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Tutoring abilities

What is smaller than zero? If you have zero cookies, you have none — but numbers can actually go **below zero**!

A **negative number** is any number that is less than zero, and we write it with a little minus sign like **$-3$**.

Where do we see these cool numbers in real life? Let's check the weather first!

A thermometer measures how warm or cold it is. When water turns into ice, the temperature is **$0$ degrees**.

When it gets super freezing outside, the temperature drops below zero into **negative temperatures** like $-5^\circ$.

<!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: transparent;
      color: #1e2945;
      display: flex;
      flex-direction: column;
      align-items: center;
      justify-content: center;
      min-height: 100%;
      padding: 12px;
      user-select: none;
      -webkit-user-select: none;
    }

    .main-layout {
      display: flex;
      flex-direction: row;
      align-items: center;
      justify-content: center;
      gap: 28px;
      width: 100%;
      max-width: 480px;
    }

    /* Thermometer Component */
    .thermo-container {
      position: relative;
      display: flex;
      align-items: center;
      height: 280px;
    }

    .ticks {
      display: flex;
      flex-direction: column;
      justify-content: space-between;
      height: 240px;
      margin-right: 8px;
      font-size: 13px;
      font-weight: 600;
      color: #64748b;
      text-align: right;
    }

    .tick-item {
      display: flex;
      align-items: center;
      justify-content: flex-end;
      gap: 4px;
      line-height: 1;
    }

    .tick-item.zero {
      color: #0284c7;
      font-weight: 800;
    }

    .tick-item.neg {
      color: #6366f1;
    }

    .tick-line {
      width: 6px;
      height: 2px;
      background: #cbd5e1;
    }

    .tick-item.zero .tick-line {
      width: 10px;
      background: #0284c7;
      height: 2px;
    }

    .stem {
      position: relative;
      width: 20px;
      height: 240px;
      background: #e2e8f0;
      border-radius: 10px 10px 0 0;
      overflow: hidden;
      box-shadow: inset 0 2px 4px rgba(0,0,0,0.08);
    }

    .mercury {
      position: absolute;
      bottom: 0;
      left: 0;
      right: 0;
      width: 100%;
      background: linear-gradient(180deg, #38bdf8 0%, #2563eb 100%);
      border-radius: 10px 10px 0 0;
      transition: height 0.4s cubic-bezier(0.4, 0, 0.2, 1), background 0.4s ease;
    }

    .bulb {
      position: absolute;
      bottom: 8px;
      left: 50%;
      transform: translateX(-50%);
      width: 38px;
      height: 38px;
      background: #2563eb;
      border-radius: 50%;
      box-shadow: 0 4px 10px rgba(37, 99, 235, 0.3);
      z-index: 2;
    }

    /* Zero Reference Line */
    .zero-marker-line {
      position: absolute;
      left: -20px;
      right: -20px;
      top: 130px;
      border-top: 2px dashed #0284c7;
      pointer-events: none;
      z-index: 1;
    }

    /* Right State Display Card */
    .info-card {
      flex: 1;
      display: flex;
      flex-direction: column;
      align-items: center;
      background: #ffffff;
      border: 1px solid #e2e8f0;
      border-radius: 16px;
      padding: 16px 14px;
      box-shadow: 0 4px 14px rgba(0, 0, 0, 0.04);
      min-width: 150px;
      text-align: center;
    }

    .weather-icon {
      font-size: 44px;
      line-height: 1;
      margin-bottom: 8px;
      height: 48px;
      display: flex;
      align-items: center;
      justify-content: center;
      transition: transform 0.3s ease;
    }

    .temp-display {
      font-size: 32px;
      font-weight: 800;
      letter-spacing: -0.5px;
      color: #1e2945;
      margin-bottom: 4px;
    }

    .zone-badge {
      display: inline-block;
      padding: 4px 10px;
      border-radius: 20px;
      font-size: 13px;
      font-weight: 700;
      margin-bottom: 12px;
    }

    .badge-pos { background: #fee2e2; color: #dc2626; }
    .badge-zero { background: #e0f2fe; color: #0284c7; }
    .badge-neg { background: #e0e7ff; color: #4338ca; }

    /* Button Controls */
    .btn-group {
      display: grid;
      grid-template-columns: 1fr 1fr;
      gap: 6px;
      width: 100%;
    }

    .temp-btn {
      background: #f8fafc;
      border: 1px solid #cbd5e1;
      border-radius: 8px;
      padding: 8px 4px;
      font-size: 13px;
      font-weight: 700;
      color: #334155;
      cursor: pointer;
      transition: all 0.2s ease;
    }

    .temp-btn:active {
      transform: scale(0.96);
    }

    .temp-btn.active {
      background: #22b7ff;
      border-color: #22b7ff;
      color: #ffffff;
      box-shadow: 0 2px 6px rgba(34, 183, 255, 0.35);
    }

