>
      <div class="node" id="n1">7</div>
      <div class="node" id="n2">10</div>
      <div class="node" id="n3">13</div>
      <div class="node" id="n4">16</div>
    </div>
  </div>

  <div class="rule-banner" id="banner">
    <span>Rule:</span>
    <span class="tag add" id="ruleTag">+3</span>
  </div>

  <div class="controls">
    <button class="ctrl-btn primary" id="playBtn" onclick="stepForward()">Jump ▶</button>
    <button class="ctrl-btn" onclick="resetState()">Reset ↺</button>
  </div>
</div>

<script>
  const presets = [
    { type: 'add', rule: '+3', nums: ['4', '7', '10', '13', '16'], mystery: false },
    { type: 'sub', rule: '-5', nums: ['35', '30', '25', '20', '15'], mystery: false },
    { type: 'add', rule: '+6', nums: ['8', '14', '20', '26', '32'], mystery: true }
  ];

  let currentMode = 0;
  let currentStep = 0;

  function setMode(idx) {
    currentMode = idx;
    document.querySelectorAll('.tab-btn').forEach((btn, i) => {
      btn.classList.toggle('active', i === idx);
    });
    resetState();
  }

  function resetState() {
    currentStep = 0;
    const config = presets[currentMode];
    
    const bannerTag = document.getElementById('ruleTag');
    bannerTag.textContent = config.rule;
    bannerTag.className = 'tag ' + config.type;

    for (let i = 0; i < 5; i++) {
      const node = document.getElementById('n' + i);
      node.className = 'node';
      if (i === 4 && config.mystery) {
        node.textContent = '?';
        node.classList.add('mystery');
      } else {
        node.textContent = config.nums[i];
      }
    }
    document.getElementById('n0').classList.add('active');

    for (let i = 0; i < 4; i++) {
      const arc = document.getElementById('arc' + i);
      arc.className = 'arc ' + config.type;
      arc.style.strokeDashoffset = '200';
      arc.setAttribute('marker-end', config.type === 'add' ? 'url(#arrowAdd)' : 'url(#arrowSub)');

      const badge = document.getElementById('badge' + i);
      badge.textContent = config.rule;
      badge.className = 'rule-badge ' + config.type;
    }
  }

  function stepForward() {
    if (currentStep < 4) {
      const arc = document.getElementById('arc' + currentStep);
      const badge = document.getElementById('badge' + currentStep);
      
      arc.style.strokeDashoffset = '0';
      badge.classList.add('show');
      
      currentStep++;
      const nextNode = document.getElementById('n' + currentStep);
      
      if (currentStep === 4 && presets[currentMode].mystery) {
        nextNode.textContent = presets[currentMode].nums[4];
        nextNode.classList.remove('mystery');
        nextNode.classList.add('revealed');
      }
      nextNode.classList.add('active');
    } else {
      resetState();
    }
  }

  resetState();
</script>

</body>
</html>

How do we figure out the secret jump rule every single time?

When numbers get bigger, we find how much is added from one number to the next.

In the pattern $3, 6, 9$, we see that $3 + 3 = 6$ and $6 + 3 = 9$, so the rule is **add 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">
<style>
  * { box-sizing: border-box; margin: 0; padding: 0; }
  body {
    font-family: system-ui, -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, sans-serif;
    background: transparent;
    color: #1e2945;
    display: flex;
    flex-direction: column;
    align-items: center;
    justify-content: center;
    min-height: 100%;
    padding: 12px;
  }

  .controls {
    display: flex;
    gap: 8px;
    margin-bottom: 24px;
    background: #f1f5f9;
    padding: 4px;
    border-radius: 999px;
  }

  .btn {
    border: none;
    background: transparent;
    padding: 6px 16px;
    border-radius: 999px;
    font-size: 14px;
    font-weight: 600;
    color: #64748b;
    cursor: pointer;
    transition: all 0.25s ease;
  }

  .btn.active {
    background: #8b5cf6;
    color: #ffffff;
    box-shadow: 0 2px 8px rgba(139, 92, 246, 0.3);
  }

  .sequence-container {
    position: relative;
    width: 100%;
    max-width: 520px;
    padding: 60px 10px 20px 10px;
    display: flex;
    justify-content: space-between;
    align-items: center;
  }

