Illuminations: Linking Length, Perimeter, Area, and Volume

# Linking Length, Perimeter, Area, and Volume

This cluster of Internet Mathematics Excursions is based on E-example 6.3 as described in the Geometry Standard and Measurement Standards. These lessons are designed for students to understand ratio, proportion, scale factor, and similarity using perimeter, area, volume and surface area of various rectangular shapes.

The first is an on-line pre-activity to build studentsâ€™ understanding of ratio, proportion and similarity. Another on-line pre-activity follows with similarity and scale factor. The third lesson involves students comparing perimeter and area ratios of similar rectangles with various scale factors using the E-example 6.3.1. E-examples 6.3.2 is the basis for the fourth and fifth lessons. The fourth lesson focuses on the relationship between scale factor and volume. The final lesson highlights the surface area for rectangular prisms in relationship to scale factor.

### Math Content

In this unit, students will:
• Compare the perimeter and area ratios of similar rectangles with various scale factors.
• Explore the relationship between the volume of two similar rectangular prisms.
• Examine the connection between the surface area of two similar rectangular prisms.
• Use an applet to discover these relationships.

### Individual Lessons

Lesson 1 - Blue Squares and Beyond

This Internet Mathematics Excursion is a pre-activity for E-example 6.3 from the NCTM Principles and Standards for School Mathematics. This is the first in a sequence of four lessons designed for students to understand ratio, proportion, scale factor, and similarity. This lesson invites students to manipulate two rectangles to create examples of similarity and to study the effects on area ratios. Students sketch similar figures, verify proportionality, and apply these concepts to structures in their world.

Lesson 2 - Go With Green Rectangles

This Internet Mathematics Excursion is based on E-example 6.3 from the NCTM Principles and Standards for School Mathematics. This is the second in a sequence of four lessons designed for students to understand ratio, proportion, scale factor, and similarity using perimeter and area of various rectangular shapes. Students manipulate 2-dimensional rectangles to focus on the relationship between the scale factor and ratio of perimeters of similar rectangles, and the relationship between scale factor and ratio of areas of similar rectangles.

Lesson 3 - Fill'r Up

This Internet Mathematics Excursion is based on E-example 6.3.2 from the NCTM Principles and Standards for School Mathematics. This is the third in a sequence of four lessons designed for students to understand scale factor and volume of various rectangular prisms. In this lesson, the student can manipulate the scale factor that links two three-dimensional rectangular prisms and learn about the relationships between edge lengths and volumes.

Lesson 4 - Purple Prisms

This Internet Mathematics Excursion is based on E-example 6.3.2 from the NCTM Principles and Standards for School Mathematics. This is the last activity in a sequence of four lessons designed for students to understand scale factor and surface area of various rectangular prisms. Students manipulate the scale factor that links two three-dimensional rectangular prisms to learn about edge lengths and surface area relationships.

### NCTM Resources

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