Geometry – Day 60 – Pick’s Theorem & Treasure Hunt

Why We’re Here:

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


  1. Pick’s Theorem Worksheet 1
  2. Pick’s Theorem Worksheet 2
  3. Treasure Hunt Stations
  4. Concept Quiz 18

The Breakdown

  1. Opener + Review (15 minutes)
  2. Pick’s Theorem Notes (25 minutes)
  3. Pick’s Theorem Classwork (10 minutes)
  4. Break (5 minutes)
  5. Show and Tell (1.5 minutes)
  6. Treasure Hunt (30 minutes)
  7. Concept Quiz (20 minutes)


Slide Deck

  1. Texas has the lowest. New Hampshire has the highest. (Houston Chronicle)
  2. Just ask them sketch the quadrilateral. Tell ‘em you aren’t giving them any side lengths. You’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.]
  3. Subtract off the triangles. Pass out the worksheet here. (Pick’s Worksheet #2)
  4. Once people start noticing the area is 12 for all of them, let them skip the rest. “See, this guy Pick — that’s Georg Pick, only one “e” in Georg — found out that the only thing that matters is the boundary points and the interior points.” Have them count those points.
  5. Just a visual representation that there’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.
  6. Test it out on our quadrilateral.
  7. I’m kind of in love with this little white floater here. Gonna have to bring that scratch space back in future episodes.
  8. Just bring it back to the start now. Nice and easy.
  9. 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. They’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:

  1. The final classwork set for Pick’s Theorem went much faster than expected.
I'm Dan and this is my blog. I'm a former high school math teacher and current head of teaching at Desmos. He / him. More here.

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