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
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
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
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
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 |