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

    .diagram-content {
      width: 100%;
      max-width: 480px;
      display: flex;
      flex-direction: column;
      gap: 20px;
    }

    /* Tape Diagram Section */
    .tapes-area {
      display: flex;
      flex-direction: column;
      gap: 12px;
      width: 100%;
    }

    .tape-row {
      display: flex;
      flex-direction: column;
      gap: 4px;
    }

    .tape-header {
      display: flex;
      justify-content: space-between;
      align-items: baseline;
      font-size: 14px;
      font-weight: 700;
    }

    .friend-text {
      color: #0f766e;
    }

    .you-text {
      color: #1d4ed8;
    }

    .tape-track {
      display: flex;
      width: 100%;
      gap: 4px;
      height: 48px;
    }

    .block {
      height: 100%;
      border-radius: 8px;
      display: flex;
      align-items: center;
      justify-content: center;
      font-weight: 800;
      font-size: 16px;
      user-select: none;
      transition: transform 0.2s ease, filter 0.2s ease;
    }

    .teal-block {
      flex: 1;
      background: #14b8a6;
      color: #ffffff;
      border: 2px solid #0d9488;
    }

    .blue-block {
      flex: 1;
      background: #3b82f6;
      color: #ffffff;
      border: 2px solid #2563eb;
    }

    .empty-spacer {
      flex: 2;
    }

    /* Ratio Badges */
    .badges-row {
      display: flex;
      justify-content: center;
      align-items: center;
      gap: 12px;
      flex-wrap: wrap;
    }

    .pill {
      background: #f8fafc;
      border: 2px solid #e2e8f0;
      border-radius: 9999px;
      padding: 8px 18px;
      font-weight: 800;
      font-size: 16px;
      color: #1e2945;
      display: flex;
      align-items: center;
      gap: 2px;
      box-shadow: 0 1px 3px rgba(0, 0, 0, 0.05);
    }

    .pill .f-val {
      color: #0f766e;
    }

    .pill .y-val {
      color: #1d4ed8;
    }

    .pill .separator {
      color: #94a3b8;
      font-weight: 600;
      margin: 0 2px;
    }

    /* Subtitle Label */
    .ratio-caption {
      text-align: center;
      font-size: 14px;
      font-weight: 600;
      color: #475569;
      background: #f1f5f9;
      padding: 8px 14px;
      border-radius: 8px;
    }

    .ratio-caption strong {
      color: #0f766e;
    }

    .ratio-caption span.you-num {
      color: #1d4ed8;
      font-weight: 700;
    }
  </style>
</head>
<body>

  <div class="diagram-content">
    
    <div class="tapes-area">
      
      <div class="tape-row">
        <div class="tape-header">
          <span class="friend-text">Friend (3 units)</span>
          <span class="friend-text">$12</span>
        </div>
        <div class="tape-track">
          <div class="block teal-block">$4</div>
          <div class="block teal-block">$4</div>
          <div class="block teal-block">$4</div>
        </div>
      </div>

      
      <div class="tape-row">
        <div class="tape-header">
          <span class="you-text">You (1 unit)</span>
          <span class="you-text">$4</span>
        </div>
        <div class="tape-track">
          <div class="block blue-block">$4</div>
          <div class="empty-spacer"></div>
        </div>
      </div>
    </div>

    
    <div class="badges-row">
      <div class="pill">
        <span class="f-val">3</span>
        <span class="separator">to</span>
        <span class="y-val">1</span>
      </div>
      <div class="pill">
        <span class="f-val">3</span>
        <span class="separator">:</span>
        <span class="y-val">1</span>
      </div>
      <div class="pill">
        <span class="f-val">3</span>
        <span class="separator">/</span>
        <span class="y-val">1</span>
      </div>
    </div>

    
    <div class="ratio-caption">
      For every <span class="you-num">1 unit</span> you have, friend has <strong>3 units</strong>
    </div>
  </div>

