Learn on PengiPengi Math (Grade 4)Chapter 6: Understanding Fractions

Lesson 3: Strategies for Comparing Fractions

In this Grade 4 lesson from Pengi Math Chapter 6, students learn multiple strategies for comparing fractions, including using benchmark numbers (0, 1/2, and 1), comparing fractions with the same denominator or same numerator, and creating common denominators with area models. Students also practice ordering fractions and placing them on a number line based on their proximity to benchmarks.

Section 1

Visualizing Benchmark Comparisons with Area Models

Property

To compare a fraction to a benchmark using an area model, shade the area representing the fraction and visually compare it to the area representing the benchmark (e.g., 12\frac{1}{2} or 11).

Examples

Section 2

Comparing Fractions with the Same Denominator

Property

To compare two fractions with the same denominator, compare their numerators.
The fraction with the greater numerator is the greater fraction.
If a>ca > c, then ab>cb\frac{a}{b} > \frac{c}{b}.

Examples

Section 3

Comparing Fractions with Like Numerators

Property

When two fractions have the same numerator, the fraction with the smaller denominator is greater because its pieces are larger.
If a>0a > 0 and b>c>0b > c > 0, then ab<ac\frac{a}{b} < \frac{a}{c}.

Examples

Section 4

Finding Common Denominators with Area Models

Property

A common denominator for two fractions, ab\frac{a}{b} and cd\frac{c}{d}, can be found visually using two identical area models.
By partitioning the first model (representing ab\frac{a}{b}) with dd horizontal lines and the second model (representing cd\frac{c}{d}) with bb vertical lines, both models are decomposed into b×db \times d equal parts.

Examples

Book overview

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

Continue this chapter

Chapter 6: Understanding Fractions

  1. Lesson 1

    Lesson 1: The Unit Fraction Concept

  2. Lesson 2

    Lesson 2: Understanding and Generating Equivalent Fractions

  3. Lesson 3Current

    Lesson 3: Strategies for Comparing Fractions

  4. Lesson 4

    Lesson 4: Decomposition, Mixed Numbers, and Improper Fractions

Lesson overview

Expand to review the lesson summary and core properties.

Expand

Section 1

Visualizing Benchmark Comparisons with Area Models

Property

To compare a fraction to a benchmark using an area model, shade the area representing the fraction and visually compare it to the area representing the benchmark (e.g., 12\frac{1}{2} or 11).

Examples

Section 2

Comparing Fractions with the Same Denominator

Property

To compare two fractions with the same denominator, compare their numerators.
The fraction with the greater numerator is the greater fraction.
If a>ca > c, then ab>cb\frac{a}{b} > \frac{c}{b}.

Examples

Section 3

Comparing Fractions with Like Numerators

Property

When two fractions have the same numerator, the fraction with the smaller denominator is greater because its pieces are larger.
If a>0a > 0 and b>c>0b > c > 0, then ab<ac\frac{a}{b} < \frac{a}{c}.

Examples

Section 4

Finding Common Denominators with Area Models

Property

A common denominator for two fractions, ab\frac{a}{b} and cd\frac{c}{d}, can be found visually using two identical area models.
By partitioning the first model (representing ab\frac{a}{b}) with dd horizontal lines and the second model (representing cd\frac{c}{d}) with bb vertical lines, both models are decomposed into b×db \times d equal parts.

Examples

Book overview

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

Continue this chapter

Chapter 6: Understanding Fractions

  1. Lesson 1

    Lesson 1: The Unit Fraction Concept

  2. Lesson 2

    Lesson 2: Understanding and Generating Equivalent Fractions

  3. Lesson 3Current

    Lesson 3: Strategies for Comparing Fractions

  4. Lesson 4

    Lesson 4: Decomposition, Mixed Numbers, and Improper Fractions