**Why We’re Here:**

- We’re going to investigate Pick’s Theorem (and then forget about it).
- We’re going to review new area formulas with a treasure hunt.

**Materials:**

**The Breakdown**

- Opener + Review (15 minutes)
- Pick’s Theorem Notes (25 minutes)
- Pick’s Theorem Classwork (10 minutes)
- Break (5 minutes)
- Show and Tell (1.5 minutes)
- Treasure Hunt (30 minutes)
- Concept Quiz (20 minutes)

**Attachments**

- Keynote
- PowerPoint
- Interactive QuickTime
- Pick’s Theorem Worksheet 1
- Pick’s Theorem Worksheet 2
- Treasure Hunt Stations
- Concept Quiz 18

**Slide Deck**

- Texas has the lowest. New Hampshire has the highest. (Houston Chronicle)
- Just ask them sketch the quadrilateral. Tell â€˜em you arenâ€™t giving them any side lengths. Youâ€™re giving them something new. Ask if they see the rectangle that fits around the vertices. [Note: It’s awfully hard to tell what’s going on here without consulting the QuickTime or original slide deck.]
- Subtract off the triangles. Pass out the worksheet here. (Pick’s Worksheet #2)
- Once people start noticing the area is 12 for all of them, let them skip the rest. â€œSee, this guy Pick — thatâ€™s Georg Pick, only one â€œeâ€ in Georg — found out that the only thing that matters is the boundary points and the interior points.â€ Have them count those points.
- Just a visual representation that thereâ€™s, indeed, a pattern. I asked my class to see if they could find a way to turn 6 and 14 into 12 that also worked for 5 and 16, 10 and 6, etc. Several got it. Some very quickly.
- Test it out on our quadrilateral.
- Iâ€™m kind of in love with this little white floater here. Gonna have to bring that scratch space back in future episodes.
- Just bring it back to the start now. Nice and easy.
- The treasure hunt is a kick. You post ten multiple-choice questions around the room. Students form groups or go solo and solve any problem they want. A correct answer sends them to another question somewhere in the room. Theyâ€™ve done it correctly if they hit each of the ten questions in the right order. Hard to set up. Infinitely re-usable.Treasure hunt answer: 1 – 5 – 9 – 2 – 4 – 7 – 3 – 6 – 8 – 10
[

**Updated**(years later): students who finish early function as docents at harder outposts, explaining and prompting as other students need help.]

**Notes & Revisions:**

- The final classwork set for Pick’s Theorem went much faster than expected.

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