</body>
</html>

Understanding Ratios as Multiplicative Comparisons

<!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;
    }

    body {
      padding: 16px;
      background: #ffffff;
      color: #1e2945;
      display: flex;
      flex-direction: column;
      align-items: center;
      justify-content: space-between;
      min-height: 100%;
      user-select: none;
    }

    .main-wrap {
      width: 100%;
      max-width: 480px;
      display: flex;
      flex-direction: column;
      gap: 16px;
    }

    /* Controls */
    .controls {
      display: flex;
      background: #f1f5f9;
      padding: 4px;
      border-radius: 12px;
      width: 100%;
    }

    .toggle-btn {
      flex: 1;
      padding: 10px 12px;
      border: none;
      background: transparent;
      font-size: 15px;
      font-weight: 600;
      color: #64748b;
      border-radius: 8px;
      cursor: pointer;
      transition: all 0.25s ease;
      text-align: center;
    }

    .toggle-btn.active {
      background: #ffffff;
      color: #0284c7;
      box-shadow: 0 2px 6px rgba(0,0,0,0.08);
    }

    /* Bar Visualization Area */
    .bars-container {
      display: flex;
      flex-direction: column;
      gap: 14px;
      background: #f8fafc;
      padding: 18px 16px;
      border-radius: 12px;
      border: 1px solid #e2e8f0;
    }

    .bar-row {
      display: flex;
      flex-direction: column;
      gap: 6px;
    }

    .bar-header {
      display: flex;
      justify-content: space-between;
      font-size: 14px;
      font-weight: 600;
    }

    .name-tag {
      color: #334155;
    }

    .val-tag {
      color: #0f172a;
      font-variant-numeric: tabular-nums;
    }

    .track {
      width: 100%;
      height: 28px;
      background: #e2e8f0;
      border-radius: 6px;
      overflow: hidden;
      position: relative;
    }

    .fill {
      height: 100%;
      border-radius: 6px;
      transition: width 0.45s cubic-bezier(0.4, 0, 0.2, 1);
      display: flex;
      align-items: center;
      padding-left: 8px;
      color: white;
      font-size: 12px;
      font-weight: 700;
    }

    .fill-maya {
      background: #38bdf8;
    }

    .fill-liam {
      background: #0284c7;
    }

    /* Comparison Metrics Grid */
    .metrics-grid {
      display: grid;
      grid-template-columns: 1fr 1fr;
      gap: 12px;
      width: 100%;
    }

    .metric-card {
      padding: 12px 14px;
      border-radius: 10px;
      display: flex;
      flex-direction: column;
      gap: 4px;
      border: 1px solid transparent;
      transition: background 0.3s ease, border-color 0.3s ease;
    }

    .metric-diff {
      background: #fef2f2;
      border-color: #fee2e2;
    }

    .metric-ratio {
      background: #f0fdf4;
      border-color: #dcfce7;
    }

    .metric-label {
      font-size: 12px;
      font-weight: 600;
      text-transform: uppercase;
      letter-spacing: 0.5px;
    }

    .metric-diff .metric-label {
      color: #b91c1c;
    }

    .metric-ratio .metric-label {
      color: #15803d;
    }

    .metric-value {
      font-size: 16px;
      font-weight: 700;
      display: flex;
      align-items: baseline;
      gap: 6px;
      flex-wrap: wrap;
    }

    .metric-diff .metric-value {
      color: #dc2626;
    }

    .metric-ratio .metric-value {
      color: #16a34a;
    }

    .badge {
      font-size: 11px;
      padding: 2px 6px;
      border-radius: 4px;
      font-weight: 600;
      white-space: nowrap;
    }

    .badge-diff {
      background: #fee2e2;
      color: #991b1b;
    }

    .badge-ratio {
      background: #dcfce7;
      color: #166534;
    }

    /* Scale Factor Indicator */
    .multiplier-tag {
      text-align: center;
      font-size: 13px;
      font-weight: 600;
      color: #64748b;
      margin-top: -4px;
    }

    .multiplier-tag span {
      color: #0284c7;
    }
  </style>
</head>
<body>
  <div class="main-wrap">
    