    /* Range slider on mobile / quick control */
    .slider-wrap {
      width: 100%;
      margin-top: 14px;
      display: flex;
      align-items: center;
      justify-content: center;
    }

    input[type=range] {
      width: 100%;
      max-width: 320px;
      height: 6px;
      border-radius: 3px;
      background: #cbd5e1;
      outline: none;
      -webkit-appearance: none;
      appearance: none;
      cursor: pointer;
    }

    input[type=range]::-webkit-slider-thumb {
      -webkit-appearance: none;
      width: 22px;
      height: 22px;
      border-radius: 50%;
      background: #22b7ff;
      box-shadow: 0 2px 6px rgba(0,0,0,0.2);
      cursor: pointer;
    }

    @media (max-width: 380px) {
      .main-layout { gap: 14px; }
      .thermo-container { height: 250px; }
      .ticks, .stem { height: 210px; }
      .temp-display { font-size: 26px; }
      .weather-icon { font-size: 38px; }
    }
  </style>
</head>
<body>

  <div class="main-layout">
    
    <div class="thermo-container">
      <div class="zero-marker-line"></div>
      <div class="ticks">
        <div class="tick-item"><span>+10°</span><div class="tick-line"></div></div>
        <div class="tick-item"><span>+5°</span><div class="tick-line"></div></div>
        <div class="tick-item zero"><span>0°</span><div class="tick-line"></div></div>
        <div class="tick-item neg"><span>-5°</span><div class="tick-line"></div></div>
        <div class="tick-item neg"><span>-10°</span><div class="tick-line"></div></div>
      </div>
      <div style="position: relative; display: flex; flex-direction: column; align-items: center;">
        <div class="stem">
          <div class="mercury" id="mercury"></div>
        </div>
        <div class="bulb" id="bulb"></div>
      </div>
    </div>

    
    <div class="info-card">
      <div class="weather-icon" id="weatherIcon">❄️</div>
      <div class="temp-display" id="tempText">-5°C</div>
      <div class="zone-badge badge-neg" id="zoneBadge">Below Zero</div>

      <div class="btn-group">
        <button class="temp-btn" onclick="setTemp(10)">+10°C</button>
        <button class="temp-btn" onclick="setTemp(5)">+5°C</button>
        <button class="temp-btn" onclick="setTemp(0)">0°C</button>
        <button class="temp-btn active" onclick="setTemp(-5)">-5°C</button>
      </div>
    </div>
  </div>

  <div class="slider-wrap">
    <input type="range" id="tempSlider" min="-10" max="10" step="1" value="-5" oninput="setTemp(this.value)">
  </div>

  <script>
    function setTemp(val) {
      val = parseInt(val, 10);
      const slider = document.getElementById('tempSlider');
      slider.value = val;

      const mercury = document.getElementById('mercury');
      const bulb = document.getElementById('bulb');
      const tempText = document.getElementById('tempText');
      const zoneBadge = document.getElementById('zoneBadge');
      const weatherIcon = document.getElementById('weatherIcon');

      // Update button active states
      document.querySelectorAll('.temp-btn').forEach(btn => {
        const btnVal = parseInt(btn.textContent.replace('°C', '').replace('+', ''), 10);
        btn.classList.toggle('active', btnVal === val);
      });

      // Range: -10 to +10 (total 20 degrees)
      // Percentage from bottom (0% at -10°C, 50% at 0°C, 100% at +10°C)
      const percent = Math.max(0, Math.min(100, ((val + 10) / 20) * 100));
      mercury.style.height = percent + '%';

      // Format text
      tempText.textContent = (val > 0 ? '+' : '') + val + '°C';

      // Zone categorization & color scheme
      if (val > 0) {
        zoneBadge.textContent = 'Above Zero';
        zoneBadge.className = 'zone-badge badge-pos';
        weatherIcon.textContent = val >= 8 ? '☀️' : '🌤️';
        mercury.style.background = 'linear-gradient(180deg, #f97316 0%, #ef4444 100%)';
        bulb.style.background = '#ef4444';
        bulb.style.boxShadow = '0 4px 10px rgba(239, 68, 68, 0.35)';
      } else if (val === 0) {
        zoneBadge.textContent = 'Freezing Point';
        zoneBadge.className = 'zone-badge badge-zero';
        weatherIcon.textContent = '🧊';
        mercury.style.background = 'linear-gradient(180deg, #38bdf8 0%, #0284c7 100%)';
        bulb.style.background = '#0284c7';
        bulb.style.boxShadow = '0 4px 10px rgba(2, 132, 199, 0.35)';
      } else {
        zoneBadge.textContent = 'Below Zero';
        zoneBadge.className = 'zone-badge badge-neg';
        weatherIcon.textContent = val <= -6 ? '🥶' : '❄️';
        mercury.style.background = 'linear-gradient(180deg, #818cf8 0%, #4338ca 100%)';
        bulb.style.background = '#4338ca';
        bulb.style.boxShadow = '0 4px 10px rgba(67, 56, 202, 0.35)';
      }
    }

    // Initialize at -5°C as referenced in lesson
    setTemp(-5);
  </script>
</body>
</html>

Can we go below zero outdoors on the earth too?

The top of the ocean water is called **sea level**, and we count it as **$0$ feet**.

