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Students find the volume and surface area of a rectangular box (e.g., a cereal box), and then figure out how to convert that box into a new, cubical box having the same volume as the original. As they construct the new, cube-shaped box from the original box material, students discover that the cubical box has less surface area than the original, and thus, a cube is a more efficient way to package things. Students then consider why consumer goods generally aren't packaged in cube-shaped boxes, even though they would require less material to produce and ultimately, less waste to discard. To display their findings, each student designs and constructs a mobile that contains a duplicate of his or her original box, the new cube-shaped box of the same volume, the scraps that are left over from the original box, and pertinent calculations of the volumes and surface areas involved.

Students find the volume and surface area of a rectangular box (e.g., a cereal box), and then figure out how to convert that box into a new, cubical box having the same volume as the original. As they construct the new, cube-shaped box from the original box material, students discover that the cubical box has less surface area than the original, and thus, a cube is a more efficient way to package things. Students then consider why consumer goods generally aren't packaged in cube-shaped boxes, even though they would require less material to produce and ultimately, less waste to discard. To display their findings, each student designs and constructs a mobile that contains a duplicate of his or her original box, the new cube-shaped box of the same volume, the scraps that are left over from the original box, and pertinent calculations of the volumes and surface areas involved.

The students will use a "real" 3D coordinate system. They will have 3 axes at right angles, and a plane (the XY plane) that will be able to slide up and down the Z axis. The students will then be given several coordinates and asked to find these points in space. They will also be asked to find the coordinates of the 8 corners of a box with given dimensions.

Perhaps this lesson cold be tweaked to include fabricated models and a fictitious map. Engineers design systems that require precise and known locations, and often use triangulation calculations to do this. Engineers use triangulation with ground data to determine where in space a satellite is located. Accurately determining a satellite's location is important to adjusting its position to keep it on course. Triangulation technology is also used to inform a robot of its current and target locations. Triangulation helps in spatial modeling to determine the area covered by cell phone transmitters, roadway noise zones, voltage maps and river high-water marks.

Engineers design systems that require precise and known locations, and often use triangulation calculations to do this. Engineers use triangulation with ground data to determine where in space a satellite is located. Accurately determining a satellite's location is important to adjusting its position to keep it on course. Triangulation technology is also used to inform a robot of its current and target locations. Triangulation helps in spatial modeling to determine the area covered by cell phone transmitters, roadway noise zones, voltage maps and river high-water marks.

Perhaps a better triangulation lesson than the other bookmark. In this activity, students will use bearing measurements to triangulate and determine objects' locations. Working in teams of two or three, students must put on their investigative hats as they take bearing measurements to specified landmarks in their classroom (or other rooms in the school) from a "mystery location."

Perhaps a better triangulation lesson than the other bookmark. In this activity, students will use bearing measurements to triangulate and determine objects' locations. Working in teams of two or three, students must put on their investigative hats as they take bearing measurements to specified landmarks in their classroom (or other rooms in the school) from a "mystery location."