    <div class="controls">
      <button class="toggle-btn active" id="btnBefore" onclick="setState(false)">1. Before Doubling</button>
      <button class="toggle-btn" id="btnAfter" onclick="setState(true)">2. After Doubling (×2)</button>
    </div>

    
    <div class="multiplier-tag" id="multTag">Original quantities</div>

    
    <div class="bars-container">
      
      <div class="bar-row">
        <div class="bar-header">
          <span class="name-tag">Maya</span>
          <span class="val-tag" id="mayaVal">6</span>
        </div>
        <div class="track">
          <div class="fill fill-maya" id="mayaFill" style="width: 16.66%;"></div>
        </div>
      </div>

      
      <div class="bar-row">
        <div class="bar-header">
          <span class="name-tag">Liam</span>
          <span class="val-tag" id="liamVal">18</span>
        </div>
        <div class="track">
          <div class="fill fill-liam" id="liamFill" style="width: 50%;"></div>
        </div>
      </div>
    </div>

    
    <div class="metrics-grid">
      
      <div class="metric-card metric-diff">
        <span class="metric-label">Difference</span>
        <div class="metric-value">
          <span id="diffVal">12</span>
          <span class="badge badge-diff" id="diffBadge" style="display: none;">Changed!</span>
        </div>
      </div>

      
      <div class="metric-card metric-ratio">
        <span class="metric-label">Ratio (Liam : Maya)</span>
        <div class="metric-value">
          <span>3 : 1</span>
          <span class="badge badge-ratio" id="ratioBadge" style="display: none;">Preserved!</span>
        </div>
      </div>
    </div>
  </div>

  <script>
    let isDoubled = false;

    function setState(doubled) {
      isDoubled = doubled;
      
      const btnBefore = document.getElementById('btnBefore');
      const btnAfter = document.getElementById('btnAfter');
      const mayaFill = document.getElementById('mayaFill');
      const liamFill = document.getElementById('liamFill');
      const mayaVal = document.getElementById('mayaVal');
      const liamVal = document.getElementById('liamVal');
      const diffVal = document.getElementById('diffVal');
      const diffBadge = document.getElementById('diffBadge');
      const ratioBadge = document.getElementById('ratioBadge');
      const multTag = document.getElementById('multTag');

      if (isDoubled) {
        btnBefore.classList.remove('active');
        btnAfter.classList.add('active');

        // Scale max width is based on 36 units (100%)
        mayaFill.style.width = '33.33%';
        liamFill.style.width = '100%';

        mayaVal.textContent = '12';
        liamVal.textContent = '36';

        diffVal.textContent = '24';
        diffBadge.style.display = 'inline-block';
        ratioBadge.style.display = 'inline-block';
        multTag.innerHTML = 'Scale factor: <span>× 2</span>';
      } else {
        btnAfter.classList.remove('active');
        btnBefore.classList.add('active');

        mayaFill.style.width = '16.66%';
        liamFill.style.width = '50%';

        mayaVal.textContent = '6';
        liamVal.textContent = '18';

        diffVal.textContent = '12';
        diffBadge.style.display = 'none';
        ratioBadge.style.display = 'none';
        multTag.innerHTML = 'Original quantities';
      }
    }
  </script>
</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;
      font-family: system-ui, -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, sans-serif;
      -webkit-tap-highlight-color: transparent;
    }

    body {
      background: #f8fafc;
      color: #1e293b;
      padding: 12px;
      display: flex;
      flex-direction: column;
      align-items: center;
      justify-content: center;
      min-height: 100%;
    }

    .toolbar {
      display: flex;
      gap: 6px;
      margin-bottom: 12px;
    }

    .toggle-btn {
      background: #ffffff;
      border: 1px solid #cbd5e1;
      color: #64748b;
      padding: 6px 12px;
      font-size: 13px;
      font-weight: 600;
      border-radius: 20px;
      cursor: pointer;
      transition: all 0.2s ease;
    }

    .toggle-btn.active {
      background: #1e293b;
      border-color: #1e293b;
      color: #ffffff;
    }

