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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).

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Tutoring abilities

Have you ever tripped over untied shoelaces, dropped your backpack because the zipper jammed, or watched your ice pop melt into a sticky puddle on your hands?

Those annoying daily moments aren't just bad luck — they are actually invitations to invent something new.

An **engineering problem** is a specific need or challenge that people can solve by designing, building, or improving a product or system.

When engineers look at the world, they ask two simple questions: *Who is struggling with something?* and *What would make this work better?*

<!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>Engineering Problems and Solutions</title>
  <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: 16px;
    }
    .diagram-content {
      width: 100%;
      max-width: 520px;
      display: flex;
      flex-direction: column;
      gap: 16px;
    }
    .toggle-bar {
      display: flex;
      background: #e2e8f0;
      padding: 4px;
      border-radius: 12px;
      gap: 4px;
    }
    .toggle-btn {
      flex: 1;
      border: none;
      background: transparent;
      padding: 10px 8px;
      border-radius: 8px;
      font-size: 14px;
      font-weight: 600;
      color: #64748b;
      cursor: pointer;
      display: flex;
      align-items: center;
      justify-content: center;
      gap: 6px;
      transition: all 0.25s ease;
    }
    .toggle-btn.active {
      background: #ffffff;
      color: #1e2945;
      box-shadow: 0 2px 8px rgba(0, 0, 0, 0.08);
    }
    .toggle-btn.active.q1 {
      color: #d97706;
    }
    .toggle-btn.active.q2 {
      color: #0284c7;
    }
    .cards-grid {
      display: grid;
      grid-template-columns: repeat(3, 1fr);
      gap: 12px;
    }
    .scenario-card {
      background: #ffffff;
      border-radius: 12px;
      padding: 16px 8px;
      text-align: center;
      box-shadow: 0 2px 8px rgba(0, 0, 0, 0.04);
      display: flex;
      flex-direction: column;
      align-items: center;
      justify-content: center;
      gap: 10px;
      min-height: 160px;
      transition: all 0.3s ease;
      cursor: pointer;
      position: relative;
    }
    .scenario-card:hover {
      box-shadow: 0 4px 12px rgba(0, 0, 0, 0.08);
    }
    .icon-box {
      font-size: 40px;
      line-height: 1;
      height: 52px;
      display: flex;
      align-items: center;
      justify-content: center;
      transition: transform 0.3s ease;
    }
    .badge {
      font-size: 13px;
      font-weight: 600;
      padding: 4px 10px;
      border-radius: 20px;
      letter-spacing: -0.2px;
      transition: all 0.3s ease;
    }
    .struggle .badge {
      background: #fef3c7;
      color: #b45309;
    }
    .solution .badge {
      background: #e0f2fe;
      color: #0369a1;
    }
    .arrow-indicator {
      font-size: 16px;
      color: #94a3b8;
    }
    .selector-dots {
      display: flex;
      justify-content: center;
      gap: 8px;
    }
    .dot-btn {
      width: 10px;
      height: 10px;
      border-radius: 50%;
      background: #cbd5e1;
      border: none;
      cursor: pointer;
      padding: 0;
      transition: background 0.2s ease;
    }
    .dot-btn.active {
      background: #22b7ff;
      transform: scale(1.2);
    }
  </style>
</head>
<body>
  <div class="diagram-content">
    <div class="toggle-bar">
      <button class="toggle-btn q1 active" id="btnStruggle">
        <span>👤</span> 1. Struggle?
      </button>
      <button class="toggle-btn q2" id="btnSolution">
        <span>💡</span> 2. Better fix?
      </button>
    </div>

    <div class="cards-grid">
      <div class="scenario-card struggle" id="card1">
        <div class="icon-box" id="icon1">🎒</div>
        <span class="badge" id="label1">Heavy load</span>
      </div>

      <div class="scenario-card struggle" id="card2">
        <div class="icon-box" id="icon2">🧗</div>
        <span class="badge" id="label2">Steep steps</span>
      </div>

      <div class="scenario-card struggle" id="card3">
        <div class="icon-box" id="icon3">🥀</div>
        <span class="badge" id="label3">Dry plant</span>
      </div>
    </div>
  </div>

