Learn on PengienVision, Mathematics, Grade 4Chapter 8: Extend Understanding of Fraction Equivalence and Ordering

Lesson 1: Equivalent Fractions: Area Models

In this Grade 4 lesson from enVision Mathematics Chapter 8, students learn to recognize and generate equivalent fractions using area models, including rectangles and circles divided into equal parts. The lesson demonstrates how fractions like 5/6 and 10/12 name the same part of a whole even when the number and size of parts differ. Students practice finding missing numerators and writing equivalent fractions to build a foundational understanding of fraction equivalence.

Section 1

Defining Equivalent Fractions

Property

Two fractions, ab\frac{a}{b} and cd\frac{c}{d}, are equivalent if they represent the same value, area, or length. This is only true if both fractions refer to the same size whole.

Examples

Section 2

Generalizing Equivalence Across Different Shapes

Property

If two models represent identical wholes, and the fractional part of Model 1 has the same size (e.g., area) as the fractional part of Model 2, the fractions are equivalent.
The shape or arrangement of the fractional parts does not affect their value.

Examples

Section 3

Connecting Area Models and Multiplication for Equivalent Fractions

Property

To generate an equivalent fraction from an area model, you can partition the model with horizontal lines.
If you create nn new horizontal sections, you are multiplying the number of shaded parts (numerator) and the total number of parts (denominator) by nn.
This visual process is represented by the numerical formula:

ab=a×nb×n\frac{a}{b} = \frac{a \times n}{b \times n}

Examples

Book overview

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Chapter 8: Extend Understanding of Fraction Equivalence and Ordering

  1. Lesson 1Current

    Lesson 1: Equivalent Fractions: Area Models

  2. Lesson 2

    Lesson 2: Equivalent Fractions: Number Lines

  3. Lesson 3

    Lesson 3: Generate Equivalent Fractions: Multiplication

  4. Lesson 4

    Lesson 4: Generate Equivalent Fractions: Division

  5. Lesson 5

    Lesson 5: Use Benchmarks to Compare Fractions

  6. Lesson 6

    Lesson 6: Compare Fractions

Lesson overview

Expand to review the lesson summary and core properties.

Expand

Section 1

Defining Equivalent Fractions

Property

Two fractions, ab\frac{a}{b} and cd\frac{c}{d}, are equivalent if they represent the same value, area, or length. This is only true if both fractions refer to the same size whole.

Examples

Section 2

Generalizing Equivalence Across Different Shapes

Property

If two models represent identical wholes, and the fractional part of Model 1 has the same size (e.g., area) as the fractional part of Model 2, the fractions are equivalent.
The shape or arrangement of the fractional parts does not affect their value.

Examples

Section 3

Connecting Area Models and Multiplication for Equivalent Fractions

Property

To generate an equivalent fraction from an area model, you can partition the model with horizontal lines.
If you create nn new horizontal sections, you are multiplying the number of shaded parts (numerator) and the total number of parts (denominator) by nn.
This visual process is represented by the numerical formula:

ab=a×nb×n\frac{a}{b} = \frac{a \times n}{b \times n}

Examples

Book overview

Jump across lessons in the current chapter without opening the full course modal.

Continue this chapter

Chapter 8: Extend Understanding of Fraction Equivalence and Ordering

  1. Lesson 1Current

    Lesson 1: Equivalent Fractions: Area Models

  2. Lesson 2

    Lesson 2: Equivalent Fractions: Number Lines

  3. Lesson 3

    Lesson 3: Generate Equivalent Fractions: Multiplication

  4. Lesson 4

    Lesson 4: Generate Equivalent Fractions: Division

  5. Lesson 5

    Lesson 5: Use Benchmarks to Compare Fractions

  6. Lesson 6

    Lesson 6: Compare Fractions