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Form 6.3: Course Outline with Assessment Ideas and Activities

Analytic GeometryModule 1: Plane Analytic Geometry – The Basics

Objective Assessment Ideas Absorb Do Connect1. compile, refine, and revise a digital class glossary

Rubric for feedback and final grade

View instructor video describing glossary entries and rubric

Write and revise glossary entry

Write and revise glossary entry

2. write reflections on learning or respond to teacher-generated prompts

Rubric for forum/blog entries

Read reflection questions/prompts

Write Reflections and/or Responses


3. solve problems involving distance formula, point-of-division formulas, and slope formula

Sample Problems Pair Practice Mastery Quiz Quiz

Read instructional materials and notes

View instructional videos including examples


4. calculate the angle from one line to another





5. plot graphs of various equations





Form adapted from Smith, R. M. Conquering the Content. San Francisco: Jossey-Bass, 2008.

6. solve for intersections of equations





7. determine an equation of a locus




Sample Problems Pair Practice Mastery Quiz

8. create a Talking Worksheet Locus Workshop rubric

View Talking Worksheet example

View instructor video discussing Talking Worksheet and rubric

Solve assigned Locus Problem

Create Talking Worksheet

Locus Talking Worksheet

9. evaluate and provide feedback for locus workshop

Locus Workshop rubric

Read rubric Solve and evaluate assigned Locus Workshop problems

Write feedback for assigned Locus Workshop problems


Analytic GeometryModule 2: Vectors




Write and revise glossary entries







3. sketch a vector, write it in component form, and calculate its unit vector

Sample Problems Pair Practice Quiz




4. sketch and calculate vector sums and differences

Pass/fail vector Simulation Lab

Video feedback Sample Problems Pair Practice Quiz

Mathematica Head to Toe Vector Addition CDF for visualization



Mathematica Head to Toe Vector Addition CDF

PhET Vector applet

Vectors Simulation Lab


5. identify endpoints of a vector Sample Problems Pair Practice Quiz


Sample Problems Pair Practice Mastery Quiz



Quiz

6. sketch and calculate scalar multiples of vector sums and differences





7. use the dot product to calculate the angle between two vectors and the projection of one vector onto another



Mathematica Dot Project CDF for visualization

Mathematica Vector Projection CDF for visualization


Mathematica Dot Project CDF

Mathematica Vector Projection CDF


8. use vectors to represent forces acting upon a body, the resultant vector of multiple forces, and to determine equilibrium

Sample Problems Pair Practice Vector Forces

Partner Activity



Sample Problems Pair Practice Vector Forces

Partner Activity


Analytic GeometryModule 3: The Line











3. express the equations of lines in point-slope, two-point, slope-intercept, and intercept form, and sketch their graphs




Sample Problems Pair Practice Mastery Quiz Quiz Nine Point Circle

Activity (w/partner)

4. create and organize a matrix that depicts characteristics of the different forms of linear equations

Matrix Activity Forms of Linear Equations Matrix

Forms of Linear Equations Matrix

5. calculate the distance between two lines





6. describe families of lines and determine when particular lines are included or excluded from a family



View instructional



videos including examples

Analytic GeometryModule 4: The Circle











3. write equations of circles in standard form and general form and sketch the graph of the circle





4. use equations of circles to solve analytic geometry problems involving arcs






Analytic GeometryModule 5: Conic Sections











3. formulate and describe a cutting conics theory

Video feedback Read instructional materials and notes

Read conic sections historical notes

NCTM Cutting Conics Applet/Activity

Create video describing Cutting Conics Theory

4. sketch a conic section and discuss its properties




Parabola, Ellipse, and Hyperbola Explorations


5. use the properties of the three conic sections to solve analytic geometry problems






6. write equations of conic sections





7. design, create and self-evaluate a multimedia presentation demonstrating real world application of conic sections

Presentation rubric

View example Presentation

View instructor video describing Presentation and rubric

Create real-world conic sections multimedia presentation

8. evaluate and provide feedback for peer multimedia presentations demonstrating real world application of conic sections

Read rubric Write feedback for assigned Conic Sections Presentations


Analytic GeometryModule 6: Transformations











3. translate conic section so its vertex is now at the origin and sketch conic along with both sets of axes




Translated Parabolas applet

Translated Ellipses applet

Translated Hyperbolas applet


4. write the equation of a translated conic section





5. identify a conic section and its attributes from its equation






6. use elimination to translate conic sections algebraicallly





7. rotate a conic section through a specified angle, write the equation of the rotated section, and sketch the curve showing the old and new coordinate systems





8. rotate axes to eliminate the xy-term and sketch the conic section both before and after rotation





9. translate conic section so its vertex is now at the origin and sketch conic along with both sets of axes






Analytic GeometryModule 7: Curve Sketching











3. analyze an equation for symmetry




Drawing with Symmetry applet


4. identify intercepts of polynomial functions





5. use intercepts, end behavior and symmetry to sketch polynomial functions





6. use limits to identify all asymptotic behavior of rational functions



Asymptote of a Curve applet

Sample Problems



Pair Practice Quiz

7. use intercepts, end behavior, asymptotic behavior, and symmetry to sketch rational functions





8. use domain and range, intercepts, end behavior, asymptotic behavior, and symmetry to sketch the graph of the relation





9. create an info-graphic summarizing the principles of curve sketch for polynomial and rational functions

Info-graphic rubric

View example info-graphic

View instructor video describing info-graphic and rubric

Info-graphic


Analytic GeometryModule 8: Polar Coordinates and Parametric Graphing











3. sketch and identify the graphs of polar equations




Graphing Polar Equations applet & activity


4. solve for intersection points of polar equations





5. convert between polar form and rectangular form




Graphing Polar Coordinates applet & activity


6. identify the type and properties of conic sections represented by polar equations






7. sketch the graphs of conic sections represented by polar equations





8. eliminate a parameter and sketch the curve represented by parametric equations




Investigate Parametric Curves Applet & Activity


9. create polar graphing art OR a presentation on real world uses of polar coordinates

Polar Art Rubric OR Polar Presentation Rubric

View example art project or presentation

View instructor video describing project, presentation and appropriate rubric

Polar Art or Polar Presentation


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