# 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.

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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.*

Retrieved from http://standards.nctm.org/document/chapter7/geom.htm

### The teacher's notes for this activity is found at: Teacher Sheet

### Follow this link to view the activity and the student work sheet: JSP Student Activity