  .term-col {
    display: flex;
    flex-direction: column;
    align-items: center;
    position: relative;
    z-index: 2;
  }

  .term-card {
    width: 54px;
    height: 54px;
    background: #ffffff;
    border: 2px solid #e2e8f0;
    border-radius: 14px;
    display: flex;
    align-items: center;
    justify-content: center;
    font-size: 20px;
    font-weight: 700;
    color: #1e2945;
    box-shadow: 0 4px 12px rgba(0, 0, 0, 0.05);
    transition: all 0.3s ease;
  }

  .term-card.highlight {
    border-color: #8b5cf6;
    background: #f5f3ff;
    color: #8b5cf6;
    transform: translateY(-2px);
    box-shadow: 0 6px 16px rgba(139, 92, 246, 0.2);
  }

  .term-card.next-term {
    border-style: dashed;
    border-color: #cbd5e1;
    color: #94a3b8;
    background: #f8fafc;
    cursor: pointer;
  }

  .term-card.next-term.revealed {
    border-style: solid;
    border-color: #10b981;
    color: #10b981;
    background: #ecfdf5;
  }

  .jump-layer {
    position: absolute;
    top: 0;
    left: 0;
    width: 100%;
    height: 100%;
    pointer-events: none;
    z-index: 1;
  }

  .rule-badge {
    margin-top: 24px;
    font-size: 15px;
    font-weight: 700;
    padding: 6px 16px;
    border-radius: 8px;
    background: #f5f3ff;
    color: #7c3aed;
    display: inline-flex;
    align-items: center;
    gap: 6px;
    border: 1px solid #ddd6fe;
  }

  .rule-badge.sub {
    background: #eff6ff;
    color: #2563eb;
    border-color: #bfdbfe;
  }

  .jump-label {
    position: absolute;
    top: 10px;
    font-size: 13px;
    font-weight: 700;
    padding: 2px 8px;
    border-radius: 999px;
    background: #8b5cf6;
    color: #ffffff;
    transform: translateX(-50%);
    box-shadow: 0 2px 6px rgba(139, 92, 246, 0.3);
    opacity: 0;
    transition: opacity 0.3s ease;
  }

  .jump-label.sub {
    background: #2563eb;
    box-shadow: 0 2px 6px rgba(37, 99, 235, 0.3);
  }

  .jump-label.visible {
    opacity: 1;
  }

  svg path.arc {
    fill: none;
    stroke-width: 2.5;
    stroke-linecap: round;
    stroke-dasharray: 200;
    stroke-dashoffset: 200;
    transition: stroke-dashoffset 0.5s ease;
  }

  svg path.arc.visible {
    stroke-dashoffset: 0;
  }
</style>
</head>
<body>

<div class="controls">
  <button class="btn active" id="btn-add" onclick="setPattern('add')">+3 Rule</button>
  <button class="btn" id="btn-sub" onclick="setPattern('sub')">-4 Rule</button>
</div>

<div class="sequence-container" id="seq-box">
  <svg class="jump-layer" id="svg-layer"></svg>

  <div class="term-col">
    <div class="term-card" id="term-0">3</div>
  </div>

  <div class="term-col">
    <div class="term-card" id="term-1">6</div>
  </div>

  <div class="term-col">
    <div class="term-card" id="term-2">9</div>
  </div>

  <div class="term-col">
    <div class="term-card" id="term-3">12</div>
  </div>

  <div class="term-col">
    <div class="term-card next-term" id="term-4" onclick="revealNext()">?</div>
  </div>

  <div class="jump-label" id="lbl-0">+3</div>
  <div class="jump-label" id="lbl-1">+3</div>
  <div class="jump-label" id="lbl-2">+3</div>
  <div class="jump-label" id="lbl-3">+3</div>
</div>