  <script src="{{VENDOR_CDN}}/classace-diagram.js"></script>
  <script>
    const scenarios = [
      {
        struggle: { icon: '🎒', label: 'Heavy load' },
        solution: { icon: '🧳', label: 'Wheels' }
      },
      {
        struggle: { icon: '🧗', label: 'Steep steps' },
        solution: { icon: '♿', label: 'Ramp' }
      },
      {
        struggle: { icon: '🥀', label: 'Dry plant' },
        solution: { icon: '💧', label: 'Drip system' }
      }
    ];

    let mode = 'struggle'; // 'struggle' | 'solution'

    const btnStruggle = $('#btnStruggle');
    const btnSolution = $('#btnSolution');
    const cards = [$('#card1'), $('#card2'), $('#card3')];
    const icons = [$('#icon1'), $('#icon2'), $('#icon3')];
    const labels = [$('#label1'), $('#label2'), $('#label3')];

    function setMode(newMode) {
      mode = newMode;
      const isStruggle = mode === 'struggle';

      btnStruggle.classList.toggle('active', isStruggle);
      btnSolution.classList.toggle('active', !isStruggle);

      cards.forEach((card, idx) => {
        card.classList.toggle('struggle', isStruggle);
        card.classList.toggle('solution', !isStruggle);
        const data = isStruggle ? scenarios[idx].struggle : scenarios[idx].solution;
        icons[idx].textContent = data.icon;
        labels[idx].textContent = data.label;
      });
    }

    onTap(btnStruggle, () => setMode('struggle'));
    onTap(btnSolution, () => setMode('solution'));

    cards.forEach((card) => {
      onTap(card, () => {
        setMode(mode === 'struggle' ? 'solution' : 'struggle');
      });
    });
  </script>
</body>
</html>

So how do you tell the difference between a problem you can engineer a fix for, and something you can't?

Engineers cannot change the weather to stop it from raining, but they *can* design a lightweight, water-repellent jacket.

To make a problem solvable, engineers turn a general frustration into a clear **need statement** that defines who needs what and why.

<!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>Engineering Need Statement</title>
  <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: #f8f9fa;
      color: #1e2945;
      display: flex;
      flex-direction: column;
      align-items: center;
      justify-content: space-between;
      min-height: 100%;
      padding: 16px;
      gap: 12px;
    }

    .scenario-tabs {
      display: flex;
      gap: 8px;
      width: 100%;
      max-width: 520px;
    }

    .tab-btn {
      flex: 1;
      border: 1px solid #e2e8f0;
      background: #ffffff;
      padding: 8px 6px;
      border-radius: 10px;
      font-size: 14px;
      font-weight: 600;
      color: #64748b;
      cursor: pointer;
      display: flex;
      align-items: center;
      justify-content: center;
      gap: 6px;
      transition: background 0.2s, color 0.2s, box-shadow 0.2s;
    }

    .tab-btn.active {
      background: #ffffff;
      color: #0284c7;
      box-shadow: 0 0 0 2px #22b7ff;
    }

    .main-stage {
      width: 100%;
      max-width: 520px;
      display: flex;
      flex-direction: column;
      gap: 12px;
    }

    .frustration-box {
      background: #ffffff;
      border-radius: 12px;
      padding: 12px 16px;
      display: flex;
      align-items: center;
      justify-content: space-between;
      box-shadow: 0 2px 6px rgba(0, 0, 0, 0.04);
    }

    .frustration-badge {
      font-size: 12px;
      font-weight: 700;
      text-transform: uppercase;
      letter-spacing: 0.5px;
      color: #e11d48;
      background: #ffe4e6;
      padding: 3px 8px;
      border-radius: 6px;
    }

    .frustration-text {
      font-size: 15px;
      font-weight: 600;
      color: #334155;
      display: flex;
      align-items: center;
      gap: 8px;
    }

    .arrow-divider {
      text-align: center;
      font-size: 18px;
      color: #94a3b8;
      font-weight: 700;
      line-height: 1;
    }

    .formula-grid {
      display: grid;
      grid-template-columns: 1fr 1fr 1fr;
      gap: 8px;
      width: 100%;
    }

    .part-card {
      background: #ffffff;
      border-radius: 12px;
      padding: 12px 8px;
      text-align: center;
      display: flex;
      flex-direction: column;
      align-items: center;
      gap: 6px;
      box-shadow: 0 2px 6px rgba(0, 0, 0, 0.04);
      cursor: pointer;
      position: relative;
      transition: transform 0.2s, box-shadow 0.2s;
    }