A bird flying in the sky is **above sea level** at $+10$ feet, but a submarine diving deep underwater is **below sea level** at $-10$ feet.

<!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>Elevation & Negative Numbers</title>
  <style>
    * {
      box-sizing: border-box;
      margin: 0;
      padding: 0;
      font-family: system-ui, -apple-system, BlinkMacSystemFont, 'Segoe UI', Roboto, sans-serif;
      user-select: none;
    }
    body {
      background: #f8f9fa;
      color: #1e2945;
      display: flex;
      flex-direction: column;
      align-items: center;
      justify-content: center;
      min-height: 100%;
      padding: 12px;
    }
    .diagram-wrap {
      width: 100%;
      max-width: 480px;
      display: flex;
      flex-direction: column;
      gap: 12px;
    }
    /* Buttons */
    .controls {
      display: grid;
      grid-template-columns: repeat(3, 1fr);
      gap: 8px;
    }
    .btn-step {
      background: #ffffff;
      border: 2px solid #e5e7eb;
      border-radius: 10px;
      padding: 8px 4px;
      font-size: 14px;
      font-weight: 600;
      color: #4b5563;
      cursor: pointer;
      display: flex;
      align-items: center;
      justify-content: center;
      gap: 6px;
      transition: all 0.25s ease;
      box-shadow: 0 1px 3px rgba(0,0,0,0.05);
    }
    .btn-step.active {
      border-color: #22b7ff;
      background: #f0f9ff;
      color: #0284c7;
      box-shadow: 0 0 0 1px #22b7ff;
    }
    /* Cross section stage */
    .stage {
      position: relative;
      height: 280px;
      border-radius: 16px;
      overflow: hidden;
      display: flex;
      box-shadow: 0 2px 8px rgba(0,0,0,0.06);
    }
    /* Background environments */
    .sky-bg {
      position: absolute;
      top: 0;
      left: 0;
      right: 0;
      height: 50%;
      background: linear-gradient(180deg, #bae6fd 0%, #e0f2fe 100%);
    }
    .sea-bg {
      position: absolute;
      bottom: 0;
      left: 0;
      right: 0;
      height: 50%;
      background: linear-gradient(180deg, #0284c7 0%, #034870 100%);
    }
    .sea-level-line {
      position: absolute;
      top: 50%;
      left: 0;
      right: 0;
      height: 2px;
      background: #ffffff;
      box-shadow: 0 0 4px rgba(255,255,255,0.8);
      z-index: 2;
    }
    .sea-level-label {
      position: absolute;
      right: 12px;
      top: calc(50% - 11px);
      background: rgba(255, 255, 255, 0.9);
      color: #0369a1;
      font-size: 11px;
      font-weight: 700;
      padding: 2px 6px;
      border-radius: 4px;
      z-index: 3;
      letter-spacing: 0.5px;
      text-transform: uppercase;
    }

    /* Vertical Number Scale */
    .scale-axis {
      position: absolute;
      left: 20px;
      top: 20px;
      bottom: 20px;
      width: 50px;
      display: flex;
      flex-direction: column;
      justify-content: space-between;
      align-items: flex-end;
      z-index: 3;
      padding-right: 8px;
      border-right: 2px dashed rgba(255, 255, 255, 0.6);
    }
    .tick {
      font-size: 13px;
      font-weight: 700;
      line-height: 1;
      position: relative;
    }
    .tick.pos {
      color: #0369a1;
    }
    .tick.zero {
      color: #ffffff;
      background: #0284c7;
      padding: 2px 4px;
      border-radius: 4px;
    }
    .tick.neg {
      color: #bfdbfe;
    }

    /* Actor & Marker */
    .actor-track {
      position: absolute;
      left: 90px;
      right: 20px;
      top: 20px;
      bottom: 20px;
      z-index: 4;
    }
    .actor-container {
      position: absolute;
      left: 50%;
      transform: translate(-50%, -50%);
      transition: top 0.6s cubic-bezier(0.34, 1.3, 0.64, 1);
      display: flex;
      align-items: center;
      gap: 12px;
    }
    .actor-icon {
      font-size: 40px;
      filter: drop-shadow(0 4px 6px rgba(0,0,0,0.2));
      transition: transform 0.3s ease;
    }
    .actor-badge {
      background: #ffffff;
      color: #1e2945;
      padding: 6px 12px;
      border-radius: 20px;
      font-size: 15px;
      font-weight: 700;
      box-shadow: 0 4px 12px rgba(0,0,0,0.15);
      white-space: nowrap;
      border: 2px solid transparent;
      transition: all 0.3s ease;
    }
    .actor-badge.pos {
      border-color: #38bdf8;
      color: #0369a1;
    }
    .actor-badge.zero {
      border-color: #94a3b8;
      color: #475569;
    }
    .actor-badge.neg {
      border-color: #60a5fa;
      color: #1d4ed8;
    }

    /* Background decorative clouds / bubbles */
    .bg-deco {
      position: absolute;
      opacity: 0.35;
      pointer-events: none;
      font-size: 20px;
    }
  </style>
</head>
<body>
  <div class="diagram-wrap">
    
