Advanced

Tutor model

i62 💰:9.4

i52 💰:7.9

🏆 i67 💰:62.5

i70 💰:125.0

i68 💰:125.0

🏆 i66 💰:75.0

i65 💰:125.0

i63 💰:62.5

i61 💰:75.0

i60 💰:9.4

i60 💰:37.5

i58 💰:62.5

i57 💰:22.5

i57 💰:37.5

i56 💰:45.0

⚡ i55 💰:11.25

i55 💰:37.5

i54 💰:62.5

i52 💰:35.0

i51 💰:37.5

i49 💰:15.0

i49 💰:62.5

i48 💰:11.3

i47 💰:7.5

i44 💰:25.0

i43 💰:37.5

i42 💰:187.5

i40 💰:5.0

i39 💰:100.0

i38 💰:37.5

i37 💰:11.0

i36 💰:187.5

i34 💰:12.5

i33 💰:37.5

i30 💰:1.0

i29 💰:1.5

i28 💰:150.0

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i20 💰:4.0

i18 💰:1.0

i16 💰:25.0

i13 💰:1.5

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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

i31 💰:11.0

i25 💰:31.3

Tutoring abilities

Why would someone buy 85 giant watermelons at the grocery store?

You see questions like that on math worksheets all the time. It is great practice, but nobody in real life has an 85-watermelon emergency!

The word **authentic** means real and genuine. An **authentic problem** is a challenge that real people actually face in everyday life.

A **practice problem** is created just to help you train a skill, like a puzzle in a game or a question on a test.

<!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: -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, sans-serif;
    }

    body {
      background: #f8f9fa;
      color: #1e2945;
      padding: 16px;
      display: flex;
      flex-direction: column;
      align-items: center;
      justify-content: center;
      min-height: 100%;
    }

    .toolbar {
      display: flex;
      gap: 8px;
      margin-bottom: 16px;
      background: #e9ecef;
      padding: 4px;
      border-radius: 20px;
    }

    .tab-btn {
      border: none;
      background: transparent;
      padding: 8px 18px;
      font-size: 14px;
      font-weight: 600;
      color: #6b7280;
      border-radius: 16px;
      cursor: pointer;
      transition: background 0.2s, color 0.2s;
    }

    .tab-btn.active {
      background: #ffffff;
      color: #1e2945;
      box-shadow: 0 2px 6px rgba(0, 0, 0, 0.08);
    }

    .display-area {
      width: 100%;
      max-width: 480px;
      display: grid;
      grid-template-columns: 1fr 1fr;
      gap: 12px;
    }

    .tile {
      background: #ffffff;
      border-radius: 12px;
      padding: 16px 12px;
      text-align: center;
      display: flex;
      flex-direction: column;
      align-items: center;
      justify-content: center;
      min-height: 140px;
      border: 2px solid transparent;
      transition: border-color 0.3s, background-color 0.3s;
    }

    .tile.practice {
      border-color: #cbd5e1;
    }

    .tile.authentic {
      border-color: #22b7ff;
      background: #f0f9ff;
    }

    .badge {
      font-size: 11px;
      text-transform: uppercase;
      font-weight: 700;
      letter-spacing: 0.5px;
      padding: 4px 8px;
      border-radius: 6px;
      margin-bottom: 8px;
    }

    .practice .badge {
      background: #e2e8f0;
      color: #475569;
    }

    .authentic .badge {
      background: #bae6fd;
      color: #0369a1;
    }

    .icon {
      font-size: 36px;
      line-height: 1;
      margin-bottom: 8px;
      display: block;
    }

    .label {
      font-size: 14px;
      font-weight: 600;
      color: #1e2945;
      line-height: 1.2;
    }

    .sub-label {
      font-size: 12px;
      color: #6b7280;
      margin-top: 4px;
    }

    .flow-indicator {
      grid-column: 1 / -1;
      display: flex;
      justify-content: center;
      gap: 6px;
      margin-top: 4px;
    }

    .dot {
      width: 8px;
      height: 8px;
      border-radius: 50%;
      background: #cbd5e1;
      cursor: pointer;
      border: none;
      padding: 0;
      transition: background 0.2s, transform 0.2s;
    }

    .dot.active {
      background: #22b7ff;
      transform: scale(1.25);
    }
  </style>
</head>
<body>

