Algebra 2 Curriculum Map 2016-17
Pacing / Unit/Essential Questions / Essential Knowledge- Content/Performance Indicators(What students must learn) / Essential Skills
(What students will be able to do) / Vocabulary / Resources
Pearson NYS Algebra 2
Sept
7–23 / Unit 1:Equations and Inequalities
How do you solve absolute value equation/inequality and plot on the number line? / Review of Algebra Topics
Student will be able to
-simplify expressions
-write and evaluate algebraic expressions
-represent mathematical phrases and real world quantities using algebraic expressions
-solve multi step equations and check
-distinguish between solution, no solution and identity
-solve literal equations
-solve multi step inequalities and graph them
-write inequality from a sentence using key word atleast, atmost, fewer, less, more …
Algebra 2 Topics
Students will be able to
-solve absolute value equations and check
-solve absolute value inequalities and check for extraneous solution
-distinguish between an “and” problem and an “or” problem and accordingly write the solution / Term
Constant term
Like terms
Coefficient
Expression
Equation
Literal Equation
Inequality
Absolute Value
Extraneous solution / 1-3: Algebraic Expressions
1-4: Solving equations.
Supplement with additional worksheets on equations with fractional coefficients
1-5: Solving Inequalities
1-6 Absolute Value Equations
Sept 26 – Oct 14 / Unit 2: Linear Equations and Functions
How do you distinguish between Direct and Inverse variation?
How do you distinguish between a relation and a function?
How do you find the domain and range of a function?
How do you transformation with functions? / Review of Algebra Topics
Student will be able to
-Determine if a function is linear
-Graph a linear function with/without a calculator.
-Find the Slope of a linear function given an equation, graph or 2 points
-Find the equation for a linear function given two points or a point and a graph.
-
Algebra 2 topics
Student will be able to
-Distinguish between a relation and a function.
-Determine if a relation is a function given a set of ordered pair, mapping diagram, graph or table of values
-Distinguish between direct and indirect variation
-Determine of a given function is direct given a function rule, graph or table of values
-Solve word problems related to direct and indirect variation (ref. to regents questions from jmap.org)
-Distinguish between parallel and perpendicular lines.
-Do linear regression using a graphing calculator
-Determine the correlation between the data sets by viewing or plotting a scatter-plot.
-Perform vertical and horizontal translations
-Graph absolute value equations and perform related translations / Relation
Function
Vertical line test
Function Rule
Function notation
Domain
Range
Direct Variation
Constant of Variation
Linear function
Linear equation
x-intercept
y-intercept
Slope
Standard form of linear function
Slope intercept form of linear function
Point slope form of linear function
Line of best fit
Scatter plot
Correlation
Correlation coefficient
Regression
Absolute value / 2.1 Relations and functions
Emphasis on domain and Range
2.2 Direct Variation
2.3 Linear Functions and slope-intercept Form
2.4 More about Linear Equations
2.5 Using Linear Model
2.6 Families of functions
2.7 Absolute value Functions and Graphs
Oct 17 – 28 / Unit 3: Linear Systems
How can you use a graph to find the solution of a system?
How do you solve a system of equations by substitution or elimination?
How can you solve a system of inequalities graphically?
How can you solve systems involving three equations? / Review of Algebra Topics
Student will be able to
-Find the point where the two lines intersect
-Identify the solution to a system of two lines
-Identify a consistent system
-Identify an inconsistent system
-Identify an independent and dependent system
-Solve a system of equations by substitution
-Solve a system of equations by elimination
-Use substitution or elimination to solve word problems
Algebra 2 Topics
Student will be able to
-Solve a system of inequalities graphically.
-Use a system of inequalities to model a real situation
-Solve a linear and absolute-value system
-solve a system of three equations using elimination /
System of equations
Linear system solution of a system
inconsistent system
consistent system
independent system
dependent system
equivalent systems
at least
at most / 3 -1 Solving System Using Tables and Graphs
3 - 2 Solving Systems Algebraically
3 - 3 Systems of
Inequalities
3 - 5 Systems with Three Variables
OPTIONAL
Oct. 31 –
Jan6 / Unit 4: Quadratic Equations and Functions
How do you perform transformations of functions?
How do you factor completely all types of quadratic expressions?
How do you use the calculator to find appropriate regression formulas?
How do you use imaginary numbers to find square roots of negative numbers?
How do you solve quadratic equations using a variety of techniques?
How do you determine the kinds of roots a quadratic will have from its equation?
How do you find the solution set for quadratic inequalities?
