The purpose of the task is to show students a situation where squaring both sides of an equation can result in an equation with more solutions than the original one. The reason for this is that it is possible to have two unequal numbers whose squares are equal.

The purpose of this task is to provide an opportunity for students to reason about equivalence of equations. The instruction to give reasons that do not depend on solving the equation is intended to focus attention on the transformation of equations as a deductive step.

Students learn about electricity and air pollution while building devices to measure volatile organic compounds (VOC) by attaching VOC sensors to prototyping boards. In the second part of the activity, students evaluate the impact of various indoor air pollutants using the devices they made.

This lesson unit is intended to help teachers assess how well students are able to solve quadratics in one variable. In particular, the lesson will help teachers identify and help students who have the following difficulties: making sense of a real life situation and deciding on the math to apply to the problem; solving quadratic equations by taking square roots, completing the square, using the quadratic formula, and factoring; and interpreting results in the context of a real life situation.

This lesson unit is intended to help teachers assess how well students are able to: recognize the differences between equations and identities; substitute numbers into algebraic statements in order to test their validity in special cases; resist common errors when manipulating expressions such as 2(x Đ 3) = 2x Đ 3; (x + 3)_ = x_ + 3_; and carry out correct algebraic manipulations. It also aims to encourage discussion on some common misconceptions about algebra.

Using a household fan, cardboard box and paper towels, student teams design and build their own evaporative cooler prototype devices. They learn about the process that cools water during the evaporation of water. They make calculations to determine a room's cooling load, and thus determine the swamp cooler size. This activity adds to students' understanding of the behind-the-scenes mechanical devices that condition and move air within homes and buildings for human health and comfort.

In this activity, students learn about creating a design directly from a CAD (computer-aided design) program. They will design a tower in CAD and manufacture the parts with a laser cutter. A competition determines the tower design with the best strength:weight ratio. Students also investigate basic structural truss concepts and stress concentrations. Partnership with a local college or manufacturing center is necessary for the completion of this project.

Students learn about the water cycle and its key components. First, they learn about the concept of a watershed and why it is important in the context of engineering hydrology. Then they learn how we can use the theory of conservation of mass to estimate the amount of water that enters a watershed (precipitation, groundwater flowing in) and exits a watershed (evaporation, runoff, groundwater out). Finally, students learn about runoff and how we visualize runoff in the form of hydrographs.

In addition to the associated lesson, this activity functions as a summative assessment for the Using Stress and Strain to Detect Cancer unit. In this activity, students will create a 1-D strain plot in Microsoft Excel depicting the location of a breast tumor amidst healthy tissue. The results of this activity will function as proof of the accuracy and reliability of the students' breast cancer detection design.