    <div class="controls">
      <button class="btn-step active" onclick="setElevation(10, '🦅', '+10 ft', 'pos', 0)">
        <span>🦅</span> +10 ft
      </button>
      <button class="btn-step" onclick="setElevation(0, '⛵', '0 ft', 'zero', 1)">
        <span>⛵</span> 0 ft
      </button>
      <button class="btn-step" onclick="setElevation(-10, '🤿', '-10 ft', 'neg', 2)">
        <span>🤿</span> -10 ft
      </button>
    </div>

    
    <div class="stage">
      <div class="sky-bg">
        <span class="bg-deco" style="top: 20%; right: 25%;">☁️</span>
        <span class="bg-deco" style="top: 50%; right: 15%; font-size: 16px;">☁️</span>
      </div>
      <div class="sea-bg">
        <span class="bg-deco" style="bottom: 25%; right: 28%; font-size: 16px;">🫧</span>
        <span class="bg-deco" style="bottom: 50%; right: 18%;">🐠</span>
      </div>
      
      <div class="sea-level-line"></div>
      <div class="sea-level-label">Sea Level (0)</div>

      
      <div class="scale-axis">
        <span class="tick pos">+10</span>
        <span class="tick pos">+5</span>
        <span class="tick zero">0</span>
        <span class="tick neg">-5</span>
        <span class="tick neg">-10</span>
      </div>

      
      <div class="actor-track">
        <div class="actor-container" id="actor" style="top: 0%;">
          <div class="actor-icon" id="actor-icon">🦅</div>
          <div class="actor-badge pos" id="actor-badge">+10 ft</div>
        </div>
      </div>
    </div>
  </div>

  <script>
    const actor = document.getElementById('actor');
    const actorIcon = document.getElementById('actor-icon');
    const actorBadge = document.getElementById('actor-badge');
    const buttons = document.querySelectorAll('.btn-step');

    // Elevation positions mapped to track percentage: +10 -> 0%, 0 -> 50%, -10 -> 100%
    function setElevation(val, icon, text, type, btnIndex) {
      // Calculate % from top (val: +10 is 0%, -10 is 100%)
      const pct = ((10 - val) / 20) * 100;
      actor.style.top = pct + '%';
      
      actorIcon.textContent = icon;
      actorBadge.textContent = text;
      
      actorBadge.className = 'actor-badge ' + type;

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

    // Auto cycle initially if untouched
    let autoCycleIndex = 0;
    const states = [
      { val: 10, icon: '🦅', text: '+10 ft', type: 'pos' },
      { val: 0, icon: '⛵', text: '0 ft', type: 'zero' },
      { val: -10, icon: '🤿', text: '-10 ft', type: 'neg' }
    ];

    let timer = setInterval(() => {
      autoCycleIndex = (autoCycleIndex + 1) % states.length;
      const s = states[autoCycleIndex];
      setElevation(s.val, s.icon, s.text, s.type, autoCycleIndex);
    }, 3200);

    // Stop auto cycling on user click
    buttons.forEach(btn => {
      btn.addEventListener('click', () => clearInterval(timer));
    });
  </script>
</body>
</html>

What happens if you want to buy a toy, but you do not have enough coins?

If you have $\$0$ in your piggy bank and borrow $\$2$ from a friend to buy a sticker, you **owe** $\$2$.

Owing money is called an **overdraft** or debt, and we write it as **$-\$2$** because you have two dollars less than zero.

<!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>Real-Life Negative Numbers</title>
  <style>
    * { box-sizing: border-box; margin: 0; padding: 0; }
    body {
      font-family: -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, sans-serif;
      color: #1e2945;
      background: #f8f9fa;
      display: flex;
      flex-direction: column;
      align-items: center;
      justify-content: space-between;
      min-height: 100%;
      padding: 12px;
      user-select: none;
    }

    .modes {
      display: flex;
      gap: 8px;
      width: 100%;
      max-width: 440px;
    }

    .mode-btn {
      flex: 1;
      border: 1px solid #e2e8f0;
      background: #ffffff;
      color: #64748b;
      padding: 8px 4px;
      border-radius: 10px;
      font-size: 14px;
      font-weight: 600;
      cursor: pointer;
      display: flex;
      align-items: center;
      justify-content: center;
      gap: 6px;
      transition: all 0.2s ease;
    }

    .mode-btn.active {
      background: #22b7ff;
      color: #ffffff;
      border-color: #22b7ff;
      box-shadow: 0 2px 8px rgba(34, 183, 255, 0.3);
    }

    .scene-container {
      width: 100%;
      max-width: 440px;
      height: 280px;
      display: flex;
      gap: 16px;
      margin: 10px 0;
      position: relative;
    }

    /* Vertical Scale */
    .scale-wrapper {
      width: 68px;
      background: #ffffff;
      border: 1px solid #e2e8f0;
      border-radius: 12px;
      display: flex;
      flex-direction: column;
      position: relative;
      padding: 6px 0;
    }

