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., or ).
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
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., or ).
Section 2
Comparing Fractions with the Same Denominator
To compare two fractions with the same denominator, compare their numerators.
The fraction with the greater numerator is the greater fraction.
If , then .
Section 3
Comparing Fractions with Like Numerators
When two fractions have the same numerator, the fraction with the smaller denominator is greater because its pieces are larger.
If and , then .
Section 4
Finding Common Denominators with Area Models
A common denominator for two fractions, and , can be found visually using two identical area models.
By partitioning the first model (representing ) with horizontal lines and the second model (representing ) with vertical lines, both models are decomposed into equal parts.
Expand to review the lesson summary and core properties.
Section 1
Visualizing Benchmark Comparisons with Area Models
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., or ).
Section 2
Comparing Fractions with the Same Denominator
To compare two fractions with the same denominator, compare their numerators.
The fraction with the greater numerator is the greater fraction.
If , then .
Section 3
Comparing Fractions with Like Numerators
When two fractions have the same numerator, the fraction with the smaller denominator is greater because its pieces are larger.
If and , then .
Section 4
Finding Common Denominators with Area Models
A common denominator for two fractions, and , can be found visually using two identical area models.
By partitioning the first model (representing ) with horizontal lines and the second model (representing ) with vertical lines, both models are decomposed into equal parts.