<!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>Parts of an Algebraic Expression</title>
  <style>
    * {
      box-sizing: border-box;
      margin: 0;
      padding: 0;
    }
    body {
      font-family: system-ui, -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, sans-serif;
      background: #ffffff;
      color: #1e2945;
      padding: 12px;
      display: flex;
      flex-direction: column;
      gap: 14px;
      user-select: none;
    }

    /* Expression Header Bar */
    .expr-container {
      display: flex;
      align-items: center;
      justify-content: center;
      gap: 6px;
      background: #f8fafc;
      border: 1px solid #e2e8f0;
      border-radius: 12px;
      padding: 10px 14px;
      font-size: 20px;
      font-weight: 700;
      letter-spacing: 0.5px;
    }

    .expr-part {
      padding: 4px 8px;
      border-radius: 8px;
      cursor: pointer;
      transition: background-color 0.2s ease, box-shadow 0.2s ease;
      display: inline-flex;
      align-items: center;
    }
    .expr-part.active {
      box-shadow: 0 0 0 2px #22b7ff;
      background: #e0f2fe;
    }

    /* Math layout */
    .frac {
      display: inline-flex;
      flex-direction: column;
      vertical-align: middle;
      text-align: center;
      font-size: 0.9em;
      line-height: 1;
      padding: 0 2px;
    }
    .frac .top {
      border-bottom: 1.5px solid currentColor;
      padding-bottom: 1px;
    }
    .frac .bottom {
      padding-top: 1px;
    }
    sup {
      font-size: 0.7em;
      vertical-align: super;
      line-height: 0;
    }

    /* Grid of breakdown columns */
    .grid {
      display: grid;
      grid-template-columns: repeat(4, 1fr);
      gap: 10px;
      width: 100%;
    }

    @media (max-width: 520px) {
      .grid {
        grid-template-columns: repeat(2, 1fr);
      }
      .expr-container {
        font-size: 17px;
      }
    }

    /* Summary Card / Column */
    .col-card {
      background: #ffffff;
      border: 1.5px solid #e2e8f0;
      border-radius: 10px;
      padding: 10px;
      display: flex;
      flex-direction: column;
      gap: 8px;
      cursor: pointer;
      transition: border-color 0.2s ease, box-shadow 0.2s ease;
    }
    .col-card.active {
      border-color: #22b7ff;
      box-shadow: 0 3px 10px rgba(34, 183, 255, 0.15);
      background: #fafcff;
    }

    .term-title {
      font-size: 16px;
      font-weight: 700;
      text-align: center;
      padding-bottom: 6px;
      border-bottom: 1px dashed #e2e8f0;
      min-height: 38px;
      display: flex;
      align-items: center;
      justify-content: center;
    }

    .meta-row {
      display: flex;
      flex-direction: column;
      gap: 3px;
    }
    .meta-label {
      font-size: 11px;
      font-weight: 600;
      text-transform: uppercase;
      letter-spacing: 0.5px;
      color: #64748b;
    }

    /* Badges */
    .badge {
      display: inline-flex;
      align-items: center;
      justify-content: center;
      font-size: 13px;
      font-weight: 700;
      padding: 4px 8px;
      border-radius: 6px;
      width: 100%;
    }
    .badge-blue {
      background: #e0f2fe;
      color: #0284c7;
      border: 1px solid #bae6fd;
    }
    .badge-coral {
      background: #ffe4e6;
      color: #e11d48;
      border: 1px solid #fecdd3;
    }
    .badge-gray {
      background: #f1f5f9;
      color: #334155;
      border: 1px solid #e2e8f0;
    }
    .badge-amber {
      background: #fef3c7;
      color: #d97706;
      border: 1px solid #fde68a;
    }

    .coral-sign {
      color: #e11d48;
      font-weight: 800;
    }
    .subtext {
      font-size: 10px;
      color: #64748b;
      text-align: center;
      margin-top: -2px;
    }
  </style>
</head>
<body>

  
  <div class="expr-container">
    <div class="expr-part" data-idx="0">
      <div class="frac"><span class="top">3x<sup>2</sup>y</span><span class="bottom">4</span></div>
    </div>
    <div class="expr-part" data-idx="1">
      <span class="coral-sign">−</span>7xy
    </div>
    <div class="expr-part" data-idx="2">
      +z
    </div>
    <div class="expr-part" data-idx="3">
      <span class="coral-sign">−</span>19
    </div>
  </div>

