Curriculum Framework
N.RN.1: Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents.
N.CN.1: Know there is a complex number 𝘪 such that 𝘪² = –1, and every complex number has the form 𝘢 + 𝘣𝘪 with 𝘢 and 𝘣 real.
N.CN.2: Use the relation 𝘪² = –1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers.
N.CN .7: Solve quadratic equations with real coefficients that have complex solutions.
A.SSE.2: Use the structure of an expression to identify ways to rewrite it.
Equivalent Algebraic Expressions II
Factoring Special Products
Modeling the Factorization of ax2+bx+c
Modeling the Factorization of x2+bx+c
Simplifying Algebraic Expressions I
Simplifying Algebraic Expressions II
Solving Algebraic Equations II
A.SSE.3: Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.
A.SSE.3.c: Use the properties of exponents to transform expressions for exponential functions.
A.APR.2: Know and apply the Remainder Theorem: For a polynomial 𝘱(𝘹) and a number 𝘢, the remainder on division by 𝘹 – 𝘢 is 𝘱(𝘢), so 𝘱(𝘢) = 0 if and only if (𝘹 – 𝘢) is a factor of 𝘱(𝘹).
Dividing Polynomials Using Synthetic Division
Polynomials and Linear Factors
A.APR.3: Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial.
Polynomials and Linear Factors
Quadratics in Factored Form
A.CED.1: Create equations and inequalities in one variable and use them to solve problems.
Absolute Value Equations and Inequalities
Arithmetic Sequences
Compound Interest
Exploring Linear Inequalities in One Variable
Exponential Growth and Decay
Geometric Sequences
Modeling and Solving Two-Step Equations
Quadratic Inequalities
Solving Linear Inequalities in One Variable
Solving Two-Step Equations
A.REI.1: Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method.
Modeling One-Step Equations
Modeling and Solving Two-Step Equations
Solving Algebraic Equations II
Solving Formulas for any Variable
A.REI.2: Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise.
A.REI.4: Solve equations and inequalities in one variable
A.REI.4.b: Solve quadratic equations by inspection (e.g., for 𝘹² = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as 𝘢 ± 𝘣𝘪 for real numbers 𝘢 and 𝘣.
Factoring Special Products
Modeling the Factorization of ax2+bx+c
Modeling the Factorization of x2+bx+c
Roots of a Quadratic
A.REI.6: Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables.
Cat and Mouse (Modeling with Linear Systems)
Solving Linear Systems (Matrices and Special Solutions)
Solving Linear Systems (Slope-Intercept Form)
A.REI.11: Explain why the 𝘹-coordinates of the points where the graphs of the equations 𝘺 = 𝘧(𝘹) and 𝘺 = 𝑔(𝘹) intersect are the solutions of the equation 𝘧(𝘹) = 𝑔(𝘹); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where 𝘧(𝘹) and/or 𝑔(𝘹) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions.
Solving Equations by Graphing Each Side
Solving Linear Systems (Slope-Intercept Form)
F.IF.4: For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship.
Distance-Time Graphs
Distance-Time and Velocity-Time Graphs
F.IF.6: Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.
Distance-Time Graphs
Distance-Time and Velocity-Time Graphs
F.IF.7: Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.
F.IF.7.c: Graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior.
Graphs of Polynomial Functions
Polynomials and Linear Factors
Quadratics in Factored Form
Quadratics in Vertex Form
Roots of a Quadratic
Zap It! Game
F.IF.7.e: Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude.
Cosine Function
Exponential Functions
Exponential Growth and Decay
Logarithmic Functions
Logarithmic Functions: Translating and Scaling
Sine Function
Tangent Function
F.IF.8: Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.
F.IF.8.b: Use the properties of exponents to interpret expressions for exponential functions.
Compound Interest
Exponential Growth and Decay
F.BF.1: Write a function that describes a relationship between two quantities.
F.BF.1.a: Determine an explicit expression, a recursive process, or steps for calculation from a context.
Arithmetic Sequences
Geometric Sequences
F.BF.2: Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms.
Arithmetic Sequences
Geometric Sequences
F.BF.3: Identify the effect on the graph of replacing 𝘧(𝘹) by 𝘧(𝘹) + 𝘬, 𝘬 𝘧(𝘹), 𝘧(𝘬𝘹), and 𝘧(𝘹 + 𝘬) for specific values of 𝘬 (both positive and negative); find the value of 𝘬 given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology.
Exponential Functions
Logarithmic Functions
Translating and Scaling Functions
Translating and Scaling Sine and Cosine Functions
Zap It! Game
F.LE.2: Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table).
Compound Interest
Exponential Functions
Exponential Growth and Decay
Point-Slope Form of a Line
Slope-Intercept Form of a Line
F.LE.4: For exponential models, express as a logarithm the solution to 𝘢𝘣 to the 𝘤𝘵 power = 𝘥 where 𝘢, 𝘤, and 𝘥 are numbers and the base 𝘣 is 2, 10, or 𝘦; evaluate the logarithm using technology.
F.LE.5: Interpret the parameters in a linear or exponential function in terms of a context.
Arithmetic Sequences
Compound Interest
Distance-Time Graphs
Distance-Time and Velocity-Time Graphs
Exponential Growth and Decay
F.TF.5: Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline.
G.GPE.2: Derive the equation of a parabola given a focus and directrix.
S.ID.6: Represent data on two quantitative variables on a scatter plot, and describe how the variables are related.
S.ID.6.a: Fit a function to the data; use functions fitted to data to solve problems in the context of the data.
Least-Squares Best Fit Lines
Solving Using Trend Lines
Zap It! Game
S.IC.4: Use data from a sample survey to estimate a population mean or proportion; develop a margin of error through the use of simulation models for random sampling.
Estimating Population Size
Polling: City
Polling: Neighborhood
S.IC.5: Use data from a randomized experiment to compare two treatments; use simulations to decide if differences between parameters are significant.
Real-Time Histogram
Sight vs. Sound Reactions
S.CP.1: Describe events as subsets of a sample space (the set of outcomes) using characteristics (or categories) of the outcomes, or as unions, intersections, or complements of other events (“or,” “and,” “not”).
Independent and Dependent Events
Probability Simulations
Theoretical and Experimental Probability
S.CP.2: Understand that two events 𝘈 and 𝘉 are independent if the probability of 𝘈 and 𝘉 occurring together is the product of their probabilities, and use this characterization to determine if they are independent.
Independent and Dependent Events
S.CP.3: Understand the conditional probability of 𝘈 given 𝘉 as 𝘗(𝘈 and 𝘉)/𝘗(𝘉), and interpret independence of 𝘈 and 𝘉 as saying that the conditional probability of 𝘈 given 𝘉 is the same as the probability of 𝘈, and the conditional probability of 𝘉 given 𝘈 is the same as the probability of 𝘉.
Independent and Dependent Events
Correlation last revised: 5/8/2018