The study of biomimicry and sustainable design promises great benefits in design applications, offering cost-effective, resourceful, non-polluting avenues for new enterprise. An important final caveat for students to understand is that once copied, species are not expendable. Biomimicry is intended to help people by identifying natural functions from which to pattern human-driven services. Biomimicry was never intended to replace species. Ecosystems remain in critical need of ongoing protection and biodiversity must be preserved for the overall health of the planet. This activity addresses the negative ramifications of species decline. For example, pollinators such as bees are a vital work force in agriculture. They perform an irreplaceable task in ensuring the harvest of most fruit and vegetable crops. In the face of the unexplained colony collapse disorder, we are only now beginning to understand how invaluable these insects are in keeping food costs down and even making the existence of these foods possible for humans.

With a continued focus on the Sonoran Desert, students are introduced to the concepts of biomes, limiting factors (resources), carrying capacity and growth curves through a PowerPoint® presentation. Abiotic factors (temperature, annual precipitation, seasons, etc.) determine the biome landscape. The vegetative component, as producers, determines the types of consumers that form its various communities. Students learn how the type and quantity of available resources defines how many organisms can be supported within the community, as well as its particular resident species. Students use mathematical models of natural relationships (in this case, sigmoid and exponential growth curves) to analyze population information and build upon it. With this understanding, students are able to explain how carrying capacity is determined by the limiting factors within the community and feeding relationships. By studying these ecological relationships, students see the connection between ecological relationships of organisms and the fundamentals of engineering design, adding to their base of knowledge towards solving the grand challenge posed in this unit.

Students are introduced to the challenge question, which revolves around proving that a cabinet x-ray system can produce bone mineral density images. Students work independently to generate ideas from the questions provided, then share with partners and then with the class as part of the Multiple Perspectives phase of this unit. Then, as part of the associated activity, students explore multiple websites to gather information about bone mineral density and answer worksheet questions, followed by a quiz on the material covered in the articles.

In their reading from activity 1 of this unit, students should have discovered the term "logarithm." It is at this point that they begin their study of logarithms. Specifically, students examine the definition, history and relationship to exponents; they rewrite exponents as logarithms and vice versa, evaluating expressions, solving for a missing piece. Students then study the properties of logarithms (multiplication/addition, division/subtraction, exponents). They complete a set of practice problems to apply the skills they have learned (rewriting logarithms and exponents, evaluating expressions, solving/examining equations for a missing variable.) Then they complete a short quiz covering what they have studied thus far concerning logarithms (problems similar to the practice problems). They consider how what they have learned moves them closer to answering the unit's challenge question.

Students revisit the mathematics required to find bone mineral density, to which they were introduced in lesson 2 of this unit. They learn the equation to find intensity, Beer's law, and how to use it. Then they complete a sheet of practice problems that use the equation.

Students examine an image produced by a cabinet x-ray system to determine if it is a quality bone mineral density image. They write in their journals about what they need to know to be able to make this judgment. Students learn about what bone mineral density is, how a BMD image can be obtained, and how it is related to the x-ray field. Students examine the process used to obtain a BMD image and how this process is related to mathematics, primarily through logarithmic functions. They study the relationship between logarithms and exponents, the properties of logarithms, common and natural logarithms, solving exponential equations and Beer's law.

Students continue an examination of logarithms in the Research and Revise stage by studying two types of logarithms—common logarithms and natural logarithm. In this study, they take notes about the two special types of logarithms, why they are useful, and how to convert to these forms by using the change of base formula. Then students see how these types of logarithms can be applied to solve exponential equations. They compute a set of practice problems and apply the skills learned in class.

The computer program's simulation of a Sonoran desert community should ultimately strengthen the student's comprehension of what is required for a natural ecosystem to sustain itself (remain in balance). This computer simulation program has great flexibility. It allows the student to manipulate the population numbers of five Sonoran Desert species. A species natural history attachment provides vital information for the students to familiarize themselves with each species' behaviors, its niche and food resource needs. The program includes two producers, the Saguaro cactus and the Ironwood Tree. It also includes 3 consumers, but their interactions both toward the producers and each other differ. The community's ability to remain in balance and sustain all five species so that none die out rests on the student's assessment skills enabling him to correctly identify these dependencies. The student learns by trial and error as he continues to fine tune the ecosystem that he maintains stewardship of.