    .scale-level {
      flex: 1;
      display: flex;
      align-items: center;
      justify-content: center;
      font-size: 14px;
      font-weight: 700;
      cursor: pointer;
      color: #64748b;
      position: relative;
      z-index: 2;
      transition: color 0.2s ease;
    }

    .scale-level.zero {
      color: #0f172a;
      font-weight: 800;
    }

    .scale-level.selected {
      color: #ffffff;
    }

    .scale-level:hover {
      background: rgba(34, 183, 255, 0.08);
      border-radius: 6px;
    }

    .slider-indicator {
      position: absolute;
      left: 4px;
      right: 4px;
      height: 34px;
      border-radius: 8px;
      background: #22b7ff;
      transition: top 0.3s cubic-bezier(0.4, 0, 0.2, 1), background 0.3s ease;
      z-index: 1;
      box-shadow: 0 2px 6px rgba(0,0,0,0.15);
    }

    /* Visual Display Card */
    .display-card {
      flex: 1;
      background: #ffffff;
      border: 1px solid #e2e8f0;
      border-radius: 12px;
      position: relative;
      overflow: hidden;
      display: flex;
      flex-direction: column;
    }

    .zone-positive {
      flex: 1;
      background: linear-gradient(180deg, #f0fdf4 0%, #e0f2fe 100%);
      position: relative;
      display: flex;
      align-items: center;
      justify-content: center;
    }

    .zero-divider {
      height: 2px;
      background: #94a3b8;
      border-top: 1px dashed #cbd5e1;
      position: relative;
      z-index: 3;
    }

    .zero-tag {
      position: absolute;
      left: 10px;
      top: -10px;
      background: #475569;
      color: #ffffff;
      font-size: 11px;
      font-weight: 700;
      padding: 1px 6px;
      border-radius: 4px;
      letter-spacing: 0.5px;
    }

    .zone-negative {
      flex: 1;
      background: linear-gradient(180deg, #fff7ed 0%, #fee2e2 100%);
      position: relative;
      display: flex;
      align-items: center;
      justify-content: center;
    }

    /* Floating Item Target */
    .target-token {
      position: absolute;
      width: 100%;
      height: 48px;
      display: flex;
      align-items: center;
      justify-content: space-around;
      padding: 0 16px;
      transition: top 0.3s cubic-bezier(0.4, 0, 0.2, 1);
      z-index: 4;
      pointer-events: none;
    }

    .token-bubble {
      background: #ffffff;
      border: 2px solid #22b7ff;
      border-radius: 20px;
      padding: 6px 14px;
      display: flex;
      align-items: center;
      gap: 8px;
      box-shadow: 0 4px 12px rgba(0,0,0,0.08);
      font-weight: 700;
      font-size: 15px;
      transition: border-color 0.3s ease;
    }

    .token-emoji {
      font-size: 24px;
      line-height: 1;
    }

    .token-tag {
      font-size: 13px;
      font-weight: 600;
      color: #64748b;
    }

    /* Controls */
    .controls {
      display: flex;
      gap: 12px;
      width: 100%;
      max-width: 440px;
      align-items: center;
      justify-content: center;
    }

    .stepper-btn {
      flex: 1;
      background: #ffffff;
      border: 1px solid #cbd5e1;
      border-radius: 8px;
      padding: 8px 12px;
      font-size: 14px;
      font-weight: 700;
      color: #1e2945;
      cursor: pointer;
      display: flex;
      align-items: center;
      justify-content: center;
      gap: 6px;
      transition: all 0.15s ease;
    }

    .stepper-btn:active {
      background: #f1f5f9;
    }
  </style>
</head>
<body>

  
  <div class="modes">
    <button class="mode-btn active" onclick="setMode('money')">🏦 Money</button>
    <button class="mode-btn" onclick="setMode('temp')">🌡️ Temp</button>
    <button class="mode-btn" onclick="setMode('depth')">🌊 Elevation</button>
  </div>

  
  <div class="scene-container">
    
    <div class="scale-wrapper">
      <div class="slider-indicator" id="slider"></div>
      <div class="scale-level" onclick="setValue(3)" id="lvl-3">+3</div>
      <div class="scale-level" onclick="setValue(2)" id="lvl-2">+2</div>
      <div class="scale-level" onclick="setValue(1)" id="lvl-1">+1</div>
      <div class="scale-level zero" onclick="setValue(0)" id="lvl-0">0</div>
      <div class="scale-level" onclick="setValue(-1)" id="lvl-m1">-1</div>
      <div class="scale-level" onclick="setValue(-2)" id="lvl-m2">-2</div>
      <div class="scale-level" onclick="setValue(-3)" id="lvl-m3">-3</div>
    </div>

    
    <div class="display-card">
      <div class="zone-positive" id="posZone"></div>
      <div class="zero-divider">
        <div class="zero-tag" id="zeroLabel">ZERO ($0)</div>
      </div>
      <div class="zone-negative" id="negZone"></div>

      
      <div class="target-token" id="token">
        <div class="token-bubble" id="tokenBubble">
          <span class="token-emoji" id="tokenEmoji">💳</span>
          <span id="tokenValue">-$2</span>
          <span class="token-tag" id="tokenTag">Overdraft</span>
        </div>
      </div>
    </div>
  </div>