    .part-card.active {
      box-shadow: 0 0 0 2px #22b7ff;
    }

    .tag-label {
      font-size: 11px;
      font-weight: 800;
      letter-spacing: 0.5px;
      text-transform: uppercase;
      padding: 2px 6px;
      border-radius: 4px;
    }

    .tag-who { background: #ede9fe; color: #7c3aed; }
    .tag-what { background: #e0f2fe; color: #0284c7; }
    .tag-why { background: #dcfce7; color: #16a34a; }

    .part-icon {
      font-size: 26px;
      line-height: 1;
      margin: 4px 0;
    }

    .part-text {
      font-size: 13px;
      font-weight: 600;
      color: #1e293b;
      line-height: 1.2;
      min-height: 32px;
      display: flex;
      align-items: center;
      justify-content: center;
    }

    .statement-summary {
      background: #ffffff;
      border-radius: 12px;
      padding: 14px 16px;
      box-shadow: 0 2px 6px rgba(0, 0, 0, 0.04);
      display: flex;
      flex-wrap: wrap;
      align-items: center;
      gap: 6px;
      font-size: 15px;
      font-weight: 500;
      color: #475569;
      line-height: 1.5;
    }

    .pill {
      font-weight: 700;
      padding: 2px 8px;
      border-radius: 6px;
      display: inline-block;
    }

    .pill-who { background: #ede9fe; color: #6d28d9; }
    .pill-what { background: #e0f2fe; color: #0369a1; }
    .pill-why { background: #dcfce7; color: #15803d; }

    .stepper-nav {
      display: flex;
      align-items: center;
      justify-content: center;
      gap: 12px;
      width: 100%;
      max-width: 520px;
    }

    .play-btn {
      background: #ffffff;
      border: 1px solid #cbd5e1;
      width: 34px;
      height: 34px;
      border-radius: 50%;
      display: flex;
      align-items: center;
      justify-content: center;
      cursor: pointer;
      color: #334155;
      font-size: 14px;
    }

    .dots {
      display: flex;
      gap: 6px;
    }

    .dot {
      width: 8px;
      height: 8px;
      border-radius: 4px;
      background: #cbd5e1;
      cursor: pointer;
      transition: background 0.2s, width 0.2s;
    }

    .dot.active {
      width: 20px;
      background: #22b7ff;
    }
  </style>
</head>
<body>

  <div class="scenario-tabs">
    <button class="tab-btn active" id="tab0">🎒 Backpack</button>
    <button class="tab-btn" id="tab1">🌱 Plants</button>
    <button class="tab-btn" id="tab2">🚴 Bike</button>
  </div>

  <div class="main-stage">
    <div class="frustration-box">
      <span class="frustration-badge">Frustration</span>
      <span class="frustration-text" id="frustText">😫 "My heavy bag hurts my shoulders"</span>
    </div>

    <div class="arrow-divider">↓ Make It Solvable ↓</div>

    <div class="formula-grid">
      <div class="part-card active" id="cardWho">
        <span class="tag-label tag-who">1. WHO</span>
        <span class="part-icon" id="iconWho">🎒</span>
        <span class="part-text" id="textWho">Students</span>
      </div>

      <div class="part-card" id="cardWhat">
        <span class="tag-label tag-what">2. WHAT</span>
        <span class="part-icon" id="iconWhat">⚖️</span>
        <span class="part-text" id="textWhat">Lighter carry weight</span>
      </div>

      <div class="part-card" id="cardWhy">
        <span class="tag-label tag-why">3. WHY</span>
        <span class="part-icon" id="iconWhy">🩺</span>
        <span class="part-text" id="textWhy">Prevent injury</span>
      </div>
    </div>

    <div class="statement-summary">
      <span class="pill pill-who" id="sumWho">Students</span>
      <span>need</span>
      <span class="pill pill-what" id="sumWhat">lighter carry weight</span>
      <span>so that</span>
      <span class="pill pill-why" id="sumWhy">they prevent injury.</span>
    </div>
  </div>

  <div class="stepper-nav">
    <button class="play-btn" id="playBtn" aria-label="Play/Pause">⏸</button>
    <div class="dots">
      <div class="dot active" id="dot0"></div>
      <div class="dot" id="dot1"></div>
      <div class="dot" id="dot2"></div>
    </div>
  </div>