How do you solve systems of linear and quadratic equations graphically and algebraically? / Review of Algebra Topics
Students will be able to
-use definitions of domain and range to sketch a quadratic
-factor the difference of two squares
-factor completely
-solve quadratic equations by factoring
-use a quadratic equation to model a real situation
-determine a quadratic equation, given integer roots
-graph linear and quadratic functions
Algebra 2Topics
Students will be able to
-perform horizontal and vertical translations of the graph of y = x2
-graph a quadratic in vertex form:f(x) =a(x - h)2 + k
-identify and label the vertex as ( h , k )
-identify and label the axis of symmetry of a parabola
-graph parabolas in the form of y = a x2with various values of a
-graph a quadratic in vertex form:
-f(x) = ax2+bx+c
-find the axis of symmetry algebraically using the standard form of the equation
-identify the y-intercept as ( 0, c )
-find the vertex of a parabola algebraically using the standard form of the equation
-identify the range of parabolas
-sketch a graph of a parabola after finding the axis of symmetry, the vertex, and the y-intercept
-use the calculator to find a quadratic regression equation
-factor using “FOIL”
-finding a GCF
-perfect square trinomials
-difference of two squares
-zero product property
-finding the sum and product of roots
-writing equations knowing the roots or knowing the sum and product of the roots
-solve by taking square roots
-solve by completing the square
-solve by using the quadratic formula
-use the discriminant to find the nature of the roots
-simplify expressions containing complex numbers (include rationalizing the denominator)
-solve quadratic inequalities
-solve systems of quadratics algebraically / Parabola
Quadratic function
Vertex form
Axis of symmetry
Vertex of the parabola
Maximum
Minimum
Standard form
Domain and Range
Regressions
Factoring
Greatest Common Factor
Perfect square trinomial
Difference of two squares
Zero of a function (root)
Discriminant
Imaginary numbers
Complex numbers
Conjugates
/ 4-1 Quadratic functions and transformations
4-2 Standard form of a quadratic function
4-3 Modeling with quadratic functions
4-4 Factoring quadratic expressions
4-5 Quadratic equations
4-6 Completing the square
4-7 Quadratic Formula
4-8 Complex Numbers
Additional resource at
Quadratic Inequalities Page 256-257
4-9 Quadratic Systems
Jan 9 – March 3 / Unit 5: Polynomials
How do you perform arithmetic operations with polynomial expressions?
How do you factor polynomials?
How do you solve polynomial equation?
How do you expand a polynomial to the nth
Order?
How do you find the nth term of a binomial expansion? / Review of Algebra Topics
Student will be able to
-combine like terms
-subtract polynomial expressions
-multiply monomials, binomials and trinomials
Algebra 2 Topics
Students will be able to
-recognize and classify polynomials
-factor polynomials using common factor extraction, difference of two perfect squares and or trinomial factoring.
-Write a polynomial function given its roots.
-Solve polynomial equations /find the roots graphically.
-Apply the Binomial Theorem to expand a binomial expression
-Find a specific term of a binomial expansion. / Polynomial
Monomial
Binomial
Trinomial
Degree
Root
Solution
Zero Property / 5-1 Polynomial Functions
5-2 Polynomials, Linear Factors and Zeros
5-3 Solving Polynomial Equations
5-4 Dividing Polynomials
5-5 Theorems About Roots of Polynomial Equations
5-6 Fundamental Theorem of Algebra
5-7 The Binomial Theorem
(2 days)
March 6-24 / Unit 6: Radical Functions, Rational Exponents, Function Operations
How do you write algebraic expressions in simplest radical form?
How do you simplify by rationalizing the denominator?
How do you express sums and differences of radical expressions in simplest form?
How do you write radicals with fractional exponents?
How do you change an expression with a fractional exponent into a radical expression?
How do you solve radical equations?
How do you add, subtract, multiply, and divide functions? / Review of Algebra Topics
Student will be able to
-Use rules of positive and negative exponents in algebraic computations
-Use squares and cubes of numbers
-Know square roots of perfect squares from 1-15
Algebra 2 Topics
Students will be able to
-Simplify radical expressions
-Multiply and divide radical expressions
-Add and subtract radical expressions
-Use rational exponents
-Solve radical equations and check for extraneous roots
-Add, subtract, multiply, and divide functions / Exponents
Conjugates
Radicals
Rationalize the denominator
Extraneous roots
f- 1(x)
inverse of a function
one to one
onto
/ Page 360 Properties of exponents
6-1 Simplify radical expressions
6-2 Multiply and divide radical expressions
6-3 Binomial Radical Expressions
6-4 Rational Exponents
6-5 Solve radical equations
March 27-Apr28 / Unit 7:Exponential and Logarithmic Functions
How do you model a quantity that changes regularly over time by the same percentage?
How are exponents and logarithms related?
How are exponential functions and logarithmic functions related? / Students will be able to:
-model exponential growth and decay
-explore the properties of functions of the form
-graph exponential functions that have base e
-write and evaluate logarithmic expressions
-graph logarithmic functions
-derive and use the properties of logarithms to simplify and expand logarithms.
-solve exponential and logarithmic equations
-evaluate and simplify natural logarithmic expressions
-solve equations using natural logarithms / asymptote
change of base formula
common logarithm
exponential equation
exponential function
exponential decay
exponential growth
logarithm
logarithmic equation
logarithmic function
natural logarithmic function / 7 -1 Exploring Exponential Models (1 day)
7 – 3 Logarithmic Functions as Inverses
(2 days)
7 - 4 Properties of Logarithms
(2 – 3 days)
7 - 5 Exponential and Logarithmic Equations
(3 days)
7 - 6 Natural Logarithms pg 478
(2 days)
May 1-Jun 2 / Unit 8: Rational Expressions and Functions
How do we perform arithmetic operations on rational expressions?
How do we simplify a complex fraction?
How do we solve a rational equation? / Review of Algebra Topics
All topics in this unit except complex fractions are taught in Integrated Algebra. In Algebra most problems involve monomials and simple polynomials. In Algebra 2 factoring becomes more complex and may require more than one step to factor completely.
Algebra 2 Topics
Students will be able to
-Simplify a rational expression to lowest terms by factoring and reducing
-State any restrictions on the variable
-Multiply and divide rational expressions
-Add and subtract rational expressions
-Simplify a complex fraction
-Solve rational equations (inequalities will be saved for the Alg 2 course) / Simplest form
Rational Expression
Common factors
Reciprocal
Least Common Multiple
Lowest Common Denominator
Common factors
Complex Fraction
Rational equation / 8-1 Inverse Variation
8-2 The reciprocal Function Family
8-3 Rational functions and Their Graphs
8-4 Rational Expressions
8-5 Adding and Subtracting Rational Expressions- includes simplifying complex fractions
8-6 Solving Rational Equations