Algebra 2 Honor


Year overview:
26ish teaching days per quarter (28 in Q3)
Q1: Functions, Quadratics, Transformations
Q2: Polynomials & Complex #s, Rational Functions
Q3: Exponents & Radicals, Exponential Functions
Q4: Inverses, Logs, Sequences & Series, Probability & Stat

Formative Assessment: Exit Tickets, mini quizzes, plickers, partner quizzes, class participation

Review: Mathbitsnotebook, Jeopardy labs

Assessment of Mastery: Unit tests, projects/presentations/writing

Engage NY, Desmos, Underground Math, Plickers, Zipgrade, jeopardy labs, math teacher mambo, http://www.kutasoftware.com/free.html

 


Q1 Learning Goals mastery check


Functions 3 days

Understand the difference between a function and a relation

Use mapping and vertical line test to identify functions

Understand function notation

Identify functions given table, equation, graph, points or description

Understand domain and range of functions and relations, input, output

Understand interval notation

Understand indep and dep variables, identify and justify indep variables

Given examples of functions and relations

Identify domain and range using correct notation and units from equation, table, graph, situation, points

Understand domain in context, discrete vs conts, integers or natural numbers

Sketch a function given domain and range

Give domain restrictions to match graph

Restrict domain/range to make a relation a function

Evaluate a function given an input (numerical, variable, binomial) or output, given table, equation or graph, multiple representations

Graph functions using technology to explore

Interpret the graph of a function in context

Understand domain restrictions from equation, graph, context

Compare functions in different representations

Understand function operations

Understand function composition, compose functions to give the desired output


4 days

Identify parent functions

Understand shared characteristics and key feature of parent functions

Graph parent functions with key features

Use a table to plot points if forget what the parent function looks like

State the symmetry of parent functions


Classify functions as even or odd

Identify even/odd functions given multiple representations

Find another point on an even/odd function

Draw an even/odd function or the other half of an even/odd function

SHOW/PROVE a function is even/odd/neither


3 days

Graph horizontal transformations of parent functions

Graph vertical transformations of parent functions

Graph vertical stretches and reflections

Graph horizontal stretches and reflections

Write transformations in function notation

Graph transformations from function notation (no equation)

Graph multiple transformations

Given eqn/graph state the transformations

Choose correct parent function to model situation

Use calculator to perform regression of data set


3 days

Graph piecewise functions given eqn/description

Give eqn piecewise functions given graph

Evaluate piecewise functions

Solve systems by graphing

Find “k” to make piecewise function continuous

Interpret piecewise functions in context


Factoring

4 days

Apply the distributive property

Understand and identify factors, terms, expressions

Find GCF of numbers and algebraic expressions

Factor trinomials, box method

Factor a>1, a, b neg

Factor polynomials using grouping

Recognize special cases difference of squares, perfect squares

Prove identities

Factor difference of squares

Factor completely

Factor with two variables

Factor with degree higher than 2--recognize the underlying structure and use subst


3 days

Equivalent expressions and graphing

Graph from factored form

Identify double roots and understand the connection to the graph

Given graph, find equation, plug in a point to find “a”

Understand the different forms of a quadratic equation: standard, vertex, factored form

Understand the key features of graph that are visible in each form

Find x and y-intercepts given any form

Graph a parabola given any form without changing it to another form

Label graphs with x, y int, vertex and line of symmetry

Complete the square to put in vertex form

Given graph, find QE in specific form

Use symmetry to graph given vertex and one other point

Given three points, find QE, including “a”

Interpret graphs and tables in context

Compare parabolas in different forms


3 days

Solve QE

Understand zero product property

Solve from factored form

Understand the difference between a factor, an x int and a root/zero

Solve using sqr roots

Solve by CTS, with a>1, with fractions

Solve literal equations

Use CTS to derive QF

Solve using QF-answers in simplest form

Choose the best method to solve

Solve application problems in context including maximization probs

Identify extraneous solutions in context


3 days

Understand how the value of the discriminant determines the number and nature of the roots

Predict the number and nature of the roots without solving using the QF

Derive -b/2a using QF

Use -b/2a to graph

Use -b/2a to put in vertex form

Use QF to derive sum/prod roots

Find eqn in standard form using sum/prod roots

Find eqn in stand form given irrat roots

Solve higher degree eqns using QF

Understand the Fundamental Theorem of Algebra


Q2 Learning Goals mastery check

Introduction to Polynomials 3 days

Distinguish between expressions, terms, variables and coefficients

Understand what a polynomial is

Identify polynomials and justify these choices

Use technology to explore polynomials

Classify polynomials by degree and number of terms

Identify and combine like terms

Put polynomials in standard form

Leading coefficient, end behavior, number of turns

Relate even/odd degrees to start/end behavior

Add, subtract and multiply polynomials

Understand closure of polynomials with respect to these operations


Factors, roots and graphing 3 days

Review factors vs zeros

Review factoring completely including hidden quadratics

Identify single, double, triple roots from factored form and from a graph

Find leading coefficient from factored form without multiplying it out, including buried negatives

Pull a negative out of a factor to predict end behavior

Given standard form, factor completely and sketch

Given description, find equation and graph

Give a graph, find the equation including “a”

Apply transformations to polynomial equations


Polynomial division 3 days

Use the box method to multiply polynomials and determine factors

Use the box method to derive the sum/difference of cubes

Divide polynomials using the box method

Divide by monomial

Divide by binomial

Divide polynomials using synthetic division

Find quotients with remainders


Solving and graphing polynomials 4 days

Use division to identify factors

Use the remainder theorem to identify roots

Solve and graph polynomial equations by factoring

Given a polynomial and a factor or root, find remaining factors, equation and graph

Use the remainder theorem to find a root, then divide, factor and graph the polynomial

Solve higher degree polynomial eqns by dividing, factoring and using the QF

Create polynomial equations to model real-world situations and use them to solve problems


Simplify Rational Expressions 3 days

Review key features and transformations of y=1/x

Simplify rational monomials by factoring

Rationalize the denominator of monomials

Review domain restrictions on rational monomials

Add/subtract and simplify rational Expressions with same and different denominators

Multiply, divide and simplify rational Expressions

Simplify complex and continued fractions, with and without tech


Solve rational equations 3 days

Identify extraneous solutions in context

Solve application problems including work problems




Midyear exam review 3 days