  <script>
    const scenarios = [
      {
        tab: "🎒 Backpack",
        frust: "😫 \"My heavy bag hurts my shoulders\"",
        who: { icon: "🎒", text: "Students", sum: "Students" },
        what: { icon: "⚖️", text: "Weight balance", sum: "better weight balance" },
        why: { icon: "🩺", text: "Prevent strain", sum: "they prevent shoulder strain." }
      },
      {
        tab: "🌱 Plants",
        frust: "🥀 \"I forget to water houseplants\"",
        who: { icon: "🏡", text: "Plant owners", sum: "Plant owners" },
        what: { icon: "💧", text: "Self-watering tool", sum: "a self-watering system" },
        why: { icon: "🌿", text: "Keep plants alive", sum: "plants survive when away." }
      },
      {
        tab: "🚴 Bike",
        frust: "🌙 \"Night biking feels dangerous\"",
        who: { icon: "🚴", text: "Night cyclists", sum: "Cyclists" },
        what: { icon: "💡", text: "Bright side light", sum: "360° side visibility" },
        why: { icon: "🛡️", text: "Ride safely", sum: "cars see them clearly." }
      }
    ];

    let currentScenario = 0;
    let currentPart = 0;
    let isPlaying = true;
    let timer = null;

    const frustText = document.getElementById('frustText');
    const iconWho = document.getElementById('iconWho');
    const textWho = document.getElementById('textWho');
    const iconWhat = document.getElementById('iconWhat');
    const textWhat = document.getElementById('textWhat');
    const iconWhy = document.getElementById('iconWhy');
    const textWhy = document.getElementById('textWhy');

    const sumWho = document.getElementById('sumWho');
    const sumWhat = document.getElementById('sumWhat');
    const sumWhy = document.getElementById('sumWhy');

    const cardWho = document.getElementById('cardWho');
    const cardWhat = document.getElementById('cardWhat');
    const cardWhy = document.getElementById('cardWhy');
    const cards = [cardWho, cardWhat, cardWhy];

    const tabs = [document.getElementById('tab0'), document.getElementById('tab1'), document.getElementById('tab2')];
    const dots = [document.getElementById('dot0'), document.getElementById('dot1'), document.getElementById('dot2')];
    const playBtn = document.getElementById('playBtn');

    function render() {
      const data = scenarios[currentScenario];

      tabs.forEach((t, i) => t.classList.toggle('active', i === currentScenario));
      dots.forEach((d, i) => d.classList.toggle('active', i === currentScenario));

      frustText.textContent = data.frust;

      iconWho.textContent = data.who.icon;
      textWho.textContent = data.who.text;
      sumWho.textContent = data.who.sum;

      iconWhat.textContent = data.what.icon;
      textWhat.textContent = data.what.text;
      sumWhat.textContent = data.what.sum;

      iconWhy.textContent = data.why.icon;
      textWhy.textContent = data.why.text;
      sumWhy.textContent = data.why.sum;

      cards.forEach((c, idx) => c.classList.toggle('active', idx === currentPart));
    }

    function step() {
      currentPart = (currentPart + 1) % 3;
      if (currentPart === 0) {
        currentScenario = (currentScenario + 1) % scenarios.length;
      }
      render();
    }

    function startTimer() {
      clearInterval(timer);
      timer = setInterval(step, 2400);
      isPlaying = true;
      playBtn.textContent = '⏸';
    }

    function stopTimer() {
      clearInterval(timer);
      isPlaying = false;
      playBtn.textContent = '▶';
    }

    tabs.forEach((tab, index) => {
      tab.addEventListener('click', () => {
        currentScenario = index;
        currentPart = 0;
        render();
        if (isPlaying) startTimer();
      });
    });

    dots.forEach((dot, index) => {
      dot.addEventListener('click', () => {
        currentScenario = index;
        currentPart = 0;
        render();
        if (isPlaying) startTimer();
      });
    });

    cards.forEach((card, index) => {
      card.addEventListener('click', () => {
        currentPart = index;
        render();
      });
    });

    playBtn.addEventListener('click', () => {
      if (isPlaying) {
        stopTimer();
      } else {
        startTimer();
      }
    });

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

What does this look like when we break down a real, messy problem step by step?

## Worked Example: The Soggy Cereal Problem

**The Observation:** Maya notices that by the time she gets halfway through her cereal, the flakes turn completely mushy and unappetizing.

