This is a task from the Illustrative Mathematics website that is one part of a complete illustration of the standard to which it is aligned. Each task has at least one solution and some commentary that addresses important asects of the task and its potential use. Here are the first few lines of the commentary for this task: For this task, the letter $i$ denotes the imaginary unit, that is, $i=\sqrt{-1}$. For each integer $k$ from 0 to 8, write $i^k$ in the form $a+bi$. Des...

This is a task from the Illustrative Mathematics website that is one part of a complete illustration of the standard to which it is aligned. Each task has at least one solution and some commentary that addresses important asects of the task and its potential use. Here are the first few lines of the commentary for this task: Let $z = 1 + i$ where $i^2 = -1$. Calculate $z^2, z^3,$ and $z^4$. Graph $z, z^2, z^3,$ and $z^4$ in the complex plane. What do you notice about the po...

Have you ever seen a problem and wanted to do something about it? Of course you have. The schools, police, government welfare offices, churches and families aren’t handling it. Others share your concerns and want to do something. That’s why you would start a nongovernmental organization, or NGO. This handbook will guide you through the steps of starting and operating an NGO.

This is a task from the Illustrative Mathematics website that is one part of a complete illustration of the standard to which it is aligned. Each task has at least one solution and some commentary that addresses important asects of the task and its potential use. Here are the first few lines of the commentary for this task: A small company wants to give raises to their 5 employees. They have $10,000 available to distribute. Imagine you are in charge of deciding how the rai...

This is a task from the Illustrative Mathematics website that is one part of a complete illustration of the standard to which it is aligned. Each task has at least one solution and some commentary that addresses important aspects of the task and its potential use.

This is a task from the Illustrative Mathematics website that is one part of a complete illustration of the standard to which it is aligned. Each task has at least one solution and some commentary that addresses important asects of the task and its potential use. Here are the first few lines of the commentary for this task: Three students disagree about what value to assign to the expression $0^0$. In each case, critically analyze the student's argument. Juan suggests that...

This is a task from the Illustrative Mathematics website that is one part of a complete illustration of the standard to which it is aligned. Each task has at least one solution and some commentary that addresses important asects of the task and its potential use. Here are the first few lines of the commentary for this task: Below is a picture of the (elliptical) orbit of a planet around the sun: The sun is at point $A$, point $P$ is where the planet is closest to the sun d...

This activity helps students understand how a motor in a LEGO MINDSTORMS(TM) NXT robot uses electricity produced by the battery to move a robot to do useful work in the form of throwing a ball. Students relate the concepts of electricity and battery to the movement of the LEGO NXT motor and connected links.

This self-paced course is based on the Nahuatl variant from the Huasteca of Veracruz that is spoken in Chicontepec, Veracruz, Mexico. The principal aim of this course is to develop the student’s oral, written, and comprehension abilities primarily through the study of grammar, listening, and reading. The intended audience for this pedagogical resource is foreign students interested in developing their language skills, as well as native teachers in bilingual schools in the Chicontepec region.

Student pairs experience the iterative engineering design process as they design, build, test and improve catching devices to prevent a "naked" egg from breaking when dropped from increasing heights. To support their design work, they learn about materials properties, energy types and conservation of energy. Acting as engineering teams, during the activity and competition they are responsible for design and construction planning within project constraints, including making engineering modifications for improvement. They carefully consider material choices to balance potentially competing requirements (such as impact-absorbing and low-cost) in the design of their prototypes. They also experience a real-world transfer of energy as the elevated egg's gravitational potential energy turns into kinetic energy as it falls and further dissipates into other forms upon impact. Pre- and post-activity assessments and a scoring rubric are provided. The activity scales up to district or regional egg drop competition scale. As an alternative to a ladder, detailed instructions are provided for creating a 10-foot-tall egg dropper rig.

Given an assortment of unknown metals to identify, student pairs consider what unique intrinsic (aka intensive) metal properties (such as density, viscosity, boiling or melting point) could be tested. For the provided activity materials (copper, aluminum, zinc, iron or brass), density is the only property that can be measured so groups experimentally determine the density of the "mystery" metal objects. They devise an experimental procedure to measure mass and volume in order to calculate density. They calculate average density of all the pieces (also via the graphing method if computer tools area available). Then students analyze their own data compared to class data and perform error analysis. Through this inquiry-based activity, students design their own experiments, thus experiencing scientific investigation and experimentation first hand. A provided PowerPoint(TM) file and information sheet helps to introduce the five metals, including information on their history, properties and uses.

