2.+Standards+for+Taxicab+Geometry

**GPS Standards** **M4G1. Students will define and identify the characteristics of geometric figures through examination and construction.** b. Describe parallel and perpendicular lines in plane geometric figures. c. Examine and classify quadrilaterals (including parallelograms, squares, rectangles, trapezoids, and rhombi) by their properties. d. Compare and contrast the relationships among quadrilaterals.

-For students to do taxicab geometry, they need to have a good understanding of the properties of shapes, especially when drawing Euclidean shapes into taxicab shapes. Also, parallel and perpendicular lines are used in grids and students should be familiar with these concepts as well.

**M4G3. Students will use the coordinate system.** a.Understand and apply ordered pairs in the first quadrant of the coordinate system. b.Locate a point in the first quadrant in the coordinate plane and name the ordered pair. c.Graph ordered pairs in the first quadrant.

-The coordinate system is fundamental to taxicab geometry. In this geometry, students use ordered pairs to plot points, create lines, and contruct shapes. Although students will have knowledge of the coordinate system, they will learn taxicab geometry to strengthen their understanding.

**M6G1. Students will further develop their understanding of plane figures.** -Refer to M4G1 reasoning.

**M7N1. Students will understand the meaning of positive and negative rational numbers and use them in computation.** a. Find the absolute value of a number and understand it as the distance from zero on a number line. -Taxicab geometry has a formula that involves the concept of absolute value. Thus, the students need to understand how absolute values affect the formula.

<span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">**M7G1. Students will construct plane figures that meet given conditions.** <span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">a. Perform basic constructions using both compass and straight edge, and appropriate technology. Constructions should include copying a segment; copying an angle; bisecting a segment; bisecting an angle; constructing perpendicular lines, including the perpendicular bisector of a line segment; and constructing a line parallel to a given line through a point not on the line. <span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">-Whenever the students draw taxicab shapes, they need to have a firm grasp on the basic constructions. Some of the constructions stated above look different in taxicab than in Euclidean geometry.

<span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">**M7A3. Students will understand relationships between two variables.** <span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">a. Plot points on a coordinate plane. <span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">-Students should know how to plot points onto a grid and understand the aspects of the x-axis versus the y-axis.

<span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">**M8G2. Students will understand and use the Pythagorean theorem.** <span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">a. Apply the properties of right triangles, including the Pythagorean theorem. <span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">-The students will work closely to right triangles but will not need to work with the Pythagorean theorem. However, the Pythagorean theorem will help the student understand how taxicab geometry and Euclidean geometry are related. Taxicab geometry builds up to the Pythagorean theorem. <span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">** References: ** <span style="display: block; font-family: 'Times New Roman',Times,serif; font-size: 110%; text-align: left;">Georgia Department of Education Kathy Cox, State Superintendent of Schools September 11, 2008 All Rights Reserved Page 9 of 16 <span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">[|http://www.learner.org/teacherslab/m][|a][|th/geometry/shape/taxicab/taxicab_background.html]-This site helped open up all the possibilities of standards that can be related.