Standards

As detailed on the syllabus, your assessment grade in this course will be determined by your proficiency on a variety of standards. (This is known as Standards Based Grading.)

Here is the list of standards that form the basis for this class, along with guiding questions that address each standard. You will be assessed on these standards throughout the semester.

What is different from the high-stakes "tests" that you might associate with a math class, there is an opportunity for you to re-assess your knowledge if you did not master the knowledge the first time around.

The Standards

Standard 1. Mathematical Collaboration. Have you met with classmates and completed the writing prompts that are assigned at regular intervals in the class?

Standard 2. Functions. Can you give the definition of a function? Can you determine if a given rule, table, or curve represents a function?

Standard 3. Cartesian Coordinates and Graphing. Can you determine the Cartesian coordinates of a given point? Can you place a point at a given coordinate pair? Given a function f and a number x, can you plot (x,f(x)) on a set of axes? Given a function f, can you plot points that lie on the graph of f?

Standard 4. Introduction to Desmos including graphing. Can you create folders and text cells in Desmos? Can you create lists of points in Desmos and connect them with line segments? Can you have Desmos produce the graph of a real function? Can you change the color and opacity of the graphs Desmos creates? Can you use parameters and sliders to visualize how the graph of a function changes when you modify its parameters?

Standard 5. Parent Function Recognition. For linear, parabolic, cubic, square root, exponential, logarithmic, and rational functions: Given the curve of a function, can you determine which type of function it represents? Given the equation of function, can you determine what shape its curve will have?

Standard 6. Implicit Functions. Do you understand the difference between a real function and an implicit function? Do you know the implicit function formulas for a circle, diamond, and astroid? Can you have Desmos produce the graph of an implicit function?

Standard 7. Elements of Art and Principles of Design.

Standard 8. The Aesthetics of Mathematical Functions.

Standard 9. Translations. Do you understand what a translation is? Can you apply desired translations to a real function? Can you apply desired translations to an implicit function? Can you determine the translation that transforms an initial curve into a final curve? Given an initial curve and a translation of the curve, and the equation of the initial curve, can you determine the equation of the translated curve?

Standard 10. Sequences and Number Patterns. Do you understand what a sequence is? Can you create a sequence from a given function? Can you determine a pattern in a given sequence of numbers? Can you write this pattern down in words? Can you write this pattern down as an equation? Can you use this equation to recreate the pattern as a list in Desmos?

Standard 11. Creating Families of Translates. Can you use Desmos to create artwork involving the translations of a parent function or implicit function?

Standard 12. Realizing Digital Art with a Pen Plotter. Can you export your Desmos file and print it on an AxiDraw Pen Plotter?

Standard 13. Reflections. Do you understand what a reflection is? Can you apply a horizontal reflection to a graph of a real (or implicit) function? A vertical reflection? A reflection across the line y=x? An absolute reflection? If you are given an initial and reflected graph, along with the equation of the initial graph, can you determine the equation of the reflected graph?

Standard 14. Dilations. Do you understand what a dilation is? Can you apply a horizontal dilation to a graph of a real (or implicit) function? A vertical dilation? If you are given an initial and dilated graph, along with the equation of the initial graph, can you determine the equation of the dilated graph?

Standard 15. Multiple Transformations. If you have a collection of transformations that are applied to an initial curve, can you determine the equation of the final curve? If you are given an equation of a composition of transformations, can you determine its graph by applying a sequence of transformations from the initial curve?

Standard 16. The Unit Circle. Can you convert between radians and degrees? Can you find specified angles on the unit circle? Can you determine the x- and y-coordinates of a point on the unit circle?

Standard 17. Sine and Cosine Functions. Do you understand how the unit circle is related to the sine curve and the cosine curve? Can you apply all the techniques of transformations, including translations, reflections, and dilations to the sine and cosine functions? Can you determine the equation of a sine or cosine function that has a specified range?

Standard 18. Polar Functions. Do you understand what a polar function is? Can you have Desmos produce the graph of a given polar function?

Standard 19. Basic Polar Functions. Do you know the polar equation of a circle? a rose? a rhodonea curve?

Standard 20. Transformations of Polar Functions. Expert: Can you apply rotations, reflections, and dilations to polar functions? What does r=af(b(θ-θ₀))+r₀ do?

Standard 21. Choosing materials intentionally.

Standard 22. Plotting Multiple Layers with a Pen Plotter.

Standard 23. Parametric Functions. Do you understand what a parametric function is? Can you plot points that lie on the graph of a basic parametric function? Can you have Desmos produce the graph of a parametric function?

Standard 24. Basic Parametric Functions. Do you know the parametric equations of a line? a circle? a Lissajous Curve? Can you convert a function of the form y=f(x) or x=g(y) into a basic parametric function of the form (p(t),q(t))?

Standard 25. Transformations of Parametric Functions. Can you apply reflections, translations, and dilations to parametric functions? How does the graph of (a•p(bt)+h,c• q(ct)+k) compare to the graph of (p(t), q(t))?

Standard 26. Rotations of Curves. Do you understand how to rotate a point (x,0) or (0,y) by an angle θ around the origin? Do you understand how to rotate a point (x,y) by an angle θ around the origin? Can you rotate parametric curves by an angle θ around the origin?

Standard 27. Linear Interpolations. Do you understand how to create a linear interpolation between two points? Do you understand how to create a linear interpolation between two curves? Can you use Desmos to create a family of parametric curves that interpolate between two curves? Expert: Can you create a non-linear interpolation between two curves?

Standard 28. Realizing Digital Art with another machine.