Illinois State University Mathematics Department

 MAT 326: Technology Tools for Secondary School Mathematics Dr. Roger Day (day@ilstu.edu)

### Session #2

27 August 2012

Warming Up: Mathematics is Everywhere!

Patio Cement Problem
Syllabus Questions?

Exploration: Quadratics Functions and Their Graphs

Last time, in small groups,  using these guidelines, you began to carry out an exploration of graphs of quadratic functions, focusing particularly on the vertex of the parabola. Prior to the end of last week's class (8/20/12), your group:
* created a non-technology conjecture related to each of the three parameters, a, b, and c, in the general quadratic function; and
* explored the accuracy of those conjectures using technology such as your graphing calculator or Geometer's SketchPad.
Your charge at the end of class was to have ready, for today's class, two sets of conjectures: your first set, non-tech based, as completed last time, and a revised set, based on evidence generated using technology. During today's class session, we'll proceed with this investigation, extending to the third and fourth stages as described on the exploration guidelines.

• Based on your updated conjectures, prove each of them. We'll discuss in class what constitutes proof.
• Complete Stage IV of the exploration by generating small-group responses to the reflection questions.

Extending the Technology: Parameters, Sliders, and Polynomials

• Study the Overview of Geogebra 1 tutorial and use that information to create a Geogebra file similar to the GSP file (GSPDay1) with sliders for exploration of quadratic graphs. Each student should submit a Geogebra file using the following file name convention:
• LASTNAMEfirstnameGGB0827.ggb
• For example, Floyd Pattersen's file would be PATTERSENfloydGGB0827.ggb
• Email that file to me.
• Study the GSP5_Slider video tutorial and use that information to create a GSP5 file, with two tabs, with sliders exploration for the following families of functions.
• y = ax + b and
• y = ax3 + bx2 + cx + d

Each student should submit a SketchPad file (two tabs, one for each family of functions) using the following file name convention:

• LASTNAMEfirstnameGSP0827.gsp
• For example, Linda Larsen's file would be LARSENlindaGSP0827.gsp
• Email that file to me.

Participating in a Research Project

Assignments for Next Time: Session #3 (3 Sept 2012)

• Continue group work on Quadratic Graphs exploration. We will bring closure to this. See 9/10/12 requirements below.
• Continue work on solving the Patio Cement Problem.
• Submit via email Geogebra (quad sliders) and GSP5 files (linear and cubic sliders) as described above. Due by midnight, Monday, 9/3/12.
• Look at this PDF file and watch this video. Practice using the equation editor by creating a file (Word or Work) that shows all the mathematical symbolism on the PDF handout. Each student should submit a Word or Work file using the following file name convention: LASTNAMEfirstnameEW10827.docx  For example, Sam Stuwart's file would be STUARTsamEW0827.docx Email the file to me by Friday, 9/7/12.

Assignments for Session #4 (10 Sept 2012)

• Continue group work on Quadratic Graphs exploration. Bring to class on Monday 9/10/12 a draft copy of your group's work, with complete responses to Stages I through IV as described in the exploration guide. One submission per small group.
• Begin to look for and critique mobile apps that focus on school mathematics, preferably secondary school mathematics. More info on this to follow.

 Session Links and Resources GSPDay1 Overview of Geogebra 1 (YouTube) GSP5_Slider (Jing)

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