  
  <div class="controls">
    <button class="stepper-btn" onclick="adjust(-1)">▼ Decrease</button>
    <button class="stepper-btn" onclick="adjust(1)">▲ Increase</button>
  </div>

  <script>
    let currentMode = 'money';
    let currentValue = -2;

    const DATA = {
      money: {
        zeroText: "ZERO ($0)",
        unit: "$",
        levels: {
          3:  { label: "+$3", tag: "Savings",   emoji: "💰", color: "#10b981" },
          2:  { label: "+$2", tag: "Savings",   emoji: "💵", color: "#10b981" },
          1:  { label: "+$1", tag: "Savings",   emoji: "🪙", color: "#10b981" },
          0:  { label: "$0",  tag: "Balance",   emoji: "⚖️", color: "#64748b" },
          "-1": { label: "-$1", tag: "Debt",      emoji: "💳", color: "#ef4444" },
          "-2": { label: "-$2", tag: "Overdraft", emoji: "📉", color: "#ef4444" },
          "-3": { label: "-$3", tag: "Overdraft", emoji: "⚠️", color: "#ef4444" }
        }
      },
      temp: {
        zeroText: "FREEZING (0°C)",
        unit: "°C",
        levels: {
          3:  { label: "+30°C", tag: "Hot",     emoji: "☀️", color: "#f59e0b" },
          2:  { label: "+20°C", tag: "Warm",    emoji: "🌤️", color: "#10b981" },
          1:  { label: "+10°C", tag: "Cool",    emoji: "🍃", color: "#06b6d4" },
          0:  { label: "0°C",   tag: "Freezing",emoji: "🧊", color: "#64748b" },
          "-1": { label: "-10°C", tag: "Cold",   emoji: "❄️", color: "#3b82f6" },
          "-2": { label: "-20°C", tag: "Freezing", emoji: "🥶", color: "#6366f1" },
          "-3": { label: "-30°C", tag: "Frost",  emoji: "🧊", color: "#8b5cf6" }
        }
      },
      depth: {
        zeroText: "SEA LEVEL (0 m)",
        unit: "m",
        levels: {
          3:  { label: "+300 m", tag: "Peak",   emoji: "🏔️", color: "#10b981" },
          2:  { label: "+200 m", tag: "Hill",   emoji: "⛰️", color: "#10b981" },
          1:  { label: "+100 m", tag: "Shore",  emoji: "🌴", color: "#06b6d4" },
          0:  { label: "0 m",    tag: "Surface",emoji: "⛵", color: "#64748b" },
          "-1": { label: "-100 m", tag: "Diver", emoji: "🤿", color: "#0284c7" },
          "-2": { label: "-200 m", tag: "Sub",   emoji: "🚢", color: "#0369a1" },
          "-3": { label: "-300 m", tag: "Abyss", emoji: "🐙", color: "#1e3a8a" }
        }
      }
    };

    const POSITIONS = {
      3: { sliderY: 6,   tokenY: 10 },
      2: { sliderY: 44,  tokenY: 48 },
      1: { sliderY: 82,  tokenY: 86 },
      0: { sliderY: 122, tokenY: 116 },
      "-1": { sliderY: 162, tokenY: 156 },
      "-2": { sliderY: 200, tokenY: 194 },
      "-3": { sliderY: 240, tokenY: 226 }
    };

    function setMode(mode) {
      currentMode = mode;
      document.querySelectorAll('.mode-btn').forEach((btn, idx) => {
        btn.classList.toggle('active', ['money','temp','depth'][idx] === mode);
      });
      update();
    }

    function setValue(val) {
      currentValue = Math.max(-3, Math.min(3, val));
      update();
    }

    function adjust(delta) {
      setValue(currentValue + delta);
    }

    function update() {
      const modeData = DATA[currentMode];
      const stepData = modeData.levels[currentValue];
      const pos = POSITIONS[currentValue];

      // Update Labels on ruler
      const keys = [3, 2, 1, 0, -1, -2, -3];
      keys.forEach(k => {
        const id = k < 0 ? `lvl-m${Math.abs(k)}` : `lvl-${k}`;
        const el = document.getElementById(id);
        const lvl = modeData.levels[k];
        el.textContent = lvl.label;
        el.classList.toggle('selected', k === currentValue);
      });

      // Update Zero Divider Label
      document.getElementById('zeroLabel').textContent = modeData.zeroText;

      // Update Slider Indicator
      const slider = document.getElementById('slider');
      slider.style.top = pos.sliderY + 'px';
      slider.style.background = stepData.color;

      // Update Token
      const token = document.getElementById('token');
      token.style.top = pos.tokenY + 'px';

      const bubble = document.getElementById('tokenBubble');
      bubble.style.borderColor = stepData.color;

      document.getElementById('tokenEmoji').textContent = stepData.emoji;
      document.getElementById('tokenValue').textContent = stepData.label;
      document.getElementById('tokenValue').style.color = stepData.color;
      document.getElementById('tokenTag').textContent = stepData.tag;
    }

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

Have you ever played a game where you lost points?

