This lesson goes over some basic elements of engineering and the paper making process. We will be using the circumference of a circle and conversions to program motors to make sure the dryer cans are going at the correct RPM's to ensure the paper machine functions correctly. This is a lesson that can be self taught or can be teacher led.

This task provides students the opportunity to make use of units to find the gas need (N-Q.1). The key point is for them to explain their choices. This task provides an opportunity for students to practice MP2, Reason abstractly and quantitatively, and MP3, Construct viable arguments and critique the reasoning of others.

The problem requires students to not only convert miles to kilometers and gallons to liters but they also have to deal with the added complication of finding the reciprocal at some point. In the USA we use distance per unit volume to measure fuel efficiency but in Europe we use volume per unit distance. Furthermore, the unit of distance is not simply 1 km but rather 100 km.

This is a challenging task, suitable for extended work, and reaching into a deep understanding of units. The task requires students to exhibit MP1, Make sense of problems and persevere in solving them. An algebraic solution is possible but complicated; a numerical solution is both simpler and more sophisticated, requiring skilled use of units and quantitative reasoning. Thus the task aligns with either A-CED.1 or N-Q.1, depending on the approach.

Pennies have a monetary face value of one cent, but they are made of material that has a market value that is usually different. It is the value of the materials that requires attention in this problem. While it is interesting to compare the face value with the value of the materials, this does not have any bearing on the calculations. Interference between these two notions of value is a possible area of difficulty for some students.

The purpose of this task is to engage students, probably working in groups, in a substantial and open-ended modeling problem. Students will have to brainstorm or research several relevant quantities, and incorporate these values into their solutions.

This task provides students with an opportunity to engage in Standard for Mathematical Practice 6, attending to precision. It intentionally omits some relevant information -- namely, that a typical soda can holds 12 oz of fluid, that a pound is equivalent to 16 dry ounces, and that an ounce of water weighs approximately 1.04 dry ounces (at the temperature of the human body) -- in the interest of having students discover that these are relevant quantities. The incompleteness of the problem statement makes the task more amenable to having students do work in groups.

This task is a modeling problem which ties in to financial decisions faced routinely by businesses, namely the balance between maintaining inventory and raising short-term capital for investment or re-investment in developing the busines

This task, while involving relatively simple arithmetic, codes to all three standards in this cluster, and also offers students a good opportunity to practice modeling (MP4), since they must attempt to make reasonable assumptions about the average length of vehicles in the traffic jam and the space between vehicles. Teachers can encourage students to compare their solutions with other students.

Unit Title: Urban Runoff and Its Impact on the Community and BeyondAuthor: Anthony Jordan, Franklin High School, Franklin Public SchoolsGrade Level: 9-12Context:  This unit of study combined mathematics, environmental science, and literacy while also incorporating a real world context. Students began the unit of study by looking at specific examples of environmental impacts of rainwater runoff and the contaminants they contain. In addition, students used these articles to build context knowledge and dive deeper through research on the reasons behind stormwater runoff, the systems in place, and solutions to solve this problem on a local, national, and global level. Afterwards students began to incorporate how to calculate the amount of stormwater runoff and utilized GIS and google earth to develop a deeper understanding of how to accurately calculate the area of impervious surfaces. Finally, students compared the amount of runoff calculated and were able to construct a project on how to address building a greener school. 

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.

While touring the central lab area at Verso Corporation, the environmental engineers gave an example of how they use mathematics within their job responsibilities. Verso is mandated to complete environmental reports showing they meet the state environmental standards. Often times when data is collected, it is not in the proper units that the state reports require. This was something that both the environmental engineer and co-op engineer were working on--properly converting rates that are specified for the reports. Students will experience finding unit rates and using conversion factors to convert measurements and rates into alternate units of measure.