EMAT 3500, Spring 2009

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

Week 0: (01/08/2009) 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 Mathematics

Georgia DOE On-Line training Materials for HS Mathematics GPS

Week 1: (01/13 & 01/15) Georgia Perfomance Standards & Characteristics of Functions

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

Week 2: (01/20 & 01/22) Number and Operations & Characteristics of Functions

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: (01/27 & 01/29) 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: (02/03 & 02/05) 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: (02/10 & 02/12) 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 (02/17 & 02/19) 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: (02/24) Midterm Practice Exam

Click here to download Dynagraphs_5.gsp

(02/26) Midterm Practice Review

Week 8: (03/03) Mid-Term Exam on Functions

(03/05) 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: (03/17 & 03/19) 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.

<>Week 10: (03/24 & 03/26) Experimental Labs with TI-Nspire
            03/24: Discussion of Experimental Labs
03/26: Experimental Labs
                Collecting data from lab experiments
                Finding function graphs to fit your data from your lab experiments

Week 11: (3/31 & 4/02) Representing and Analyzing Data from Experimental Labs           

                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
Line of best fit for a set of data pairs: Signed, Absolute and Squared deviations
                Discussion of implications of labs for teaching

Week 12: (04/07 & 04/09) Data Explorations & Probability

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: (04/14 & 04/16) 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: (04/21 & 04/23) Modelling with GSP (continued)

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

Proposals for Final Projects due

Week 15: (04/28)  Work on final projects

Final Projects due on Monday, May 4 before 5:00 p.m.

Final Exam (Project Presentations): TBD
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