## Teacher Resources for Taxicab Geometry

__The Standards for Mathematical Practice__

- Make sense of problems and persevere in solving them.
- Reason abstractly and quantitatively.
- Construct viable arguments and critique the reasoning of others.
- Model with mathematics.
- Use appropriate tools strategically.
- Attend to precision.
- Look for and make use of structure.
- Look for and express regularity in repeated reasoning.

Taxicab Geometry is a very unique non-euclidean geometry, in the sense that it's fairly easy to understand if you have a basic knowledge of Euclidean Geometry. Because of this, we believe that students should be able to see, learn about, and investigate different topics within Taxicab Geometry. On top of that, it's easy to see that all of the above standards of mathematical can be met by investigating Taxicab Geometry within the middle or high school mathematics classroom setting.

There are a plethora of resources, especially online, for teachers to use at any grade level to implement Taxicab Geometry into their classrooms. One basic resource is an applet that allows the user to select a location on a city grid in which to hide the “treasure”, and the applet then computes the taxicab distance it takes to reach the treasure:

The applet can be found at the following link: http://www.learner.org/teacherslab/math/geometry/shape/taxicab/

There is also a wikispace that shows how Taxicab Geometry can be implemented in 4th-6th grade classrooms and then also in 6th grade and up classrooms. It also provides a plethora of task and resources needed to implement these tasks that incorporate Taxicab Geometry. These can be found at the following link: http://emat-5290-spring-2012-group-5-taxicab.wikispaces.com/1.+Taxicab+Home

There is also on lesson plan on Shodor that incorporates Taxicab Geometry: http://shodor.org/succeed-1.0/curriculum/MCN_NEW/lessons/nonEuclid.html

There is a student project presented by Prentice-Hall to assess student learning in regards to this geometry: http://cwx.prenhall.com/bookbind/pubbooks/esm_masingila_mathelem_1/chapter1/custom1/deluxe-content.html

A worksheet tailored to high school students uses a map of Texas with a road grid to introduce the concept of Taxicab Geometry: http://www.teacherspayteachers.com/Product/Introduction-to-Taxicab-Geometry-Road-Trip-Worksheet-1061744

An article explaining how a group of teachers implemented Taxicab Geometry in their classrooms provides a variety of tasks and an analysis of how their students benefitted from participating in them: http://www.math.oregonstate.edu/~tevian/OMLI/JMTE.pdf

An NCTM article presents a variety of Taxicab Geometry-based problems for students in high school along with an answer key (and it’s free for members!): http://www.nctm.org/publications/article.aspx?id=22334

Texas Instruments provides an interactive activity for introducing Taxicab Geometry: http://education.ti.com/en/us/activity/detail?id=30A1673412FF45358F291B1E289D51F1

This link provides a means of linking Euclidean and Taxicab Geometry through the use of “school bus geometry”: http://math.rice.edu/~lanius/Geom/schbus1.html

This link provides a variety of lessons and activities to assess whether students understand the basic concepts of Taxicab Geometry, including perpendicular bisectors: http://www.pasadenaisd.org/Curr_Instr/math/images/Geometry/Geometry%20Curriculum%20Resources/Geometry%20Structure/taxicab.pdf

For possible CCGPS Standards where these assignments, and Taxicab Geometry in general can be implemented, click the button below.

There is also a wikispace that shows how Taxicab Geometry can be implemented in 4th-6th grade classrooms and then also in 6th grade and up classrooms. It also provides a plethora of task and resources needed to implement these tasks that incorporate Taxicab Geometry. These can be found at the following link: http://emat-5290-spring-2012-group-5-taxicab.wikispaces.com/1.+Taxicab+Home

There is also on lesson plan on Shodor that incorporates Taxicab Geometry: http://shodor.org/succeed-1.0/curriculum/MCN_NEW/lessons/nonEuclid.html

There is a student project presented by Prentice-Hall to assess student learning in regards to this geometry: http://cwx.prenhall.com/bookbind/pubbooks/esm_masingila_mathelem_1/chapter1/custom1/deluxe-content.html

A worksheet tailored to high school students uses a map of Texas with a road grid to introduce the concept of Taxicab Geometry: http://www.teacherspayteachers.com/Product/Introduction-to-Taxicab-Geometry-Road-Trip-Worksheet-1061744

An article explaining how a group of teachers implemented Taxicab Geometry in their classrooms provides a variety of tasks and an analysis of how their students benefitted from participating in them: http://www.math.oregonstate.edu/~tevian/OMLI/JMTE.pdf

An NCTM article presents a variety of Taxicab Geometry-based problems for students in high school along with an answer key (and it’s free for members!): http://www.nctm.org/publications/article.aspx?id=22334

Texas Instruments provides an interactive activity for introducing Taxicab Geometry: http://education.ti.com/en/us/activity/detail?id=30A1673412FF45358F291B1E289D51F1

This link provides a means of linking Euclidean and Taxicab Geometry through the use of “school bus geometry”: http://math.rice.edu/~lanius/Geom/schbus1.html

This link provides a variety of lessons and activities to assess whether students understand the basic concepts of Taxicab Geometry, including perpendicular bisectors: http://www.pasadenaisd.org/Curr_Instr/math/images/Geometry/Geometry%20Curriculum%20Resources/Geometry%20Structure/taxicab.pdf

For possible CCGPS Standards where these assignments, and Taxicab Geometry in general can be implemented, click the button below.