<div class="rule-badge" id="rule-display">
  Rule: <strong>Add 3</strong>
</div>

<script>
const patterns = {
  add: {
    terms: [3, 6, 9, 12, 15],
    ruleText: "Add 3",
    jumpText: "+3",
    color: "#8b5cf6",
    isSub: false
  },
  sub: {
    terms: [20, 16, 12, 8, 4],
    ruleText: "Subtract 4",
    jumpText: "-4",
    color: "#2563eb",
    isSub: true
  }
};

let currentMode = 'add';
let isRevealed = false;

function drawArcs() {
  const container = document.getElementById('seq-box');
  const svg = document.getElementById('svg-layer');
  const cRect = container.getBoundingClientRect();
  
  svg.setAttribute('viewBox', `0 0 ${cRect.width} ${cRect.height}`);
  svg.innerHTML = '';

  const cfg = patterns[currentMode];

  for (let i = 0; i < 4; i++) {
    const t1 = document.getElementById(`term-${i}`).getBoundingClientRect();
    const t2 = document.getElementById(`term-${i+1}`).getBoundingClientRect();

    const x1 = t1.left + t1.width / 2 - cRect.left;
    const x2 = t2.left + t2.width / 2 - cRect.left;
    const y = t1.top - cRect.top + 6;

    const midX = (x1 + x2) / 2;
    const peakY = y - 36;

    const path = document.createElementNS('http://www.w3.org/2000/svg', 'path');
    path.setAttribute('d', `M ${x1} ${y} Q ${midX} ${peakY} ${x2} ${y}`);
    path.setAttribute('class', 'arc' + (i < 3 || isRevealed ? ' visible' : ''));
    path.setAttribute('id', `arc-${i}`);
    path.setAttribute('stroke', cfg.color);
    svg.appendChild(path);

    const lbl = document.getElementById(`lbl-${i}`);
    lbl.style.left = `${midX}px`;
    lbl.style.top = `${peakY - 14}px`;
    lbl.textContent = cfg.jumpText;
    lbl.className = 'jump-label ' + (cfg.isSub ? 'sub' : '') + (i < 3 || isRevealed ? ' visible' : '');
  }
}

function updatePatternUI() {
  const cfg = patterns[currentMode];
  
  for (let i = 0; i < 4; i++) {
    document.getElementById(`term-${i}`).textContent = cfg.terms[i];
  }

  const nextEl = document.getElementById('term-4');
  if (isRevealed) {
    nextEl.textContent = cfg.terms[4];
    nextEl.className = 'term-card next-term revealed';
  } else {
    nextEl.textContent = '?';
    nextEl.className = 'term-card next-term';
  }

  const badge = document.getElementById('rule-display');
  badge.innerHTML = `Rule: <strong>${cfg.ruleText}</strong>`;
  badge.className = 'rule-badge' + (cfg.isSub ? ' sub' : '');

  drawArcs();
}

function setPattern(mode) {
  currentMode = mode;
  isRevealed = false;
  document.getElementById('btn-add').className = 'btn' + (mode === 'add' ? ' active' : '');
  document.getElementById('btn-sub').className = 'btn' + (mode === 'sub' ? ' active' : '');
  updatePatternUI();
}

function revealNext() {
  if (!isRevealed) {
    isRevealed = true;
    updatePatternUI();
  }
}

window.addEventListener('resize', drawArcs);
window.addEventListener('load', () => updatePatternUI());
</script>

</body>
</html>

Each number in a number pattern is called a **term**.

To calculate subsequent terms, apply your rule ($d$) to the most recent value: $\text{Next Term} = \text{Current Term} + d$.

With our rule of $+3$, starting from the **Current Term** $9$ gives a **Next Term** of $9 + 3 = 12$.

Each number in a pattern is called a **term**.

To calculate subsequent terms, consistently apply the identified rule to the most recent term: $\text{Next Term} = \text{Current Term} + d$.

What happens when the numbers count down and get smaller instead?

When numbers get smaller, we take away the same amount on each step.

Look at $10, 8, 6$. Since $10 - 2 = 8$ and $8 - 2 = 6$, our rule is **subtract 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">
<style>
  * { box-sizing: border-box; margin: 0; padding: 0; }
  body {
    font-family: -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, sans-serif;
    background-color: #f8f9fa;
    color: #1e2945;
    display: flex;
    flex-direction: column;
    align-items: center;
    justify-content: center;
    min-height: 100%;
    padding: 16px 8px;
  }

  .diagram-area {
    width: 100%;
    max-width: 480px;
    display: flex;
    flex-direction: column;
    align-items: center;
    gap: 20px;
  }

