Rewriting Quadratic Expressions in Factored Form (Part 4)

5 min

Narrative

This Warm-up prompts students to compare four quadratic 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.

Launch

Arrange students in groups of 2–4. Display the expressions for all to see. Give students 1 minute of quiet think time, and ask them to indicate when they have noticed three expressions that go together and can explain why. Next, tell students to share their response with their group, and then together find as many sets of three as they can.

Student Task

Which three go together? Why do they go together?

  1. (x+4)(x−3)(x+4)(x-3)
  2. 3x2−8x+53x^2-8x+5
  3. x2−25x^2-25
  4. x2+2x+3x^2+2x+3

Sample Response

Sample responses:

  • A, B, and C go together because they can be written in factored form.
  • A, B, and D go together because they have a linear term when written in standard form.
  • A, C, and D go together because the coefficient of the quadratic term is 1 when written in standard form.
  • B, C, and D go together because they are written in standard form.

Synthesis

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 the reasons given are correct.

During the discussion, ask students to explain the meaning of any terminology they use, such as “standard form,” “factors,” and “coefficient.” Also, press students on unsubstantiated claims.

Standards
Addressing
  • A-SSE.A·Interpret the structure of expressions
  • HSA-SSE.A·Interpret the structure of expressions.

15 min

15 min

25 min