    .comparison-grid {
      display: grid;
      grid-template-columns: 1fr 1fr;
      gap: 12px;
      width: 100%;
      max-width: 640px;
    }

    @media (max-width: 480px) {
      .comparison-grid {
        grid-template-columns: 1fr;
        gap: 10px;
      }
    }

    .concept-card {
      background: #ffffff;
      border: 1px solid #e2e8f0;
      border-radius: 12px;
      padding: 14px;
      display: flex;
      flex-direction: column;
      gap: 12px;
      transition: opacity 0.3s ease, transform 0.2s ease, box-shadow 0.2s ease;
    }

    .concept-card.dimmed {
      opacity: 0.35;
    }

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

    .card-title {
      font-size: 14px;
      font-weight: 700;
      letter-spacing: 0.2px;
    }

    .tag-add {
      color: #059669;
      background: #ecfdf5;
      font-size: 11px;
      font-weight: 700;
      padding: 2px 8px;
      border-radius: 6px;
    }

    .tag-mult {
      color: #2563eb;
      background: #eff6ff;
      font-size: 11px;
      font-weight: 700;
      padding: 2px 8px;
      border-radius: 6px;
    }

    .visual-area {
      display: flex;
      flex-direction: column;
      gap: 8px;
      padding: 8px 0;
    }

    .row-label {
      font-size: 12px;
      font-weight: 600;
      color: #64748b;
      display: flex;
      justify-content: space-between;
      margin-bottom: 3px;
    }

    /* Additive Grid Styles */
    .unit-bar {
      display: grid;
      grid-template-columns: repeat(12, 1fr);
      gap: 2px;
      height: 22px;
    }

    .unit {
      border-radius: 3px;
      height: 100%;
    }

    .unit.blue {
      background: #3b82f6;
    }

    .unit.green-base {
      background: #93c5fd;
    }

    .unit.green-diff {
      background: #10b981;
    }

    .bracket-container {
      position: relative;
      margin-top: 2px;
      height: 26px;
    }

    .bracket-line {
      position: absolute;
      left: 33.33%;
      width: 66.66%;
      height: 8px;
      border: 2px dashed #10b981;
      border-top: none;
      border-radius: 0 0 4px 4px;
    }

    .bracket-label {
      position: absolute;
      top: 10px;
      left: 33.33%;
      width: 66.66%;
      text-align: center;
      font-size: 11px;
      font-weight: 700;
      color: #059669;
    }

    /* Multiplicative Block Styles */
    .mult-bar-container {
      display: flex;
      flex-direction: column;
      gap: 8px;
    }

    .single-group {
      display: flex;
      width: 33.33%;
      background: #3b82f6;
      color: #ffffff;
      height: 22px;
      border-radius: 4px;
      align-items: center;
      justify-content: center;
      font-size: 11px;
      font-weight: 700;
    }

    .multi-groups {
      display: grid;
      grid-template-columns: repeat(3, 1fr);
      gap: 4px;
    }

    .group-block {
      background: #3b82f6;
      color: #ffffff;
      height: 22px;
      border-radius: 4px;
      display: flex;
      align-items: center;
      justify-content: center;
      font-size: 11px;
      font-weight: 700;
      position: relative;
    }

    .group-block.scale-extra {
      background: #2563eb;
    }

    .scale-legend {
      display: flex;
      justify-content: space-around;
      font-size: 11px;
      font-weight: 600;
      color: #2563eb;
      margin-top: 4px;
    }

    .math-pill {
      background: #f8fafc;
      border: 1px solid #e2e8f0;
      border-radius: 8px;
      padding: 8px 10px;
      font-size: 13px;
      font-weight: 700;
      text-align: center;
    }

    .math-pill.add {
      color: #059669;
    }

    .math-pill.mult {
      color: #2563eb;
    }
  </style>
</head>
<body>

  <div class="toolbar">
    <button class="toggle-btn active" data-mode="both">Both</button>
    <button class="toggle-btn" data-mode="add">Additive (+8)</button>
    <button class="toggle-btn" data-mode="mult">Multiplicative (×3)</button>
  </div>