  /* Sequence row */
  .sequence-container {
    position: relative;
    width: 100%;
    display: flex;
    justify-content: space-between;
    align-items: flex-end;
    padding-top: 50px;
  }

  .term-col {
    display: flex;
    flex-direction: column;
    align-items: center;
    z-index: 2;
    flex: 1;
  }

  .term-tile {
    width: 58px;
    height: 58px;
    background: #ffffff;
    border-radius: 14px;
    display: flex;
    align-items: center;
    justify-content: center;
    font-size: 24px;
    font-weight: 700;
    color: #1e2945;
    box-shadow: 0 3px 10px rgba(0, 0, 0, 0.06);
    border: 2px solid #e6e6e6;
    transition: border-color 0.3s ease, color 0.3s ease, background-color 0.3s ease;
  }

  .term-tile.active {
    border-color: #ff6b6b;
    color: #ff6b6b;
  }

  .term-tile.target {
    border-style: dashed;
    border-color: #cbd5e1;
    color: #94a3b8;
    background: #f8fafc;
  }

  .term-tile.revealed {
    border-style: solid;
    border-color: #10b981;
    color: #10b981;
    background: #ecfdf5;
  }

  /* SVG Jump Arcs */
  .arcs-svg {
    position: absolute;
    top: 0;
    left: 0;
    width: 100%;
    height: 100%;
    pointer-events: none;
    z-index: 1;
  }

  .jump-path {
    fill: none;
    stroke: #e2e8f0;
    stroke-width: 3;
    stroke-linecap: round;
    transition: stroke 0.3s ease, stroke-dashoffset 0.4s ease;
  }

  .jump-path.active {
    stroke: #ff6b6b;
  }

  .jump-path.success {
    stroke: #10b981;
  }

  .jump-tag {
    position: absolute;
    top: 6px;
    transform: translateX(-50%);
    background: #ffffff;
    border: 2px solid #e2e8f0;
    color: #64748b;
    font-size: 13px;
    font-weight: 700;
    padding: 3px 8px;
    border-radius: 12px;
    opacity: 0.3;
    transition: all 0.3s ease;
  }

  .jump-tag.active {
    border-color: #ff6b6b;
    background: #ff6b6b;
    color: #ffffff;
    opacity: 1;
  }

  .jump-tag.success {
    border-color: #10b981;
    background: #10b981;
    color: #ffffff;
    opacity: 1;
  }

  /* Rule summary badge */
  .rule-badge {
    display: inline-flex;
    align-items: center;
    gap: 6px;
    background: #ffffff;
    padding: 8px 16px;
    border-radius: 20px;
    border: 1px solid #e2e8f0;
    font-size: 15px;
    font-weight: 600;
    color: #475569;
    box-shadow: 0 2px 6px rgba(0, 0, 0, 0.04);
  }

  .rule-badge strong {
    color: #ff6b6b;
  }

  /* Navigation steps */
  .nav-controls {
    display: flex;
    align-items: center;
    gap: 8px;
    margin-top: 4px;
  }

  .step-btn {
    border: 1px solid #cbd5e1;
    background: #ffffff;
    color: #475569;
    padding: 6px 14px;
    border-radius: 20px;
    font-size: 13px;
    font-weight: 600;
    cursor: pointer;
    transition: all 0.2s ease;
  }

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

  .play-toggle {
    width: 32px;
    height: 32px;
    border-radius: 50%;
    border: 1px solid #cbd5e1;
    background: #ffffff;
    color: #1e2945;
    display: flex;
    align-items: center;
    justify-content: center;
    cursor: pointer;
    font-size: 12px;
    margin-left: 4px;
  }
</style>
</head>
<body>

<div class="diagram-area">
  <div class="sequence-container" id="seqContainer">
    
    <svg class="arcs-svg" viewBox="0 0 360 120" preserveAspectRatio="none">
      
      <path id="arc0" class="jump-path" d="M 45 60 Q 90 10, 135 60" />
      
      <path id="arc1" class="jump-path" d="M 135 60 Q 180 10, 225 60" />
      
      <path id="arc2" class="jump-path" d="M 225 60 Q 270 10, 315 60" />
    </svg>

    
    <div id="tag0" class="jump-tag" style="left: 25%;">-2</div>
    <div id="tag1" class="jump-tag" style="left: 50%;">-2</div>
    <div id="tag2" class="jump-tag" style="left: 75%;">-2</div>

