GPS Alignment Course

The purpose of this course is for teachers to:

• Develop mathematical content knowledge
• Explore mathematical investigations using technology
• Become more technology proficient
• Align mathematical investigations with Georgia Performance Standards

The participants in this course will be expected to:

• Complete 5 write-ups and align work with the GPS's
• Complete 5 write-ups that align to given GPS's
• Complete 2 lesson plans aligning with GPS's

Week 1  Number Concept – Integers                   

1. Introduction to InterMath
2. Discussion of GPS's
3. Group investigations
       How Old are Three Daughters?
       McNugget Numbers
4. Introduction to Excel
5. Discussion of write-up and Individual Investigations
       Planning Cruises
       The Frog Race
       Locker Counting

Week 2  Number Concept – Integers

1. Group investigations
       Want to be a Millionaire?
       Square Root Patterns
2. Discussion of GPS’s and write-up
3. More on Excel
4. Individual investigations
       Double Exponents & Same Base Multiples & Exponents
       Irrational to Rational
       The Last Digit
5. Write-up to include GPS’s that could come up in class discussion and how they could come out.

Week 3   Number Concept – Rational Numbers

1. Group investigations
       Creating Integers
       The Salesman and the Eggs
2. Discussion of GPS’s and write-up
3. More on Excel
4. Individual investigations
       Ordering Fractions
       Fractional Parts
       Johnny's Rule
       Buying Pollywogs
5. Write-up to include GPS’s that could come up in class discussion and how they could come out.

Week 4  Algebra – Patterns

1. Group investigations
       Arranging Toothpicks
       Pascal's Patterns
2. Discussion of GPS’s and write-up
3. Individual investigation of problem found by participants that should elicit discussion of given GPS’s
       Consecutive Odds and Evens
       Going Fishing
       Tri-Square Trios
4. Write-up to include GPS’s that could come up in class discussion and how they could come out.

Week 5  Algebra – Patterns

1. Group investigations
       Theater Seating
       Gretel's Goldfish
2. Discussion of GPS’s and write-up
3. Individual investigations
       Hot Air Balloons
       Counting Stones
       Squares on a Checkerboard
       Hypatia's Triumph
4. Write-up to include GPS’s that could come up in class discussion and how they could come out.

Week 6  Algebra – Functions

1. Group investigations
       Modifying the Slope and Y-Intercept
       Triangle from a Line
2. Introduction to Graphing Calculator
3. Discussion of GPS’s and write-up
4. Individual investigations
       Multiple Inequalities
       Burglar Alarm
       Counting Coins
5. Write-up to include GPS’s that could come up in class discussion and how they could come out.

Week 7  Algebra – Functions

1. Group investigations
       Intersecting Functions
       Composite Functions
2. Review of Graphing Calculator
3. Discussion of GPS’s and write-up
4. Individual investigations
       Multiple Solutions
       Bouncing Ball
       Supper with Skiing
       Using Roots to Generate an Equation
5. Write-up to include GPS’s that could come up in class discussion and how they could come out.

Week 8  Algebra – Graphing

1. Group investigations
       Comparing Lines
       Intersecting Graphs
2. Review of Graphing Calculator
3. Discussion of GPS’s and write-up
4. Individual investigations
       Coefficients that Effect the Graph
       Temperature Comparisons
       Solving Graphically
       X-Intercept Transformation
5. Write-up to include GPS’s that could come up in class discussion and how they could come out.

Week 9  Geometry – Points, Lines, and Planes

1. Group Investigations
       All Swimmed Out
       Sum of Exterior Angles
2. Introduction to Geometer’s Sketchpad
3. Discussion of GPS’s and write-up
4. Individual Investigations
       Intersecting Chords
       Constructing Quadrilaterals
       Intersecting Circles
5. Write-up to include GPS’s that could come up in class discussion and how they could come out.

Week 10 Geometry – Circles

1. Group Investigations
       Maximal Volume of a Cone
       Angles in a Circle
2. Discussion of GPS’s and write-up
3. Individual Investigations
       Tangent Along the Diameter
       N-Sided Circle
       Changes in the Circumference
4. Write-up to include GPS’s that could come up in class discussion and how they could come out.

Week 11  Geometry – Triangles

1. Group Investigations
       Triangle Inside a Rectangle
       Half as Much May be Right
2. Discussion of GPS’s and write-up
3. Individual Investigations
       Classified Information
       Capture the Flag
       Casting Shadows
4. Write-up to include GPS’s that could come up in class discussion and how they could come out.

Week 12  Geometry – Quadrilaterals

1. Group Investigations    
       Two Squares
       Penning for Pony
2. Discussion of GPS’s and write-up
3. Individual Investigations
       Mystery Quadrilaterals
       Water Stop
       Minimum Perimeter
4. Write-up to include GPS’s that could come up in class discussion and how they could come out.

Week 13  Geometry – Polygons

1. Group Investigations    
       Tessellation Restrictions    
       Sum of Angles in a Polygon
2. Discussion of GPS’s and write-up
3. Individual Investigations
       Apothem and Area
       Symmetry Lines
       Pentagram Triangles
4. Write-up to include GPS’s that could come up in class discussion and how they could come out.

Week 14  Data Analysis – Probability

1. Group Investigations
       Adding Marbles
       Rolling Die
2. Discussion of GPS’s and write-up
3. Individual Investigations
       Increasing Your Chances
       One Probability
       Varying Probabilities
4. Write-up to include GPS’s that could come up in class discussion and how they could come out.

Week 15  Data Analysis - Statistics

1. Group Investigations
       Ten Apart and Introducing Outliers    
       Taking Classes   
2. Discussion of GPS’s and write-up
3. Individual Investigations
       Computer Usage
       Transformations of Data
       Favorite Dessert
4. Write-up to include GPS’s that could come up in class discussion and how they could come out.

Note to Instructor: The instructor pages include GPS alignment and how we envision the mathematical content could develop in a class discussion or an individual exploration. What we have outlined for each GPS alignment is merely a possibility and may or may not appear in your class discussion. Likewise, you may find other GPS's that align with a given investigation that we have not included.