# CTE Resource Center - Verso - Sustainability and Renewable Technologies Task 954512751

# Analyze linear and cyclical approaches to life cycles of common technological products.

## Definition

Analysis should include describing linear (cradle-to-grave) and cyclical (cradle-to-cradle) lifelines of products and materials. A linear approach considers the product or material from the time of acquisition to disposal. A cyclical approach considers the product or material from the time of its acquisition to its being reused, remanufactured, and/or recycled.

Examples of products to analyze may include oil, water, soil, compost, biological waste, cell phones, tennis shoes, tires, hamburgers, and refrigerators.

## Process/Skill Questions

• How does the cradle-to-grave approach handle the end-of-life stage of a product?
• What is remanufacturing?
• How can a given product be redesigned to become reusable?
• Why is it important to think about a product's life cycle?
• What is more economically efficient for a business, a linear or cyclical approach?
Resource:

## Mathematics

### A.7

The student will investigate and analyze function (linear and quadratic) families and their characteristics both algebraically and graphically, including
1. determining whether a relation is a function;
2. domain and range;
3. zeros of a function;
4. x- and y-intercepts;
5. finding the values of a function for elements in its domain; and
6. making connections between and among multiple representations of functions including concrete, verbal, numeric, graphic, and algebraic.

### A.8

The student, given a situation in a real-world context, will analyze a relation to determine whether a direct or inverse variation exists, and represent a direct variation algebraically and graphically and an inverse variation algebraically.

### A.9

The student will collect and analyze data, determine the equation of the curve of best fit in order to make predictions, and solve practical problems, using mathematical models of linear and quadratic functions.