  <div class="toolbar" role="tablist">
    <button class="tab-btn active" id="tab0">Origin</button>
    <button class="tab-btn" id="tab1">Users</button>
    <button class="tab-btn" id="tab2">Impact</button>
  </div>

  <div class="display-area">
    
    <div class="tile practice">
      <span class="badge">Practice</span>
      <span class="icon" id="icon-practice">📝</span>
      <span class="label" id="label-practice">Made Up</span>
      <span class="sub-label" id="sub-practice">Test question</span>
    </div>

    
    <div class="tile authentic">
      <span class="badge">Authentic</span>
      <span class="icon" id="icon-authentic">🌍</span>
      <span class="label" id="label-authentic">Real World</span>
      <span class="sub-label" id="sub-authentic">Actual situation</span>
    </div>

    
    <div class="flow-indicator">
      <button class="dot active" id="dot0" aria-label="Step 1"></button>
      <button class="dot" id="dot1" aria-label="Step 2"></button>
      <button class="dot" id="dot2" aria-label="Step 3"></button>
    </div>
  </div>

  <script>
    const steps = [
      {
        pIcon: '📝',
        pLabel: 'Made Up',
        pSub: 'Test or game',
        aIcon: '🌍',
        aLabel: 'Real World',
        aSub: 'Real situation'
      },
      {
        pIcon: '👤',
        pLabel: 'Solo Learner',
        pSub: 'Only for practice',
        aIcon: '👥',
        aLabel: 'Real People',
        aSub: 'Helps a community'
      },
      {
        pIcon: '💯',
        pLabel: 'Single Score',
        pSub: 'Right or wrong',
        aIcon: '💡',
        aLabel: 'Real Value',
        aSub: 'Practical change'
      }
    ];

    let current = 0;
    let timer = null;

    function render(index) {
      current = index;
      const data = steps[index];

      // Update Practice tile
      document.getElementById('icon-practice').textContent = data.pIcon;
      document.getElementById('label-practice').textContent = data.pLabel;
      document.getElementById('sub-practice').textContent = data.pSub;

      // Update Authentic tile
      document.getElementById('icon-authentic').textContent = data.aIcon;
      document.getElementById('label-authentic').textContent = data.aLabel;
      document.getElementById('sub-authentic').textContent = data.aSub;

      // Update tabs and dots
      for (let i = 0; i < steps.length; i++) {
        document.getElementById('tab' + i).classList.toggle('active', i === index);
        document.getElementById('dot' + i).classList.toggle('active', i === index);
      }
    }

    function startAutoCycle() {
      stopAutoCycle();
      timer = setInterval(() => {
        const next = (current + 1) % steps.length;
        render(next);
      }, 3500);
    }

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

    for (let i = 0; i < steps.length; i++) {
      const tab = document.getElementById('tab' + i);
      const dot = document.getElementById('dot' + i);

      const handler = () => {
        stopAutoCycle();
        render(i);
      };

      tab.addEventListener('click', handler);
      dot.addEventListener('click', handler);
    }

    render(0);
    startAutoCycle();
  </script>
</body>
</html>

How can you be sure whether a problem is authentic or made up?

To spot an authentic problem, you can act like a detective and check for three clues.

<!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>3 Clues of an Authentic Problem</title>
  <script src="https://cdn.jsdelivr.net/npm/classace-diagram@latest/dist/index.js"></script>
  <style>
    * { box-sizing: border-box; margin: 0; padding: 0; font-family: system-ui, -apple-system, BlinkMacSystemFont, 'Segoe UI', Roboto, sans-serif; }
    
    body {
      background: #f8f9fa;
      color: #1e2945;
      padding: 16px;
      display: flex;
      flex-direction: column;
      align-items: center;
      justify-content: center;
      min-height: 100%;
    }

    .main-stage {
      width: 100%;
      max-width: 540px;
      display: flex;
      flex-direction: column;
      align-items: center;
      gap: 16px;
    }

    /* Clue Grid */
    .clues-grid {
      display: grid;
      grid-template-columns: repeat(3, 1fr);
      gap: 12px;
      width: 100%;
    }

    .clue-card {
      background: #ffffff;
      border: 2px solid #e2e8f0;
      border-radius: 14px;
      padding: 14px 8px;
      display: flex;
      flex-direction: column;
      align-items: center;
      text-align: center;
      cursor: pointer;
      user-select: none;
      transition: border-color 0.25s ease, box-shadow 0.25s ease, background-color 0.25s ease;
      position: relative;
    }

