EMAT 3500, Fall 2009

Exploring Concepts (with Technology) in Secondary School mathematics
Outline (Subject to adjustments as needed)

Week 1: (08/18 & 08/20) National and State Standards for Mathematics Teaching

Setting up electronic communications (email and network)

Introduction and discussion of NCTM Principals & Standards

Introduction to the new Georgia Performance Standards for Mathematics 6-12.
Georgia Department of Education Resource page for GPS.

Georgia DOE On-Line training Materials for HS Mathematics GPS
Sharing e-Examples from the NCTM Principles & Standards
Introduction to GSP4 and Excel

Explore Task 1 from Unit 1 (Exploring Functions with Fiona) of the GPS Math 1 Frameworks using the Excel Spreadsheet.

<>Explore the Fences and Functions task from Unit 1 of the GPS Frameworks using Matt Winking's GSP Sketch

Week 2: (08/25 & 08/27) Number and Operations & Characteristics of Functions

Explore Matt Winkings On-line Resources for Units 1 and 2 of the 9th Grade GPS Frameworks.

Chapter 6 from Transforming Mathematics with GSP

The Slide Rule (download GSP Slide Rule)
Constructing a product of two numbers on a number line using dilation (connecting with transformational geometry) (download GSP sketch)
(Download Numberline Tool)
Investigating arithmetic relations dynamically: Mystery Machines

Mystery Combinations

Chapter 7 from Transforming Mathematics with GSP

Dynamic algebraic functions using transformations
Constructing a linear function through dilation and translation
Constructing powers of x through dilation
Comparing Functions on parallel number lines

Week 3: (09/01 & 09/03) Exploring Functions with GSP

Click on the following links to download GSP sketches for these activities:

Click here to download a starting dynagraph sketch

Exploring the behavior of functions with Dynagraphs
Composing functions using a sequence of Dynagraphs

From Dynagraphs to Rectangular Coordinates.

Investigating different functions using both Dynagraphs and Rectangular Coordinates

Operations on functions using multiple coordinate systems

Week 4: (09/08 & 09/10) Further Explorations of Functions with GSP

Download Classwork from 9/11/07
Activity 7.4 from
Transforming Mathematics with GSP:
Transformations of the quadratic function
Using GSP4 as a function-grapher

Explore Matt Winking's GSP sketch for Unit 5 of the 9th grade GPS Framework

Week 5: (09/15 & 09/17) Trigonometry of the unit circle with GSP

Chapter 8 from Transforming Mathematics with GSP
Click here to download a starter sketch for the trig functions based on a unit circle

Week 6 (09/22 & 09/24) Investigating Functions

Sorting Functions
Conic functions through paper folding
    Download Chapter 13 from
Transforming Mathematics with GSP: Conic Sections
GSP Simulation of paper folded conics

Week 7: (09/29) Midterm Practice Exam

Click here to download Dynagraphs_5.gsp

(10/01) Midterm Practice Review

Week 8: (10/06) Mid-Term Exam on Functions

(10/08) Introduction to Probability
Download Unit 4 from the Math 1 Frameworks. Look through the definitions for calculating probabilities of random events using the idea of Random Spinners. Design a Random Spinner using GSP.

Week 9: (10/13) Introduction to the TI-Nspire Handheld technology

Download the Intro-BeginningTI-Nspire.pdf document. We shall work through this introduction.
Download the NumOps-USPopulation-Student.pdf document and the PTE-NumOps-USPopulation_EN.tns TI-Nspire file. We shall work through this example in class.

(10/15) Visit to GCTM Annual Conference at Rock Eagle

Week 10: (10/20 & 10/22)
            (10/20) Reports of Visit to GCTM Conference

Discussion of Experimental Labs

(10/22) TI-nSpire Training with Data Collection Devices
Experimental Lab Preparations

Week 11: (10/27 & 10/29) Using TI-nSpire and Fathom to Collect and Analyze Data

        (10/27) Experimental Labs
                Collecting data from lab experiments
                Finding function graphs to fit your data from your lab experiments

        (10/30) Representing and Analyzing Data from Experimental Labs           
                Click here to access the TI-Nspire files for each group's data
Line of best fit for a set of data pairs: Signed, Absolute and Squared deviations
                Discussion of implications of labs for teaching

Week 12: (11/03 & 11/05) Data Explorations & Probability

Activities from: Discovering Algebra 1 with the TI-nSpire (From Key Curriculum Press, copyright 2009)
                    Simulation of Radioactive Decay (pages 67-69 of Exponential Equations PDF)

Download the TI-nSpire file Radioactive Decay.tns

More Activities from Discovering Algebra 1 with the TI-nSpire
Polynomial Factoring--Maximum Area of a Folded Triangle (pages 119-121 of Quadratics and Higher Degree Polynomials PDF)  

An example Integrated Mathematical Exploration
Geometric Probability and Curve Fitting using Fathom and/or TI-nSpire
Click here to download the Fathm activity.
Click here to download the TI-nSpire document Monte Carlo.tns
Week 13: (11/10 & 11/12) Modelling with GSP

Chapter 9 from Transforming Mathematics with GSP
        Using GSP to model physical situations and generate data:
The Biggest Box Problem (click here to download a sophisticated sketch of the problem)

The Cardboard View-Tube Problem (Click here to download a starter sketch)

Week 14: (11/17 & 11/19) Modelling with GSP (continued)

Discussion of simulations from the Biggest Box and View-Tube experiments

Proposals for Final Projects due

Week 15: (12/01 & 12/03)  Work on final projects

Final Projects due on Tuesday, December 8th before 5:00 p.m.

Final Exam (Project Presentations): Tuesday, December 15, 8:00-11:00 a.m. in room 111/113
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