  
  <div class="grid">
    
    <div class="col-card" data-idx="0">
      <div class="term-title">
        <div class="frac"><span class="top">3x<sup>2</sup>y</span><span class="bottom">4</span></div>
      </div>
      <div class="meta-row">
        <span class="meta-label">Coefficient</span>
        <span class="badge badge-blue">
          <div class="frac"><span class="top">3</span><span class="bottom">4</span></div>
        </span>
      </div>
      <div class="meta-row">
        <span class="meta-label">Variables</span>
        <span class="badge badge-gray">x<sup>2</sup>, y</span>
      </div>
    </div>

    
    <div class="col-card" data-idx="1">
      <div class="term-title">
        <span class="coral-sign">−</span>7xy
      </div>
      <div class="meta-row">
        <span class="meta-label">Coefficient</span>
        <span class="badge badge-coral">−7</span>
      </div>
      <div class="meta-row">
        <span class="meta-label">Variables</span>
        <span class="badge badge-gray">x, y</span>
      </div>
    </div>

    
    <div class="col-card" data-idx="2">
      <div class="term-title">+z</div>
      <div class="meta-row">
        <span class="meta-label">Coefficient</span>
        <span class="badge badge-blue">1</span>
        <span class="subtext">1z = z</span>
      </div>
      <div class="meta-row">
        <span class="meta-label">Variables</span>
        <span class="badge badge-gray">z</span>
      </div>
    </div>

    
    <div class="col-card" data-idx="3">
      <div class="term-title">
        <span class="coral-sign">−</span>19
      </div>
      <div class="meta-row">
        <span class="meta-label">Type</span>
        <span class="badge badge-amber">Constant</span>
      </div>
      <div class="meta-row">
        <span class="meta-label">Value</span>
        <span class="badge badge-coral">−19</span>
      </div>
    </div>
  </div>

  <script>
    const parts = document.querySelectorAll('.expr-part');
    const cards = document.querySelectorAll('.col-card');

    function setActive(idx) {
      parts.forEach((p, i) => p.classList.toggle('active', i === idx));
      cards.forEach((c, i) => c.classList.toggle('active', i === idx));
    }

    cards.forEach((card, i) => {
      card.addEventListener('click', () => setActive(i));
    });

    parts.forEach((part, i) => {
      part.addEventListener('click', () => setActive(i));
    });
  </script>
</body>
</html>

Parts of an Algebraic Expression: Terms, Coefficients, Constants

<!DOCTYPE html>
<html lang="en">
<head>
  <meta charset="UTF-8">
  <meta name="viewport" content="width=device-width, initial-scale=1.0">
  <title>Finding Coefficients: Traps vs. Correct Analysis</title>
  <style>
    * {
      box-sizing: border-box;
      margin: 0;
      padding: 0;
    }

    body {
      font-family: system-ui, -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, sans-serif;
      color: #1e293b;
      background: transparent;
      padding: 10px;
      line-height: 1.4;
    }

    .math-var {
      font-style: italic;
      font-family: "Cambria Math", "Times New Roman", Times, serif;
    }

    .fraction {
      display: inline-flex;
      flex-direction: column;
      vertical-align: -0.35em;
      text-align: center;
      font-size: 0.9em;
      line-height: 1;
      padding: 0 1px;
    }

    .fraction .num {
      border-bottom: 1.5px solid currentColor;
      padding-bottom: 1px;
    }

    .fraction .den {
      padding-top: 1px;
    }

    .hero-container {
      background: #f8fafc;
      border: 1.5px solid #e2e8f0;
      border-radius: 10px;
      padding: 10px 14px;
      margin-bottom: 12px;
      text-align: center;
    }

    .hero-label {
      font-size: 11px;
      font-weight: 700;
      text-transform: uppercase;
      letter-spacing: 0.5px;
      color: #64748b;
      margin-bottom: 4px;
    }

    .expr-hero {
      display: flex;
      align-items: center;
      justify-content: center;
      gap: 6px;
      font-size: 22px;
      font-weight: 700;
      flex-wrap: wrap;
    }

    .interactive-term {
      cursor: pointer;
      padding: 3px 8px;
      border-radius: 6px;
      border: 1.5px solid transparent;
      transition: background-color 0.15s ease, border-color 0.15s ease;
      display: inline-flex;
      align-items: center;
      user-select: none;
    }

