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...

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.

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

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.

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.

Students learn about frequency and period, particularly natural frequency using springs. They learn that the natural frequency of a system depends on two things: the stiffness and mass of the system. Students see how the natural frequency of a structure plays a big role in the building surviving an earthquake or high winds.

This article provides background information related to natural resources of the poles, and renewable and non-renewable energy.

In this lesson, students will identify the Earth's natural resources and classify them as renewable or non-renewable. They will simulate the distribution of resources and discuss the fairness and effectiveness of the distribution. Students will identify ways that they use and waste natural resources, and they will explore ways that engineers interact with natural resources.

This activity uses a cultural story to excite kinesthetic homework, nature journaling and daily adventure in a child's own back yard or kitchen flower pot.

This activity is a classroom lesson on how a slinky relates to sound waves and how sound waves relate to the human ear.

Students will follow the scientific method for self discovery of the nature of the land around the school to then determine as a class what plants and grasses would flourish in the area.

In this activity, students explore the importance of charts to navigation on bodies of water. Using one worksheet, students learn to read the major map features found on a real nautical chart. Using another worksheet, students draw their own nautical chart using the symbols and identifying information learned.

For thousands of years, navigators have looked to the sky for direction. Today, celestial navigation has simply switched from using natural objects to human-created satellites. A constellation of satellites, called the Global Positioning System, and hand-held receivers allow for very accurate navigation. In this lesson, students investigate the fundamental concepts of GPS technology trilateration and using the speed of light to calculate distances.

This task applies geometric concepts, namely properties of tangents to circles and of right triangles, in a modeling situation. The key geometric point in this task is to recognize that the line of sight from the mountain top towards the horizon is tangent to the earth. We can then use a right triangle where one leg is tangent to a circle and the other leg is the radius of the circle to investigate this situation.

This learning strategy provides discussion and visualizations of the neuron and its function, as well as components and functions of different parts of the nervous system, including the human brain.

This collection uses primary sources to explore the New Woman ideal. Digital Public Library of America Primary Source Sets are designed to help students develop their critical thinking skills and draw diverse material from libraries, archives, and museums across the United States. Each set includes an overview, ten to fifteen primary sources, links to related resources, and a teaching guide. These sets were created and reviewed by the teachers on the DPLA's Education Advisory Committee.

This activity illustrates the interrelationship between science and engineering in the context of extinction prevention. There are two parts to the activity. The first part challenges students to think like scientists as they generate reports on endangered species and give presentations worthy of a news channel or radio broadcast. The second part puts students in the shoes of engineers, designing ways to help the endangered species.

In this Interactive Lecture Demonstration, students will attempt to predict the content of articles on the Health Science pages of French newspapers by reading headlines. They then read the actual articles and reflect on the actual content of the news articles.