Understand congruence and similarity using physical models, transparencies, or geometry software.
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8.G.1 Verify experimentally the properties of rotations, reflections, and translations.
8.G.2 Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them.
8.G.4 Understand that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar two-dimensional figures, describe a sequence that exhibits the similarity between them.
Expert
Tomb Raider (Transformations)
After years of searching, treasure hunters Li and Sara have found the treasure in Egypt. The crypt door is locked by a strange lock. It appears to be a puzzle. The pieces are stuck to the wall and can come off but can be moved. The tablet on the wall says: completing the square using only rigid transformations will unlock the door. Can you complete the puzzle and open the crypt door?
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8.G.3 Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates.
Beginner
Batman (Dilations)
This is a scene from Tim Burton's 1989 Batman. This scene at the end of the movie is the unveiling of the Batsignal. The mayor reads a message from Batman. Please inform the citizens of Gotham that Gotham City has earned a rest from crime. But if the forces of evil should rise again to cast a shadow on the heart of the city, call me. Batman has given the city of Gotham a signal. It is a spotlight with a bat on it, and when it's turned on, a bat will appear in the night sky. In this project you will recreate this scene.
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8.G.4 Understand that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar two-dimensional figures, describe a sequence that exhibits the similarity between them.
8.G.5 Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles.
National Treasure
Understand and apply the Pythagorean Theorem.
8.G.6 Explain a proof of the Pythagorean Theorem and its converse.
8.G.7 Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in problems in two and three dimensions.
Die Hard
Potter Wand
8.G.8 Apply the Pythagorean Theorem to find the distance between two points in a coordinate system.
Expert
Drone Delivery (Pythagorean Theorem)
Story A: Our drones deliver packages all over the city. The process is mostly flawless, with just a few minor hiccups. They are programmed to go to the nearest charging station, when the battery runs low. Our issue is that each charging station has space for only four drones. Can you calculate how far each drone is from each charging station and determine which ones it can safely reach.
Story B: Our drones deliver packages all over the city. The process is mostly flawless, with just a few minor hiccups. They are programmed to go to the nearest charging station, when the battery runs low. Our issue is that each charging station has space for only five drones. Can you safely reroute any drones that need to be rerouted?
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Solve real-world and mathematical problems involving volume of cylinders, cones, and spheres.
8.G.9 Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve problems.
Intermediate
Tiny House (Volume of Cylinders, Spheres, and Cones)
Li’s company, SiloBuild, uses unused silos to build tiny houses for its clients. Clients have 3 floor plans to choose from. Nia wants a home that gives her family the most space. Which one should she choose?
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Intermediate
Vases (Volume of Cylinders, Spheres, and Cones)
Andrew is at a pottery shop buying new vases. As a botanist, he knows how much flower food needs to be added to the water, so it is important that he knows how much water each vase can hold. Nia, who makes the vases, doesn't know how much water each vase can hold, but she can write down the measurements of each vase for him in the magazine. Andrew needs vases that can comfortably hold 55 fluid ounces of water for an upcoming wedding. Which vases can he choose from?
Extension: The couple for whom Andrew is arranging the flowers likes the cone. Since it is not big enough, Andrew needs to figure out how to change the size to make it work.
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