The goal of this task is to give students experience applying and reasoning about reflections of geometric figures using their growing understanding of the properties of rigid motions. In the case of reflecting a rectangle over a diagonal, the reflected image is still a rectangle and it shares two vertices with the original rectangle.

This activity is one in a series of tasks using rigid transformations of the plane to explore symmetries of classes of triangles, with this task in particular focusing on the class of equilaterial triangles. In particular, the task has students link their intuitive notions of symmetries of a triangle with statements proving that the said triangle is unmoved by applying certain rigid transformations.

This task examines some of the properties of reflections of the plane which preserve an equilateral triangle: these were introduced in ''Reflections and Isosceles Triangles'' and ''Reflection and Equilateral Triangles I''. The task gives students a chance to see the impact of these reflections on an explicit object and to see that the reflections do not always commute.

This activity is one in a series of tasks using rigid transformations of the plane to explore symmetries of classes of triangles, with this task in particular focussing on the class of isosceles triangles.

This task serves as a bridge between understanding place-value and using strategies based on place-value structure for addition.

A quantitative illustration of how non-renewable resources are depleted while renewable resources continue to provide energy. Students remove beads (units of energy) from a bag (representing a country). A certain number of beads are removed from the bag each "year." At some point, no non-renewable beads remain. Student groups have different ratios of renewable and non-renewable energy beads. A comparison of the remaining beads and time when they ran out of energy shows the value of utilizing a greater proportion of renewable resources as a sustainable energy resources.

Students analyze real-world data for five types of renewable energy, as found on the online Renewable Energy Living Lab. They identify the best and worst locations for production of each form of renewable energy, and then make recommendations for which type that state should pursue.

The purpose of the task is to have students reflect on the meaning of repeating decimal representation through approximation. A formal explanation requires the idea of a limit to be made precise, but 7th graders can start to wrestle with the ideas and get a sense of what we mean by an "infinite decimal."

This task presents students with some creative geometric ways to represent the fraction one half. The goal is both to appeal to students' visual intuition while also providing a hands on activity to decide whether or not two areas are equal.

This task provides a context for indentifying different ways of representing half of a rectangle.

As a behavior-management tool, response effort seems like simple common sense: We engage less in behaviors that we find hard to accomplish. Teachers often forget, however, that response effort can be a useful part of a larger intervention plan. To put it simply, teachers can boost the chances that a student will take part in desired behaviors (e.g., completing homework or interacting appropriately with peers) by making these behaviors easy and convenient to take part in. However, if teachers want to reduce the frequency of a behavior (e.g., a child's running from the classroom), they can accomplish this by making the behavior more difficult to achieve (e.g., seating the child at the rear of the room, far from the classroom door).

The task is intended to address standards regarding sample space, independence, probability distributions and permutations/combinations.

Student pairs reverse engineer objects of their choice, learning what it takes to be an engineer. Groups each make a proposal, create a team work contract, use tools to disassemble a device, and sketch and document their full understanding of how it works. They compile what they learned into a manual and write-up that summarizes the object's purpose, bill of materials and operation procedure with orthographic and isometric sketches. Then they apply some of the steps of the engineering design process to come up with ideas for how the product or device could be improved for the benefit of the end user, manufacturer and/or environment. They describe and sketch their ideas for re-imagined designs (no prototyping or testing is done). To conclude, teams compile full reports and then recap their reverse engineering projects and investigation discoveries in brief class presentations. A PowerPoint(TM) presentation, written report and oral presentation rubrics, and peer evaluation form are provided.

In this task students draw the graphs of two functions from verbal descriptions. Both functions describe the same situation but changing the viewpoint of the observer changes where the function has output value zero. This small twist forces the students to think carefully about the interpretation of the dependent variable.

Students write a biographical sketch of an artist or athlete who lives on the edge, riding the gravity wave, to better understand how these artists and athletes work with gravity and manage risk. Note: The literacy activities for the Mechanics unit are based on physical themes that have broad application to our experience in the world concepts of rhythm, balance, spin, gravity, levity, inertia, momentum, friction, stress and tension.

This task provides a good opportunity to use isosceles triangles and their properties to show an interesting and important result about triangles inscribed in a circle: the fact that these triangles are always right triangles is often referred to as Thales' theorem. It does not have a lot of formal prerequisites, just the knowledge that the sum of the three angles in a triangle is 180 degrees.

The result here complements the fact, presented in the task ``Right triangles inscribed in circles I,'' that any triangle inscribed in a circle with one side being a diameter of the circle is a right triangle. A second common proof of this result rotates the triangle by 180 degrees about M and then shows that the quadrilateral, obtained by taking the union of these two triangles, is a rectangle.

The purpose of this task is to give students an opportunity to explore various aspects of exponential models (e.g., distinguishing between constant absolute growth and constant relative growth, solving equations using logarithms, applying compound interest formulas) in the context of a real world problem with ties to developing financial literacy skills.

Students build on their understanding and feel for flow rates, as gained from the associated Faucet Flow Rate activity, to estimate the flow rate of a local river. The objective is to be able to relate laboratory experiment results to the environment. They use the U.S. Geological Survey website (http://waterdata.usgs.gov/nwis/rt) to determine the actual flow rate data for their river, and compare their estimates to the actual flow rate. For this activity to be successful, choose a nearby river and take a field trip or show a video so students gain a visual feel for the flow of the nearby river.