**Step 1 (Identify the user & goal):** Maya needs her cereal flakes to stay crunchy until she is ready to eat them.

**Step 2 (Identify the root cause):** The flakes sit submerged in liquid milk for too long before reaching her spoon.

**Step 3 (Formulate the problem):** Design a bowl that separates dry cereal from milk until the moment a bite is taken.

<!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>Formulating a Problem</title>
  <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: 100vh;
      padding: 12px;
    }

    .stepper-nav {
      display: flex;
      gap: 8px;
      margin-bottom: 14px;
      width: 100%;
      max-width: 420px;
    }

    .step-btn {
      flex: 1;
      padding: 8px 4px;
      border: 2px solid #e2e8f0;
      background: #ffffff;
      border-radius: 8px;
      font-size: 13px;
      font-weight: 600;
      color: #64748b;
      cursor: pointer;
      text-align: center;
      transition: all 0.25s ease;
    }

    .step-btn.active {
      border-color: #22b7ff;
      background: #f0f9ff;
      color: #0284c7;
      box-shadow: 0 2px 4px rgba(34, 183, 255, 0.15);
    }

    .stage-container {
      position: relative;
      width: 100%;
      max-width: 420px;
      height: 250px;
      background: #ffffff;
      border-radius: 16px;
      border: 1px solid #e2e8f0;
      overflow: hidden;
      display: flex;
      flex-direction: column;
      align-items: center;
      justify-content: center;
    }

    .step-view {
      position: absolute;
      inset: 0;
      display: flex;
      flex-direction: column;
      align-items: center;
      justify-content: center;
      opacity: 0;
      pointer-events: none;
      transition: opacity 0.35s ease;
      padding: 16px;
    }

    .step-view.active {
      opacity: 1;
      pointer-events: auto;
    }

    /* Step 1 Visual: Standard Bowl with Soggy Cereal */
    .bowl-svg {
      width: 180px;
      height: 120px;
    }

    /* Step 2 Visual: Timer & Separation */
    .timer-ring {
      font-size: 40px;
      margin-bottom: 6px;
    }

    /* Step 3 Visual: Partitioned Bowl */
    .tag {
      margin-top: 12px;
      padding: 6px 14px;
      border-radius: 20px;
      font-size: 14px;
      font-weight: 600;
      display: inline-flex;
      align-items: center;
      gap: 6px;
    }

    .tag-symptom {
      background: #fef2f2;
      color: #dc2626;
      border: 1px solid #fecaca;
    }

    .tag-cause {
      background: #fffbeb;
      color: #d97706;
      border: 1px solid #fde68a;
    }

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</head>
<body>

  
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        <path d="M 60 90 L 100 90" stroke="#64748b" stroke-width="4" stroke-linecap="round"/>
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      <div class="tag tag-formulation">Problem: Separate until bite</div>
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A common mistake is jumping straight to a solution before fully understanding what the real problem is.

If Maya assumed 'cereal is bad' and gave up, she would never invent a better bowl — always separate the **symptom** (soggy flakes) from the **cause** (prolonged liquid contact).

How do different types of engineers tackle everyday problems around us?

## Different Engineers, Different Solutions

Depending on the problem, different branches of engineering step in with specialized tools.

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Take a look around the room you are sitting in right now — what is one small thing that is noisy, slow, or frustrating to use?

technology

What Is a Problem We Want to Solve?. Learners identify problems in everyday life that engineering and design can help solve.

Early Level Technologies: Designing and Problem Solving

STEM from the START: Problem Solving and Materials Engineering

Engineering Design Process: Solving Everyday Problems

At Early Level (P1 / ages 4-6), the learning experience must be grounded in tactile, real-world context and play-based inquiry. Teachers should begin with a 'Problem Mystery Box' or classroom scavenger hunt where pupils examine common tools (scissors, pegs, water bottles, umbrellas) and articulate what life would be like without that specific product. Emphasize talk routines using the sentence frame: 'The problem was ___, so someone designed a ___ to help us ___.' This builds early technological literacy and oral vocabulary while fulfilling Curriculum for Excellence benchmark TCH 0-12a.

What Is a Problem We Want to Solve?

What Is an Engineering Problem?

Problems We Can Engineer

Worked Example: The Soggy Cereal Problem