    .clue-card:hover {
      border-color: #cbd5e1;
    }

    .clue-card.active {
      border-color: #22b7ff;
      background: #f0f9ff;
      box-shadow: 0 4px 14px rgba(34, 183, 255, 0.18);
    }

    .clue-num {
      font-size: 11px;
      font-weight: 700;
      color: #64748b;
      background: #f1f5f9;
      border-radius: 20px;
      padding: 2px 8px;
      margin-bottom: 8px;
    }

    .clue-card.active .clue-num {
      background: #22b7ff;
      color: #ffffff;
    }

    .clue-icon {
      font-size: 32px;
      line-height: 1;
      margin-bottom: 8px;
      filter: grayscale(0.8);
      opacity: 0.6;
      transition: filter 0.25s ease, opacity 0.25s ease;
    }

    .clue-card.active .clue-icon {
      filter: grayscale(0);
      opacity: 1;
    }

    .clue-label {
      font-size: 14px;
      font-weight: 700;
      color: #334155;
      line-height: 1.2;
    }

    .clue-card.active .clue-label {
      color: #0369a1;
    }

    /* Central Authentic Detective Target */
    .authentic-box {
      width: 100%;
      background: #ffffff;
      border: 2px solid #e2e8f0;
      border-radius: 16px;
      padding: 18px 16px;
      display: flex;
      flex-direction: column;
      align-items: center;
      gap: 12px;
      box-shadow: 0 2px 6px rgba(0, 0, 0, 0.04);
    }

    .detective-visual {
      display: flex;
      align-items: center;
      justify-content: center;
      gap: 14px;
    }

    .badge-icon {
      font-size: 36px;
      line-height: 1;
    }

    .badge-text {
      font-size: 16px;
      font-weight: 800;
      letter-spacing: 0.5px;
      color: #1e2945;
    }

    .checks-row {
      display: flex;
      gap: 12px;
    }

    .check-pill {
      display: flex;
      align-items: center;
      gap: 6px;
      background: #f1f5f9;
      border-radius: 20px;
      padding: 6px 12px;
      font-size: 13px;
      font-weight: 600;
      color: #94a3b8;
      transition: background-color 0.3s ease, color 0.3s ease;
    }

    .check-pill.lit {
      background: #ecfdf5;
      color: #059669;
    }

    .check-pill .chk-icon {
      font-size: 13px;
    }

    /* Controls */
    .controls {
      display: flex;
      align-items: center;
      justify-content: center;
      gap: 12px;
      margin-top: 2px;
    }

    .nav-btn {
      background: #ffffff;
      border: 1px solid #cbd5e1;
      border-radius: 50%;
      width: 34px;
      height: 34px;
      display: flex;
      align-items: center;
      justify-content: center;
      font-size: 13px;
      cursor: pointer;
      color: #475569;
      transition: background 0.2s ease, border-color 0.2s ease;
    }

    .nav-btn:hover {
      background: #f1f5f9;
      border-color: #94a3b8;
    }

    .dots-container {
      display: flex;
      gap: 8px;
    }

    .dot {
      width: 10px;
      height: 10px;
      border-radius: 50%;
      background: #cbd5e1;
      cursor: pointer;
      transition: background-color 0.25s ease, width 0.25s ease;
    }

    .dot.active {
      background: #22b7ff;
      width: 20px;
      border-radius: 10px;
    }

    @media (max-width: 400px) {
      .clue-icon { font-size: 26px; }
      .clue-label { font-size: 13px; }
      .badge-text { font-size: 14px; }
      .check-pill { padding: 4px 8px; font-size: 12px; }
    }
  </style>
</head>
<body>
  <div class="main-stage">
    
    
    <div class="clues-grid">
      <div class="clue-card active" data-step="0">
        <span class="clue-num">CLUE 1</span>
        <div class="clue-icon">👥</div>
        <span class="clue-label">Real<br>People</span>
      </div>

      <div class="clue-card" data-step="1">
        <span class="clue-num">CLUE 2</span>
        <div class="clue-icon">⚠️</div>
        <span class="clue-label">Real<br>Need</span>
      </div>

