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 examine different types of fabric and their characteristics. Using magnifying glasses and sandpaper, they test and observe the weave and wear quality of fabric samples. By comparing the qualities of different fabrics they come to understand why so many different types of fabric exist and are able to recognize or suggest different uses for them.

In small groups, students experiment and observe the similarities and differences between human-made objects and objects from nature. They compare the function and structure of hollow bones with drinking straws, bird beaks, tool pliers, bat wings and airplane wings. Observations are recorded in a compare & contrast chart, and then shared in a classroom discussion, along with follow up assessment activities such as journal writing and Venn diagrams.

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.

Computer science is the study of computational systems and their use in representing important problems in science and society. Major topics include computational science, software systems, network systems, theory of computation, machine learning, and human-computer interaction.

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.

In this lesson, students find their location on a map using Latitude and Longitudinal coordinates. They determine where they should go to be rescued and how best to get there.

Students gain experience with the software/system design process, closely related to the engineering design process, to solve a problem. First, they learn about the Mars Curiosity rover and its mission, including the difficulties that engineers must consider and overcome to operate a rover remotely. Students observe a simulation of a robot being controlled remotely. These experiences guide discussion on how the design process is applied in these scenarios. The lesson culminates in a hands-on experience with the design process as students simulate the remote control of a rover. In the associated activity, students gain further experience with the design process by creating an Android application using App Inventor to control one aspect of a remotely controlled vehicle. (Note: The lesson requires a LEGO® MINDSTORMS® Education NXT base set.)

Students perform DNA forensics using food coloring to enhance their understanding of DNA fingerprinting, restriction enzymes, genotyping and DNA gel electrophoresis. They place small drops of different food coloring ("water-based paint") on strips of filter paper and then place one paper strip end in water. As water travels along the paper strips, students observe the pigments that compose the paint decompose into their color components. This is an example of the chromatography concept applied to DNA forensics, with the pigments in the paint that define the color being analogous to DNA fragments of different lengths.

Students conduct Internet research to investigate the purpose and current functioning status of some of the largest dams throughout the world. They investigate the success or failure of eight dams and complete a worksheet. While researching the dams, they also gain an understanding of the scale of these structures by recording and comparing their reservoir capacities. Students come to understand that dams, like all engineered structures, have a finite lifespan and require ongoing maintenance and evaluation for their usefulness.

Education in a free society must prepare citizens to make informed choices in all areas of their lives. They must be able to grasp the information being presented, analyze it, and make reasoned decisions. To accomplish these goals, students learn to collect, organize, and display relevant data to answer questions that can be addressed with data; use appropriate statistical methods and predictions that are based on data; develop and evaluate inferences and predictions that are based on data; and apply basic concepts of probability. Probability is the study of chance and the possibility that an event will occur.

Students learn about and practice converting between fractions, decimals and percentages. Using a LEGO® MINDSTORMS® NXT robot and a touch sensor, each group inputs a fraction of its choosing. Team members convert this same fraction into a decimal, and then a percentage via hand calculations, and double check their work using the NXT robot. Then they observe the robot moving forward and record that distance. Students learn that the distance moved is a fraction of the full distance, based on the fraction that they input, so if they input ½, the robot moves half of the original distance. From this, students work backwards to compute the full distance. Groups then compete in a game in which they are challenged to move the robot as close as possible to a target distance by inputting a fraction into the NXT bot.

In this first part of a two-part lab activity, students use triple balance beams and graduated cylinders to take measurements and calculate the densities of several common, irregularly shaped objects with the purpose to resolve confusion about mass and density. After this activity, conduct the associated Density Column Lab - Part 2 activity before presenting the associated Density & Miscibility lesson for discussion about concepts that explain what students have observed.

Concluding a two-part lab activity, students use triple balance beams and graduated cylinders to take measurements and calculate densities of several household liquids and compare them to the densities of irregularly shaped objects (as determined in Part 1). Then they create density columns with the three liquids and four solid items to test their calculations and predictions of the different densities. Once their density columns are complete, students determine the effect of adding detergent to the columns. After this activity, present the associated Density & Miscibility lesson for a discussion about why the column layers do not mix.

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.

Students acquire a basic understanding of the science and engineering of space travel as well as a brief history of space exploration. They learn about the scientists and engineers who made space travel possible and briefly examine some famous space missions. Finally, they learn the basics of rocket science (Newton's third law of motion), the main components of rockets and the U.S. space shuttle, and how engineers are involved in creating and launching spacecraft.

Students are introduced to detail drawings and the importance of clearly documenting and communicating their designs. They are introduced to the American National Standards Institute (ANSI) Y14.5 standard, which controls how engineers communicate and archive design information. They are introduced to standard paper sizes and drawing view conventions, which are major components of the Y14.5 standard.

Students disassemble and analyze retractable pens. Through the process of "reverse engineering," they learn how the ink pens work.

Students discover the mathematical constant phi, the golden ratio, through hands-on activities. They measure dimensions of "natural objects"—a star, a nautilus shell and human hand bones—and calculate ratios of the measured values, which are close to phi. Then students learn a basic definition of a mathematical sequence, specifically the Fibonacci sequence. By taking ratios of successive terms of the sequence, they find numbers close to phi. They solve a squares puzzle that creates an approximate Fibonacci spiral. Finally, the instructor demonstrates the rule of the Fibonacci sequence via a LEGO® MINDSTORMS® NXT robot equipped with a pen. The robot (already created as part of the companion activity, The Fibonacci Sequence & Robots) draws a Fibonacci spiral that is similar to the nautilus shape.

Students explore the concept of optical character recognition (OCR) in a problem-solving environment. They research OCR and OCR techniques and then apply those methods to the design challenge by developing algorithms capable of correctly "reading" a number on a typical high school sports scoreboard. Students use the structure of the engineering design process to guide them to develop successful algorithms. In the associated activity, student groups implement, test and revise their algorithms. This software design lesson/activity set is designed to be part of a Java programming class.