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GBK Geometry

GBK Geometry. Jordan Johnson. Today’s plan. Greeting Supplies Check / Pre-write Two Problems: The Surfer and Spotter Homework / Questions Clean-up. Supplies. Take out and be ready to show me… compass ruler protractor notebook/graph paper 3 colors of pen or pencil

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GBK Geometry

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  1. GBK Geometry Jordan Johnson

  2. Today’s plan • Greeting • Supplies Check / Pre-write • Two Problems: The Surfer and Spotter • Homework / Questions • Clean-up

  3. Supplies • Take out and be ready to show me… • compass • ruler • protractor • notebook/graph paper • 3 colors of pen or pencil • 2 composition books (or one plus a binder)

  4. Quick pre-write(Name, Date, Period @ top-right) • What do you know about… • …points? • …lines? • …line segments? • …planes? (Not the flying kind…) • If you know these words, tell what they mean: • collinear / noncollinear • coplanar / noncoplanar • concurrent • What shapes are formed by intersecting lines? • What about intersecting planes?

  5. Equilateral triangles • Take out • your notes • your equilateral triangle construction from yesterday

  6. The Surfer’s & Spotter’s puzzles Spotter: Wants access to all corners Surfer: Wants access to all sides

  7. The Island • Equilateral triangular island • 12km on each side

  8. The Spotter • Goal: • Choose a location for his house • Minimize the sum of the distances from the house to the vertices A, B, and C.

  9. The Spotter • Scale drawing of the island: 1cm = 1km • Example 1: • House at D • AD = 4.4km, DB = 9.1km, DC = 7.9km • Total distance: 21.4km • Example 2: • House at E • AE = 10.4km, EB = 5.1km, EC = 6.9km • Total distance: 22.4km.

  10. The Spotter • Using your triangle from yesterday or a new one (12cm on each side) as a model: • Choose several points on the island • For each point: • Measure the distance to each corner • Add up the distances. • What do you believe is the best place for the house? • …and how many km of path must the spotter clear? • What about the worst place? • …and how many km to clear from there?

  11. The Surfer • Goal: • Minimize the sum of the distances from his house to the sides of the island. • Note: • The shortest path from the house to a side is perpendicular to the side.

  12. The Surfer • Example. • This time you can measure them.

  13. The Surfer • Using your triangle from yesterday or a new one (12cm on each side) as a model: • Choose several points on the island • For each point: • Measure the distance to each side (again, perpendicular!) • Add up the distances. • What do you believe is the best place for the house? • …and how many km of path must the surfer clear? • What about the worst place? • …and how many km to clear from there?

  14. Homework • By Friday: Introduction email(subject: Period __ Geometry: Introduction) • Instructions on Schoology • Tonight: 10 minutes work on Khan Academy • Choose a topic you need to work on from the pre-test • Watch a video and work the associated problem(s)

  15. Clean-up / Reminders • Pick up all trash / items. • Push in chairs (at front and back tables). • See you tomorrow!

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