# Technology and Secondary School Mathematics

## Spring Semester 2016

This is the web site page devoted to EMAT 4680/6680 Technology and Secondary School Mathematics at the University of Georgia as led by Jim Wilson. The development of this course was assisted by my involvement in the Learning and Performance Support Laboratory, University of Georgia. A little support was provided from grants GRA/GCATT94.02 and GRA/GCATT94.03 of the Georgia Research Alliance and the Georgia Center for Advanced Telecommunications Technology.

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Send e-mail to jwilson@uga.edu

EMAT 4680/6680 Student Pages

## Some Papers

Roots 2 and 5. This paper examines sets of equations that have graphs crossing the x-axis only at 2 and 5. For a preview on one family of such graphs, click here.

Exploration of a Triangle Ratios Problem. Given a triangle ABC and an interior point M. Extend a segment from each vertex through M to its intersecion with the opposite side creating segments AD, BE, and CF. The exploration will evaluate some ratios of segments within the triangle.

EMAT 4680/6680 Documentation

EMAT 4680/6680 Syllabus - General information about the objectives and operation of the course.

EMAT 4680/6680 Explorations 00 This set of mathematics explorations is to help develop familiarity with graphing of relations and functions using various technology applications.

EMAT 4680/6680 Explorations 01 - Problems and explorations with graphing functions and relations.

EMAT 4680/6680 Explorations 02 - Problems and explorations with second degree equations.

EMAT 4680/6680 Explorations 03 - Quadratic and Cubic Equations.

EMAT 4680/6680 Explorations 04 - Centers of a Triangle.

EMAT 4680/6680 Explorations 05 - Making and using scripts.

EMAT4680/6680 Explorations 06 - Problems.

EMAT 4680/6680 Explorations 07 - Tangent Circles.

EMAT 4680/6680 Explorations 08 - Altitudes and Orthocenters.

EMAT 4680/6680 Explorations 09 - Pedal Triangles.

EMAT4680/6680 Explorations 10 - Parametric Equations.

EMAT 4680/6680 Explorations 11 - Polar Equations.

Mathematics Problems and explorations with spreadsheets.

Challenges

The "Challenges" are some extracurricular activity for the course -- that is, they are explorations that may be boring,  attention grabbing, waste of time, or other derogatory descriptions.    But hey, so was Star Wars.  Take a look as this section grows.

Challenge 1.     Can you figure out how to generate this pattern.
Click on the Challenge link to see a full size picture.

Challenge 2.     Try to mentally calculate the yellow area.  What different ways might successful problem solvers use?  The challenge is to find several rather than looking for "the best."

Challenge 3.    Find an equation to draw this figure.

a. With Graphing Calculator
b. With Geogebra
c. With Desmos
d. Plot without technology

### Course Feedback

(This link will be made active near the end of the semester)

### What is a WRITE-UP?

Write-Up #1 (Graphs). The first write-up is a problem from Exploratons 1 -- you select.

Write-Up #2 (Quadratics). The second write-up is a problem from Explorations 2 -- you select.

Write-Up #3 (Quadratic Equations). This is Explorations 3.

Write-Up #4 (Concurrencies of a triangle). Something from Explorations 4 on the Centers of a Triangle exercises.

Write-Up #5 (GSP Script Library). Make a link to your web page to connect to your file of GSP Scripts. This will be expanding throughout the quarter.

Write-Up #6 (Problems). Select one of the 10 explorations in Explorations 6 for a Write-up.

Write-Up #7 (Tangent Circles). The investigation explores the set of circles tangent to two given circles and the locus of their centers. The write-up is to select some aspect of the investigation for a discussion.

Write-Up #8 (Altitudes and Orthocenters). Select one of the explorations in Problems 1 - 9 of Explorations 8 for a Write-up.

Write-Up #9 (Pedal Triangles). The investigation explores aspects of the Pedal Triangle associated with a Pedal Point of a triangle. The write-up is to select some aspect of the investigation for a discussion.

Write-Up #10 (Parametric Equations). Select one of the 12 explorations in Explorations 10 for a Write-up.

Write-Up #11 (Polar Equations). Select one of the 5 explorations in Explorations 11 for a Write-up.

Write-Up #12 (Spreadsheets). Select one of the 12 explorations in Explorations 12 for a Write-up.