Mathematics 7. Add, subtract, and multiply polynomials, showing that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication.
Unpacked Content
Evidence Of Student Attainment:
Students:
Use the repeated reasoning from prior knowledge of properties of arithmetic on integers to progress consistently to rules for arithmetic on polynomials.
Accurately perform combinations of operations on various polynomials. Teacher Vocabulary:
Polynomials
Closure
Analogous system Knowledge:
Students know:
Corresponding rules of arithmetic of integers, specifically what it means for the integers to be closed under addition, subtraction, and multiplication, and not under division.
Procedures for performing addition, subtraction, and multiplication on polynomials. Skills:
Students are able to:
Communicate the connection between the rules for arithmetic on integers and the corresponding rules for arithmetic on polynomials.
Accurately perform combinations of operations on various polynomials. Understanding:
Students understand that:
There is an operational connection between the arithmetic on integers and the arithmetic on polynomials. Diverse Learning Needs:
Essential Skills:
Learning Objectives: ALGI.7.1: Combine like terms of a given expression
ALGI.7.2: Define monomial, term, binomial, trinomial and polynomial.
ALGI.7.3: Multiply polynomial expressions (quadratic).
ALGI.7.4: Multiply polynomial expressions (linear).
ALGI.7.5: Subtract polynomial expressions.
ALGI.7.6: Add polynomial expressions.
ALGI.7.7: Use order of operations to evaluate and simplify algebraic and numerical expressions.
ALGI.7.8: Identify the terms in a polynomial expressions.
ALGI.7.9: Explain the distributive property.
Prior Knowledge Skills:
Identify properties of exponents.
Give examples of the properties of operations including distributive, commutative, and associative.
Recall how to find the greatest common factor.
Combine like terms of a given expression.
Recognize the property demonstrated in a given expression.
Simplify expressions with parentheses (Ex. 5(4 + x) = 20 + 5x).
Simplify an expression by dividing by the greatest common factor (Ex. 18x + 6y= 6(3x + y).
Define linear expression, rational, coefficient, and rational coefficient.
Combine terms that are alike of a given expression.