      <div class="clue-card" data-step="2">
        <span class="clue-num">CLUE 3</span>
        <div class="clue-icon">🌟</div>
        <span class="clue-label">Real<br>Impact</span>
      </div>
    </div>

    
    <div class="authentic-box">
      <div class="detective-visual">
        <span class="badge-icon">🔍</span>
        <span class="badge-text">Authentic Problem</span>
      </div>

      <div class="checks-row">
        <div class="check-pill lit" id="check-0">
          <span class="chk-icon">✓</span>
          <span>People</span>
        </div>
        <div class="check-pill" id="check-1">
          <span class="chk-icon">✓</span>
          <span>Need</span>
        </div>
        <div class="check-pill" id="check-2">
          <span class="chk-icon">✓</span>
          <span>Impact</span>
        </div>
      </div>
    </div>

    
    <div class="controls">
      <button class="nav-btn" id="prevBtn" title="Previous">◀</button>
      <div class="dots-container">
        <div class="dot active" data-step="0"></div>
        <div class="dot" data-step="1"></div>
        <div class="dot" data-step="2"></div>
      </div>
      <button class="nav-btn" id="nextBtn" title="Next">▶</button>
    </div>

  </div>

  <script>
    const cards = document.querySelectorAll('.clue-card');
    const dots = document.querySelectorAll('.dot');
    const pills = [
      document.getElementById('check-0'),
      document.getElementById('check-1'),
      document.getElementById('check-2')
    ];

    let currentStep = 0;
    let timer = null;

    function setStep(idx) {
      currentStep = idx;

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

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

      pills.forEach((pill, i) => {
        pill.classList.toggle('lit', i <= currentStep);
      });
    }

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

    function prevStep() {
      setStep((currentStep - 1 + 3) % 3);
    }

    function startAutoPlay() {
      stopAutoPlay();
      timer = setInterval(nextStep, 3500);
    }

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

    cards.forEach((card, idx) => {
      card.addEventListener('click', () => {
        stopAutoPlay();
        setStep(idx);
      });
    });

    dots.forEach((dot, idx) => {
      dot.addEventListener('click', () => {
        stopAutoPlay();
        setStep(idx);
      });
    });

    document.getElementById('nextBtn').addEventListener('click', () => {
      stopAutoPlay();
      nextStep();
    });

    document.getElementById('prevBtn').addEventListener('click', () => {
      stopAutoPlay();
      prevStep();
    });

    // Start pedagogical slow loop
    setStep(0);
    startAutoPlay();
  </script>
</body>
</html>

Let's put these three clues to work on two different stories.

Imagine a story where a wizard needs 50 magic crystals to fly his broom. This is a made-up problem because wizards and flying brooms are not in our real world.

Now imagine kids slipping on wet tile near the hallway water fountain after gym class. That is an authentic problem because real kids can get hurt, and a solution protects them.

<!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: -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, sans-serif; }
  body {
    background: transparent;
    display: flex;
    flex-direction: column;
    align-items: center;
    justify-content: center;
    min-height: 100%;
    padding: 12px;
    color: #1e2945;
    user-select: none;
  }
  .switcher {
    display: flex;
    gap: 8px;
    margin-bottom: 16px;
    background: #e2e8f0;
    padding: 4px;
    border-radius: 24px;
  }
  .btn {
    border: none;
    background: transparent;
    padding: 8px 16px;
    border-radius: 20px;
    font-size: 14px;
    font-weight: 700;
    color: #64748b;
    cursor: pointer;
    transition: all 0.25s ease;
  }
  .btn.active {
    background: #ffffff;
    color: #0284c7;
    box-shadow: 0 2px 6px rgba(0,0,0,0.08);
  }
  .stage {
    position: relative;
    width: 100%;
    max-width: 380px;
    height: 240px;
  }
  .view {
    position: absolute;
    inset: 0;
    display: flex;
    flex-direction: column;
    align-items: center;
    justify-content: center;
    background: #ffffff;
    border-radius: 16px;
    border: 2px solid #e2e8f0;
    box-shadow: 0 4px 12px rgba(0,0,0,0.04);
    opacity: 0;
    pointer-events: none;
    transform: translateY(6px);
    transition: opacity 0.3s ease, transform 0.3s ease;
  }
  .view.active {
    opacity: 1;
    pointer-events: auto;
    transform: translateY(0);
  }
  .icon-row {
    display: flex;
    align-items: center;
    justify-content: center;
    gap: 16px;
    font-size: 44px;
    margin-bottom: 12px;
  }
  .arrow {
    font-size: 24px;
    color: #94a3b8;
  }
  .tag {
    font-size: 13px;
    font-weight: 700;
    text-transform: uppercase;
    letter-spacing: 0.5px;
    padding: 4px 12px;
    border-radius: 12px;
    margin-bottom: 6px;
  }
  .tag-practice {
    background: #f1f5f9;
    color: #475569;
  }
  .tag-authentic {
    background: #e0f2fe;
    color: #0284c7;
  }
  .outcome {
    font-size: 18px;
    font-weight: 800;
    display: flex;
    align-items: center;
    gap: 6px;
  }
  .pulse-hazard {
    animation: hazardGlow 2s infinite ease-in-out;
  }
  @keyframes hazardGlow {
    0%, 100% { transform: scale(1); }
    50% { transform: scale(1.08); }
  }
</style>
</head>
<body>

