Pick A Point

Here’s my favorite moment from a workshop in Spokane last week:

It’s about the quickest and most concise illustration I can offer of Guershon Harel’s necessity principle. The moment of need is brief, but really hard to miss. It sounds a lot like laughter.

2014 Feb 19. Christine Lenghaus adapts the interaction for naming angles:

I drew a large triangle and then lots of various sized ones inside it and asked the students to pick an acute angle. I asked a student to describe the one they were thinking about and then another student to come up and mark it! This lead to discussion on how best to label so that we both agree on which angle we were talking about. Gold!

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Joel Patterson:

There’s an easy way to do this in Geogebra.
Open up blank Geogebra file, viewing only the Geometry window (no Algebra window).

Click the point tool and make a bunch of points like in Dan’s video.

Then there is a small button AA with one A in black and the other in grey. This button shows and hides labels for all points.

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Hans Freudenthal:

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I'm Dan and this is my blog. I'm a former high school teacher, former graduate student, and current head of teaching at Desmos. More here.

23 Comments

  1. Clara

    February 12, 2014 - 11:13 am

    Wow. Now I just have to find these moments in the mundane and exploit them. Without any comment. I have students who would respond: why didn’t you put the points on there in the first place! Thank you!

  2. William Carey

    February 12, 2014 - 11:32 am

    Another thing this beautifully highlights is that math is fundamentally about communication. We name points so we can talk about them, either with other people or with ourselves.

  3. Jeff Naslund

    February 12, 2014 - 10:39 pm

    Thanks for the intellectual perturbation!

  4. Carlo

    February 13, 2014 - 8:00 pm

    Awesome!! What program did you use to make this?

  5. Dan Meyer

    February 13, 2014 - 8:33 pm

    Just Keynote for the two slides in class.

    I made this video using Final Cut Pro.

  6. Andrew Stadel

    February 15, 2014 - 9:12 am

    Simple.
    Clean.
    Effective.
    Necessary.
    I think you’re also creating a need for communication between students and for them to be as descriptive as possible while keeping each other accountable.
    Great design.

  7. Tom

    February 17, 2014 - 8:19 pm

    With more time, it might be fun to name them by numbers first.

  8. Jeff

    February 19, 2014 - 10:24 am

    Love the idea! I hated teaching this in geometry. One idea I would try out too: I have worked with students on developing mathematical basics/tools to solve other math problems. Instead of just picking a point and describing it as the end goal, what if you had them work on picking 2 points to put a line through (so that naming points is a mathematical necessity)? Then they would have to describe 2 points…almost battleship style? It could also lead into similar x-y coordinate plane activities too.

  9. Joel Patterson

    August 28, 2014 - 10:56 am

    There’s an easy way to do this in Geogebra.
    Open up blank Geogebra file, viewing only the Geometry window (no Algebra window).

    Click the point tool and make a bunch of points like in Dan’s video.

    Then there is a small button AA with one A in black and the other in grey. This button shows and hides labels for all points.

  10. Dan Meyer

    August 28, 2014 - 3:26 pm

    @Joel, great hack! Added it to the top post.