The three tasks (including part 1 and part 3) in this set are not examples of tasks asking students to compute using the standard algorithms for multiplication and division because most people know what those kinds of problems look like. Instead, these tasks show what kinds of reasoning and estimation strategies students need to develop in order to support their algorithmic computations.

Students use real-world data to calculate the potential for solar and wind energy generation at their school location. After examining maps and analyzing data from the online Renewable Energy Living Lab, they write recommendations as to the optimal form of renewable energy the school should pursue.

Students use real-world data to evaluate whether solar power is a viable energy alternative for several cities in different parts of the U.S. Working in small groups, they examine maps and make calculations using NREL/US DOE data from the online Renewable Energy Living Lab. In this exercise, students analyze cost and availability for solar power, and come to conclusions about whether solar power is a good solution for four different locations.

Students learn the concept of angular momentum and its correlation to mass, velocity and radius. They experiment with rotation and an object's mass distribution. In an associated literacy activity, students use basic methods of comparative mythology to consider why spinning and weaving are common motifs in creation myths and folktales.

Students explore whether rooftop gardens are a viable option for combating the urban heat island effect. Can rooftop gardens reduce the temperature inside and outside houses? Teams each design and construct two model buildings using foam core board, one with a "green roof" and the other with a black tar paper roof. They measure and graph the ambient and inside building temperatures while under heat lamps and fans. Then students analyze the data and determine whether the rooftop gardens are beneficial to the inhabitants.

Students use their knowledge about how healthy heart valves function to design, construct and implant prototype replacement mitral valves for hypothetical patients' hearts. Building on what they learned in the associated lesson about artificial heart valves, combined with the testing and scoring of their prototype heart valve designs in this activity, students discover the pros and cons of different types of artificial heart valves based on materials, surgery requirements, and lifespan.

The earliest explorers did not have computers or satellites to help them know their exact location. The most accurate tool developed was the sextant to determine latitude and longitude. In this activity, the sextant is introduced and discussed with the class. Students will learn how a sextant can be a reliable tool that is still being used by today's navigators and how computers can help assure accuracy when measuring angles. Also, this activity will show how computers can be used to understand equations even when knowing how to do the math is unknown.

Students investigate the critical nature of foundations as they learn differences between shallow and deep foundations, including the concepts of bearing pressure and settlement. Using models representing a shallow foundation and a deep pile foundation, they test, see and feel the effects in a cardboard box test bed composed of layers of pebbles, soil and sand. They also make bearing pressure calculations and recommendations for which type of foundations to use in various engineering scenarios.

Students learn about the major factors that comprise the design and construction cost of a modern bridge. Before a bridge design is completed, engineers provide overall cost estimates for construction of the bridge. Students learn about the components that go into estimating the total cost, including expenses for site investigation, design, materials, equipment, labor and construction oversight, as well as the trade-off between a design and its cost.

Through a five-lesson series with five activities, students are introduced to six simple machines inclined plane, wedge, screw, lever, pulley, wheel-and-axle as well as compound machines, which are combinations of two or more simple machines. Once students understand about work (work = force x distance), they become familiar with the machines' mechanical advantages, and see how they make work easier. Through an introduction to compound machines, students begin to think critically about machine inventions and their pervasive roles in our lives. After learning about Rube Goldberg contraptions absurd inventions that complete simple tasks in complicated ways they evaluate the importance and usefulness of the many machines around them. Through the hands-on activities, students draw designs for contraptions that could move a circus elephant into a rail car, create a construction site ramp design by measuring different inclined planes and calculating the ideal vs. actual mechanical advantage of each, compare the theoretical and actual mechanical advantages of different pulley systems conceived to save a whale, build and test grape catapults made with popsicle sticks and rubber bands, and follow the steps of the engineering design process to design and build Rube Goldberg machines.

Students examine collisions between two skateboards with different masses to learn about conservation of momentum in collisions.

Students learn about the strength of bones and methods of helping to mend fractured bones. During a class demonstration, a chicken bone is broken by applying a load until it reaches a point of failure (fracture). Then, working as biomedical engineers, students teams design their own splint or cast to help repair a fractured bone, learning about the strength of materials used.

Students learn about the variety of materials used by engineers in the design and construction of modern bridges. They also find out about the material properties important to bridge construction and consider the advantages and disadvantages of steel and concrete as common bridge-building materials to handle compressive and tensile forces.

Students culture cells in order to find out which type of surfactant (in this case, soap) is best at removing bacteria. Groups culture cells from unwashed hands and add regular bar soap, regular liquid soap, anti-bacterial soap, dishwasher soap, and hand sanitizer to the cultures. The cultures are allowed to grow for two days and then the students assess which type of soap design did the best job of removing bacteria cells from unwashed hands. Students extend their knowledge of engineering and surfactants for different environmental applications.

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.

Through a series of activities, students discover that the concept of mechanical advantage describes reality fairly well. They act as engineers creating a design for a ramp at a construction site by measuring four different inclined planes and calculating the ideal mechanical advantage versus the actual mechanical advantage of each. Then, they use their analysis to make recommendations for the construction site.

In this activity, students will learn how to read a topographical map and how to triangulate with just a map. True triangulation requires both a map and compass, but to simplify the activity and make it possible indoors, the compass information is given. Students will practice converting a compass measurement to a protractor measurement, as well as reverse a bearing direction (i.e., if they know a tree's bearing is 100 degrees from you, they can determine what bearing they are from the tree). Students will use the accompanying worksheets to take a bearing of certain landmarks and then start at those landmarks to work backwards to figure out where they are.

In this activity, students will learn how to actually triangulate using a compass, topographical (topo) map and view of outside landmarks. It is best if a field trip to another location away from school is selected. The location should have easily discernable landmarks (like mountains or radio towers) and changes in elevation (to illustrate the topographical features) to enhance the activity. A national park is an ideal location, and visiting a number of parks, especially parks with hiking trails, is especially beneficial.

Student teams use the engineering design process to create a useful product of their choice out of recyclable items and "trash." The class is given a "landfill" of reusable items, such as aluminum cans, cardboard, paper, juice boxes, chip bags, egg cartons, milk cartons, etc., and each group is allowed a limited amount of bonding materials, such as duct tape, hot glue and string. This activity addresses the importance of reuse and encourages students to look at ways they can reuse items they would otherwise throw away.