The purpose of this task is to give students practice interpreting statements using function notation. It can be used as a diagnostic if students seem to be having trouble with function notation, for example interpreting f(x) as the product of f and x.

Students set up a simple way to indirectly observe and quantify the amount of respiration occurring in yeast-molasses cultures. Each student adds a small amount of baking yeast to a test tube filled with diluted molasses. A second, smaller test tube is then placed upside-down inside the solution. As the yeast cells respire, the carbon dioxide they produce is trapped inside the inverted test tube, producing a growing bubble of gas that is easily observed and measured. Students are presented with the procedure for designing an effective experiment; they learn to think critically about experimental results and indirect observations of experimental events.

I intend this book to be, firstly, a introduction to calculus based on the hyperreal number system. In other words, I will use infinitesimal and infinite numbers freely. Just as most beginning calculus books provide no logical justification for the real number system, I will provide none for the hyperreals. The reader interested in questions of foundations should consult books such as Abraham Robinson's Non-standard Analysis or Robert Goldblatt's Lectures on the Hyperreals. Secondly, I have aimed the text primarily at readers who already have some familiarity with calculus. Although the book does not explicitly assume any prerequisites beyond basic algebra and trigonometry, in practice the pace is too fast for most of those without some acquaintance with the basic notions of calculus.

This version of YAINTT has a particular emphasis on connections to cryptology. The cryptologic material appears in Chapter 4 and §§5.5 and 5.6, arising naturally (I hope) out of the ambient number theory. The main cryptologic applications – being the RSA cryptosystem, Diffie-Hellman key exchange, and the ElGamal cryptosystem – come out so naturally from considerations of Euler’s Theorem, primitive roots, and indices that it renders quite ironic G.H. Hardy’s assertion [Har05] of the purity and eternal inapplicability of number theory. Note, however, that once we broach the subject of these cryptologic algorithms, we take the time to make careful definitions for many cryptological concepts and to develop some related ideas of cryptology which have much more tenuous connections to the topic of number theory. This material therefore has something of a different flavor from the rest of the text – as is true of all scholarly work in cryptology (indeed, perhaps in all of computer science), which is clearly a discipline with a different culture from that of “pure”mathematics. Obviously, these sections could be skipped by an uninterested reader, or remixed away by an instructor for her own particular class approach.

In Yoga Minds, Writing Bodies, Christy Wenger argues for the inclusion of Eastern-influenced contemplative education within writing studies. She observes that, although we have "embodied" writing education in general by discussing the rhetorics of racialized, gendered, and disabled bodies, we have done substantially less to address the particular bodies that occupy our classrooms. She proposes that we turn to contemplative education practices that engages student bodies through fusing a traditional curriculum with contemplative practices including yoga, meditation, and the martial arts. Drawing strength from the recent "quiet revolution" (Zajonc) of contemplative pedagogy within postsecondary education and a legacy of field interest attributable to James Moffett, this project draws on case studies of first-year college writers to present contemplative pedagogy as a means of teaching students mindfulness of their writing and learning in ways that promote the academic, rhetorical work accomplished in first-year composition classes while at the same time remaining committed to a larger scope of a writer's physical and emotional well-being.

Students are introduced to the role of electricity and magnetism as they build speakers. They also explore the properties of magnets, create electromagnets, and determine the directions of magnetic fields. They conduct a scientific experiment and show cause-effect relationships by monitoring changes in the speaker's movement as the amount or the direction of the current change.

Students learn about archives and primary sources as they research original historical documents. While preparing an imaginative first-person account as if witnessing an historical event, they learn to appreciate the value of the first-person, eye-witness account and understand its limitations. 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.

Contamination in drinking water sources or watersheds can negatively affect the organisms that come in contact with it. The affects can be severe causing illness or, in some cases, even death. It is important for people to understand how they can contribute to the contaminants in drinking water and what treatment can be done to counter these harmful effects. Students will learn about the various methods developed by environmental engineers for treating drinking water in the United States.

Students will have to solve the real world problem of locker smell leakage by building an air filter that will cover the vents on the top of a locker. This project goes well with a curriculum on the particle nature of gases and phase changes.

This lesson introduces students to the concepts of evolution, specifically the evolution of humans. So often our students assume that humans are well adapted to our environments because we are in control of our evolutionary destiny. The goal is to change these types of misconceptions and get our students to link the concepts learned in their DNA, protein synthesis, and genetics units to their understanding of evolution. Students will also discover that humans are still evolving and learn about the traits that are more recent adaptations to our environment. The lesson is designed to take two one-hour class periods to complete. The activities will allow students to draw connections between environmental pressures and selected traits, both through data analysis and modeling. Most activities can be done without any special materials, although the Modeling Natural Selection activity needs either a tri-colored pasta, or tricolored beans, to be completed effectively.

The internet is full of catchy headlines and outrageous images, all to make us curious and get our attention. But kids don't usually realize: What you click on isn't always what you get. Show your students the best ways to avoid clickbait online.

This text is meant to be used in any first year College Composition class or as a general guide to college writing. The book focuses on writing as a process, not a product. The goal is to help students discover their own writing process, trying out different methods and strategies to find what works best for them.

In addition to the associated lesson, this activity functions as a summative assessment for the Using Stress and Strain to Detect Cancer unit. In this activity, students will create a 1-D strain plot in Microsoft Excel depicting the location of a breast tumor amidst healthy tissue. The results of this activity will function as proof of the accuracy and reliability of the students' breast cancer detection design.

This is a simple task touching on two key points of functions. First, there is the idea that not all functions have real numbers as domain and range values. Second, the task addresses the issue of when a function admits an inverse, and the process of "restricting the domain" in order to achieve an invertible function.

This textbook companion is a resource to help students successfully navigate through their first year at Kansas State University. It serves as part of the K-State First mission to create an outstanding university experience for every first-year student by helping with the transition to college-level learning and college life. The textbook helps improve chances for student success by focusing on fostering campus community, offering resources for diverse activities, highlighting academic expectations, and empowering students with personal responsibility and social agency. Instructors are encouraged to use the textbook in their K-State First classes, and it is also offered as a direct resource for students. In any university setting there are often unwritten rules that students are expected to understand, and this guide addresses and answers those questions directly. Ultimately, this guide encourages students to be engaged learners and to enjoy all facets of education, both inside and outside the classroom.

Teaching digital citizenship is all about helping kids think beyond themselves and recognize the ripple effects of their actions. Personal responsibility is important, but understanding their responsibilities to others can help kids unlock new ways to learn and connect with their communities -- and even change those communities for the better.

Students perform a macroinvertebrate survey to gauge the health of a local river. They collect water samples and count macroinvertebrates to learn how the health of a river's ecosystem can be determined by its river insect population.

The purpose of this activity is to demonstrate Newton's 3rd Law of Motion, which is the physical law that governs thrust in aircraft. The students will do several activities that show that for every action there is an equal and opposite reaction.

To explore different ways of using solar energy, students build a model solar water heater and determine how much it can heat water in a given amount of time. Solar water heaters work by solar radiation and convection.