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A1-A-3-2

Page history last edited by Brenda Butz 6 years, 2 months ago

A1.A.3.2 Simplify polynomial expressions by adding, subtracting or multiplying.

In a Nutshell

Students will apply their knowledge of operations and exponents to polynomial expressions. Understanding the reasons behind these operations, they will be able to create equivalent expressions and provide justification for their processes.

Student Actions	Teacher Actions
Students will develop accurate and appropriate procedural fluency as they work with like terms and exponents to simplify polynomial expressions. Students will apply previous knowledge of whole numbers, including operations with exponent properties, to polynomials to generate equivalent expressions, working to develop mathematical reasoning as they make conjectures about how operations will change expressions and justify their processes. Students will justify their processes to teachers and peers, using appropriate mathematical notation as written or verbal statements, developing the ability to communicate mathematically.	Focus on helping students show evidence of their thinking as they justify operations (relying on the properties learned in pre-algebra) related to both whole numbers and polynomials rather than having students memorize a series of steps. Create examples and pose purposeful questions that highlight what parts of an expression change and what parts stay the same when working with polynomials. Assist students in discussing and using proper use of mathematical notation, guiding students toward meaningful and accurate mathematical discourse.
Key Understandings	Misconceptions
Produce equivalent expressions and give justification for their equivalence when using operations including addition, subtraction, multiplication and properties of exponents. Examples: 3x2 -4y+8x +9y-5x2 (2x-5)(3x-8) 3x(5x2-2x+5) Focus on the reasons expressions are equivalent rather than memorizing a set of rules.	Students may misuse exponent properties, often confusing multiplication with powers. i.e. 2*x² and (x²)² Students will incorrectly manipulate the base when using powers. i.e. (2x²)³=(8x)³ Students will raise the variable by the power and forget to raise the coefficient by the same power. Ie (2x²)²=2x⁴ Student will incorrectly add non like terms. Students will neglect partial products. i.e. (x-3)²=x²-3² When subtracting expressions, students only subtract the first term of the second expression then add the other terms.