5.+Taxicab+Geometry+Tasks

The tasks below are created to help the students see that the following quote is held true: "What is targeted through project-based learning, which presents real life problems, is students' recognition that, in real life, Taxicab geometry may be more practical than Euclidean. (Tuba and Aytaç, p. 109)
 * Tasks for Taxicab Geometry **

**Task #1** **Materials Needed:** A classroom with desks that resemble a grid and a long piece of string, or a material that is like string. ** Intro: ** Create a replica city street in the classroom to represent a coordinate plan as a way to get students to see the difference between Euclidean geometry and taxicab geometry. **Procedure:** Follow the lesson plan in the file below. After this activity is done, you must further explain it on a coordinate plane. By showing that points A and B have specific coordinates, it is easy to begin scaffolding towards understanding the distance in terms of Taxicab Geometry. 

**Task #2** **Materials Needed:** Cardboard, empty cans, empty cartons, markers, toy cars, and string.  **Intro:** The students will work in groups and make a five block by five block replica of a city using materials provided. The materials given to the students will be a piece of cardboard for the base of the city. Also, the students will be given empty cans and cartons for the buildings. The students need to make up road names and how the city looks. The main restriction is that the roads have to look like the [|Example Grid]. The teacher if wanted can have the students include one way streets and road blocks to see how it affects the travel distance from one point to another. **Procedure:** The teacher at one point will give the students a toy car for the students to see how their car goes around the model. Then, the teacher will give each group a length of a string and have the students draw on a piece of paper all the different ways the string can take to get from point A and point B. The teacher will then enforce that a road block due to a car wreck happens on "such and such street." The students then have to figure out how many ways the taxi can get to the finishing point. Next, the teacher will tell the students that the mayor changed two roads into one way direction streets. The teacher will ask the class how this will affect the travel distance of two points.

<span style="font-family: 'Times New Roman',Times,serif;">Task 1 was made by Audr é Williams (including the graphics)

<span style="font-family: 'Times New Roman',Times,serif;">Task 2 was made up by Philip Peavy and the grid was found at <span style="font-family: 'Times New Roman',Times,serif;">http://etc.usf.edu/clipart/42600/42669/grid_42669.htm.