In many video games and board games, winning a challenge gives you **positive points** like $+5$.

If your score is $0$ and you hit a red hazard block that takes away $3$ points, your new score becomes **$-3$**!

<!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">
  <title>Real-Life Negative Numbers</title>
  <style>
    * {
      box-sizing: border-box;
      margin: 0;
      padding: 0;
      font-family: system-ui, -apple-system, BlinkMacSystemFont, 'Segoe UI', Roboto, sans-serif;
      user-select: none;
      -webkit-user-select: none;
    }
    body {
      background: #f8f9fa;
      color: #1e2945;
      padding: 12px;
      display: flex;
      flex-direction: column;
      align-items: center;
      justify-content: center;
      min-height: 100%;
    }
    .diagram {
      width: 100%;
      max-width: 480px;
      display: flex;
      flex-direction: column;
      gap: 12px;
    }
    /* Scenario selector tabs */
    .tabs {
      display: flex;
      gap: 8px;
      justify-content: center;
      width: 100%;
    }
    .tab-btn {
      flex: 1;
      padding: 8px 4px;
      font-size: 14px;
      font-weight: 600;
      border: 2px solid #e2e8f0;
      background: #ffffff;
      color: #64748b;
      border-radius: 10px;
      cursor: pointer;
      display: flex;
      align-items: center;
      justify-content: center;
      gap: 4px;
      transition: all 0.2s ease;
    }
    .tab-btn.active {
      background: #22b7ff;
      border-color: #22b7ff;
      color: #ffffff;
      box-shadow: 0 4px 10px rgba(34, 183, 255, 0.25);
    }
    /* Visual container */
    .scale-card {
      background: #ffffff;
      border: 1px solid #e2e8f0;
      border-radius: 14px;
      padding: 14px 16px;
      display: flex;
      flex-direction: column;
      gap: 8px;
      box-shadow: 0 2px 6px rgba(0,0,0,0.03);
    }
    .zone-badge {
      font-size: 11px;
      font-weight: 700;
      text-transform: uppercase;
      letter-spacing: 0.5px;
      padding: 3px 8px;
      border-radius: 6px;
      align-self: flex-start;
    }
    .badge-pos {
      background: #e0f2fe;
      color: #0284c7;
    }
    .badge-neg {
      background: #fee2e2;
      color: #dc2626;
    }
    /* Vertical number scale */
    .meter-wrap {
      display: grid;
      grid-template-columns: 50px 1fr;
      gap: 12px;
      align-items: center;
    }
    .track {
      position: relative;
      height: 240px;
      display: flex;
      flex-direction: column;
      justify-content: space-between;
      align-items: center;
      padding: 6px 0;
    }
    .track-line {
      position: absolute;
      top: 10px;
      bottom: 10px;
      width: 4px;
      background: #cbd5e1;
      border-radius: 2px;
      z-index: 1;
    }
    .tick-node {
      position: relative;
      z-index: 2;
      background: #ffffff;
      border: 2px solid #94a3b8;
      color: #334155;
      font-size: 13px;
      font-weight: 700;
      width: 44px;
      height: 26px;
      border-radius: 6px;
      display: flex;
      align-items: center;
      justify-content: center;
      transition: all 0.25s ease;
    }
    .tick-node.zero {
      border-color: #f59e0b;
      background: #fef3c7;
      color: #b45309;
      font-size: 14px;
      box-shadow: 0 0 0 2px rgba(245, 158, 11, 0.2);
    }
    .tick-node.pos {
      border-color: #38bdf8;
      color: #0369a1;
    }
    .tick-node.neg {
      border-color: #f87171;
      color: #b91c1c;
    }

    /* Right side item display */
    .stages {
      position: relative;
      height: 240px;
      display: flex;
      flex-direction: column;
      justify-content: space-between;
    }
    .item-row {
      display: flex;
      align-items: center;
      gap: 10px;
      background: #f8fafc;
      border: 1px solid #e2e8f0;
      padding: 6px 10px;
      border-radius: 10px;
      height: 48px;
      transition: all 0.3s ease;
    }
    .item-row.highlight-pos {
      background: #f0f9ff;
      border-color: #bae6fd;
    }
    .item-row.highlight-zero {
      background: #fffbeb;
      border-color: #fde68a;
    }
    .item-row.highlight-neg {
      background: #fef2f2;
      border-color: #fecaca;
    }
    .item-emoji {
      font-size: 24px;
      line-height: 1;
    }
    .item-info {
      display: flex;
      flex-direction: column;
    }
    .item-val {
      font-size: 15px;
      font-weight: 800;
      letter-spacing: -0.2px;
    }
    .pos-val { color: #0284c7; }
    .zero-val { color: #d97706; }
    .neg-val { color: #dc2626; }