Is the food chain shown above accurate? Does the first link depict a producer, the second link a herbivore, and the third link an omnivore / carnivore? Students must correctly determine whether a species is a producer or consumer, and what type of consumer; herbivore, omnivore, or carnivore. Students are provided with a list of Sonoran Desert species and asked to construct, within their groups, several food chains. These food chains are then be used to construct a food web. In order to complete this activity, students must first research the individual species to understand their feeding habits.

Students are challenged to design a permanent guest village within the Saguaro National Park in Arizona. The design must provide a true desert experience to visitors while emphasizing sustainable design, protection of the natural environment, and energy and resource conservation. To successfully address and respond to this challenge, students must acquire an understanding of desert ecology, environmental limiting factors, species adaptations and resource utilization. Following theintroduction, students generate ideas and consider the knowledge required to complete the challenge. The lectures and activities that follow serve to develop this level of comprehension. To introduce the concepts of healthy ecosystems, biomimetics and the importance of sustainable environmental design, students watch three video clips of experts. These clips provide direction for student research and challenge design solutions.

The Challenge Question of the Legacy Cycle draws the student into considering the engineering ingenuity of nature. It will force him to analyze, appreciate and understand the wisdom of these designs as the student team focuses on meeting each of the challenge's requirements. The student is asked, with his team members, to envision a sustainable design for a future guest village within the Saguaro National Park, outside of Tucson, Arizona. What issues need to be addressed to support the comforts of park visitors without compromising the natural resources or endangering the endemic species of the area? A deeper scope of application will reveal extensions of this design in the incorporation of urban planning and systems design. It also strengthens the concept of manufacturing and building without producing waste or pollution.

Students experiment with an online virtual laboratory set at a skate park. They make predictions of graphs before they use the simulation to create graphs of energy vs. time under different conditions. This simulation experimentation strengths their comprehension of conservation of energy solely between gravitational potential energy and kinetic energy

In Activity 5, as part of the Going Public step, students demonstrate their knowledge of how potential energy may be transferred into kinetic energy. Students design, build and test vehicle prototypes that transfer various types of potential energy into motion.

This activity utilizes hands on learning with the conservation of energy with the inclusion of elastic potential energy. Students use pogo sticks to experience the elastic potential energy and its conversion to gravitational potential energy.

This activity utilizes hands-on learning with the conservation of energy and the interaction of friction. Students use a roller coaster track and collect position data. The students then calculate velocity, and energy data. After the lab, students relate the conversion of potential and kinetic energy to the conversion of energy used in a hybrid car.

Students act as an engineering consulting firm with the task to design and sell their idea for a new vehicle power system. During the brainstorming activity (Generate Ideas), students determine and comprehend what type of information is important to learn in order to accomplish the task. Then they watch several video clips as part of the Multiple Perspectives phase. The new input contributes to changing and focusing their original ideas.

In this activity, students will explore two given websites to gather information on Bone Mineral Density and how it is measured. They will also learn about X-rays in general, how they work and their different uses, along with other imaging modalities. They will answer guiding questions as they explore the websites and take a short quiz after to test the knowledge they gained while reading the articles.

With a continued focus on the Sonoran Desert, students are introduced to the concepts of food chains and food webs through a PowerPoint® presentation. They learn the difference between producers and consumers and study how these organisms function within their communities as participants in various food chains. They further understand ecosystem differences by learning how multiple food chains link together to form intricate and balanced food webs. At lesson end, students construct food webs using endemic desert species.

Students investigate different forms of hybrid engines as well as briefly conclude a look at the different forms of potential energy, which concludes the Research and Revise step of the legacy cycle. Students are introduced to basic circuit schematics and apply their understanding of the difference between series and parallel circuits to current research on hybrid cars.

Through four lessons and four hands-on associated activities, this unit provides a way to teach the overarching concept of energy as it relates to both kinetic and potential energy. Within these topics, students are exposed to gravitational potential, spring potential, the Carnot engine, temperature scales and simple magnets. During the module, students apply these scientific concepts to solve the following engineering challenge: "The rising price of gasoline has many effects on the US economy and the environment. You have been contracted by an engineering firm to help design a physical energy storage system for a new hybrid vehicle for Nissan. How would you go about solving this problem? What information would you consider to be important to know? You will create a small prototype of your design idea and make a sales pitch to Nissan at the end of the unit." This module is built around the Legacy Cycle, a format that incorporates findings from educational research on how people best learn. This module is written for a first-year algebra-based physics class, though it could easily be modified for conceptual physics.