This problem provides students with an opportunity to discover algebraic structure in a geometric context. More specifically, the student will need to divide up the given polygons into triangles and then use the fact that the sum of the angles in each triangle is 180_.

Parts (d) and (e) of this task constitute a very advanced application of the skill of making use of structure: in (d) students are being asked to use the defining property of even and odd functions to manipulate expressions involving function notation. In (e) they are asked to see the structure in the system of two equations involving functions.

The intent of this problem is to have students think about how function addition works on a fundamental level, so formulas have been omitted on purpose.

Use this hands-on activity to demonstrate rotational inertia, rotational speed, angular momentum, and velocity. Students build at least two simple spinners to conduct experiments with different mass distributions and shapes, as they strive to design and build the spinner that spins the longest.

In an activity that integrates science and art, students see, experience and harness the phenomenon of surface tension as they create beautiful works of art. Students conduct two experiments related to surface tension floating objects on the surface of water and creating original artwork using floating inks. They also learn historical and cultural information through an introduction to the ancient Japanese art form of suminagashi. They take the topic a step further by discussing how an understanding of surface tension can be applied to solve real-world engineering problems and create useful inventions.

This lesson introduces the concepts of longitudinal and transverse waves. Students see several demonstrations of waves and characterize them by transverse and longitudinal behavior. This lesson also introduces the Sunken Treasure theme of the Sound and Light unit a continuous story line throughout the lessons.

Students use a table-top-sized tsunami generator to observe the formation and devastation of a tsunami. They see how a tsunami moves across the ocean and what happens when it reaches the continental shelf. Students make villages of model houses and buildings to test how different material types are impacted by the huge waves. They further discuss how engineers design buildings to survive tsunamis. Much of this activity setup is the same as for the Mini-Landscape activity in Lesson 4 of the Natural Disasters unit.

The purpose of this task is to address the concept of opportunity cost through a real world context involving money.

This task asks students to determine a recursive process from a context. Students who study computer programming will make regular use of recursive processes.

In his book, MacKay explores our population's addiction to fossil fuels and the problems faced with sustainability. Two issues faced with fossil fuels are they will eventually run out and they are harming our environment during use. McKay does not give one simple solution to the problem, but contrast various advanced technologies and how they may be applied to improve our environment and sustainability. More information may be found at http://www.withouthotair.com/.

Using a household fan, cardboard box and paper towels, student teams design and build their own evaporative cooler prototype devices. They learn about the process that cools water during the evaporation of water. They make calculations to determine a room's cooling load, and thus determine the swamp cooler size. This activity adds to students' understanding of the behind-the-scenes mechanical devices that condition and move air within homes and buildings for human health and comfort.

In this activity, learners use a chemical reaction to visualize where moisture forms on the body. Learners use the Minor's iodine-starch test, a diagnostic test that doctors use to detect hyperhidrosis (excessive sweating), to identify where moisture is forming. Learners also use this method to test the effectiveness of different antiperspirants.

When manatees were first seen by Columbus, he thought they were mermaids..but he had been at sea for a long time! Today these gentle marine mammals are threatened by loss of habitat and collisions with boats. This video segment explores the endangered manatees of Florida and their struggle to survive, as well as some of the people who are working to save them. Please see the accompanying lesson plan for educational objectives, discussion points and classroom activities.

Students examine the motion of pendulums and come to understand that the longer the string of the pendulum, the fewer the number of swings in a given time interval. They see that changing the weight on the pendulum does not have an effect on the period. They also observe that changing the angle of release of the pendulum has negligible effect upon the period.

This activity demonstrates how potential energy (PE) can be converted to kinetic energy (KE) and back again. Given a pendulum height, students calculate and predict how fast the pendulum will swing by understanding conservation of energy and using the equations for PE and KE. The equations are justified as students experimentally measure the speed of the pendulum and compare theory with reality.

This activity shows students the engineering importance of understanding the laws of mechanical energy. More specifically, it demonstrates how potential energy can be converted to kinetic energy and back again. Given a pendulum height, students calculate and predict how fast the pendulum will swing by using the equations for potential and kinetic energy. The equations will be justified as students experimentally measure the speed of the pendulum and compare theory with reality.

Students experientially learn about the characteristics of a simple physics phenomenon the pendulum by riding on playground swings. They use pendulum terms and a timer to experiment with swing variables. They extend their knowledge by following the steps of the engineering design process to design timekeeping devices powered by human swinging.

In this hands-on activity, students construct a simple switch and determine what objects and what types of materials can be used to close a switch in a circuit and light a light bulb.

Students are directed to read through a Web-based tutorial on Symmetry and Tilings in the form of an short and colorful article entitled Tilings and Tesselations; afterwards, they answer several questions on tilings (tessellations), tiling terminology, types of symmetry (isometries), periodic tilings and Penrose tilings.

The goal of this task is to help students understand the commutative property of addition by examining the addition facts for single digit numbers. This is important as it gives students a chance, at a young age, to do more than memorize these arithmetic facts which they will use throughout their education.