This is the last problem of seven in a series about ratios set in the context of a classroom election. Since the number of voters is not known, the problem is quite abstract and requires a deep understanding of ratios and their relationship to fractions.

This is the first and most basic problem in a series of seven problems, all set in the context of a classroom election. Every problem requires students to understand what ratios are and apply them in a context. The problems build in complexity and can be used to highlight the multiple ways that one can reason about a context involving ratios.

This is the second in a series of tasks that are set in the context of a classroom election. It requires students to understand what ratios are and apply them in a context. The simple version of this question just asked how many votes each gets. This has the extra step of asking for the difference between the votes.

This problem, the third in a series of tasks set in the context of a class election, is more than just a problem of computing the number of votes each person receives. In fact, that isnŐt enough information to solve the problem. One must know how many votes it takes to make one half of the total number of votes. Although the numbers are easy to work with, there are enough steps and enough things to keep track of to lift the problem above routine.

This is the fourth in a series of tasks about ratios set in the context of a classroom election. What makes this problem interesting is that the number of voters is not given. This information isnŐt necessary, but at first glance some students may believe it is.

As the standards in statistics and probability unfold, students will not yet know the rules of probability for compound events. Thus, simulation is used to find an approximate answer to these questions. In fact, part b would be a challenge to students who do know the rules of probability, further illustrating the power of simulation to provide relatively easy approximate answers to wide-ranging problems.

In this activity, students participate in a series of timed relay races using their skeletal muscles. The compare the movement of skeletal muscle and relate how engineers help astronauts exercise skeletal muscles in space.

After students have complete the associated activity to collect and graph acceleration data from walking human subjects, they learn more about gait analysis---the study of human motion, which is used as biometric data for human medical diagnostics and (non-human) comparative biomechanics. They learn about the steps that comprise the universal process of engineering analysis—data collection, data analysis, mathematical modeling and reporting—and consider how these steps could be applied to analyze a person's gait, which prepares them to conduct the second associated activity.

This task is meant to be a straight-forward assessment task of graph reading and interpreting skills. This task helps reinforce the idea that when a variable represents time, t=0 is chosen as an arbitrary point in time and positive times are interpreted as times that happen after that.

Students observe and discuss a simple model of a wet scrubber to understand how this pollutant recovery method functions in cleaning industrial air pollution.

People use energy in all aspects of their lives for cooking, lighting and entertainment. Much of this energy use takes place in buildings, such as our homes. To save money and reduce the impact on our environment, many people are reducing their energy use. One way is to hire engineers to perform home energy audits to understand the ways we use energy and identify ways we can conserve energy. In this activity, students act as energy conservation engineers and identify the ways energy is conserved or wasted. They also learn many ways to personally conserve energy everyday.

Students use inclined planes as they recreate the difficult task of raising a monolith of rock to build a pyramid. They compare the push and pull of different-sized blocks up an inclined plane, determine the angle of inclination, and learn the changes that happen when the angle is increased or decreased.

This problem asks the student to evaluate six numerical expressions that contain the same integers and operations yet have differing results due to placement of parentheses. It helps students see the purpose of using parentheses.

This problem asks the student to evaluate three numerical expressions that contain the same integers yet have differing results due to placement of parentheses.

Students observe a model waterwheel to investigate the transformations of energy involved in turning the blades of a hydro-turbine. Students work as engineers to create model waterwheels while considering resources such as time and materials, in their design. Students also discuss and explore the characteristics of hydropower plants.

Students learn the history of the waterwheel and common uses for water turbines today. They explore kinetic energy by creating their own experimental waterwheel from a two-liter plastic bottle. They investigate the transformations of energy involved in turning the blades of a hydro-turbine into work, and experiment with how weight affects the rotational rate of the waterwheel. Students also discuss and explore the characteristics of hydroelectric plants.

Building on an introduction to statics, dynamics free-body diagrams, combustion and thermodynamics provided by the associated lesson, students design, construct and test their own rocket engines using sugar and potassium nitrate an opportunity to apply their knowledge of stoichiometry. This activity helps students understand that the energy required to launch a rocket comes from the chemical energy stored in the rocket fuel. The performance of each engine is tested during a rocket launch, after which students determine the reasons for the success or failure of their rockets.

Students discuss the characteristics of storms, including the relationship of weather fronts and storms. Using everyday materials, they develop models of basic lightning detection systems (similar to a Benjamin Franklin design) and analyze their models to determine their effectiveness as community storm warning systems.

In this unit, students learn the basics about weather and the atmosphere. They investigate materials engineering as it applies to weather and the choices available to us for clothing to counteract the effects of weather. Students have the opportunity to design and analyze combinations of materials for use in specific weather conditions. In the next lesson, students also are introduced to air masses and weather forecasting instrumentation and how engineers work to improve these instruments for atmospheric measurements on Earth and in space. Then, students learn the distinguishing features of the four main types of weather fronts that accompany high and low pressure air masses and how those fronts are depicted on a weather map. During this specific lesson, students learn different ways that engineers help with storm prediction, analysis and protection. In the final lesson, students consider how weather forecasting plays an important part in their daily lives by learning about the history of weather forecasting and how improvements in weather technology have saved lives by providing advance warning of natural disasters.

The principal purpose of the task is to explore a real-world application problem with algebra, working with units and maintaining reasonable levels of accuracy throughout.