<!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;
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    body {
      font-family: system-ui, -apple-system, BlinkMacSystemFont, 'Segoe UI', Roboto, sans-serif;
      background: #ffffff;
      color: #1e2945;
      display: flex;
      flex-direction: column;
      align-items: center;
      justify-content: center;
      min-height: 100vh;
      padding: 16px;
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    .diagram {
      width: 100%;
      max-width: 480px;
      display: flex;
      flex-direction: column;
      gap: 16px;
    }

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

    .mode-btn {
      flex: 1;
      border: none;
      background: transparent;
      padding: 8px 12px;
      font-size: 14px;
      font-weight: 600;
      color: #64748b;
      border-radius: 6px;
      cursor: pointer;
      transition: all 0.2s ease;
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    .mode-btn.active {
      background: #ffffff;
      color: #1e2945;
      box-shadow: 0 1px 3px rgba(0,0,0,0.1);
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    .row {
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      align-items: center;
      gap: 12px;
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    .label {
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      font-weight: 600;
      color: #1e2945;
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    .tape-track {
      flex: 1;
      display: flex;
      align-items: center;
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    .block {
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      font-weight: 700;
      font-size: 16px;
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    .block-empty {
      flex: 2;
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    .block.diff-extra {
      background: #38bdf8;
      border: 2px dashed #0284c7;
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    .total-val {
      width: 44px;
      font-size: 16px;
      font-weight: 700;
      text-align: right;
      color: #1e2945;
    }

    .comparison-card {
      background: #f8fafc;
      border: 1px solid #e2e8f0;
      border-radius: 10px;
      padding: 14px 16px;
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      flex-direction: column;
      gap: 8px;
      text-align: center;
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    .sub-math {
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      font-weight: 600;
      letter-spacing: 0.5px;
    }
  </style>
</head>
<body>

  <div class="diagram">
    <div class="mode-toggle">
      <button class="mode-btn active" id="btnQuotient">Quotient (×3)</button>
      <button class="mode-btn" id="btnDiff">Difference (+$8)</button>
    </div>

    
    <div class="row">
      <span class="label">You</span>
      <div class="tape-track">
        <div class="block">$4</div>
        <div class="block-empty"></div>
      </div>
      <span class="total-val">$4</span>
    </div>

    
    <div class="row">
      <span class="label">Friend</span>
      <div class="tape-track">
        <div class="block" id="b1">$4</div>
        <div class="block" id="b2">$4</div>
        <div class="block" id="b3">$4</div>
      </div>
      <span class="total-val">$12</span>
    </div>

    
    <div class="comparison-card">
      <div class="main-math" id="mathText">3 times as many ($12 ÷ $4 = 3)</div>
      <div class="sub-math" id="badgeText">Ratio: 12 : 4 = 3 : 1</div>
    </div>
  </div>

  <script>
    const btnQuotient = document.getElementById('btnQuotient');
    const btnDiff = document.getElementById('btnDiff');
    const b2 = document.getElementById('b2');
    const b3 = document.getElementById('b3');
    const mathText = document.getElementById('mathText');
    const badgeText = document.getElementById('badgeText');

    function showQuotient() {
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      btnDiff.classList.remove('active');
      b2.classList.remove('diff-extra');
      b3.classList.remove('diff-extra');
      mathText.textContent = '3 times as many ($12 ÷ $4 = 3)';
      badgeText.textContent = 'Ratio: 12 : 4 = 3 : 1';
      badgeText.style.background = '#e0f2fe';
      badgeText.style.color = '#0369a1';
    }

    function showDiff() {
      btnDiff.classList.add('active');
      btnQuotient.classList.remove('active');
      b2.classList.add('diff-extra');
      b3.classList.add('diff-extra');
      mathText.textContent = '$8 more ($12 − $4 = $8)';
      badgeText.textContent = 'Difference: +$8';
      badgeText.style.background = '#e0f2fe';
      badgeText.style.color = '#0369a1';
    }

    btnQuotient.addEventListener('click', showQuotient);
    btnDiff.addEventListener('click', showDiff);
  </script>
</body>
</html>

Comparing Numbers Using Differences and Quotients

<!DOCTYPE html>
<html lang="en">
<head>
  <meta charset="UTF-8">
  <meta name="viewport" content="width=device-width, initial-scale=1.0">
  <meta name="aspect-ratio" content="4:3">
  <style>
    * {
      box-sizing: border-box;
      margin: 0;
      padding: 0;
      font-family: system-ui, -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, sans-serif;
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    body {
      background: #ffffff;
      color: #1e2945;
      padding: 12px;
      display: flex;
      flex-direction: column;
      justify-content: center;
      min-height: 100%;
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    .comparison-grid {
      display: grid;
      grid-template-columns: repeat(auto-fit, minmax(240px, 1fr));
      gap: 14px;
      width: 100%;
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    .col-card {
      background: #ffffff;
      border-radius: 12px;
      padding: 14px;
      display: flex;
      flex-direction: column;
      gap: 12px;
      transition: box-shadow 0.2s ease;
      cursor: pointer;
    }

