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Factoring Quadratic Equations,a=1

Lesson Plan

Factoring Quadratic Equations,a=1

Grade Levels

9th Grade

Course, Subject

Algebra I, Mathematics
Related Academic Standards
A2.1.3.1.1 A2.1.3.1.1
Write and/or solve quadratic equations (including factoring and using the Quadratic Formula).
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  • Big Ideas
    Families of functions exhibit properties and behaviors that can be recognized across representations. Functions can be transformed, combined, and composed to create new functions in mathematical and real world situations.
    Mathematical functions are relationships that assign each member of one set (domain) to a unique member of another set (range), and the relationship is recognizable across representations.
    Numbers, measures, expressions, equations, and inequalities can represent mathematical situations and structures in many equivalent forms.
    Patterns exhibit relationships that can be extended, described, and generalized.
    Relations and functions are mathematical relationships that can be represented and analyzed using words, tables, graphs, and equations.
    There are some mathematical relationships that are always true and these relationships are used as the rules of arithmetic and algebra and are useful for writing equivalent forms of expressions and solving equations and inequalities.
  • Concepts
    Algebraic properties, processes and representations
    Exponential functions and equations
    Polynomial functions and equations
    Quadratic functions and equations
  • Competencies
    Extend algebraic properties and processes to quadratic, exponential, and polynomial expressions and equations and to matrices, and apply them to solve real world problems.
    Represent a polynomial function in multiple ways, including tab les , graphs, equations, and contextual situations, and make connections among representations; relate the solution of the associated polynomial equation to each representation.
    Represent a quadratic function in multiple ways, including tab les , graphs, equations, and contextual situations, and make connections among representations; relate the solution of the associated quadratic equation to each representation.

Common Core Standards

 

Seeing Structure in Expressions A-SSE

Rationale

Vocabulary

Binomial, Coefficient, Factor (noun), Factor (verb), Factor a monomial, Factor a polynomial, Greatest common Factor (GCF), Monomial, Polynomial, Quadratic Equation, Trinomial

Objectives

  • Students will be able to factor quadratic trinomials in which a=1.
  • Students will recognize if a trinomial is the difference of two squares and be able to factor it.
  • Students will recognize if a trinomial is a perfect square trinomial and be able to factor it.
  • Students will write rules for factoring quadratic trinomials

Lesson Essential Question(s)

 How can we show that algebraic properties and processes are extensions of arithmetic properties and processes, and how can we use algebraic properties and processes to solve problems?

How do you decide which functional representation to choose when modeling a real world situation, and how would you explain your solution to the problem?

Duration

90 minutes

Materials

 

 

Suggested Instructional Strategies

W:

 The students will be presented with the task and prior knowledge will be discussed, along with what acceptable responses entail.
H:

 The task will require students to apply the content from the previous lessons in reverse order.
E:

 Students will work in groups and use techniques, such as think-pair-share, to have individual time to work and group support as well.
R:

Students will work in groups and defend their arguments to each other and to the class
E:

Students will present their group work and explain it to the class.  They will field questions from their classmates in a discussion.
T:

Students will be working in groups and be able to work together if they get stuck.  If they can't figure it out in the group, I will use assessing/advancing questions to get that student back on track.
O:

 The task builds for students from concrete to creating an abstract rule, during a multiple day task.

Instructional Procedures

  • Students will work on the following warm-up problem as class begins:Describe, in words, the steps you take to multiply two binomials.  Write a problem multiplying two binomials and solve it.
  • As students are working on their warm-up, pass out “Notes: Factoring Quadratic Trinomials, a = 1.” 
  • After students complete the warm-up, using random reporter, have a few students put their problems on the board and solve them.  While students are writing their work, have other students share their steps for multiplying binomials.  Have students who wrote their work on the board explain what they did.
  • Explain to students that they will be working backwards from what we have been doing.  Ask them what they are going to discover. (Answer: The inverse of multiplying two binomials).
  • Explain to students that they are to work on this worksheet in their groups and in order, by section.  Go over the directions with students to ensure they understand what they are supposed to do.  Remind students to write out all of their work neatly, they will need it for multiple days.
  • Before having students begin to work, give students 1minute to write down everything they know about quadratic equations on their own.
  • Give students about 15-20 minutes to complete Sections I-III (pages 1-3) of notes in their groups at their desks.  Circulate the room to answer student questions and assess student discussion.
  • As students are finishing up, pass out poster paper & markers.
  • Assign each group a problem to present (Section I, B #4-7, Section II, B #4 & 5, Section III, B #8 & 10).  If there aren’t 8 groups, assign multiple problems to each group.
  • (If periods are 40-45 minutes): Have students make their posters and write what they have learned so that they can present their posters the following day.
  • Have students present their posters in order, up to Section III.  They are to explain how they solved the problems and what led them to that conclusion.
  • After presenting the problems from Sections I & II, discuss #8 from Section I.  Using the random reporter, ask 3 students to write their rules on the board.  Allow time for students to explain their work and ask each other questions. 
  • Have students turn to the fourth page and complete the Conclusions page, filling in the blanks by writing rules for the each case, up through the Perfect Square Trinomial section.
  • Have students who were assigned problems from Section III present their posters, explaining what they did. 
  • Discuss Section III, Part A, #7 as a class.
  • Discuss #14-15 in Section III.  Ask students about the differences and how they change how they factor.  Using the random reporter, have 2 students write their rules on the board.  Allow students time to challenge/discuss these rules.
  • Have students turn to the fourth page and complete the Conclusions page, and fill in the Difference of Squares section.
  • After giving students some time to write their rules and notes for this section, conclude the class by reviewing these rules as a group to ensure that all students have the correct rules written out.
  • Pass out “Practice Factoring Quadratic Trinomials, a=1.” If there is time, give students time to practice and discuss the problems.  Assign part of the problems (odds) for students to finish for practice.

Formative Assessment

Students will be working in groups and discussing their worksheets.  I will be listening to their conversations as they work to assess how they're learning.  Students will also be asked to present how they solved problems or conclusions they came to after completing the task at hand.

Related Materials & Resources

Distributing and Factoring Using Area - Activity for practicing factoring.

https://www.khanacademy.org/video/factoring-quadratic-expressions?playlist=ck12.org%20Algebra%201%20Examples - Videos explaining how to factoring quadratic equations with links to special products.

Author

Ashley Lester

Date Published

July 22, 2011
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