1. Enrich Transformations and Polynomials Instruction with Technology Using Geometer’s Sketchpad to Model Binomial and Trinomial Expressions iLearn Grade 8 Math 6 out of 8

2. Focusing Questions How are the second and third items of a factorable trinomial related to the binomial factors? How can Geometer’s Sketchpad be used to model how to expand binomial expressions and factor polynomial expressions?

3. Instruction

4. Framing The Session How can the algebra tiles in Geometer’s Sketchpad be used to illustrate how to expand binomials and factor trinomials?

5. Teaching You will learn how to manipulate Geometer’s Sketchpad algebra tiles. We will open binomial.gsp and expand binomials using algebra tiles. Then we will open trinomial.gsp and use algebra tiles to factor a polynomial expression.

6. Guided Practice Part 1: Expanding binomials. Go to page 3 of binomials.gsp. Use the custom tools to build the product (y + 1) (y + 4) on the outside edges of the corner piece. Use the custom tools to build a rectangle whose dimensions are (y + 1) by (y + 4) inside the corner piece. Write the expanded expression represented by the rectangle each time. Be sure to combine like terms.

7. Guided Practice Part 2: Factoring trinomials. Go to page 2 of trinomials.gsp. Use the custom tools to build a rectangle inside the corner piece to represent the trinomial x2 + 5x + 6. Note: You need to use five x pieces, but it’s not clear how many should be horizontal and how many vertical. Think of it as a puzzle—experiment until you get an arrangement in which the six unit squares fit to form a rectangle. Build the rectangle’s length and width outside the corner piece. Write the factored expression represented by these dimensions.

8. Work Time

9. Getting Started Working in pairs, solve problems involving expanding binomials and factoring polynomials. How are the second and third terms of a factorable trinomial related to the binomial factors?

10. Work Time Work in the binomials.gsp to complete IMPACT page 375 Problem Set A, #3–5 and Share and Summarize. >Expand:  (x + 7) (x + 2)  (w + 2) 2 >Factor:  y 2 + 6y + 3y + 18  y 2 + 5y + 6 Go to http://ilearn-math.wikispaces.com to answer the session question.http://ilearn-math.wikispaces.com

11. Share

12. How are the second and third terms of a factorable trinomial related to the binomial factors? What did you discover? Go to the discussion board and answer the posted question. Share

13. How does this work address the questions that began the session? How does Geometer’s Sketchpad facilitate learning to expand binomial expressions? How does Geometer’s Sketchpad facilitate the understanding of how to factor polynomial expressions? How are the second and third terms of a factorable trinomial related to the binomial factors?

14. For more information Office of Instructional Technology oittc@schools.nyc.gov www.nyc.gov/schools