This lesson includes several summative application activities. There are two optional activities that involve going outside or to a room with very high ceilings to use indirect measurement to measure an object. In the first optional activity, students use mirrors (or shallow bowls of water) and in the second, they choose their own tools (MP5). The time estimates given are for doing each activity separately. If students do both the mirror method and the alternate method on the same trip outside, the activities will take less time.
The other activities focus on similar triangles and scale factors. Students explore the geometry of bank shots on pool tables, first estimating and then precisely calculating the path of the ball. They have a chance to reason abstractly and quantitatively (MP2) as they compare their estimated path with their calculated path using similar triangles and the physics of reflection.
Bank Shot works best when each student has access to devices that can run the GeoGebra applet because students will benefit from seeing the relationship in a dynamic way.
- Use similarity and proportional reasoning to solve problems in context and interpret the results (using words and other representations).
- Let’s use similarity to solve problems.
For Indirect Measurement (Mirrors): Determine a location for the experiment where you can place the mirrors so students will be able to see the top of the object being measured and the Sun won’t be too bright on the mirrors. If mirrors are not available, shallow bowls of water, especially dark bowls or bowls with dark paper at the bottom work well.
Devices are required for the digital version of the activity, Bank Shot.
- I can solve and interpret problems involving similar right triangles.