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A2.A-SSE.1a, 1b, 2 2011 Domain: Seeing Structure in Expressions Cluster: Interpret the structure of expressions Standards: 1. Interpret expressions that represent a quantity in terms of its context. a. Interpret parts of an expression, such as terms, factors, and coefficients. b. Interpret complicated expressions by viewing one or more of their parts as a single entity. For example, interpret P(1+r)n as the product of P and a factor not depending on P. 2. Use the structure of an expression to identify ways to rewrite it. For example, see x4 – y4 as (x2)2 – (y2)2, thus recognizing it as a difference of squares that can be factored as (x2 – y2)(x2 + y2). Essential Questions What are the vocabulary names of various parts of an expression? How do you simplify algebraic expressions with exponents? What are some special product patterns and how are higher degree polynomials factored? Content Statements Enduring Understandings Recognize the importance of symbolism and interpretation within the language of algebra. Understanding the key terms of various parts of an expression will improve communication with simplifying all types of algebraic expressions. Activities, Investigation, and Student Experiences Mathematical modeling problems: Area model – difference of two squares and squares of binomials Pascal’s Triangle Volume of a cube A2.A-SSE.1a, 1b, 2 Identify the different parts of the expression and explain their meaning within the context of a problem. Decompose expressions and make sense of the multiple factors and terms by explaining the meaning of the individual parts. Rewrite algebraic expressions in different equivalent forms such as factoring or combining like terms. Use factoring techniques such as common factors, grouping, the difference of two squares, the sum or difference of two cubes, or a combination of methods to factor completely. Simplify expressions including combining like terms, using the distributive property and other operations with polynomials. Assessments Factor the following polynomials: 4x2-25y2 (2x – 5y)(2x + 5y) x3-8 (x – 2)(x2 + 2x +4) x2 + 14x + 49 (x + 7)2 x6+64y6 (x2 + 4y2)(x4 – 4x2y2 + 16y4) 2011 A2.A-SSE.1a, 1b, 2 2011 x3 + x2 – 9x – 9 (x + 1)(x + 3)(x – 3) Equipment Needed: Internet access Teacher Resources: http://www.teacherschoice.com.au/maths_library/algebra/alg_7. htm http://www.khanacademy.org/video/binomial-theorem--part2?playlist=Precalculus North Carolina Department of Public Instruction