Christa Tucker - Tech Grads

Identify concept and sub-topics:

Concept: Quadrilaterals

Sub-topics: a. trapezoids b. parallelograms c. kites

Dimensions of understanding:

Students will discuss polygons (quadrilaterals) by classifying them and describing attributes (properties) of the various figures they present.

Geometric structure:

(G.1) Geometric structure: knowledge and skills and performance descriptions.

The student understands the structure of, and relationships within, an axiomatic system.

(A) The student develops an awareness of the structure of a mathematical system, connecting definitions, postulates, logical reasoning, and theorems.

(G.2) The student analyzes geometric relationships in order to make and verify conjectures.

(A) The student uses constructions to explore attributes of geometric figures and to make conjectures about geometric relationships.

(B) The student makes conjectures about angles, lines, polygons, circles, and three-dimensional figures and determines the validity of the conjectures, choosing from a variety of approaches such as coordinate, transformational, or axiomatic.

(G.3) The student applies logical reasoning to justify and prove mathematical statements.

(D) The student uses inductive reasoning to formulate a conjecture.

New topics/relations:

In order for students to be prepared for the rigor in higher level mathematics courses such as AP Calculus or Pre-AP mathematics courses, the depth and breadth of 8^th grade geometry TEKS should not be treated equally.  Therefore, the Dana Center has established clarifying activities on those TEKS in order for students to apply higher order thinking skills to concepts such as identifying and making conjectures about the distinguishing properties of the polygons that make up the quadrilateral family.  For example, which properties distinguish a kite from a parallelogram.

Instructional Technology:

In order for students to make conjectures they should use technology such as GeoGebra and Inspiration.  GeoGebra is an interactive geometry application with graphical features.  Also, student may utilized Inspiration Mind Mapping software or Inspiration Map iPad app to create Venn Diagram of the quadrilateral family.

 

References

Mathematics TEKS Toolkit (2012). Charles A. Dana Center at The University of Texas at Austin. Retrieved from http://www.utdanacenter.org/mathtoolkit/instruction/lessons/geo_quad.php

Texas Essential Knowledge and Skills (2010). Texas Education Agency. Retrieved from http://ritter.tea.state.tx.us/rules/tac/chapter111/ch111c.html