    .interactive-term:hover,
    .interactive-term.active {
      background: #e0f2fe;
      border-color: #38bdf8;
    }

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

    @media (max-width: 520px) {
      .main-grid {
        grid-template-columns: 1fr;
        gap: 10px;
      }
      .expr-hero {
        font-size: 19px;
      }
    }

    .card-panel {
      background: #ffffff;
      border-radius: 10px;
      border: 1.5px solid #e2e8f0;
      overflow: hidden;
      display: flex;
      flex-direction: column;
    }

    .card-header {
      padding: 9px 12px;
      font-weight: 700;
      font-size: 13px;
      display: flex;
      align-items: center;
      justify-content: space-between;
      letter-spacing: 0.2px;
    }

    .trap-header {
      background: #fee2e2;
      color: #991b1b;
      border-bottom: 1.5px solid #fecaca;
    }

    .correct-header {
      background: #dcfce7;
      color: #166534;
      border-bottom: 1.5px solid #bbf7d0;
    }

    .card-body {
      padding: 10px;
      display: flex;
      flex-direction: column;
      gap: 8px;
      flex: 1;
    }

    .row-item {
      background: #f8fafc;
      border-radius: 8px;
      border: 1.5px solid #e2e8f0;
      padding: 8px 10px;
      display: flex;
      align-items: center;
      justify-content: space-between;
      transition: background-color 0.15s ease, border-color 0.15s ease;
      min-height: 56px;
    }

    .row-item.highlight {
      border-color: #0284c7;
      background: #f0f9ff;
    }

    .term-col {
      display: flex;
      flex-direction: column;
      gap: 2px;
    }

    .term-box {
      font-size: 15px;
      font-weight: 700;
      color: #0f172a;
      display: inline-flex;
      align-items: center;
    }

    .arrow {
      color: #94a3b8;
      font-size: 14px;
      margin: 0 4px;
      font-weight: bold;
    }

    .result-group {
      display: flex;
      align-items: center;
      gap: 6px;
      flex-shrink: 0;
    }

    .val-badge {
      font-size: 13px;
      font-weight: 700;
      padding: 3px 8px;
      border-radius: 6px;
      display: inline-flex;
      align-items: center;
      justify-content: center;
      line-height: 1.2;
    }

    .badge-trap {
      background: #fee2e2;
      color: #b91c1c;
      border: 1px solid #fca5a5;
    }

    .badge-correct {
      background: #dcfce7;
      color: #15803d;
      border: 1px solid #86efac;
    }

    .icon-status {
      font-size: 14px;
      font-weight: 900;
      line-height: 1;
      display: inline-flex;
      align-items: center;
      justify-content: center;
      width: 18px;
      height: 18px;
      border-radius: 50%;
    }

    .icon-x {
      background: #fee2e2;
      color: #dc2626;
    }

    .icon-check {
      background: #dcfce7;
      color: #16a34a;
    }

    .note-text {
      font-size: 11px;
      color: #64748b;
      line-height: 1.2;
    }

    .interactive-hint {
      font-size: 11px;
      color: #94a3b8;
      text-align: center;
      margin-top: 6px;
    }
  </style>
</head>
<body>

  
  <div class="hero-container">
    <div class="hero-label">Target Expression</div>
    <div class="expr-hero" id="expressionBar">
      <span class="interactive-term" data-term="term-const" title="Constant term">6</span>
      <span class="interactive-term" data-term="term-a" title="Click or hover to inspect">− 5<span class="math-var">a</span></span>
      <span class="interactive-term" data-term="term-x" title="Click or hover to inspect">+ <span class="fraction"><span class="num"><span class="math-var">x</span></span><span class="den">3</span></span></span>
    </div>
  </div>

  <div class="main-grid">
    
    <div class="card-panel">
      <div class="card-header trap-header">
        <span>⚠️ Common Trap</span>
        <span class="icon-status icon-x">✕</span>
      </div>
      <div class="card-body">
        <div class="row-item" id="trap-a" data-term="term-a">
          <div class="term-col">
            <span class="term-box">−5<span class="math-var">a</span></span>
            <span class="note-text">Dropped negative sign</span>
          </div>
          <div class="result-group">
            <span class="arrow">→</span>
            <span class="val-badge badge-trap">5</span>
            <span class="icon-status icon-x">✕</span>
          </div>
        </div>

