Learning+Center


 * A. Center Information**

//1) Author:// Michael Ginter

//2) Title of the Centers:// Polynomial Practice Centers

//3) Grade Level:// 9-12

//4) Content Area:// Algebra 2

//5) Type of Centers:// Combination of Skill Centers and Enrichment Centers

//6) Organization of Centers:// Rotational/Small Group – students will travel in groups of 2 or 3 and pick (with guidance) which stations they will complete

//7) Number of Centers:// 7 (students must complete 5)

//8) Time Needed:// 20 minutes per station --2 Block Periods


 * B. Learning Objective**

~ Given review material relating to polynomial multiplication, factoring, and rational polynomials, the students will be able to accurately solve the practice problems, achieving at least 85% correct answers.

~ Students will understand the relationship between word problems and 3-dimensaionl representations by learning how to represent such word problems and solutions with 3-dimensional objects.

~ Students will understand the Complex and Real Number Systems by learning -- how the tiered Real Number subset system is created and utilized -- how to represent the intangible Complex Number System with tangible objects


 * C. Materials**


 * Handouts for each center
 * Random assortment of materials for center 7 (see description for specific materials)
 * 3-Dimensional objects for center 5 (variety of shoe boxes, tissue boxes, blocks, geometry models)
 * Real Number chart for center 6


 * D. Center Activity Description**

The learning center activities are designed to take two 80 minute periods with students traveling around in groups of 2 or 3. There are 7 possible centers and students are to complete 5 of the centers. Four of the centers are basic skill reviews. All students must complete three of these four centers based upon individual need. Three of the centers are enrichment centers. Students must pick two of these centers to complete based upon individual interest.

The centers are set up around the room in groups of desks with all the appropriate materials at each location. Students travel from station to station in a manner that they pick with the understanding that there is only enough space at each center for a set number of small groups. Throughout the centers activity, the teacher will be available to walk around the room and help individuals or small groups as necessary.

__Center 1: Skill Review – Multiplication of Polynomials __ The purpose of the first station is to have students review the process of multiplying polynomials. Moreover, the students will then review combining the process of multiplication with the processes of addition and subtraction. Students will have the answers available at this station to check themselves as they progress.

__Center 2: Skill Review – Factoring __ At this station, the students will review the important concept of factoring. Students will have to combine all the methods we discussed in class (gcf, a is 1, a is not 1, difference of squares) in order to fully factor the problems. As I tell the students in class, you can never practice factoring too much in Algebra II. The answers will be available for students to check their own progress.

__Center 3: Skill Review— Polynomial Word Problems __ The students will further develop their problem solving skills by reviewing typical polynomial word problems. Specifically, students will look at the following types: ~ Two dimensional geometry applications ~ Consecutive integer problems. The answers will be available for students to check their progress.

__Center 4: Skill Review – Rational Polynomials __ The purpose of this station is to have students sharpen their skills in relation to simplifying rational polynomials. Students will be presented with a variety of procedural and slightly higher order questions all relating to simplifying rational polynomials and determining domain restrictions. Answers will be provided so that students can self-monitor their progress during this station.

__Center 5: Enrichment Activity – Hands-on Polynomial Word Problems __ At this station, students will be presented with 3-dimensional polynomial word problems and 3-dimensional objects to manipulate. In their small groups, the students will read the available problems and then pick one to complete on paper and demonstrate the solution on their 3-dimensional object. Students will leave their problem with their object to allow for teach evaluation and suggestion.

__Center 6: Enrichment Activity – Real-Number System Enrichment __ Students have been using the real number system throughout their mathematics careers and have learned about parts of the real number system in isolation from time to time in different classes. This enrichment activity isgeared toward helping students discover the relationship between the parts of the real number system by looking at the tiered system of subsets. Guided discovery along with higher order questions helps the students to achieve this goal.

__Center 7: Enrichment Activity – Creating the Imaginary Number System __ Students have learned about the Complex Number System and its relation to the Real Number System. This station allows the students to flex their creative muscle as they are presented with a variety of random materials (plastic Easter eggs, shipping labels, tape, markers, plastic straws, cotton balls, clothes pins, muffin cups, etc …) that they form into a visual/tangible representation of the Complex Number System. Guiding questions allow the students to explain and reflect on their representation.


 * E. Assessments:**
 * Students will be able to self-monitor for centers 1-4 with the answers available (just the answers, not the work for each problem)
 * Summary questions built into Center 6
 * Informal teacher evaluation of models created in Centers 5 and 7
 * Teacher will collect the skills practice from centers 1-4 in order to evaluate if students reached the 85% correct rate stated in the behavioral objective
 * Summary questions completed and discussed as a class after the centers activites:
 * Which of the skills centers did you choose and why?
 * Which of the enrichment centers did you choose and why?
 * What changes would you make to any of the centers?
 * The centers come toward the end of the unit and the skills addressed will be formally assessed with a unit test not too long after the centers activities


 * F. Handouts and Worksheets:** See the links in each center description