  <div class="comparison-grid">
    
    <div class="concept-card" id="card-add">
      <div class="card-header">
        <span class="card-title">Additive Thinking</span>
        <span class="tag-add">Difference</span>
      </div>

      <div class="visual-area">
        <div>
          <div class="row-label"><span>You</span><span>$4</span></div>
          <div class="unit-bar">
            <div class="unit blue"></div>
            <div class="unit blue"></div>
            <div class="unit blue"></div>
            <div class="unit blue"></div>
          </div>
        </div>

        <div>
          <div class="row-label"><span>Friend</span><span>$12</span></div>
          <div class="unit-bar">
            <div class="unit green-base"></div>
            <div class="unit green-base"></div>
            <div class="unit green-base"></div>
            <div class="unit green-base"></div>
            <div class="unit green-diff"></div>
            <div class="unit green-diff"></div>
            <div class="unit green-diff"></div>
            <div class="unit green-diff"></div>
            <div class="unit green-diff"></div>
            <div class="unit green-diff"></div>
            <div class="unit green-diff"></div>
            <div class="unit green-diff"></div>
          </div>

          <div class="bracket-container">
            <div class="bracket-line"></div>
            <div class="bracket-label">+8 more</div>
          </div>
        </div>
      </div>

      <div class="math-pill add">
        12 − 4 = +8
      </div>
    </div>

    
    <div class="concept-card" id="card-mult">
      <div class="card-header">
        <span class="card-title">Multiplicative Thinking</span>
        <span class="tag-mult">Scale Ratio</span>
      </div>

      <div class="visual-area">
        <div>
          <div class="row-label"><span>You (1 group)</span><span>$4</span></div>
          <div class="single-group">$4</div>
        </div>

        <div style="margin-top: 3px;">
          <div class="row-label"><span>Friend (3 groups)</span><span>$12</span></div>
          <div class="multi-groups">
            <div class="group-block">$4</div>
            <div class="group-block scale-extra">$4</div>
            <div class="group-block scale-extra">$4</div>
          </div>
          <div class="scale-legend">
            <span>1×</span>
            <span>2×</span>
            <span>3×</span>
          </div>
        </div>
      </div>

      <div class="math-pill mult">
        4 × 3 = 12 (3× as much)
      </div>
    </div>
  </div>

  <script>
    const buttons = document.querySelectorAll('.toggle-btn');
    const cardAdd = document.getElementById('card-add');
    const cardMult = document.getElementById('card-mult');

    buttons.forEach(btn => {
      btn.addEventListener('click', () => {
        buttons.forEach(b => b.classList.remove('active'));
        btn.classList.add('active');

        const mode = btn.getAttribute('data-mode');
        if (mode === 'both') {
          cardAdd.classList.remove('dimmed');
          cardMult.classList.remove('dimmed');
        } else if (mode === 'add') {
          cardAdd.classList.remove('dimmed');
          cardMult.classList.add('dimmed');
        } else if (mode === 'mult') {
          cardAdd.classList.add('dimmed');
          cardMult.classList.remove('dimmed');
        }
      });
    });
  </script>
</body>
</html>

