Why do we care about air? Breathe in, breathe out, breathe in... …
Why do we care about air? Breathe in, breathe out, breathe in... most, if not all, humans do this automatically. Do we really know what is in the air we breathe? In this activity, students use M&M(TM) candies to create pie graphs that show their understanding of the composition of air. They discuss why knowing this information is important to engineers and how engineers use this information to improve technology to better care for our planet.
This tasks gives a verbal description for computing the perimeter of a …
This tasks gives a verbal description for computing the perimeter of a rectangle and asks the students to find an expression for this perimeter. Students then have to use the expression to evaluate the perimeter for specific values of the two variables.
This task is a natural follow up for task Rectangle Perimeter 1. …
This task is a natural follow up for task Rectangle Perimeter 1. After thinking about and using one specific expression for the perimeter of a rectangle, students now extend their thinking to equivalent expressions for the same quantity.
This task is a reasonably straight-forward application of rigid motion geometry, with …
This task is a reasonably straight-forward application of rigid motion geometry, with emphasis on ruler and straightedge constructions, and would be suitable for assessment purposes.
The goal of this task is to give students an opportunity to …
The goal of this task is to give students an opportunity to experiment with reflections of triangles on a coordinate grid. Students are not prompted in the question to list the coordinates of the different triangle vertices but this is a natural extension of the task.
The goal of this task is to give students experience applying and …
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 …
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 …
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 …
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.
A quantitative illustration of how non-renewable resources are depleted while renewable resources …
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 …
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 …
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 …
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.
Student pairs reverse engineer objects of their choice, learning what it takes …
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 …
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.
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