        <div class="row-item" id="trap-x" data-term="term-x">
          <div class="term-col">
            <span class="term-box"><span class="fraction"><span class="num"><span class="math-var">x</span></span><span class="den">3</span></span></span>
            <span class="note-text">Missed fraction coefficient</span>
          </div>
          <div class="result-group">
            <span class="arrow">→</span>
            <span class="val-badge badge-trap">no coefficient</span>
            <span class="icon-status icon-x">✕</span>
          </div>
        </div>
      </div>
    </div>

    
    <div class="card-panel">
      <div class="card-header correct-header">
        <span>✓ Correct Analysis</span>
        <span class="icon-status icon-check">✓</span>
      </div>
      <div class="card-body">
        <div class="row-item" id="correct-a" data-term="term-a">
          <div class="term-col">
            <span class="term-box">−5<span class="math-var">a</span></span>
            <span class="note-text">Sign stays with the number</span>
          </div>
          <div class="result-group">
            <span class="arrow">→</span>
            <span class="val-badge badge-correct">−5</span>
            <span class="icon-status icon-check">✓</span>
          </div>
        </div>

        <div class="row-item" id="correct-x" data-term="term-x">
          <div class="term-col">
            <span class="term-box">
              <span class="fraction"><span class="num"><span class="math-var">x</span></span><span class="den">3</span></span>
              &nbsp;=&nbsp;
              <span class="fraction"><span class="num">1</span><span class="den">3</span></span><span class="math-var">x</span>
            </span>
            <span class="note-text">Dividing by 3 is multiplying by <sup>1</sup>/<sub>3</sub></span>
          </div>
          <div class="result-group">
            <span class="arrow">→</span>
            <span class="val-badge badge-correct"><span class="fraction"><span class="num">1</span><span class="den">3</span></span></span>
            <span class="icon-status icon-check">✓</span>
          </div>
        </div>
      </div>
    </div>
  </div>

  <div class="interactive-hint">💡 Hover or tap terms above or rows below to inspect coefficient rules</div>

  <script>
    document.addEventListener('DOMContentLoaded', () => {
      const termElements = document.querySelectorAll('.interactive-term');
      const rows = {
        'term-a': [document.getElementById('trap-a'), document.getElementById('correct-a')],
        'term-x': [document.getElementById('trap-x'), document.getElementById('correct-x')]
      };

      function setHighlight(termKey) {
        // Clear all highlights
        Object.keys(rows).forEach(key => {
          rows[key].forEach(el => el && el.classList.remove('highlight'));
        });
        termElements.forEach(t => t.classList.remove('active'));

        // Apply highlight
        if (termKey && rows[termKey]) {
          rows[termKey].forEach(el => el && el.classList.add('highlight'));
          const activeSpan = document.querySelector(`.interactive-term[data-term="${termKey}"]`);
          if (activeSpan) activeSpan.classList.add('active');
        }
      }

      function clearHighlight() {
        Object.keys(rows).forEach(key => {
          rows[key].forEach(el => el && el.classList.remove('highlight'));
        });
        termElements.forEach(t => t.classList.remove('active'));
      }

      termElements.forEach(el => {
        el.addEventListener('mouseenter', () => setHighlight(el.dataset.term));
        el.addEventListener('mouseleave', clearHighlight);
        el.addEventListener('click', (e) => {
          e.stopPropagation();
          const isActive = el.classList.contains('active');
          clearHighlight();
          if (!isActive) setHighlight(el.dataset.term);
        });
      });

      document.querySelectorAll('.row-item').forEach(row => {
        const key = row.dataset.term;
        row.addEventListener('mouseenter', () => setHighlight(key));
        row.addEventListener('mouseleave', clearHighlight);
        row.addEventListener('click', (e) => {
          e.stopPropagation();
          const isActive = row.classList.contains('highlight');
          clearHighlight();
          if (!isActive) setHighlight(key);
        });
      });

      document.addEventListener('click', clearHighlight);
    });
  </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: #0f172a;
      padding: 12px;
      display: flex;
      flex-direction: column;
      gap: 12px;
      user-select: none;
    }

    /* Mode Bar */
    .mode-bar {
      display: flex;
      flex-wrap: wrap;
      gap: 6px;
      justify-content: center;
    }

