## Reflection: Student Ownership Quiz and Intro to Graphs of Polynomials - Section 3: Group Time to Generate Questions

In my own enthusiasm for the content, it can sometimes be difficult to stop myself from simply dictating what is interesting or intriguing to me. It can be equally difficult to trust that, if left to their own devices, students can and will recognize their own patterns and ask their own questions. By the time students reach high school it is sadly common that their enthusiasm for inquiry has been stifled. It takes time to get it back, but is well worth the effort.

In this exercise, I ask students to look at some mathematics and ask their own questions: first individually, then in collaboration with a small group of peers, and finally as a large group analysis of the ‘best questions.’ Hesitant students might need an initial probe from me. I might ask, “If you were a scientist and wanted to sort these graphs, how would you do that? How about the equations? Do your sorted groups help you see any patterns?”

It would be a lot faster and easier if I simply wrote my question on the board at the start: “Is there a relationship between the degree of a polynomial and the shape of its graph?” However, when the students inevitably ask this question themselves, along with several other probing questions, they own this lesson and are more motivated to find the answers. There is hardly a question they can ask that will not take us in a direction that is rich, useful, and even standards aligned.

Directing Student Inquiry
Student Ownership: Directing Student Inquiry

# Quiz and Intro to Graphs of Polynomials

Unit 4: Polynomial Theorems and Graphs
Lesson 8 of 15

## Big Idea: The graph of a polynomial can look a variety of ways depending on the degree, lead coefficient, and linear factors.

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Standards:
Subject(s):
fundamental theorem of algebra, Math, Polynomial and Rational Functions, Algebra 2, polynomial division, Remainder Theorem, graphing polynomial function, polynomial identities, Algebra
90 minutes

### Colleen Werner

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