Reflection: Complex Tasks A Gallery of Cubic Functions, Day 1 of 2 - Section 3: Solving Problems Collaboratively


Since this problem set is so complex, you can expect quite a few errors along the way.  Watch carefully for them, but don't rush to correct every one of them immediately.  I often find that my students learn more when then are given time and space to recognize their errors for themselves.  Once they realize that something doesn't make sense, they will be motivated to look for a solution and recognize its significance.

It's common for students to mismatch a few graphs.  This may happen because they're being too hasty, or it may be due to some deeper misconception.  Typically, they notice this mistake when they try using the roots visible on the graph to find the factors of the equation.  In this case, I'll ask how they went about matching graphs to equations.  From here, I can typically help them to see that this particular graph doesn't match this equation.

I also find students sometimes spend a long time trying to factor a quadratic equation that does not have real solutions (I'm thinking of the second & third equations).  In this case, I want to encourage them to use the graph!  If they've found the correct graph for these equations, they can see that this function only has one real root.  If they've already found one linear factor, they can be pretty confident there aren't any more.

Finally, I've found that some of my students seem to forget that they already know how to solve quadratic equations.  For some reason, when they find a quadratic factor of a cubic equation, they are hesitant to treat it like other quadratics.  If I suggest making use of the discriminant of the quadratic formula, for instance, they may ask, "Does that still work in this case?"

  Errors to Watch For
  Complex Tasks: Errors to Watch For
Loading resource...

A Gallery of Cubic Functions, Day 1 of 2

Unit 3: Cubic Functions
Lesson 5 of 13

Objective: SWBAT match graphs to equations for a variety of cubic functions. SWBAT convert a cubic equation from expanded form to factored form when roots are given.

Big Idea: The equation helps us identify the graph, and the graph helps us factor the equation!

  Print Lesson
Math, cubic equations, polynomial functions, Polynomial Roots, Graphing (Algebra), Algebra 2, master teacher project, cubic functions, Algebra 2, function
  45 minutes
art exhibition
Similar Lessons
Sketching Graphs of Polynomial Functions
12th Grade Math » Polynomial and Rational Functions
Big Idea: Build upon existing knowledge of second and third degree functions to sketch graphs of other polynomial functions.
Troy, MI
Environment: Suburban
Tim  Marley
Choosing a Method to Find x-intercepts
Algebra I » Quadratics!
Big Idea: Students take a step back from their work to examine a variety of quadratic functions and reflect on why they might choose one method over another.
Boston, MA
Environment: Urban
Amanda Hathaway
Rational Roots and Remainders: Important Theorems of Polynomials
12th Grade Math » Polynomial Functions and Equations
Big Idea: Using polynomial division students discover the Remainder Theorem & then learn about the Rational Root Test.
Phoenix, AZ
Environment: Urban
Tiffany Dawdy
Something went wrong. See details for more info
Nothing to upload