This is a task from the Illustrative Mathematics website that is one part of a complete illustration of the standard to which it is aligned. Each task has at least one solution and some commentary that addresses important asects of the task and its potential use. Here are the first few lines of the commentary for this task: The following is a student solution to the inequality \frac{5}{18} - \frac{x-2}{9} \leq \frac{x-4}{6}. \begin{align} \frac{5}{18} - \frac{x-2}{9} & \le...

At this point in the unit, students have learned about Pascal's law, Archimedes' principle, Bernoulli's principle, and why above-ground storage tanks are of major concern in the Houston Ship Channel and other coastal areas. In this culminating activity, student groups act as engineering design teams to derive equations to determine the stability of specific above-ground storage tank scenarios with given tank specifications and liquid contents. With their floatation analyses completed and the stability determined, students analyze the tank stability in specific storm conditions. Then, teams are challenged to come up with improved storage tank designs to make them less vulnerable to uplift, displacement and buckling in storm conditions. Teams present their analyses and design ideas in short class presentations.

A collection of relevant lessons to supplement your units in Algebra I/II. Mix these lessons into your course to show students the algebraic reasoning behind social issues, public health, the environment, business, sports, and more.

Bernoulli's principle relates the pressure of a fluid to its elevation and its speed. Bernoulli's equation can be used to approximate these parameters in water, air or any fluid that has very low viscosity. Students learn about the relationships between the components of the Bernoulli equation through real-life engineering examples and practice problems.

In this activity, students examine how different balls react when colliding with different surfaces. Also, they will have plenty of opportunity to learn how to calculate momentum and understand the principle of conservation of momentum.

Students observe Pascal's law, Archimedes' principle and the ideal gas law as a Cartesian diver moves within a closed system. The Cartesian diver is neutrally buoyant and begins to sink when an external pressure is applied to the closed system. A basic explanation and proof of this process is provided in this activity, and supplementary ideas for more extensive demonstrations and independent group activities are presented.

Students investigate the property dependence between concentrations and boiling point. In section 1, students first investigate the boiling point of various liquid solutions. In section 2, they analyze data collected by the entire class to generate two boiling point curves, one for salt solutions and one for sugar solutions. Finally, in section 3, students use the data they have analyzed to determine how to create a solution that has a particular boiling point and is a cost-effective design.

Students teams design and build shoe prototypes that convert between high heels and athletic shoes. They apply their knowledge about the mechanics of walking and running as well as shoe design (as learned in the associated lesson) to design a multifunctional shoe that is both fashionable and functional.

The students discover the basics of heat transfer in this activity by constructing a constant pressure calorimeter to determine the heat of solution of potassium chloride in water. They first predict the amount of heat consumed by the reaction using analytical techniques. Then they calculate the specific heat of water using tabulated data, and use this information to predict the temperature change. Next, the students will design and build a calorimeter and then determine its specific heat. After determining the predicted heat lost to the device, students will test the heat of solution. The heat given off by the reaction can be calculated from the change in temperature of the water using an equation of heat transfer. They will compare this with the value they predicted with their calculations, and then finish by discussing the error and its sources, and identifying how to improve their design to minimize these errors.

This lesson unit is intended to help teachers assess how well students are able to use linear inequalities to create a set of solutions. In particular, the lesson will help teachers identify and assist students who have difficulties in: representing a constraint by shading the correct side of the inequality line; and understanding how combining inequalities affects a solution space.

Students investigate circuits and their components by building a basic thermostat. They learn why key parts are necessary for the circuit to function, and alter the circuit to optimize the thermostat temperature range. They also gain an awareness of how electrical engineers design circuits for the countless electronic products in our world.

Students are presented with a hypothetical scenario that delivers the unit's Grand Challenge Question: To apply an understanding of nanoparticles to treat, detect and protect against skin cancer. Towards finding a solution, they begin the research phase by investigating the first research question: What is electromagnetic energy? Students learn about the electromagnetic spectrum, ultraviolet radiation (including UVA, UVB and UVC rays), photon energy, the relationship between wave frequency and energy (c = λν), as well as about the Earth's ozone-layer protection and that nanoparticles are being used for medical applications. The lecture material also includes information on photo energy and the dual particle/wave model of light. Students complete a problem set to calculate frequency and energy.

We all know that it takes energy to provide us with the basics of shelter: heating, cooling, lighting, electricity, sanitation and cooking. To create energy-efficient housing that is practical for people to use every day requires combining many smaller systems that each perform a function well, and making smart decisions about the sources of power we use. Through five lessons on the topics of heat transfer, circuits, daylighting, electricity from renewable energy sources, and passive solar design, students learn about the science, math and engineering that go into designing energy-efficient components of smart housing that is environmentally friendly. Through numerous design/build/analyze activities, students create a solar water heater, swamp cooler, thermostat, model houses for testing, model greenhouse, and wind and water turbine prototypes. It is best if students are concurrently taking Algebra 1 in order to complete some of the worksheets.

This activity utilizes hands on learning with the conservation of energy with the inclusion of elastic potential energy. Students use pogo sticks to experience the elastic potential energy and its conversion to gravitational potential energy.

This activity utilizes hands-on learning with the conservation of energy and the interaction of friction. Students use a roller coaster track and collect position data. The students then calculate velocity, and energy data. After the lab, students relate the conversion of potential and kinetic energy to the conversion of energy used in a hybrid car.

Explore what it means for a mathematical statement to be balanced or unbalanced by interacting with objects on a balance. Discover the rules for keeping it balanced. Collect stars by playing the game!

To become familiar with the transfer of energy in the form of quantum, students perform flame tests, which is one way chemical engineers identify elements by observing the color emitted when placed in a flame. After calculating and then preparing specific molarity solutions of strontium chloride, copper II chloride and potassium chloride (good practice!), students observe the distinct colors each solution produces when placed in a flame, determine the visible light wavelength, and apply that data to identify the metal in a mystery solution. They also calculate the frequency of energy for the solutions.

During this engineering design/build project, students investigate many different solutions to a problem. Their design challenge is to find a way to get school t-shirts up into the stands during home sporting events. They follow the steps of the engineering design process to design and build a usable model, all while keeping costs under budget.

Through four lessons and four hands-on associated activities, this unit provides a way to teach the overarching concept of energy as it relates to both kinetic and potential energy. Within these topics, students are exposed to gravitational potential, spring potential, the Carnot engine, temperature scales and simple magnets. During the module, students apply these scientific concepts to solve the following engineering challenge: "The rising price of gasoline has many effects on the US economy and the environment. You have been contracted by an engineering firm to help design a physical energy storage system for a new hybrid vehicle for Nissan. How would you go about solving this problem? What information would you consider to be important to know? You will create a small prototype of your design idea and make a sales pitch to Nissan at the end of the unit." This module is built around the Legacy Cycle, a format that incorporates findings from educational research on how people best learn. This module is written for a first-year algebra-based physics class, though it could easily be modified for conceptual physics.

Accounting is the process of identifying, measuring, recording, and communicating an organization’s economic activities to users. Users need information for decision making. With an emphasis on the corporate form of business organization, this lesson will examine how financial transactions are analyzed and then reported using four financial statements: the income statement, statement of changes in equity, balance sheet, and statement of cash flows. This lesson introduces each statement using an example based on a fictitious corporate organization called Big Dog Carworks Corp.