    .col-card.purple {
      border: 1.5px solid #ddd6fe;
      background: #faf5ff;
    }

    .col-card.purple:hover, .col-card.purple.active {
      box-shadow: 0 4px 12px rgba(139, 92, 246, 0.15);
    }

    .col-card.green {
      border: 1.5px solid #a7f3d0;
      background: #f0fdf4;
    }

    .col-card.green:hover, .col-card.green.active {
      box-shadow: 0 4px 12px rgba(16, 185, 129, 0.15);
    }

    .header-row {
      display: flex;
      align-items: center;
      justify-content: space-between;
    }

    .badge {
      display: inline-flex;
      align-items: center;
      gap: 5px;
      font-size: 11px;
      font-weight: 700;
      text-transform: uppercase;
      letter-spacing: 0.5px;
      padding: 4px 9px;
      border-radius: 20px;
    }

    .badge-purple {
      background: #8b5cf6;
      color: #ffffff;
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    .badge-green {
      background: #10b981;
      color: #ffffff;
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    .equation {
      font-size: 20px;
      font-weight: 800;
      letter-spacing: -0.5px;
    }

    .equation.purple { color: #6d28d9; }
    .equation.green { color: #047857; }

    .bars-container {
      background: #ffffff;
      border-radius: 8px;
      padding: 10px;
      border: 1px solid #e2e8f0;
      display: flex;
      flex-direction: column;
      gap: 8px;
    }

    .bar-row {
      display: flex;
      align-items: center;
      gap: 8px;
      font-size: 13px;
      font-weight: 600;
    }

    .bar-label {
      width: 42px;
      color: #64748b;
      font-size: 12px;
    }

    .track {
      flex: 1;
      height: 28px;
      display: flex;
      border-radius: 6px;
      overflow: hidden;
      background: #f1f5f9;
      position: relative;
    }

    /* Additive Bar Segments */
    .seg-base {
      width: 25%;
      height: 100%;
      background: #cbd5e1;
      display: flex;
      align-items: center;
      justify-content: center;
      font-size: 12px;
      font-weight: 700;
      color: #334155;
    }

    .seg-diff {
      width: 75%;
      height: 100%;
      background: #8b5cf6;
      color: #ffffff;
      display: flex;
      align-items: center;
      justify-content: center;
      font-size: 12px;
      font-weight: 700;
      transition: opacity 0.2s ease;
    }

    /* Multiplicative Bar Segments */
    .seg-unit {
      flex: 1;
      height: 100%;
      background: #10b981;
      color: #ffffff;
      display: flex;
      align-items: center;
      justify-content: center;
      font-size: 12px;
      font-weight: 700;
      border-right: 1.5px solid #f0fdf4;
    }

    .seg-unit:last-child {
      border-right: none;
    }

    .footer-text {
      font-size: 13px;
      font-weight: 700;
      display: flex;
      align-items: center;
      gap: 6px;
    }

    .footer-text.purple { color: #6d28d9; }
    .footer-text.green { color: #047857; }

    .highlight-pill {
      font-size: 11px;
      padding: 2px 6px;
      border-radius: 4px;
      font-weight: 800;
    }

    .pill-purple { background: #ede9fe; color: #6d28d9; }
    .pill-green { background: #d1fae5; color: #047857; }
  </style>
</head>
<body>

  <div class="comparison-grid">
    
    <div class="col-card purple active" id="additiveCard">
      <div class="header-row">
        <span class="badge badge-purple">− Difference</span>
        <span class="equation purple">20 − 5 = 15</span>
      </div>

      <div class="bars-container">
        <div class="bar-row">
          <span class="bar-label">Leo</span>
          <div class="track">
            <div class="seg-base">5</div>
            <div class="seg-diff">+15</div>
          </div>
        </div>
        <div class="bar-row">
          <span class="bar-label">Maya</span>
          <div class="track">
            <div class="seg-base">5</div>
          </div>
        </div>
      </div>

      <div class="footer-text purple">
        <span>Leo has <span class="highlight-pill pill-purple">15 more</span> stickers</span>
      </div>
    </div>

    
    <div class="col-card green active" id="multiplicativeCard">
      <div class="header-row">
        <span class="badge badge-green">÷ Quotient</span>
        <span class="equation green">20 ÷ 5 = 4</span>
      </div>