Writing and Interpreting Ratio Language

Part-to-Part and Part-to-Whole Ratios

Using Tape Diagrams to Solve Ratio Problems

Using Double Number Lines to Solve Ratio Problems

Simplifying Ratios to Lowest Terms

Ratios with Different Units of Measurement

math

Foundations of Ratios and Visual Models

Concepto de número racional y representación fraccionaria

Fracciones propias, impropias y números mixtos

Fracciones equivalentes por amplificación y simplificación

Fracción irreducible y simplificación máxima

Ubicación de fracciones positivas y negativas en la recta

Comparación de fracciones con distinto denominador

Densidad de los números racionales

Fracciones como operadores de cantidades y medidas

Problemas de comparación y medición con fracciones

Números racionales: Fracciones y equivalencia

Concepto de inverso multiplicativo o recíproco

División de fracciones por el método del recíproco

División con fracciones y números mixtos

Operaciones combinadas con fracciones y jerarquía

Problemas verbales aditivos con fracciones en medidas

Problemas verbales multiplicativos y de división con fracciones

División, operaciones combinadas y problemas con fracciones

Estructura posicional y descomposición polinomial decimal

Conversión entre fracciones y decimales exactos

Decimales periódicos puros y mixtos

Comparación y orden de números decimales en la recta

Redondeo y truncamiento de números decimales

Representación y propiedades de los números decimales

Adición y sustracción alineada de decimales

Multiplicación de números decimales

Multiplicación y división de decimales por potencias de 10

División de decimales entre enteros

División entre números decimales

Problemas contextuales con decimales y dinero

Estimación frente a cálculo exacto con decimales

Operaciones y problemas con números decimales

Understanding Ratio Language: For Every and To Every

Writing and Simplifying Ratios Using Colon Notation

Connecting Ratios to Fractions of a Whole

Sharing Amounts into Two Unequal Parts Using Bar Models

Sharing Amounts into Three or More Unequal Parts

Finding the Whole When One Part Is Known

Finding Parts When the Difference Between Parts Is Known

Ratio Foundations and Unequal Sharing

Using Multiples to Scale Recipes Up and Down

Unequal Grouping Problems with Multiples

Solving Best-Buy and Unit Cost Problems

Mixing Paint and Liquids in Given Proportions

Unequal Sharing Word Problems with Money and Measures

Multi-Step Ratio and Proportion Word Problems

Mastering Ratio and Proportion Reasoning

Proportion, Rates, and Multi-Step Problem Solving

认识比例尺及其意义（比例尺=图上距离:实际距离）

数值比例尺与线段比例尺的相互转化

已知比例尺求实际距离或图上距离

认识放大比例尺（如5:1、10:1）与精密零件设计

在方格纸上按比例将简单图形放大或缩小

探究图形放大缩小后边长与面积的变化规律

比例尺与图形的放大与缩小

Understanding Percentages as Fractions of 100

Converting Between Fractions, Decimals and Percentages

Finding a Percentage of a Quantity

Finding 10%, 25% and 50% Mentally

Using Multiplication to Find a Fraction of a Number

Representing Whole Number × Fraction with Area Models

Using Properties with Fraction Multiplication

Finding the Whole When a Percentage Is Given

Understanding Percentages and Fraction Calculations

Calculating Percentage Discounts

Finding the Sale Price After a Discount

Comparing Prices with Different Discounts

Estimating with Percentages in Real Life

Estimating with Fractions and Decimals

Approximating Solutions in Financial Contexts

Rounding and Approximation in Money Problems

Percentage Discounts and Estimation in Financial Contexts

Concepto de razón y formas de representación

Razones equivalentes y tablas de razón

Concepto de tasa y tasa unitaria

Comparación de precios unitarios para la mejor compra

Concepto de proporcionalidad directa y constante k

Ecuaciones de proporcionalidad directa: y = kx

Gráficas de proporcionalidad directa en el plano

Regla de tres simple directa

Problemas de velocidad constante, distancia y tiempo

Factores de conversión unitarios con proporcionalidad

Razones, tasas y proporcionalidad directa

Introducing Ratios and Ratio Language

Writing Ratios in Three Formats

Understanding Part-to-Part Ratios

Understanding Part-to-Whole Ratios

Representing Ratios with Pictures and Models

Understanding Equivalent Ratios

Building Ratio Tables

Finding Missing Values in Ratio Tables

Understanding Ratios

Modelling Real-World Problems with Rational Numbers

Choosing Operations for Multi-Step Problems

