This Warm-up prompts students to compare four expressions. It gives students a reason to use language precisely (MP6). It gives the teacher an opportunity to hear how students use terminology and talk about characteristics of the items in comparison to one another.

Invite each group to share one reason why a particular set of three go together. Record and display the responses for all to see. After each response, ask the class if they agree or disagree. Since there is no single correct answer to the question of which three go together, attend to students’ explanations, and ensure that the reasons given are correct.

During the discussion, prompt students to explain the meaning of any terminology they use, such as “coefficient,” “term,” “constant,” and “exponent,” and to clarify their reasoning as needed. Consider asking:

• “How do you know ?”
• “What do you mean by ?”
• “Can you say that in another way?”

If not brought up in students’ explanations, remind them of vocabulary such as coefficient, leading coefficient, and term. For example, “The term with the largest exponent has a coefficient of 1,” can be rephrased to say, “The leading coefficient is 1.”

Then, introduce students to degree, the largest exponent on a variable in a polynomial, as one way polynomials are classified. It may be helpful to show students that expression A, a 3rd-degree polynomial, can be written as , so even if an expression for a polynomial is written in factored form, the distributive property can always be used to rewrite it to more clearly identify features like the degree. More about how to do this will be addressed in future lessons.

In this activity, students analyze representations and structures closely and make connections (MP7). There is no need to formalize these connections at this time, since the activity is meant as an introduction to the mathematical work ahead and an opportunity for students to develop some basic intuition for what polynomials can look like.

Students should focus on the structure of the expressions, such as the constant term or the value of the expression at specific values of , in order to identify which expressions and graphs belong to the same polynomial function, so graphing technology is not an appropriate tool. Instead, making scientific calculators available gives students an opportunity to choose appropriate tools strategically (MP5).

Students continue to develop their understanding of how the shape and features of the graph representing a polynomial connect to the structure of the expression (MP7). This activity is meant to be an informal study in which students experiment with different coefficients and degrees using graphing technology, preparing students for future work with polynomials and building fluency graphing and changing graphing windows as appropriate for the technology.