# Taco Truck

Dan Meyer’s Taco Cart 3-Act task has long been a favorite among the Desmos teaching faculty. Two people are on a beach and decide to buy lunch from a taco vendor on the nearby boardwalk. The two disagree about the fastest route, so they go their own ways and rendez-vous at the cart. Who gets there first? Is there a faster route than either person takes? What if you had a beach wheelchair? Can a dog do this math? So many great questions present themselves in this context.

This task has several other elements going for it as well:

• It creates an intellectual need for the Pythagorean Theorem.
• The exposition is short, focused, and connected to existing student thinking.

In remaking this task in the medium of Activity Builder, we thought hard about what opportunities and constraints came along with this transition.

Here are some aspects that are new in the Desmos version we have recently publicly released at teacher.desmos.com:

• New Artwork. We rebuilt the scene from scratch. Now, people and a taco truck are visible! We increased the contrast to make the mathematical structures pop and the scene come alive.
• Progressive Disclosure. A paper textbook version of this problem might give all of the necessary information to the students up front. With paper, there isn’t much choice. Dan’s original version was an improvement on that: it sets up the problem and then asks students for a guess and what information is necessary. The Desmos version keeps all of that and goes a step further: we invite the student to imagine they are on the beach and ask for a sketch of their preferred route before we zero in on two specific routes. Perhaps you’d like to greet your friend under the umbrella on your way to lunch, or rinse the sand off your feet before pausing to put on your shoes for the stroll.
• The Plot Thickens. After students determine the time it takes to walk two specified routes, they get the opportunity to improve on those routes by determining and calculating one of their own. They test their preferred route in a delightful race to the taco line in which everyone in the class participates.
• Interpretive Feedback. In the original version, the climax of the task comes with a “reveal,” where a video shows how long each person takes to walk to the taco cart and students can compare these numbers to their own. We love the dramatic tension this creates. Yet after the reveal, the cat is out of the bag! Desmos Activity Builder gives us another option: interpretive feedback. If you tell us a person must walk 100 seconds to the Taco Cart, we’ll show you how far the person is after 100 seconds. If you’re wrong, you can revise because you don’t yet know the solution.
• Accessibility. We like problems that can be represented visually for many reasons, but one drawback is that visually-impaired students can be excluded from the fun. At Desmos we believe that math is for everyone, and so we made sure - as we do for nearly all our lessons - that any scenario that could be visually animated in this activity also is dynamically described for students using screen readers.

Want to know the fastest way to an engaging and delightful Pythagorean Theorem problem? Click here!