      <div class="bars-container">
        <div class="bar-row">
          <span class="bar-label">Leo</span>
          <div class="track">
            <div class="seg-unit">5</div>
            <div class="seg-unit">5</div>
            <div class="seg-unit">5</div>
            <div class="seg-unit">5</div>
          </div>
        </div>
        <div class="bar-row">
          <span class="bar-label">Maya</span>
          <div class="track">
            <div class="seg-base">5</div>
          </div>
        </div>
      </div>

      <div class="footer-text green">
        <span>Leo has <span class="highlight-pill pill-green">4 times</span> as many</span>
      </div>
    </div>
  </div>

</body>
</html>

<!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: #ffffff;
      color: #1e2945;
      width: 100%;
      height: 100%;
      display: flex;
      flex-direction: column;
      align-items: center;
      justify-content: center;
      padding: 16px;
      user-select: none;
    }
    .toggle-row {
      display: flex;
      gap: 8px;
      margin-bottom: 16px;
    }
    .toggle-btn {
      padding: 6px 14px;
      font-size: 14px;
      font-weight: 600;
      border: 1px solid #e2e8f0;
      border-radius: 20px;
      background: #f8fafc;
      color: #64748b;
      cursor: pointer;
      transition: background 0.2s ease, color 0.2s ease, border-color 0.2s ease;
    }
    .toggle-btn.active {
      background: #1e2945;
      color: #ffffff;
      border-color: #1e2945;
    }
    .svg-wrap {
      width: 100%;
      max-width: 480px;
      aspect-ratio: 4 / 3;
    }
    svg {
      width: 100%;
      height: 100%;
      overflow: visible;
    }
    .mode-diff, .mode-mult {
      transition: opacity 0.3s ease;
    }
    .hidden {
      opacity: 0;
      pointer-events: none;
    }
    .visible {
      opacity: 1;
    }
  </style>
</head>
<body>

  <div class="toggle-row">
    <button id="btnDiff" class="toggle-btn active" onclick="setMode('diff')">Difference (+ $8)</button>
    <button id="btnMult" class="toggle-btn" onclick="setMode('mult')">Quotient (3× as much)</button>
  </div>

  <div class="svg-wrap">
    <svg viewBox="0 0 460 300">
      
      <line x1="170" y1="35" x2="170" y2="155" stroke="#94a3b8" stroke-width="1.5" stroke-dasharray="4 4" />

      
      <text x="20" y="68" font-size="16" font-weight="700" fill="#1e2945">You</text>
      <rect x="90" y="44" width="80" height="38" rx="6" fill="#2563eb" />
      <text x="130" y="68" font-size="16" font-weight="700" fill="#ffffff" text-anchor="middle">$4</text>

      
      <text x="20" y="134" font-size="16" font-weight="700" fill="#1e2945">Friend</text>
      
      
      <rect x="90" y="110" width="80" height="38" rx="6" fill="#f97316" />
      
      <rect x="170" y="110" width="160" height="38" rx="6" fill="#f97316" />
      
      
      <line x1="170" y1="110" x2="170" y2="148" stroke="#ffffff" stroke-width="2" />
      <line x1="250" y1="110" x2="250" y2="148" stroke="#ffffff" stroke-width="2" />

      
      <text x="130" y="134" font-size="15" font-weight="700" fill="#ffffff" text-anchor="middle">$4</text>
      <text x="210" y="134" font-size="15" font-weight="700" fill="#ffffff" text-anchor="middle">$4</text>
      <text x="290" y="134" font-size="15" font-weight="700" fill="#ffffff" text-anchor="middle">$4</text>

      
      <text x="340" y="134" font-size="15" font-weight="700" fill="#f97316">Total: $12</text>

      
      <g id="diffGroup" class="mode-diff visible">
        
        <path d="M 172 162 L 172 178 Q 172 184 180 184 L 242 184 Q 250 184 250 192 Q 250 184 258 184 L 322 184 Q 330 184 330 178 L 330 162" 
              fill="none" stroke="#f97316" stroke-width="2" stroke-dasharray="4 3" />

        <rect x="160" y="206" width="180" height="32" rx="16" fill="#fff7ed" stroke="#fdba74" stroke-width="1.5" />
        <text x="250" y="227" font-size="14" font-weight="700" fill="#ea580c" text-anchor="middle">+ $8 difference</text>
        <text x="250" y="260" font-size="13" font-weight="600" fill="#64748b" text-anchor="middle">$12 − $4 = $8</text>
      </g>

      
      <g id="multGroup" class="mode-mult hidden">
        
        <path d="M 92 162 L 92 176 Q 92 182 100 182 L 202 182 Q 210 182 210 190 Q 210 182 218 182 L 322 182 Q 330 182 330 176 L 330 162" 
              fill="none" stroke="#2563eb" stroke-width="2" />