    .mode-btn {
      background: #ffffff;
      border: 1px solid #cbd5e1;
      color: #475569;
      padding: 6px 12px;
      border-radius: 9999px;
      font-size: 13px;
      font-weight: 600;
      cursor: pointer;
      transition: all 0.25s ease;
      outline: none;
    }

    .mode-btn:hover {
      border-color: #94a3b8;
      color: #1e2945;
    }

    .mode-btn.active {
      background: #1e2945;
      border-color: #1e2945;
      color: #ffffff;
      box-shadow: 0 2px 6px rgba(30, 41, 69, 0.25);
    }

    /* Main Math Display */
    .math-display {
      background: #ffffff;
      border: 1px solid #e2e8f0;
      border-radius: 12px;
      padding: 14px 8px;
      display: flex;
      justify-content: center;
      align-items: center;
      gap: 8px;
      box-shadow: 0 1px 3px rgba(0,0,0,0.03);
    }

    .math-term-group {
      display: inline-flex;
      align-items: center;
      gap: 3px;
      padding: 4px 6px;
      border-radius: 8px;
      border: 1px solid transparent;
      transition: all 0.25s ease;
      cursor: pointer;
    }

    .math-term-group:hover {
      background: #f1f5f9;
    }

    .math-token {
      font-family: 'Cambria Math', 'Times New Roman', Georgia, serif;
      font-size: 26px;
      line-height: 1;
      padding: 2px 5px;
      border-radius: 6px;
      transition: all 0.25s ease;
      display: inline-block;
    }

    .coef {
      background: #eff6ff;
      color: #1d4ed8;
      border: 1px solid #bfdbfe;
    }

    .var {
      background: #f5f3ff;
      color: #7c3aed;
      border: 1px solid #ddd6fe;
    }

    .const {
      background: #fffbeb;
      color: #b45309;
      border: 1px solid #fde68a;
    }

    /* Grid of Component Cards */
    .cards-grid {
      display: grid;
      grid-template-columns: repeat(3, 1fr);
      gap: 10px;
    }

    @media (max-width: 520px) {
      .cards-grid {
        grid-template-columns: 1fr;
      }
      .math-token {
        font-size: 22px;
      }
      .mode-btn {
        font-size: 12px;
        padding: 5px 10px;
      }
    }

    .term-card {
      background: #ffffff;
      border: 1px solid #e2e8f0;
      border-radius: 10px;
      padding: 10px;
      display: flex;
      flex-direction: column;
      gap: 8px;
      cursor: pointer;
      transition: all 0.25s ease;
    }

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

    .term-card-header {
      font-weight: 700;
      font-size: 14px;
      color: #1e2945;
      display: flex;
      align-items: center;
      justify-content: space-between;
      border-bottom: 1px solid #f1f5f9;
      padding-bottom: 6px;
    }

    .term-card-header span.sym {
      font-family: 'Cambria Math', Georgia, serif;
      font-size: 16px;
    }

    .badges {
      display: flex;
      flex-direction: column;
      gap: 5px;
    }

    .badge {
      font-size: 12px;
      font-weight: 600;
      padding: 4px 8px;
      border-radius: 6px;
      display: flex;
      justify-content: space-between;
      align-items: center;
      transition: all 0.25s ease;
    }

    .badge .val {
      font-family: 'Cambria Math', Georgia, serif;
      font-size: 14px;
    }

    .badge-blue {
      background: #eff6ff;
      color: #1d4ed8;
      border: 1px solid #bfdbfe;
    }

    .badge-purple {
      background: #f5f3ff;
      color: #7c3aed;
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What Are Algebraic Expressions?