Representing Problems with Number Sentences

Communicating Solutions in Terms of the Situation

Solving Financial Problems with Percentages

Rational Numbers in Daily Life: Length, Weight, and Capacity

Calculations With Both Common and Decimal Fractions

Modelling and Solving Real-World Problems with Rational Numbers

Concepto de proporcionalidad inversa

Tablas y gráficas de proporcionalidad inversa

Regla de tres simple inversa

Comparación entre proporcionalidad directa e inversa

Concepto de porcentaje y equivalencias fracción-decimal

Cálculo del porcentaje de una cantidad

Hallar la cantidad total a partir de un porcentaje

Porcentaje de aumento y descuento comercial

Cálculo de impuestos (IVA) y propinas

Interés simple: fórmula y aplicaciones

Variación porcentual: incremento y decremento

Proporcionalidad inversa, porcentajes y finanzas

Understanding Unit Rate Language

Calculating Unit Rates from Ratios

Finding Unit Rates with Whole Numbers

Finding Unit Rates with Fractions

Comparing Unit Rates to Find the Best Value

Ratios in Real-World Contexts

Unit Rates in Real-World Contexts

Ratios and Rates Vocabulary Review

Understanding Rates and Unit Rates

Writing Ratios to Compare Same-Attribute Quantities

Understanding Rates as Comparison by Division

Writing Rates as Quotients

Finding Unit Rates

Using Unit Rates to Compare Prices

Understanding Ratios, Rates, and Unit Rates

Understanding Relative Sizes and the Language of Ratio

Representing Ratios with Bar Models and Objects

Using the Ratio Symbol and Notation

Finding Equivalent Ratios Using Multiplication

Simplifying Ratios Using Common Factors

Scaling Recipes Up and Down Using Integer Multipliers and Divisors

Finding Missing Quantities Using Scale Factors

Foundations of Ratio and Scaling

Making Tables of Equivalent Ratios

Finding Missing Values in Equivalent Ratio Tables

Plotting Ratio Pairs on the Coordinate Plane

Comparing Ratios Using Tables

Solving Problems with Equivalent Ratio Tables

Solving Ratio Problems with Equivalent Ratios

Using Ratio Tables to Solve Problems

Solving Proportions Using Cross-Multiplication

Predicting with Ratios in Real-World Problems

Comparing Quantities Using Ratios

Real-World Rate Problems: Speed and Distance

Real-World Rate Problems: Unit Pricing

Qualitative Reasoning with Ratios and Rates

Justifying Ratio and Rate Solutions with Precise Language

Solving Problems with Ratios, Rates, and Proportions

Solving Proportion Problems Using the Unitary Method

Solving Ratio and Proportion Problems with Bar Models

Comparing Quantities Using Direct Proportion in Real-World Contexts

Scale Drawing and Map Problems Involving Scaling

Converting Units of Measure Using Ratio and Scaling

Multi-Step Problem Solving with Ratio and Proportion

Direct Proportion and Real-World Applications

Representing Ratios with Concrete Models

Representing Percents with 10×10 Grids

Representing Ratios and Percents as Fractions

Representing Ratios and Percents as Decimals

Benchmark Fractions on 10×10 Grids

Benchmark Percents on 10×10 Grids

Representing Ratios, Percents, and Fractions with Grid Models

Solving Unit Pricing Problems

Solving Constant Speed Problems

Unit Rate Word Problems: Speed and Distance

Finding Distance Given Speed and Time

Finding Speed Given Distance and Time

Finding Time Given Distance and Speed

Unit Rate and Speed Problem Solving

Estructura del plano cartesiano: cuadrantes y ejes

Localización y graficación de puntos con coordenadas enteras

Puntos con coordenadas fraccionarias y decimales en el plano

Distancia entre puntos horizontales y verticales en el plano

Figuras geométricas y polígonos en el plano cartesiano

Variables independientes y dependientes en tablas

Graficación de relaciones lineales a partir de ecuaciones

Interpretación de gráficas de dos variables en contextos reales

Sistemas de coordenadas geográficas: latitud y longitud

El plano cartesiano y relaciones lineales

Partilha em partes desiguais: o conceito

Razão entre partes e entre parte e todo

Partilha usando relações aditivas

Partilha usando relações multiplicativas

Problemas de partilha em partes desiguais

Partilha de quantidades em partes desiguais

Mixed Ratio Reasoning Word Problems

Ratio and Rate Problem-Solving Assessment

Visual Strategies for Ratio Problem Solving

OGM.7.RP.1

Aligned learning resources

Related diagrams