Building on their fifth grade experiences with operations on decimal numbers, sixth grade students should find the task to be relatively easy. The emphasis here is on whether students are actually fluent with the computations, so teachers could use this as a formative assessment task if they monitor how students solve the problem.

In this lesson, students are introduced to both potential energy and kinetic energy as forms of mechanical energy. A hands-on activity demonstrates how potential energy can change into kinetic energy by swinging a pendulum, illustrating the concept of conservation of energy. Students calculate the potential energy of the pendulum and predict how fast it will travel knowing that the potential energy will convert into kinetic energy. They verify their predictions by measuring the speed of the pendulum.

Students observe and discuss a vacuum cleaner model of a baghouse to better understand how this pollutant recovery method functions in cleaning industrial air pollution.

Students are introduced to the correct technical vocabulary for lighting, which is different than layperson's terms. They learn about lamp (light bulb) technology and how to identify the various types of lighting in their spaces. They are also introduced to lighting controls as a means for saving energy- reducing costs, human energy consumption, and greenhouse gas emissions on the environment. Using an accompanying worksheet, students embark on a guided audit in which they survey the lighting in their classroom and identify the potential savings from using controls.

Students take a hands-on look at the design of bridge piers (columns). First they brainstorm types of loads that might affect a Colorado bridge. Then they determine the maximum possible load for that scenario, and calculate the cross-sectional area of a column designed to support that load. Choosing from clay, foam or marshmallows, they create model columns and test their calculations.

Students are introduced to the structure, function and purpose of locks and dams, which involves an introduction to Pascal's law, water pressure and gravity.

In this activity, students gain first-hand experience with the mechanical advantage of pulleys. Students are given the challenge of helping save a whale by moving it from an aquarium back to its natural habitat into the ocean. They set up different pulley systems, compare the theoretical and actual mechanical advantage of each and discuss their recommendations as a class.

The purpose of this lesson is to help students understand the relationship between the mass and the weight of an object. Students will study the properties of common materials and why airplanes use specific materials.

The application of engineering principles is explored in the creation of mobiles. As students create their own mobiles, they take into consideration the forces of gravity and convection air currents. They learn how an understanding of balancing forces is important in both art and engineering design.

The purpose of this task is for students to solve problems involving decimals in a context involving a concept that supports financial literacy, namely inflation.

Students find the volume and surface area of a rectangular box (e.g., a cereal box), and then figure out how to convert that box into a new, cubical box having the same volume as the original. As they construct the new, cube-shaped box from the original box material, students discover that the cubical box has less surface area than the original, and thus, a cube is a more efficient way to package things.

Students work in engineering teams to optimize cleaner energy solutions for cooking and heating in rural China. They choose between various options for heating, cooking, hot water, and lights and other electricity, balancing between the cost and health effects of different energy choices.

The purpose of this lesson is to introduce the students to the Sun. They explore various aspects of the Sun including its composition, its interior workings, and its relationship to the Earth.

In this unit, students learn the very basics of navigation, including the different kinds of navigation and their purposes. The concepts of relative and absolute location, latitude, longitude and cardinal directions are explored, as well as the use and principles of maps and a compass. Students discover the history of navigation and learn the importance of math and how it ties into navigational techniques. Understanding how trilateration can determine one's location leads to a lesson on the global positioning system and how to use a GPS receiver. The unit concludes with an overview of orbits and spacecraft trajectories from Earth to other planets.

Students follow the steps of the engineering design process while learning more about assistive devices and biomedical engineering applied to basic structural engineering concepts. Their engineering challenge is to design, build and test small-scale portable wheelchair ramp prototypes for fictional clients. They identify suitable materials and demonstrate two methods of representing design solutions (scale drawings and simple models or classroom prototypes). Students test the ramp prototypes using a weighted bucket; successful prototypes meet all the student-generated design requirements, including support of a predetermined weight.

Students use their knowledge of scales and areas to determine the best locations in Alabraska for the underground caverns. They cut out rectangular paper pieces to represent caverns to scale with the maps and place the cut-outs on the maps to determine feasible locations.

Students design and build their own model levees. Acting as engineers for their city, teams create sturdy barriers to prevent water from flooding a city in the event of a hurricane.

On the topic of energy related to motion, this summary lesson is intended to tie together the concepts introduced in the previous four lessons and show how the concepts are interconnected in everyday applications. A hands-on activity demonstrates this idea and reinforces students' math skills in calculating energy, momentum and frictional forces.

In this hands-on activity rolling a ball down an incline and having it collide into a cup the concepts of mechanical energy, work and power, momentum, and friction are all demonstrated. During the activity, students take measurements and use equations that describe these energy of motion concepts to calculate unknown variables, and review the relationships between these concepts.

The three tasks 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.