        <rect x="160" y="206" width="180" height="32" rx="16" fill="#eff6ff" stroke="#93c5fd" stroke-width="1.5" />
        <text x="250" y="227" font-size="14" font-weight="700" fill="#2563eb" text-anchor="middle">3 × as much</text>
        <text x="250" y="260" font-size="13" font-weight="600" fill="#64748b" text-anchor="middle">$12 ÷ $4 = 3</text>
      </g>
    </svg>
  </div>

  <script>
    function setMode(mode) {
      const btnDiff = document.getElementById('btnDiff');
      const btnMult = document.getElementById('btnMult');
      const diffGroup = document.getElementById('diffGroup');
      const multGroup = document.getElementById('multGroup');

      if (mode === 'diff') {
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        btnMult.classList.remove('active');
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        multGroup.classList.add('visible');
        diffGroup.classList.remove('visible');
        diffGroup.classList.add('hidden');
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</body>
</html>

Understanding Rates and Unit Rates in Context

Solving Unit Rate and Unit Price Problems

Identifying Direct Proportionality in Tables and Equations

Solving Direct Proportionality Problems

Understanding Inverse Proportionality Concepts

Solving Inverse Proportionality Problems

Comparing Direct and Inverse Proportionality Scenarios

math

Rates, Unit Rates, and Proportional Relationships

Propiedades asociativa y conmutativa de la multiplicación

Multiplicación de tres o más factores

Estimación de productos mediante redondeo

Problemas multiplicativos de grupos iguales y arreglos

Problemas multiplicativos de comparación: tantas veces más

Problemas multiplicativos de combinatoria y cartesiano

Duplicar y partir a la mitad como estrategia mental

Detección y corrección de errores en la multiplicación

Problemas multiplicativos de dos pasos con dinero y cantidades

Cálculo mental y problemas multiplicativos

Multiplying Whole Numbers by 10, 100, and 1,000 Using Place Value Charts

Dividing Whole Numbers by 10, 100, and 1,000 Giving Whole Answers

Dividing Whole Numbers by 10 and 100 Resulting in Decimals

Multiplying Decimals with 1 Decimal Place by 10, 100, and 1,000

Multiplying Decimals with 2 Decimal Places by 10, 100, and 1,000

Dividing Decimals by 10, 100, and 1,000

Finding Missing Numbers in Multiplication and Division by Powers of 10

Applying Powers of 10 to Metric Conversions in Context

Solving Word Problems Involving Scaling by 10, 100, and 1,000

Multiplying and Dividing by 10, 100, and 1,000

Understanding the Equals Sign as a Symbol of Equivalence

Balancing Equations with Mixed Operations on Both Sides

Order of Operations: Using Brackets in Calculations

Solving Problems Involving Scaling Quantities Up and Down

Scaling Quantities by Simple Unit Fractions

Scaling Quantities by Non-Unit Fractions

Solving Problems Involving Simple Rates and Unit Costs

Two-Step Problems Combining Multiplication and Addition or Subtraction

Multi-Step Problems Combining All Four Operations

Bar Modelling for Complex Four-Operations Word Problems

Multi-Step Problem Solving & Equivalence

Concepto de razón como comparación por cociente

Razones equivalentes y simplificación de razones

Tablas de razones y patrones de escalamiento

Tasas unitarias en la vida cotidiana: velocidad y rendimiento

Concepto de proporción y la propiedad fundamental

Proporcionalidad directa: identificación y constante de proporcionalidad

Regla de tres simple directa en la resolución de problemas

Representación gráfica de la proporcionalidad directa

Razones, tasas y proporcionalidad directa

Concepto de proporcionalidad inversa: cuando una crece, la otra disminuye

Regla de tres simple inversa: tiempo, obreros y velocidad

Situaciones de producto de medidas: combinación de dimensiones

Escalas en mapas y planos arquitectónicos

Porcentaje calculado como proporción directa

Modelado y análisis de dependencia en tablas y gráficos

Proporcionalidad inversa y aplicaciones

Traslación de figuras en el plano: vector de desplazamiento

Reflexión de figuras respecto a un eje horizontal o vertical

Rotación de figuras alrededor de un vértice: giros de 90° y 180°

Conservación de forma y tamaño en las transformaciones rígidas

Homotecias y escalamiento en el plano: ampliación y reducción

Diseño de patrones, murales y frisos mediante transformaciones

Graficación de relaciones numéricas y tablas de valores

Resolución de desafíos de coordenadas y mapas del tesoro

Transformaciones geométricas en el plano

OGM.6.OA.5

OGM.6.OA.5

Aligned learning resources

Related diagrams