QUADRATIC FUNCTIONS

This unit introduces students to four ways of solving quadratic equations, graphing, factoring, completing the square, and the quadratic formula. The instructor uses Two-Column Notes and Triple-Entry Vocabulary Journals to support student learning and build comprehension. Knowledge Rating Guides serve as self assessments for the students, both before and after the unit. To integrate technology into the unit, the instructor utilizes Geogebra, free mathematics software that can be downloaded at http://www.geogebra.org/cms/.


  • LEARNING AND INSTRUCTIONAL GOALS

    • ENDURING UNDERSTANDINGS:
      How and why quadratic equations are used.
      How to determine which method of solving is best to use given the situation.


      ESSENTIAL QUESTIONS
      How are quadratic equations used in the “real” world?
      What are the different ways to solve quadratic equations and when is each appropriate?

      STUDENTS WILL KNOW/UNDERSTAND:
      Students will develop several ways to solve quadratic equations and be able to decide which way is appropriate to the situation.

      STUDENTS WILL BE ABLE TO:
      Use Two-column Notes to help organize questions from each section and then use them to help review for the final assessment.
      Use Triple Entry Vocabulary Journals to learn vocabulary and to demonstrate mastery of terms. This will be added to the previous unit’s vocabulary to construct a vocabulary digital notebook from year to year.
      Knowledge Rating Guide at beginning of unit to activate previous knowledge and at end to reinforce important words and concepts.

      MAINE LEARNING RESULTS/NCTM:

      MAINE

      Real numbers:
      1b, estimate the value(s) of roots and use technology to approximate them.
      1e, understand that some quadratic equations do not have real solutions and that there exist other number systems to allow for solutions to these equations.

      Equations and inequalities:
      2b, solve quadratic equations graphically, by factoring in cases where factoring is efficient, and by applying the quadratic formula.

      Functions and relations:
      4a, recognize the graphs and sketch graphs of the basic functions.
      4b, apply functions from these families to problem situations.
      4c, use concepts such as domain, range, zeros, intercepts, and maximum and minimum values.

      NCTM

      Number and operations
      Algebra
      Geometry
      Data analysis and probability
      Problem solving
      Reasoning and proof
      Communication
      Connections
      Representations


  • ASSESSMENTS

    • FORMATIVE:
      Pre-assessment to help activate prior knowledge and help determine length of time needed to spend on each section of the unit. The results will help the instructor to assess whether students have retained knowledge on factoring and graphing to help determine if extra time will be needed to review these topics.

      Knowledge Rating Guide will also offer instructor insight into what vocabulary should be reinforced and which is completely new and will need introduction.

      Homework will offer insight into students’ understanding of class information, and will inform teacher if students are ready to move on or need more practice.

      Exit Slips to help instructor assess each day’s lessons and concepts.

      SUMMATIVE:
      Two quizzes will be given during the unit. The first after the first two sections and the second after the third and fourth sections. Quizzes will also help inform instruction by indicating if more time needs to be spent on the material that is covered on the quiz.

      The post-assessment, which will have similar questions to the pre-assessment, will be used to show the growth of the students’ understanding throughout the unit.

  • TECHNOLOGY INTEGRATION

    • NeoOffice will be used as students build their high school math digital notebooks. These notebooks will help students to organize and study. Students will have each unit’s vocabulary, Two-column Notes for review, and Knowledge Rating Guides. These tools are used throughout the unit.

      Geogebra will be used to help students visualize quadratic equations. Students will also be able to easily manipulate and create multiple representations of the material, which will help reinforce the lessons as well as give students multiple opportunities to analyze the graphs and how they relate to the given situations in the problems.

  • LITERACY SUPPORT

    • Students will be expected to recognize quadratic functions and be able to discuss and understand different ways to solve these functions. They will also then need to evaluate which method is appropriate for the given situation.

      The literacy skills required will be two types of note taking, which are a Triple Entry Vocabulary Journal and Two-column Notes. Students will also use a Knowledge Rating Guide to activate prior knowledge and then to access their learning at the end of the unit.

      Model for students using LCD projector and Smart Board the use of the digital versions of Triple Entry Vocabulary Journal and Two-column Notes. Using a gradual release method, students will take ownership of these tools for themselves.

      Exit Slips and Knowledge Rating Guides are used in other classes, so just reinforce their use and importance in the learning environment.

  • INSTRUCTIONAL SEQUENCE

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QUADRATIC FUNCTIONS


Name of Instructor(s):

Allison Willard

   
Subject:

Mathematics Algebra 2

   
Grade Level: High School
   
Duration: 11 days
   
Videos:  
Quadratic Equations Video #1—Literacy: Triple Entry Vocabulary Journal and Two-Column Notes

Quadratic Equations Video #2—Technology: Geogebra
   
Rationale and Context:
This unit follows the unit on polynomials and deepens student’s understanding of specifically quadratic polynomials and how they may encounter them. The unit following this deals with other polynomial functions.

Quadratic functions are used to model real life situations and data.

Students need to be familiar with graphing functions, simplifying rational expressions, and multiplying and factoring polynomial expressions.

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