gr9_polynomials

Patterns and Relations (Polynomials)

//It is expected that students will://
 * **Prescribed Learning Outcomes**

B5. demonstrate an understanding of polynomials Iimited to polynomials of degree less than or equal to 2) [C, CN, R, V]

B6. model, record, and explain the operations of addition and subtraction of polynomial expressions, concretely, pictorially, and symbolically (limited to polynomials of degree less than or equal to 2) [C, CN, PS, R, V]

B7. model, record, and explain the operations of multiplication and division of polynomial expressions (limited to polynomials of degree less than or equal to 2) by monomials, concretely, pictorially, and symbolically [C, CN, R, V] || Have students develop algebraic expressions and challenge each other to represent them using algebra tiles or diagrams. Have students identify and correct errors in each other's work. determining a simplified expression for the area and perimeter of a rectangle with one of the sides being a monomial and the other any polynomial of degree less than or equal to 2. Then have the students evaluate the area and permeter or the rectangle for the different values of the variables
 * **Planning for Assessment** || **Assessment Strategies** ||
 * B5. Students will:
 * Be able to identify and define the following terms: variable, degree, number of terms, coefficient, monomial, binomial, trinomial, polynomial and format these definitions in one of the following ways: Frayer model, concept map, dictionary, or vocabulary list
 * Be able to illustrate their understanding of the vocabulary by linking the meaning to symbols
 * Students will work in pairs to create a model (concrete, pictorial, manipulative) that illustrates the relationship between the vocabulary and symbols
 * Students will then re-pair to share and explain their model enabling further understanding of polynomials || * Formative Assessment: (Vocabulary) Accurately be able to define and provide examples for: variable, degree, number of terms, coefficient, monomial, binomial, trinomial, polynomial
 * Summative Assessment: Ability to identify the characteristics of polynomials given a set of questions ||
 * B6/B7. Students will:
 * Be able to use and understand how models (concrete, pictorial, manipulative) illustrate how to add/subtract/multiply/divide polynomials
 * Be able to illustrate their understanding of combining polynomials through the identification of equivalent polynomials and polynomials that have been combined incorrectly
 * Students will work through a set of questions with solutions to determine which are equivalent, correct, or incorrect - models can be used to find solution.
 * Students can further illustrate understanding of polynomials by solving senarios that involve:

determining a simplified expression for the area and perimeter of a triangle given a polynomial expression (of degree less than or equal to 2) for each of the sides and a monomial expression for the height. Then have the students evaluate the area and perimeter of the triangle for different values of the variable.

determining an expression for the surface area of triangular and rectangular based prisms, given polynomial expressions for the dimensions of the prisms. Then have students evaluate the surface area for different values of the variable.

determining an expression for the length of a rectangle given either an expression for the perimeter and the width of the rectangle or an expression for the area and the width. Note when given a polynomial expression for the area the width must be a monomial expression in order to calculate the length. || * Formative Assessment: Can use model to illustrate how polynomials are added/subtracted/multiplied/divided
 * Summative Assessment: Accurately solve question sets of polynomials ||