The Taco Cart problem

(This is one of Dan Meyer’s 3 Act Tasks)

I gave this problem to my Calculus class while we were studying Optimization. The first three parts of the problem are understandably below the students’ level as they only require the basic use of the Pythagoras theorem. However, the students seemed to enjoy watching Dan’s reveal videos confirming their solutions that I let them tackle the first three parts as a fun and “warm up” exercise!

Part three, determining the position of the Taco Cart so that both Dan and Ben reach it at the same time, allowed me to introduce the students to

The

What excited me most was that when I looked around the room at the students working on their vertical boards, I saw examples of numeric, graphic,

The groups using the numeric method soon realized that it wasn’t the most efficient method for determining an exact solution. At that point, I had all groups share and show their strategies to the whole class. The students were then asked to solve the problem using all three methods, first manually and then with the help of

I found this to be a great problem because it can be tackled by students from all grades from Math 9 to Calculus, since each part of the problem can be approached numerically, graphically, algebraically, and through the use of Calculus concepts.

It was also a great problem to do with Vertical Non-Permanent Surfaces as it eased the collaboration process within groups and allowed many opportunities for students to share their strategies with the entire class. It also facilitated discussion with the teacher, because I could immediately see which groups needed help and which groups were doing something unique.

The student groups’ solutions and reflections on the whole problem can be viewed by clicking on the links below:

Group 1

Group 2

Group 3

Group 4

Group 5

Group 6

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The Hot Dog Showdown!

(This problem was originally created by

The Taco Cart problem

(This is one of Dan Meyer’s 3 Act Tasks)

I gave this problem to my Calculus class while we were studying Optimization. The first three parts of the problem are understandably below the students’ level as they only require the basic use of the Pythagoras theorem. However, the students seemed to enjoy watching Dan’s reveal videos confirming their solutions that I let them tackle the first three parts as a fun and “warm up” exercise!

Part three, determining the position of the Taco Cart so that both Dan and Ben reach it at the same time, allowed me to introduce the students to

*Desmos*and*Wolfram Alpha*for the first time. The students created an algebraic model and used the two tools to confirm their answers graphically and algebraically.The

*Sequel*was where it got interesting. Finding the fastest path to the Taco Cart is certainly a fun application for the Optimization section of Calculus.What excited me most was that when I looked around the room at the students working on their vertical boards, I saw examples of numeric, graphic,

__and__algebraic methods being used. All with literally no guidance from me! It was so great to see the students select a method that they felt most comfortable with.The groups using the numeric method soon realized that it wasn’t the most efficient method for determining an exact solution. At that point, I had all groups share and show their strategies to the whole class. The students were then asked to solve the problem using all three methods, first manually and then with the help of

*Desmos*and*Wolfram Alpha*.I found this to be a great problem because it can be tackled by students from all grades from Math 9 to Calculus, since each part of the problem can be approached numerically, graphically, algebraically, and through the use of Calculus concepts.

It was also a great problem to do with Vertical Non-Permanent Surfaces as it eased the collaboration process within groups and allowed many opportunities for students to share their strategies with the entire class. It also facilitated discussion with the teacher, because I could immediately see which groups needed help and which groups were doing something unique.

The student groups’ solutions and reflections on the whole problem can be viewed by clicking on the links below:

Group 1

Group 2

Group 3

Group 4

Group 5

Group 6

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The Hot Dog Showdown!

(This problem was originally created by

__Robert Kaplinsky__)I showed my class the following MasterCard commercial, featuring World Hot Dog eating champions Kobayashi and Sonya:

__commercial__.

I then asked the students to formulate and discuss any interesting mathematical questions or ideas emerging from the video that were worth exploring. Given below are two samples that students submitted as a product to present their learning in the form of a Prezi. (The files are in zipped form.)

Hot Dog Problem 1

Hot Dog Problem 2