REGIONAL EDUCATIONAL LAB ~ APPALACHIA

1. REGIONAL EDUCATIONAL LAB ~ APPALACHIA The Effects of Kentucky Virtual High School’s Hybrid Course in Algebra I on Teaching Practices, Classroom Quality, and Adolescent Learning ACT 7: OPERATIONS WITH POLYNOMIALS On-Line Professional Development JULY 15, 2009

2. Agenda • Welcome and Introductions • Equipment check-in • Updates: • Discussion of ACT 7 • Mini-Lesson and interactive word wall • Connections to KYVS ALG I: 10.2,10.3,20.1 &.2,22.3 • Linking to KET Encyclomedia • Assignment for ACT 8 Discussion: Wednesday, July 22, 2009

3. Discussion of ACT 7: Operations with Polynomials Highlights regarding content, instructional strategies, and/or reflections Pedagogy Quiz

4. ACT 7: Scenes 1- 3 How Do I Teach This? • Discovery Approach • Manipulatives - Algebra Tiles • Game Playing • Mnemonics – FOIL • Graphic Organizers • Problem Solving

5. Vocabulary for Polynomials GCF FOIL (3x – 4) PRODUCT PRIME FACTORIZATION TRINOMIAL 2xy + 6x – 16 POLYNOMIAL DISTRIBUTIVE PROPERTY Binomial FACTORS SCIENTIFIC NOTATION CHECK FACTORS ADDITIVE INVERSE PROPERTY TRIAL & ERROR 2(xy + 3x – 8) EXPONENT BASE ax2 + bx + c

6. Exponential Rules • Show examples of using exponents with numbers 23 = 2 x 2 x 2 34 = 3 x 3 x 3 x 3 • Since the exponent is the number of times the base is used as a factor, then: (a + b)2 = (a + b)·(a + b) Defn of exponents = a(a + b) + b(a + b)    Distributive Prop = a2 + ab + ba + b2 Distributive Prop = a2 + ab + ab + b2Commutative Prop = a2 + 2ab + b2 CLT

7. Discussion: Multiplying Binomials • Use a matrix array to support/model the use of the Distributive Property. • Use tiles to create the area model display. • Make Connections amongst the approaches. • Take students through a numerical approach and discussion: (5 + 3)2 = 82 = 64 as compared to 52 + 32 = 25 + 9 = 34. A2 + AB + BA + B2 = A2 + 2AB + B2 is the simplified form.

8. Connections: KYVS Algebra to SpotLight on Algebra SPOTLIGHT ON ALGEBRA: ACT 7, Operations with Polynomials & Exponents KYVS ALGEBRA I COURSE: Unit 5, Exponents, Monomials, and Polynomials • Lesson 20: Properties of Exponents • Lesson 21: Monomials • Lesson 22: Polynomials • Lesson 23: Factoring polynomials • Lesson 24: Factoring special polynomials

9. Investigate Lessons & Tracking Tools Assignments: Within the Breakout Room: Investigate the Lesson; Use the Tracking Tool developed for that Lesson and make suggestions for edits; Report back whole group. • 10.2 (Solutions to an Equation; • 10.3 (Intercepts of Lines); • 20.1 & 20.2 (Exponents); • 22.3 ( Multiplying Polynomials)

10. KYVS Algebra I Attends to • Use of mathematical language (vocabulary and properties) • Connects to the properties- providing a conceptual framework for the structures of algebra • Use of manipulatives- supports moving from the concrete to the abstract • Embeds review & practice of concepts from previous lessons • Requires a student tracking tool - provides a record of concepts learned, place to work through problems, organizer for- thinking, recording questions, and connecting to • prior learning/applications.

11. KET- Encyclomedia • ALGEBRA SUPPORT FOR: • Providing an authentic purpose • Connecting to the world • Engaging students to learn the concept • Visualizing • Promoting student thinking/discussion http://www.ket.org/education/encyclomedia.htm

12. Expectations for Next Steps • Work through ACT 8 for July 22, 2009 : take notes and be prepared to discuss. • Choose a KYVS Lesson to investigate: create/adapt a tracking tool for that Lesson, and bring to the July 22 session. All will be shared and posted on the wiki. • Send in the School Technology Database. • Investigate KET Encyclomedia & find one segment that provides an access point for some critical ALG I concept. • Dates to Remember: • On-Line PD Make-up is Tuesday, August 4, 2009; • Extension of Bb training is Thursday, August 13 in Louisville, JCTC.

13. Thanks for Sharing! Your thinking makes a difference with your students! See you Wednesday, July 22, 2009!