Download IG_Algebra 1_Unit 4 - allianceprincipalresources

Algebra
Subject:____________________
Unit Title:
Monomials and Polynomials
4
Unit:_______________________
2 (October 17th
Quarter:_____________________
– December
30th)
Unit Overview
Unit 4: Monomials and Polynomials
In this unit, students are introduced to nonlinear functions. Students first learn about polynomials and operations involving monomials and
polynomials. An expression involving the division of variables is not a monomial. Monomials that are real numbers are called constants. When
multiplying monomials, you can use the commutative and associative properties to group constants together and group powers with the same base
together. Monomials can also be divided. To divide two powers that have the same base, subtract the exponents. To find the power of a quotient, find
the power of the numerator and power of the denominator. A fraction that has a negative exponent can be rewritten as its reciprocal of the same
number with the opposite, or positive power. A polynomial is a monomial or a sum (or difference) of monomials. The sum of two monomials is
called a binomial, and the sum of three monomials is called a trinomial. Polynomials with more than three monomials have no special names. The
degree of a polynomial is the greatest degree of any monomial in the polynomial. To find the degree of a monomial, add the exponents of all its
variables. The degree of a polynomial should not be confused with the number of terms in the polynomial.
Polynomials may be added and subtracted by combining like terms. If the variable parts of two terms are exactly the same, the terms are called like
terms. The Distributive property is used to find the product of a monomial and a polynomial. Multiply each term of the polynomial by the monomial,
using the rules for monomial multiplication. If the monomial is negative, don’t forget to apply the rules for multiplying real numbers. Some
binomials have products that follow a specific pattern (e.g. square of sum or a difference and product of a sum and difference of the same two terms).
1
Math Literacy
Key Vocabulary: binomial, constant, degree of a monomial, degree of a polynomial, difference of two squares, monomial, polynomial, zero product
property, trinomial, standard form, leading coefficient
Supporting Vocabulary: distributive property, like terms, coefficient
Common Core State Standard Alignment

ASSE.1a Interpret expressions that represent a quantity in terms of its context. Interpret parts of an expression, such as terms, factors, and
coefficients.

ASSE.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).

A.APR.1 Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition,
subtraction, and multiplication; add, subtract, and multiply polynomials.
Sample Essential Questions
•
When could a nonlinear function be used to model a real-world situation?
•
How would you factor a cubic polynomial?
•
Describe the pattern formed when expanding squares and cubes of binomials?
Anchor Standards/Central Concepts
10.0 Students add, subtract, multiply, and divide monomials and polynomials. Students solve multistep problems, including word problems, by using
these techniques.
2
# CST Items
Standard
Learning Targets/
Key Concepts and Skills



10.0 Students add, subtract, multiply, and divide
monomials and polynomials. Students solve multistep problems, including word problems, by using
these techniques

4


2.0 Students understand and use such operations as
taking the opposite, finding the reciprocal, taking a
root, and raising to a fractional power. They
understand and use the rules of exponents.
4

10a I can add/subtract
polynomials
10b I can multiply polynomials
10c I can divide polynomials
(using exponent rules)
10d I can perform operations on
polynomials involving word
problems
10e I can write polynomials in
standard form.
10f I can solve equations
involving the products of
monomials and polynomials.
2a I can divide polynomials (using
exponent rules)
College-Ready Sample Assessment
Questions

The length of the rectangle above is 6
units shorter than the width. What
expression can be used to represent the
area?

Simplify:
2(𝑥 2 + 3𝑥 + 2) − 4(𝑥 2 − 4𝑥 + 1)

Simplify:
10𝑥 2 + 15𝑥 2 − 5𝑥
5𝑐

Write an expression equivalent to 𝑥 3 𝑥11

Simplify
2
83
Vertical Alignment
 Multiply and divide monomials 7AF2.2

Simplify numerical expressions and justify the process used 7.AF1.3

Operations on polynomials, including long division 2A.3.0
Additional Sample College-Ready Assessments Questions

Sample College-Ready Assessment Questions
3
4