Section 1
Defining Equivalent Fractions
Property
Two fractions, and , are equivalent if they represent the same value, area, or length. This is only true if both fractions refer to the same size whole.
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
Two fractions, and , are equivalent if they represent the same value, area, or length. This is only true if both fractions refer to the same size whole.
Section 2
Generalizing Equivalence Across Different Shapes
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.
Section 3
Connecting Area Models and Multiplication for Equivalent Fractions
To generate an equivalent fraction from an area model, you can partition the model with horizontal lines.
If you create new horizontal sections, you are multiplying the number of shaded parts (numerator) and the total number of parts (denominator) by .
This visual process is represented by the numerical formula:
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Section 1
Defining Equivalent Fractions
Two fractions, and , are equivalent if they represent the same value, area, or length. This is only true if both fractions refer to the same size whole.
Section 2
Generalizing Equivalence Across Different Shapes
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.
Section 3
Connecting Area Models and Multiplication for Equivalent Fractions
To generate an equivalent fraction from an area model, you can partition the model with horizontal lines.
If you create new horizontal sections, you are multiplying the number of shaded parts (numerator) and the total number of parts (denominator) by .
This visual process is represented by the numerical formula:
Book overview
Jump across lessons in the current chapter without opening the full course modal.
Continue this chapter