How do you give students the opportunity to practice “I can use appropriate tools strategically”?
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.
Students sketched the path of point A. How far does A travel?
Students used paper and polydrons, their hands and string.
I sent a poll to find out what they were thinking about the distance traveled.
Students then interacted with dynamic geometry software. Does seeing the figure dynamically move help you better see the path?
Does seeing the path help you calculate how far A travels?
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.
One student figured that out by the time the bell rang.
I look forward to redeeming this lesson this year, as the journey continues …
Easing the Hurry Syndrome 
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
Any feedback on this? https://drive.google.com/open?id=0B35kHulwJHubRGlURHZFRGxMZDQ
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
Amy Zimmer
August 25, 2016 at 10:52 pm
Love this interaction!