Geometry – Day 68 – Pythagorean Word Problems & Distance Formula

Come for:

  1. Some difficult Pythagorean Word Problems
  2. A discussion of the distance formula.

Stay for:

  1. Some really pretty slide work.
  2. Some really sturdy distance formula scaffolding.


  1. None


Slide Deck

  1. Louisianans, Mainers, Nutmeggers, New Jersey-ites, Bay Staters (Massholes, more locally).
  2. I cut the word problem assignment waaay back. Painful.
  3. Ask if the baseball bat (34 in.) fits in vertically. Where’s the right triangle?
  4. Didn’t get to this.
  5. Monterey Bay, CA.
  6. I want to know the distance, by air, from Pebble Beach to the Presidio. Each box in the grid is a square mile. (Not true, but let’s roll with it for argument’s sake.)
  7. They’ll count squares here.
  8. They’ll count squares here too.
  9. Here, they can’t count squares. So what do you do?
  10. Give what they’ve done on the last several problems, have them derive the formula.
  11. Again we’re Pythagorizing, but looking for a rule, a pattern.

Notes & Revisions:

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.


  1. Hey dan, just peeking in at your stuff here…GREAT JOB!

    Have you tried using Google Earth to show actual distances to check your work on problems like the Monterey-Pythagorean one?

    Very cool…students get a kick out of it.

    And answering your question about teaching Geometry w/o a projector:

    Did it w/o one for eight years, have one now, would pay for it out-of-pocket if I had to…

    Geo Sketchpad/WinGeom/ppt/Mimio/’net make the course so much more dynamic…even if I don’t bring my kids to a computer lab…

  2. The fact that I haven’t used Sketchpad this entire year is some kind of shameful badge. I mean, we aren’t exactly drowning in software licenses but that’s only barely an excuse, particularly when I think about how many concepts it would’ve clarified for my kids.

    Mimio, though? Looks like I’ve got some Googling ahead of me.

    Thanks for dropping off the references. This is the sort of thing I was hoping for when I started posting lessons.