The purpose of this task is to engage students in geometric modeling, and in particular to deduce algebraic relationships between variables stemming from geometric constraints. The modelling process is a challenging one, and will likely elicit a variety of attempts from the students.

This instructional task requires students to add four numbers to find the solution.

In this activity, students learn how engineers design faucets. Students will learn about water pressure by building a simple system to model faucets and test the relationship between pressure, area and force. This is a great outdoor activity on a warm day.

Through a series of activities, students discover that the concept of mechanical advantage describes reality fairly well. They act as engineers creating a design for a ramp at a construction site by measuring four different inclined planes and calculating the ideal mechanical advantage versus the actual mechanical advantage of each. Then, they use their analysis to make recommendations for the construction site.

In this activity, students will learn how to read a topographical map and how to triangulate with just a map. True triangulation requires both a map and compass, but to simplify the activity and make it possible indoors, the compass information is given. Students will practice converting a compass measurement to a protractor measurement, as well as reverse a bearing direction (i.e., if they know a tree's bearing is 100 degrees from you, they can determine what bearing they are from the tree). Students will use the accompanying worksheets to take a bearing of certain landmarks and then start at those landmarks to work backwards to figure out where they are.

In this activity, students will learn how to actually triangulate using a compass, topographical (topo) map and view of outside landmarks. It is best if a field trip to another location away from school is selected. The location should have easily discernable landmarks (like mountains or radio towers) and changes in elevation (to illustrate the topographical features) to enhance the activity. A national park is an ideal location, and visiting a number of parks, especially parks with hiking trails, is especially beneficial.

Students learn about tornadoes, the damage they cause, and how to rate tornadoes. Specifically, students investigate the Enhanced Fujita Damage Scale of tornado intensity, and use it to complete a mock engineering analysis of damage caused by a tornado. Additional consideration is given to tornado warning systems and how these systems can be improved to be safer. Lastly, students learn basic tornado safety procedures.

Students will analyze data of tornadoes throughout the United States. They will create a bar graph of the number of tornadoes for the top ten states in the country and then calculate the median and the mode of the data.

The purpose of this task is to provide students with the opportunity to determine experimental probabilities by collecting data.

Parts (a) and (b) of the task ask students to find the unit rates that one can compute in this context. Part (b) does not specify whether the units should be laps or km, so answers can be expressed using either one.

Students simulate the spread of a virus such as HIV through a population by "sharing" (but not drinking) the water in a plastic cup with several classmates. Although invisible, the water in a few of the cups has already be tainted with the "virus" (sodium carbonate). After all the students have shared their liquids, the contents of the cups are tested for the virus with phenolphthalein, a chemical that causes a striking color change in the presence of sodium carbonate. Students then set about trying to determine which of their classmates were the ones originally infected with the virus.

In which Stan Muller teaches you about our third branch of Intellectual Property, trademarks. A lot of people confuse trademark and copyright. Trademarks apply to things like company and product names and logos, packaging designs, and commercial designs. Basically, copyright protects ideas, but trademarks protect the things that help consumers tell companies apart. This ensures that consumers know the source of the goods they're buying. Without trademarks, it would be really difficult to buy the same product twice, and very easy for unscrupulous companies to pass off fakes and knock offs of the products you want. I'm telling you, you like trademarks.

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.

It is much easier to visualize division of fraction problems with contexts where the quantities involved are continuous. It makes sense to talk about a fraction of an hour. The context suggests a linear diagram, so this is a good opportunity for students to draw a number line or a double number line to solve the problem.

This task examines, in a graphical setting, the impact of adding a scalar, multiplying by a scalar, and making a linear substitution of variables on the graph of a function f. The setting here is abstract as there is no formula for the function f. The focus is therefore on understanding the geometric impact of these three operations.

Students collect, categorize, weigh and analyze classroom solid waste. The class collects waste for a week and then student groups spend a day sorting and analyzing the garbage with respect to recyclable and non-recyclable items. They discuss ways that engineers have helped to reduce the accumulation of solid waste.

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.

Students explore how sound waves move through liquids, solids and gases in a series of simple sound energy experiments. Understanding the properties of sound and how sound waves travel helps engineers determine the best room shape and construction materials when designing sound recording studios, classrooms, libraries, concert halls and theatres.

This task gives students a chance to explore several issues relating to rigid motions of the plane and triangle congruence. As an instructional task, it can help students build up their understanding of the relationship between rigid motions and congruence.

The purpose of this task is to emphasize the adjective "geometric" in the "geometric" series, namely, that the algebraic notion of a common ratio between terms corresponds to the geometric notion of a repeated similarity transformation.