# Reema Alnizami

Mathematics Education

North Carolina State University

Modelin activity

Hello Ma 581 students, This is my Modeling activity work sheet ModelAct and this is the Fthom document associated with the activity FathomModelAct. The students will also be given the population-data sheet that we used in class.

### The Geometric Mean & the Right Triangle

This interactive activity is designed with the follwoing standards and objectives in mind:

NCTM process standards (2004):

• Reasoning and proof: make and investigate mathematical conjectures (2.02).
• Communication: communicate their mathematical thinking coherently and clearly to peers, teachers, and others (3.02).
• Connections: understand how mathematical ideas interconnect and build on one another to produce a coherent whole (4.02).

NC Standard Course of Study objectives (2004): In grades 9-12, all students should

• Analyze characteristics and properties of two-dimensional and three-dimensional geometric shapes and develop a mathematical argument about geometric relationships: - Explore relationships (including congruence and similarity) among classes of two-and three-dimensional geometric objects, make and test conjectures about them, and solve problems involving them (1.02);
• Use visualization, spatial reasoning, and geometric modeling to solve problems: - visualize three-dimensional objects and spaces from different perspectives and analyze their cross sections (4.02).

Performance objectives:

• Given a right triangle with the altitude drawn to the hypotenuse, students will use similarity of the three resulting right triangles to conclude proportions.
• Given a right triangle with the altitude drawn to the hypotenuse, the student will state the three geometric means.
• Given length parameters of a right triangle with an altitude drawn to the hypotenuse, the student will calculate other parameters using the definition of the geometric mean.

References
Geometry standard for grades 9–12 (2004). National Council of Teachers of Mathematics.