<div class="switcher">
  <button class="btn active" id="btn-practice" onclick="show('practice')">🧩 Practice</button>
  <button class="btn" id="btn-authentic" onclick="show('authentic')">⚠️ Authentic</button>
</div>

<div class="stage">
  
  <div class="view active" id="view-practice">
    <div class="tag tag-practice">Exercise</div>
    <div class="icon-row">
      <span>📝</span>
      <span class="arrow">➔</span>
      <span>🎯</span>
    </div>
    <div class="outcome" style="color: #475569;">
      Builds Skills
    </div>
  </div>

  
  <div class="view" id="view-authentic">
    <div class="tag tag-authentic">Real World</div>
    <div class="icon-row">
      <span class="pulse-hazard">💧🚶</span>
      <span class="arrow">➔</span>
      <span>🛡️</span>
    </div>
    <div class="outcome" style="color: #0284c7;">
      Protects People
    </div>
  </div>
</div>

<script>
  function show(mode) {
    const isPractice = mode === 'practice';
    document.getElementById('btn-practice').classList.toggle('active', isPractice);
    document.getElementById('btn-authentic').classList.toggle('active', !isPractice);
    document.getElementById('view-practice').classList.toggle('active', isPractice);
    document.getElementById('view-authentic').classList.toggle('active', !isPractice);
  }
</script>

</body>
</html>

Practice problems are still super helpful for building your skills, but designers and inventors look for authentic problems when they want to make real life better.

Next time you look around your classroom, home, or playground, see if you can spot an authentic problem waiting for a great idea.

- An **authentic problem** is a real-world dilemma or challenge faced by real people, animals, or communities where the outcome matters beyond just a classroom assignment.

- A **made-up practice problem** is an artificial scenario created solely to practice a specific school skill (e.g., 'Sam has 14 apples and buys 12 more') that typically has one preset correct answer and no real-life consequence.

- Authentic problems are **open-ended**, meaning they have multiple possible pathways, creative designs, and viable solutions rather than a single predetermined answer key.

- Solving authentic problems requires empathy and user-centered thinking: students must ask, *'Who is affected by this problem, and what do they actually need?'*

- Authentic problem solving follows an iterative **design process** (Ask, Imagine, Plan, Create, Test, Reflect/Improve), where testing and learning from failure are essential steps.

What Makes a Problem Authentic?. Learners will distinguish between made-up practice problems and authentic problems that real people face.

Engineering Design Process for Early Elementary: Defining Real-World Problems

Authenticity in Project-Based Learning: Real-World Contexts for Young Learners

Inventing for Real People: Empathy and Problem Identification in the Design Loop

For 2nd grade students, abstract definitions of 'authenticity' must be grounded in physical, classroom, or community contexts. Begin instruction with an 'empathy walk' around the school building where students observe and record actual minor pain points (e.g., loose book bins, backpack traffic jams, messy crayon boxes). Guide students to compare these direct observations with closed-format worksheet tasks using the '3-Question Decision Compass'. Reinforce that authentic problem-solving embraces open-ended exploration and iterative testing, aligning directly with TEKS 126.3(b)(3)(B).

What Makes a Problem Authentic?

Real vs. Made-Up

The Three Clues

Spotting the Difference