## 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

# A Gallery of Cubic Functions, Day 1 of 2

Unit 3: Cubic Functions
Lesson 5 of 13

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

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Subject(s):
Math, cubic equations, polynomial functions, Polynomial Roots, Graphing (Algebra), Algebra 2, master teacher project, cubic functions, Algebra 2, function
45 minutes

### Jacob Nazeck

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