Informed by a writing philosophy that values both spontaneity and discipline, Michelle Bonczek Evory’s Naming the Unnameable: An Approach to Poetry for New Generations offers practical advice and strategies for developing a writing process that is centered on play and supported by an understanding of America’s rich literary traditions. With consideration to the psychology of invention, Bonczek Evory provides students with exercises aimed to make writing in its early stages a form of play that gives way to more enriching insights through revision, embracing the writing of poetry as both a love of language and a tool that enables us to explore ourselves and better understand the world. The volume includes resources for students seeking to publish and build a writing-centered lifestyle or career. Poets featured range in age, subject, and style, and many are connected to colleges in the State University of New York system. Naming the Unnameable promotes an understanding of poetry as a living art of which students are a part, and provides ways for students to involve themselves in the growing contemporary poetry community that thrives in America today.

The goal of this task is to show that when the whole is not specified, which fraction is being represented is left ambiguous.

Through two lessons and four activities, students learn about nanotechnology, its extreme smallness, and its vast and growing applications in our world. Embedded within the unit is a broader introduction to the field of material science and engineering and its vital role in nanotechnology advancement. Engaging mini-lab activities on ferrofluids, quantum dots and gold nanoparticles introduce students to specific fields within nanoscience and help them understand key concepts as the basis for thinking about engineering and everyday applications that use next-generation technology nanotechnology.

Watson and Crick noted that the size of a viral genome was insufficient to encode a protein large enough to encapsidate it and reasoned, therefore that a virus shell must be composed of multiple, but identical subunits. Today, high resolution structures of virus capsids reveal the basis of this genetic economy as a highly symmetrical structure, much like a geodesic dome composed of protein subunits. Crystallographic structures and cryo-electron microscopy reconstructions combined with molecular data are beginning to reveal how these nano-structures are built. Topics covered in the course will include basic principles of virus structure and symmetry, capsid assembly, strategies for enclosing nucleic acid, proteins involved in entry and exit, and the life cycles of well understood pathogens such as HIV, influenza, polio, and Herpes. A review of cutting edge structural methods is also covered.

This course focuses on the latest scientific developments and discoveries in the field of nanomechanics, the study of forces and motion on extremely tiny (10-9 m) areas of synthetic and biological materials and structures. At this level, mechanical properties are intimately related to chemistry, physics, and quantum mechanics. Most lectures will consist of a theoretical component that will then be compared to recent experimental data (case studies) in the literature. The course begins with a series of introductory lectures that describes the normal and lateral forces acting at the atomic scale. The following discussions include experimental techniques in high resolution force spectroscopy, atomistic aspects of adhesion, nanoindentation, molecular details of fracture, chemical force microscopy, elasticity of single macromolecular chains, intermolecular interactions in polymers, dynamic force spectroscopy, biomolecular bond strength measurements, and molecular motors.

Student teams learn how water filtration systems that use nanoparticles and nanotechnology can remove organic compounds from water. First they learn about the role nanoparticles play in water filtration. Then they are introduced to the basics of nanoparticles and nanotechnology, focusing on the impacts and benefits this innovative technology has on our daily lives. Using methylene blue and methyl orange solutions, students test for the efficiency of photocatalytic nanoparticles to sanitize water. They expose a solution sample of water and methyl orange (the microbe indicator) with their newly-made water sanitation filters under UV light (sunlight) to activate the photocatalytic properties of three specific nanoparticles. They visually compare them with control samples to determine the best photocatalytic nanoparticle to sanitize water.

Students apply the knowledge gained from the previous lessons and activities in this unit to write draft grant proposals to the U.S. National Institutes of Health outlining their ideas for proposed research using nanoparticles to protect against, detect or treat skin cancer. Through this exercise, students demonstrate their understanding of the environmental factors that contribute to skin cancer, the science and mathematics of UV radiation, the anatomy of human skin, current medical technology applications of nanotechnology and the societal importance of funding research in this area, as well as their communication skills in presenting plans for specific nanoscale research they would conduct using nanoparticles.

Through a scavenger hunt, students are introduced to the world of nanotechnology. In the form of a competition, groups race to locate symbols that correlate to an answer to a general nanotechnology question. Each team receives paper slips with questions; the remaining questions are hidden behind QR codes. Groups need to answer eight total questions in the correct order. Because this is an intro to nanotechnology and its associated engineering, students need to use problem-solving skills in order to identify the correct answers. After the initial scavenger hunt, a brief class discussion explores advances in nanotechnology. Next, students work in teams to research different areas of nanotechnology as they create their own scavenger hunt games.

Students learn about the biomedical use of nanoparticles in the detection and treatment of cancer, including the use of quantum dots and lasers that heat-activate nanoparticles. They also learn about electrophoresis a laboratory procedure that uses an electric field to move tiny particles through a channel in order to separate them by size. They complete an online virtual mini-lab, with accompanying worksheet, to better understand gel electrophoresis. This prepares them for the associated activity to write draft research proposals to use nanoparticles to protect against, detect or treat skin cancer.