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MP5: The Traveling Point

23 Aug

How do you give students the opportunity to practice “I can use appropriate tools strategically”?
MP5

When we have a new type of problem to think about, I am learning to have students give their best guess of the solution first. I’ve written about The Traveling Point before.

1 Screen Shot 2016-08-18 at 6.13.30 PM.png

Students sketched the path of point A. How far does A travel?

Students used paper and polydrons, their hands and string.

2 Screen Shot 2016-08-18 at 6.24.31 PM.png

3 IMG_0946.JPG

I sent a poll to find out what they were thinking about the distance traveled.

4 Screen Shot 2016-08-18 at 6.23.31 PM.png

Students then interacted with dynamic geometry software. Does seeing the figure dynamically move help you better see the path?

Traveling Point 1.gif

5 Screen Shot 2016-08-18 at 6.23.44 PM.png

Does seeing the path help you calculate how far A travels?

Traveling Point 2.gif

6 Screen Shot 2016-08-18 at 6.23.53 PM.png

And so the journey to make the Math Practices our habitual practice in learning mathematics continues …


And the journey for my own learning continues. Thanks to Howard for correcting me. The second two moves do not travel a distance of 6, but the length of the circumference of the quarter circle.

Screen Shot 2016-08-24 at 10.38.58 AM.png

One student figured that out by the time the bell rang.

I look forward to redeeming this lesson this year, as the journey continues …

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8 Comments

Posted by on August 23, 2016 in Geometric Measure & Dimension, Geometry

 

Tags: , , , , ,

8 responses to “MP5: The Traveling Point

  1. howardat58

    August 23, 2016 at 3:05 pm

    Nice one, but….
    I rolled the stick 90deg, I rolled the circumference 90deg and I rolled the stick 90deg
    The stick and the circumference each get 3pi/2, 3 of them is 9pi/2, not 6 +3pi

     
    • jwilson828

      August 24, 2016 at 10:35 am

      Thank you for correcting me! It took me watching it for a long time to get it. Maybe the original static image with the four quarter circles is misleading. Do you have a suggestion for changing that?

       
      • howardat58

        August 24, 2016 at 1:05 pm

        You could put a picture of the centre position, on its curved middle, and show the two either side with an overlap. Then the curved rolling part will get 1/4 of the whole circle. Diagrams !!!!!!!!!!

         
      • jwilson828

        August 25, 2016 at 4:18 pm

         
      • howardat58

        August 25, 2016 at 5:18 pm

        I also thought of some computer organised thing but it seemed very complicated. To see somthing rolling it has to be a real object. The bit in the middle, the rolling bit, could be made out of thick card, and so it will roll one quarter of the circle, and the A point will do the straight line bit at the one quarter of the circle rate, 3pi/2, the same as the outside bits.
        Computers can only give simulations !

         
      • jwilson828

        August 26, 2016 at 5:29 am

        Thank you, Howard.

         
      • howardat58

        August 28, 2016 at 10:08 am

        I just found this, from Larry Cuban

         
  2. Amy Zimmer

    August 25, 2016 at 10:52 pm

    Love this interaction!

     

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