Ruth and the Taco Cart

I love Dan Meyer's Taco Cart if you have never heard of it, here is the task it is great it is wonderful.

http://threeacts.mrmeyer.com/tacocart/

We were recently doing this activity in Algebra 2, because I love how it uses the Pythagorean Theorem and one of my students asks, "what if you split the angle in half and walked that, because that is what I would do." I thought that would be a wonderful geometry question.

Ruth and the Taco Cart

I posed this question to my geometry students, we weren't really learning about angle bisectors, but we had already learned it as well as trigonometry. It took them about 15 minutes to use pythagorean theorem and find the time it would take. However, Ruth was much more difficult.

After students completed the time section I asked what they needed to find the angle and the distance Ruth would have to go.

There were lots of good questions. I gave the rest of it as homework and only a few were able to do it completely.


For students that did the work, I had them work in a group and work on a couple of extension problems:

  • If Ruth didn't want to talk alone, how long would she have to wait for the other to catch up?
  • What if she took a different angle?
  • Does changing the angle effect the time it takes for her to get to her destination?
The other students continued to work on the problem and were given some of these extension problems as they got the answer.

I loved the use of geometry, I will definitely use this when we are learning trigonometry.


4 comments:

  1. I'd love to know more details about what your students did with the extension problems. For instance, did any of them generate solutions for the extension tasks? What strategies did they use? Did anybody mess around with dynamic geometry software to model the problem? (I think I'm going to try to do that. I'll share my sketch once I have something worked up for you.)

    ReplyDelete
    Replies
    1. I think a dynamic geometry software would have been good for this, we didn't really use it at my previous school but wondering how I might use it this year now.

      Delete
  2. Here's a sketch I made in GeoGebra to support exploration of the task. This is a first attempt, so I'm sure it could be improved. Drag the slider to change the number of seconds elapsed. The input boxes enable your students to explore changes in walking speeds and distances. Let me know your thoughts!
    https://ggbm.at/ufqajdv3

    ReplyDelete
  3. I love that Geogebra applet, it would be good to have something like that at the end for them to see an answer visually.

    ReplyDelete