    
    <div class="term-col">
      <div class="term-tile" id="tile0">10</div>
    </div>
    <div class="term-col">
      <div class="term-tile" id="tile1">8</div>
    </div>
    <div class="term-col">
      <div class="term-tile" id="tile2">6</div>
    </div>
    <div class="term-col">
      <div class="term-tile target" id="tile3">?</div>
    </div>
  </div>

  <div class="rule-badge" id="ruleBadge">
    Rule: <strong>Subtract 2</strong>
  </div>

  <div class="nav-controls">
    <button class="step-btn active" onclick="setStep(0)">Step 1</button>
    <button class="step-btn" onclick="setStep(1)">Step 2</button>
    <button class="step-btn" onclick="setStep(2)">Step 3</button>
    <button class="play-toggle" id="playBtn" onclick="togglePlay()" aria-label="Play/Pause">⏸</button>
  </div>
</div>

<script>
  let currentStep = 0;
  let isPlaying = true;
  let timer = null;

  const tiles = [
    document.getElementById('tile0'),
    document.getElementById('tile1'),
    document.getElementById('tile2'),
    document.getElementById('tile3')
  ];

  const arcs = [
    document.getElementById('arc0'),
    document.getElementById('arc1'),
    document.getElementById('arc2')
  ];

  const tags = [
    document.getElementById('tag0'),
    document.getElementById('tag1'),
    document.getElementById('tag2')
  ];

  const stepBtns = document.querySelectorAll('.step-btn');
  const playBtn = document.getElementById('playBtn');

  function renderState() {
    // Reset all elements
    tiles.forEach((t, i) => {
      t.className = 'term-tile';
      if (i === 3) {
        t.className = 'term-tile target';
        t.textContent = '?';
      }
    });

    arcs.forEach(a => a.className = 'jump-path');
    tags.forEach(t => t.className = 'jump-tag');

    stepBtns.forEach((b, i) => {
      b.classList.toggle('active', i === currentStep);
    });

    if (currentStep === 0) {
      tiles[0].classList.add('active');
      tiles[1].classList.add('active');
      arcs[0].classList.add('active');
      tags[0].classList.add('active');
    } else if (currentStep === 1) {
      tiles[1].classList.add('active');
      tiles[2].classList.add('active');
      arcs[0].classList.add('active');
      tags[0].classList.add('active');
      arcs[1].classList.add('active');
      tags[1].classList.add('active');
    } else if (currentStep === 2) {
      arcs[0].classList.add('active');
      tags[0].classList.add('active');
      arcs[1].classList.add('active');
      tags[1].classList.add('active');

      tiles[2].classList.add('active');
      arcs[2].classList.add('success');
      tags[2].classList.add('success');
      tiles[3].className = 'term-tile revealed';
      tiles[3].textContent = '4';
    }
  }

  function setStep(step) {
    currentStep = step;
    renderState();
  }

  function nextStep() {
    currentStep = (currentStep + 1) % 3;
    renderState();
  }

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

  function togglePlay() {
    isPlaying = !isPlaying;
    playBtn.textContent = isPlaying ? '⏸' : '▶';
    if (isPlaying) {
      startTimer();
    } else {
      if (timer) clearInterval(timer);
    }
  }

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

To find the missing number after $6$, take away $2$ to get $4$.

Always test your jump between two different pairs of neighbors to be sure the rule stays the same!

math

Identifying Term-to-Term Addition and Subtraction Rules. Find the constant difference in arithmetic sequences and use it to calculate subsequent terms.

Number Patterns and Sequences - Curriculum for Excellence Second Level Maths

Introduction to Arithmetic Sequences and Common Difference

Arithmetic Sequences: Find the Next Term and Term-to-Term Rule

Pedagogical delivery should bridge concrete representations (Unifix cubes, bead strings) to semi-concrete visual models (number line jumps, hundred square patterns) and abstract numerical notation. Emphasize verbalizing patterns using clear sentence stems such as 'The pattern starts at ___ and the rule is to add/subtract ___ each time' before moving directly to standard mathematical notation.

Identifying Term-to-Term Addition and Subtraction Rules

Finding the Plus Rule