Students learn about complex networks and how to use graphs to represent them. They also learn that graph theory is a useful part of mathematics for studying complex networks in diverse applications of science and engineering, including neural networks in the brain, biochemical reaction networks in cells, communication networks, such as the internet, and social networks. Students are also introduced to random processes on networks. An illustrative example shows how a random process can be used to represent the spread of an infectious disease, such as the flu, on a social network of students, and demonstrates how scientists and engineers use mathematics and computers to model and simulate random processes on complex networks for the purposes of learning more about our world and creating solutions to improve our health, happiness and safety.

This lesson will introduce students to environmental issues. Students will recognize environmental opinions and perspective, which will help them define themselves and others as either preservationists or conservationists. Students also learn about the importance of teamwork in engineering.

Student groups use the Java programming language to implement the algorithms for optical character recognition (OCR) that they developed in the associated lesson. They use different Java classes (provided) to test and refine their algorithms. The ultimate goal is to produce computer code that recognizes a digit on a scoreboard. Through this activity, students experience a very small part of what software engineers go through to create robust OCR methods. This software design lesson/activity set is designed to be part of a Java programming class.

In this 4-lesson unit, students identify, compare, and analyze attributes of two- and three-dimensional shapes, and develop geometric vocabulary. Students use basic linear measurement, understand and create scale representations, and explore perimeter and area measurement as they design their clubhouses. Activity sheets (pdf), lesson extensions and other commentary are provided.

This lesson helps students explore the functions of the kidney and its place in the urinary system. Students learn how engineers design instruments to help people when kidneys are not functioning properly or when environmental conditions change, such as kidney function in space.

In this lesson, students develop an understanding of the critical role communication plays in an engineer's life. Students create products to communicate their learning about the engineering role in the environment.

Through two lessons and five activities, students explore the structure and function of cell membranes. Specific transport functions, including active and passive transport, are presented. In the legacy cycle tradition, students are motivated with a Grand Challenge question. As they study the ingress and egress of particles through membranes, students learn about quantum dots and biotechnology through the concept of intracellular engineering.

Students are presented with a real-life problem as a challenge to investigate, research and solve. Specifically, they are asked to investigate why salt water helps a sore throat, and how engineers apply this understanding to solve other problems. Students read a medical journal article and listen to an audio talk by Dr. Z. L. Wang to learn more about quantum dots. After students reflect and respond to the challenge question, they conduct the associated activity to perform journaling and brainstorming.

Students journal their thoughts and responses to the questions associated with the grand challenge question presented in the associated lesson. For the Generate Ideas" step, they answer the questions: "What are your initial ideas about how this challenge can be answered? What background knowledge is needed? Have you tried this before?" After students have individually written responses to these questions, the class brainstorms together to reach consensus on the main ideas that need to be explored to solve the challenge question.

Students use a LEGO® ball shooter to demonstrate and analyze the motion of a projectile through use of a line graph. This activity involves using a method of data organization and trend observation with respect to dynamic experimentation with a complex machine. Also, the topic of line data graphing is covered. The main objective is to introduce students graphs in terms of observing and demonstrating their usefulness in scientific and engineering inquiries. During the activity, students point out trends in the data and the overall relationship that can be deduced from plotting data derived from test trials with the ball shooter.

This lesson focuses on the importance of airplanes in today's society. Airplanes of all shapes and sizes are used for hundreds of different reasons, including recreation, commercial business, public transportation, and delivery of goods, among many others. From transporting people to crop-dusting, our society and our economy have come to depend on airplanes. Students will discuss their own experiences with airplanes and learn more about the role of airplanes in our world.

The learning of linear functions is pervasive in most algebra classrooms. Linear functions are vital in laying the foundation for understanding the concept of modeling. This unit gives students the opportunity to make use of linear models in order to make predictions based on real-world data, and see how engineers address incredible and important design challenges through the use of linear modeling. Student groups act as engineering teams by conducting experiments to collect data and model the relationship between the wall thickness of the latex tubes and their corresponding strength under pressure (to the point of explosion). Students learn to graph variables with linear relationships and use collected data from their designed experiment to make important decisions regarding the feasibility of hydraulic systems in hybrid vehicles and the necessary tube size to make it viable.

In this 6-lesson unit students develop concepts of number, relationships between numbers, and equality. They make groups of 10 to 20 objects, connect number names to the groups, compose and decompose numbers, and use numerals to record the size of a group. Each lesson includes visual, auditory, and kinesthetic activities, as well as student activity sheets, questions for teachers and students, ideas for assessment and extensions, and links to electronic applets.

This 5-lesson unit is intended to help children who already understand the meanings of addition to develop fluency with addition facts. The activities and games take advantage of commutativity, the additive identity, doubles, and number patterns to develop operation sense and foster retention. Lessons include student materials, questions for students and teachers, assessment ideas, and links to interactive applets.

Students explore methods employing simple machines likely used in ancient pyramid building, as well as common modern-day material transportation. They learn about the wheel and axle as a means to transport materials from rock quarry to construction site. They also learn about different types and uses of a lever for purposes of transport. In an open-ended design activity, students choose from everyday materials to engineer a small-scale cart and lever system to convey pyramid-building materials.

Working as a team, students discover that the value of pi (3.1415926...) is a constant and applies to all different sized circles. The team builds a basic robot and programs it to travel in a circular motion. A marker attached to the robot chassis draws a circle on the ground as the robot travels the programmed circular path. Students measure the circle's circumference and diameter and calculate pi by dividing the circumference by the diameter. They discover the pi and circumference relationship; the circumference of a circle divided by the diameter is the value of pi.

The life sciences investigate the diversity, complexity, and interconnectedness of life on earth. Students are naturally drawn to examine living things, and as they progress through the grade levels, they become capable of understanding the theories and models that scientists use to explain observations of nature.

In this lesson, students learn about the physical properties of the Moon. They compare these to the properties of the Earth to determine how life would be different for astronauts living on the Moon. Using their understanding of these differences, they are asked to think about what types of products engineers would need to design for us to live comfortably on the Moon.

This activity is an experiment where students learn about angles of reflection and use that knowledge to reflect a light beam around obstacles to a target across the classroom.

Using the engineering design process,students will be designing and building a lantern that they will hypothetically be taking with them as they explore a newly discovered cave. The criteria of the completed lantern will include: hands need to be free for climbing, the lantern must have an on/off switch, it must point ahead when they are walking so they can see in the dark, and the lantern must be able to stay lit for at least 15 minutes. The constraints of the activity will be limited materials with which to build. At the completion of the activity, the students will present their final lantern to the class explaining how they revised and adapted the lantern to meet the criteria of the project. Students will include in the presentation the sketch of the model they created prior to building showing the labeled circuit they designed. This activity was one of numerous engineering lessons from the Virginia Children's Engineering Council geared towards Grades 1-5. http://www.childrensengineering.org/technology/designbriefs.php