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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.