Identifying Terms in Algebraic Expressions

Identifying Factors in Algebraic Expressions

Identifying Coefficients in Algebraic Expressions

Distinguishing Terms, Factors, and Coefficients

math

Anatomy of Algebraic Expressions

Interpreting Variable Components in Applied Formulas

Equivalent Expressions in Real-World Contexts

Analyzing Expression Structure to Predict Values

Rewriting Expressions by Factoring and Grouping

Modeling Complex Financial and Geometric Scenarios

Structure and Interpretation of Algebraic Expressions

Interpreting Expressions in Real-World Context

Viewing Parts of Expressions as Single Entities

Interpreting Expressions with Exponents as Products

Interpreting Expressions with Grouping Symbols

Matching Expressions to Real-World Situations

Interpreting Algebraic Expressions in Context

Translating Words to Algebraic Expressions

Writing Expressions for Geometric Contexts

Identifying Structure in Complex Expressions

Interpreting Compound Interest Expressions

Writing and Interpreting Multi-Part Expressions

Writing Algebraic Expressions from Context

Propiedades de la potenciación con exponentes enteros

Simplificación de expresiones con exponentes enteros

Concepto de notación científica y orden de magnitud

Conversión entre notación decimal y notación científica

Suma y resta en notación científica

Multiplicación y división en notación científica

Notación científica y operaciones

Potenciación con exponentes enteros y notación científica

Recognizing Common Factor Structure

Recognizing Difference of Squares Structure

Recognizing Perfect Square Trinomial Structure

Recognizing Sum and Difference of Cubes Structure

Using Substitution to Reveal Hidden Structure

Factoring by Grouping: A Structural Approach

Recognizing and Applying Basic Factoring Structures

Identifying Hidden Quadratic Structure

Rewriting to Reveal Factoring Opportunities

Recognizing Structure in Rational Expressions

Using Structure to Factor Higher-Degree Polynomials

Matching Expressions to Their Factored Forms

Rewriting Expressions with Multiple Structural Features

Advanced Structural Rewriting and Synthesis

Relación entre potencias fraccionarias y raíces

Propiedades fundamentales de los radicales

Extracción e introducción de factores en un radical

Suma y resta de radicales semejantes

Multiplicación y división de radicales de igual y distinto índice

Racionalización de denominadores monomios

Racionalización de denominadores binomios con el conjugado

Radicación: propiedades, operaciones y racionalización

Choosing Equivalent Forms Strategically

Factoring Quadratics with Leading Coefficient 1

Factoring Trinomials with a Leading Coefficient Other Than 1

Factoring Quadratics with a Negative Leading Coefficient

Factoring a Quadratic to Reveal Its Zeros

Completing the Square to Find Vertex Form

Completing the Square to Reveal Maximum or Minimum

Converting Between Standard and Vertex Form

Choosing Between Factored and Vertex Form

Revealing Properties Through Equivalent Forms

Equivalent Forms of Quadratic Expressions

Using Exponent Properties to Transform Expressions

Rewriting Exponential Expressions with Different Bases

Converting Between Annual and Monthly Growth Rates

Rewriting Exponential Expressions for Different Time Units

Factoring Out Common Exponential Factors

Transforming Exponential Expressions for Comparison

Writing Equivalent Forms to Solve Problems

Equivalent Forms of Exponential Expressions

Traducción de lenguaje común a lenguaje algebraico

Elementos de un término algebraico y clasificación

Valor numérico de una expresión algebraica

Reducción de términos semejantes

Adición y sustracción de polinomios

Multiplicación de monomio por monomio y por polinomio

Multiplicación de polinomio por polinomio

Lenguaje algebraico y operaciones con polinomios

Interpretación geométrica de la multiplicación algebraica

Cuadrado de la suma y de la diferencia de un binomio

Producto de la suma por la diferencia de dos cantidades

Producto de dos binomios con un término común

Cubo de la suma y de la diferencia de un binomio

Triángulo de Pascal y teorema del binomio

Productos notables y teorema del binomio

División de monomios y de polinomio entre monomio

División larga de polinomios

División sintética o regla de Ruffini

Teorema del residuo y del factor

Modelación algebraica de patrones y conjeturas

División de polinomios y modelación algebraica

Concepto de factorización y descomposición factorial

Factor común monomio

Factor común polinomio

Factor común por agrupación de términos

Factorización por factor común

Factorización de diferencia de cuadrados perfectos

