In some textbooks, a distinction is made between a ratio, which is …

In some textbooks, a distinction is made between a ratio, which is assumed to have a common unit for both quantities, and a rate, which is defined to be a quotient of two quantities with different units (e.g. a ratio of the number of miles to the number of hours). No such distinction is made in the common core and hence, the two quantities in a ratio may or may not have a common unit. However, when there is a common unit, as in this problem, it is possible to add the two quantities and then find the ratio of each quantity with respect to the whole (often described as a part-whole relationship).

Students use real-world data to evaluate whether solar power is a viable …

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 explore whether rooftop gardens are a viable option for combating the …

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 learn about how engineers design and build shake tables to test …

Students learn about how engineers design and build shake tables to test the ability of buildings to withstand the various types of seismic waves generated by earthquakes. Just like engineers, students design and build shake tables to test their own model buildings made of toothpicks and mini marshmallows. Once students are satisfied with the performance of their buildings, they put them through a one-minute simulated earthquake challenge.

This lesson unit is intended to help teachers assess how well students …

This lesson unit is intended to help teachers assess how well students are able to solve a real-world modeling problem. There are several correct approaches to the problem, including some that involve proportional relationships.

Students learn about the major factors that comprise the design and construction …

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.

Student teams use the engineering design process to create a useful product …

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.

This is the first and most basic problem in a series of …

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 …

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 …

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 …

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.

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