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.

Students learn about complex networks and how to represent them using graphs. They also learn that graph theory is a useful mathematical tool for studying complex networks in diverse applications of science and engineering, such as neural networks in the brain, biochemical reaction networks in cells, communication networks, such as the internet, and social networks. Topics covered include set theory, defining a graph, as well as defining the degree of a node and the degree distribution of a graph.

In a multi-week experiment, students monitor the core temperatures of two compost piles, one control and one tended, to see how air and water affect microbial activity. They daily aerate and wet the "treated" pile and collect 4-6 weeks' worth of daily temperature readings. Once the experiment is concluded, students plot and analyze their data to compare the behavior of the two piles. They find that the treated pile becomes hotter, an indication that more microbes are active and releasing heat. Through this activity, students see that microbes play a role in composting and how composting can be used as a carbon management process.

Accuracy of measurement in navigation depends very much on the situation. If a sailor's target is an island 200 km wide, sailing off center by 10 or 20 km is not a major problem. But, if the island were only 1 km wide, it would be missed if off just the smallest bit. Many of the measurements made while navigating involve angles, and a small error in the angle can translate to a much larger error in position when traveling long distances.

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.

Students investigate the property dependence between concentrations and boiling point. In section 1, students first investigate the boiling point of various liquid solutions. In section 2, they analyze data collected by the entire class to generate two boiling point curves, one for salt solutions and one for sugar solutions. Finally, in section 3, students use the data they have analyzed to determine how to create a solution that has a particular boiling point and is a cost-effective design.

Students learn how the total solar irradiance hitting a photovoltaic (PV) panel can be increased through the use of a concentrating device, such as a reflector or lens. This is the final lesson in the Photovoltaic Efficiency unit and is intended to accompany a fun design project (see the associated Concentrating on the Sun with PVs activity) to wrap up the unit. However, it can be completed independently of the other unit lessons and activities.

Students design, build and test reflectors to measure the effect of solar reflectance on the efficiency of solar PV panels. They use a small PV panel, a multimeter, cardboard and foil to build and test their reflectors in preparation for a class competition. Then they graph and discuss their results with the class. Complete this activity as part of the Photovoltaic Efficiency unit and in conjunction with the Concentrated Solar Power lesson.

Students are introduced to the idea of improving efficiency by examining a setting that is familiar to many teenagers fast food restaurants. More specifically, they learn about the concepts of trade-offs, constraints, increasing efficiency and systems thinking. They consider how to improve efficiency in a struggling restaurant through delegating tasks, restructuring employee responsibilities and revising a floor plan, all while working within limitations and requirements. Finally, students summarize and defend their suggested changes in argumentative essays.

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.

Bluetooth is everywhere—from smartphones to computers to cars. Even though students are exposed to this technology, many are not aware of how they can use it themselves to wirelessly control their own creative projects! For this challenge, students build on what they learned during a previous Arduino maker challenge, Make and Control a Servo Arm with Your Computer, and learn how to control a servo with an Android phone (iPhones do not work with the components used in this challenge). By the end of the exercise, expect students to be wirelessly controlling a servo with a simple phone application!

Students act as mining engineers and simulate ore mining production by using chocolate chip cookies. They focus on the cost-benefit analysis of the chocolate ore production throughout the simulation, which helps them understand the cost of production. As students “mine” with tools such as paperclips and toothpicks, they keep records of their costs—land (cookie), equipment used, cookie size before and after production, and time spent. While the goal is to make as much profit as possible, other costs and goals are taken into consideration—as in real-world mining engineering. For example, mining engineers also consider the resulting amount of destruction to the lithosphere when deciding the best method to obtain ore. Thus, a line item for land reclamation cost is included from the beginning. A provided worksheet serves as a profit and loss statement.

A brief refresher on the Cartesian plane includes how points are written in (x, y) format and oriented to the axes, and which directions are positive and negative. Then students learn about what it means for a relation to be a function and how to determine domain and range of a set of data points.

Students write poems using rhyme and meter as they come to understand the mechanical concept of rhythm, based on the principle of oscillation, in a broader biological and cultural context, as seen in dance and sports, poetry and other literary forms, and communication in general. Note: The literacy activities for the Mechanics unit are based on physical themes that have broad application to our experience in the world — concepts of rhythm, balance, spin, gravity, levity, inertia, momentum, friction, stress and tension.

The students discover the basics of heat transfer in this activity by constructing a constant pressure calorimeter to determine the heat of solution of potassium chloride in water. They first predict the amount of heat consumed by the reaction using analytical techniques. Then they calculate the specific heat of water using tabulated data, and use this information to predict the temperature change. Next, the students will design and build a calorimeter and then determine its specific heat. After determining the predicted heat lost to the device, students will test the heat of solution. The heat given off by the reaction can be calculated from the change in temperature of the water using an equation of heat transfer. They will compare this with the value they predicted with their calculations, and then finish by discussing the error and its sources, and identifying how to improve their design to minimize these errors.

Students learn about the physical force of linear momentum movement in a straight line by investigating collisions. They learn an equation that engineers use to describe momentum. Students also investigate the psychological phenomenon of momentum; they see how the "big mo" of the bandwagon effect contributes to the development of fads and manias, and how modern technology and mass media accelerate and intensify the effect.

Students put their STEAM knowledge and skills to the test by creating indoor light fixture “clouds” that mimic current weather conditions or provide other colorful lighting schemes they program and control with smartphones. Groups fabricate the clouds from paper lanterns and pillow stuffing, adding LEDs to enable the simulation of different lighting conditions. They code the controls and connect the clouds to smart devices and the Internet cloud to bring their floating clouds to life as they change color based on the weather outside.

Students are introduced to servos and the flex sensor as they create simple, one-jointed, finger robots controlled by Arduino. Servos are motors with feedback and are extensively used in industrial and consumer applications—from large industrial car-manufacturing robots that use servos to hold heavy metal and precisely weld components together, to prosthetic hands that rely on servos to provide fine motor control. Students use Arduino microcontrollers and flex sensors to read finger flexes, which they process to send angle information to the servos. Students create working circuits; use the constrain, map and smoothing commands; learn what is meant by library and abstraction in a coding context; and may even combine team finger designs to create a complete prosthetic hand of bendable fingers.

Student teams design and then create small-size models of working filter systems to simulate multi-stage wastewater treatment plants. Drawing from assorted provided materials (gravel, pebbles, sand, activated charcoal, algae, coffee filters, cloth) and staying within a (hypothetical) budget, teams create filter systems within 2-liter plastic bottles to clean the teacher-made simulated wastewater (soap, oil, sand, fertilizer, coffee grounds, beads). They aim to remove the water contaminants while reclaiming the waste material as valuable resources. They design and build the filtering systems, redesigning for improvement, and then measuring and comparing results (across teams): reclaimed quantities, water quality tests, costs, experiences and best practices. They conduct common water quality tests (such as turbidity, pH, etc., as determined by the teacher) to check the water quality before and after treatment.

Students create silver nanoparticles using a chemical process; however, since these particles are not observable to the naked eye, they use empirical evidence and reasoning to discover them. Students first look for evidence of a chemical reaction by mixing various solutions and observing any reactions that may occur. Students discover that copper and tannic acids from tea reduce silver nitrate, which in turn form silver. They complete the reaction, allow the water to evaporate, and observe the silver nanoparticles they created in plastic dishes using a stereo microscope. Students iterate on their initial process and test to see if they can improve the manufacturing process of silver nanoparticles.