Factorización de trinomio cuadrado perfecto

Factorización de trinomios completando el cuadrado

Factorización de trinomios de la forma x^2 + bx + c

Factorización de trinomios de la forma ax^2 + bx + c por aspa

Factorización de trinomios ax^2 + bx + c por multiplicación y división

Factorización de suma y diferencia de cubos perfectos

Factorización de binomios y trinomios cuadráticos

Factorización de suma y diferencia de potencias iguales impares

Factorización por evaluación y regla de Ruffini

Estrategia general para la combinación de casos de factorización

Aplicación de la factorización al cálculo de áreas y volúmenes

Factorización avanzada y aplicaciones

从数字到字母：用字母表示数量关系与运算律

列代数式：用代数语言刻画现实数量关系

公式的查阅、理解与代数表达构建

代数式的代入求值与整体代入技巧

用字母表示数与代数式建模

Dominio y valores indeterminados en fracciones algebraicas

Simplificación de fracciones algebraicas por factorización

Mínimo común múltiplo de expresiones algebraicas

Suma y resta de fracciones algebraicas con igual denominador

Suma y resta de fracciones algebraicas con distinto denominador

Multiplicación de fracciones algebraicas

División de fracciones algebraicas

Fracciones algebraicas complejas

Ecuaciones racionales reducibles a primer grado

Problemas de velocidad, trabajo compartido y proporciones inversas

Fracciones algebraicas y expresiones racionales

Concepto de igualdad, ecuación e identidad

Propiedades de las igualdades y transposición de términos

Resolución de ecuaciones lineales con paréntesis

Resolución de ecuaciones lineales con coeficientes fraccionarios

Clasificación de ecuaciones lineales: solución única, infinita o vacía

Despeje de variables en fórmulas de física y geometría

Planteamiento y resolución de problemas verbales lineales

Ecuaciones lineales en una variable

Propiedades de las desigualdades en los reales

Resolución de inecuaciones lineales en una variable

Inecuaciones lineales compuestas con conjunción y disyunción

Inecuaciones con valor absoluto

Problemas contextuales con desigualdades e inecuaciones

Inecuaciones lineales en una variable

Razón de cambio constante y concepto de pendiente

Clasificación de pendientes: positiva, negativa, cero e indefinida

Función lineal directa y proporcionalidad (y = mx)

Función afín y ecuación pendiente-intercepto (y = mx + b)

Ecuación punto-pendiente de la recta

Ecuación de la recta que pasa por dos puntos

Forma general de la ecuación de la recta (Ax + By + C = 0)

Rectas paralelas y perpendiculares: criterio de pendientes

Interceptos con los ejes coordenados

Modelado de costos, tarifas y planes de pago con funciones afines

Función lineal y afín: ecuaciones de la recta

Concepto de sistema de ecuaciones lineales y conjunto solución

Método gráfico y clasificación de sistemas lineales

Método de sustitución paso a paso

Método de igualación

Método de reducción o eliminación

Método de determinantes: regla de Cramer

Sistemas con coeficientes fraccionarios y signos de agrupación

Elección del método más eficiente según la estructura del sistema

Resolución de sistemas de ecuaciones lineales 2x2

Problemas contextuales con sistemas de ecuaciones

Problemas de mezclas y aleaciones con sistemas 2x2

Problemas de cinemática y velocidad relativa con sistemas 2x2

Introducción a los sistemas de ecuaciones lineales 3x3

Aplicaciones de sistemas 2x2 e introducción a sistemas 3x3

Definición y forma estándar de la ecuación cuadrática

Resolución de ecuaciones cuadráticas incompletas: puras y mixtas

Resolución de ecuaciones cuadráticas por factorización

Resolución completando el trinomio cuadrado perfecto

Deducción y aplicación de la fórmula general

Fórmula general para ecuaciones cuadráticas

El discriminante y la naturaleza de las soluciones

Relación entre raíces y coeficientes: propiedades de Vieta

Resolución de ecuaciones cuadráticas

代数推理的意义与图形点阵规律探求

用字母表征连续整数、奇数与偶数的代数性质

日历数表与数学魔术背后的代数恒等推导

多位数的特征数整除性质的代数式证明

代数推理与规律探究

Funciones cuadráticas: gráfica de la parábola

Vértice, eje de simetría y forma canónica del vértice

Interceptos y análisis completo de la parábola

Problemas de optimización: máximos y mínimos cuadráticos

Modelado de trayectorias de proyectiles y caída libre

Funciones cuadráticas y parábolas

Diferencia entre crecimiento lineal, cuadrático y exponencial

Funciones exponenciales: gráficas y modelos

Modelado de crecimiento poblacional y bacteriano

Interés compuesto y matemática financiera básica

Decaimiento radiactivo y vida media

Funciones logarítmicas

Ecuaciones exponenciales resueltas con bases iguales y logaritmos

Funciones racionales: asíntotas y gráficas

Funciones exponenciales y modelos de variación

OGM.10.ALG.1

Aligned learning resources

Related diagrams