    .item-desc {
      font-size: 12px;
      color: #64748b;
      font-weight: 500;
    }
    .zero-line {
      position: absolute;
      left: -12px;
      right: 0;
      top: 50%;
      height: 2px;
      background: repeating-linear-gradient(90deg, #f59e0b 0, #f59e0b 4px, transparent 4px, transparent 8px);
      pointer-events: none;
      z-index: 3;
    }
  </style>
</head>
<body>

<div class="diagram">
  
  <div class="tabs">
    <button class="tab-btn active" onclick="setScenario(0)">🌊 Sea Level</button>
    <button class="tab-btn" onclick="setScenario(1)">🌡️ Temp</button>
    <button class="tab-btn" onclick="setScenario(2)">🎮 Score</button>
  </div>

  
  <div class="scale-card">
    <div class="meter-wrap">
      
      <div class="track">
        <div class="track-line"></div>
        <div class="tick-node pos" id="tick-top">+10</div>
        <div class="tick-node zero" id="tick-mid">0</div>
        <div class="tick-node neg" id="tick-bot">−10</div>
      </div>

      
      <div class="stages">
        
        <div class="item-row highlight-pos" id="card-pos">
          <span class="item-emoji" id="emoji-pos">🦅</span>
          <div class="item-info">
            <span class="item-val pos-val" id="val-pos">+10 m</span>
            <span class="item-desc" id="desc-pos">Above sea level</span>
          </div>
        </div>

        
        <div class="item-row highlight-zero" id="card-zero">
          <span class="item-emoji" id="emoji-zero">⛵</span>
          <div class="item-info">
            <span class="item-val zero-val" id="val-zero">0 m</span>
            <span class="item-desc" id="desc-zero">Sea surface</span>
          </div>
        </div>

        
        <div class="item-row highlight-neg" id="card-neg">
          <span class="item-emoji" id="emoji-neg">🐟</span>
          <div class="item-info">
            <span class="item-val neg-val" id="val-neg">−10 m</span>
            <span class="item-desc" id="desc-neg">Below sea level</span>
          </div>
        </div>
      </div>
    </div>
  </div>
</div>

<script>
  const data = [
    {
      ticks: ['+10', '0', '−10'],
      pos: { emoji: '🦅', val: '+10 m', desc: 'Above sea level' },
      zero: { emoji: '⛵', val: '0 m', desc: 'Sea surface' },
      neg: { emoji: '🐟', val: '−10 m', desc: 'Below sea level' }
    },
    {
      ticks: ['+20°', '0°', '−10°'],
      pos: { emoji: '☀️', val: '+20 °C', desc: 'Warm air' },
      zero: { emoji: '🧊', val: '0 °C', desc: 'Freezing point' },
      neg: { emoji: '❄️', val: '−10 °C', desc: 'Below freezing' }
    },
    {
      ticks: ['+50', '0', '−20'],
      pos: { emoji: '⭐', val: '+50 pts', desc: 'Bonus stars' },
      zero: { emoji: '🎯', val: '0 pts', desc: 'Starting score' },
      neg: { emoji: '👾', val: '−20 pts', desc: 'Hazard penalty' }
    }
  ];

  function setScenario(idx) {
    const btns = document.querySelectorAll('.tab-btn');
    btns.forEach((btn, i) => {
      btn.classList.toggle('active', i === idx);
    });

    const item = data[idx];
    document.getElementById('tick-top').textContent = item.ticks[0];
    document.getElementById('tick-mid').textContent = item.ticks[1];
    document.getElementById('tick-bot').textContent = item.ticks[2];

    document.getElementById('emoji-pos').textContent = item.pos.emoji;
    document.getElementById('val-pos').textContent = item.pos.val;
    document.getElementById('desc-pos').textContent = item.pos.desc;

    document.getElementById('emoji-zero').textContent = item.zero.emoji;
    document.getElementById('val-zero').textContent = item.zero.val;
    document.getElementById('desc-zero').textContent = item.zero.desc;

    document.getElementById('emoji-neg').textContent = item.neg.emoji;
    document.getElementById('val-neg').textContent = item.neg.val;
    document.getElementById('desc-neg').textContent = item.neg.desc;
  }
</script>

</body>
</html>

Next time you look at ice cubes, look at a fish in the sea, or play a game, see if you can spot the **negative numbers** hiding below zero!

math

Real-Life Situations With Negative Numbers. Identify and represent temperatures below zero, bank overdrafts, elevations below sea level, and sports scores.

Negative Numbers and Real-World Scenarios: Elevation, Temperature, and Balance

Curriculum for Excellence Third Level Mathematics: Negative Numbers in Context

Understanding Integers: Real-World Word Problems and Number Lines

When introducing real-world negative numbers under Curriculum for Excellence (MNU 3-04a), pedagogical best practice begins with vertical models (thermometers and sea depth) before transitioning to horizontal models (financial ledgers and golf/sports scoring). Emphasize that zero is not an empty absence, but a defined baseline (sea level, $0^\circ\text{C}$, $\text{\pounds}0$ balance, level par). Use concrete storytelling and contextual manipulatives to bridge conceptual understanding before introducing formal sign rules.

Real-Life Situations With Negative Numbers

Freezing Cold Temperatures

Diving Below Sea Level