UT--Core Standards

SIII.MP.1.a: Explain the meaning of a problem and look for entry points to its solution. Analyze givens, constraints, relationships, and goals. Make conjectures about the form and meaning of the solution, plan a solution pathway, and continually monitor progress asking, “Does this make sense?” Consider analogous problems, make connections between multiple representations, identify the correspondence between different approaches, look for trends, and transform algebraic expressions to highlight meaningful mathematics. Check answers to problems using a different method.

Biconditional Statements

Estimating Population Size

Linear Inequalities in Two Variables

Modeling One-Step Equations

Solving Equations on the Number Line

Using Algebraic Equations

Using Algebraic Expressions

SIII.MP.3.a: Understand and use stated assumptions, definitions, and previously established results in constructing arguments. Make conjectures and build a logical progression of statements to explore the truth of their conjectures. Justify conclusions and communicate them to others. Respond to the arguments of others by listening, asking clarifying questions, and critiquing the reasoning of others.

SIII.MP.4.a: Apply mathematics to solve problems arising in everyday life, society, and the workplace. Make assumptions and approximations, identifying important quantities to construct a mathematical model. Routinely interpret mathematical results in the context of the situation and reflect on whether the results make sense, possibly improving the model if it has not served its purpose.

Determining a Spring Constant

Estimating Population Size

SIII.MP.7.a: Look closely at mathematical relationships to identify the underlying structure by recognizing a simple structure within a more complicated structure. See complicated things, such as some algebraic expressions, as single objects or as being composed of several objects.

Arithmetic Sequences

Finding Patterns

Geometric Sequences

SIII.MP.8.a: Notice if reasoning is repeated, and look for both generalizations and shortcuts. Evaluate the reasonableness of intermediate results by maintaining oversight of the process while attending to the details.

Arithmetic Sequences

Arithmetic and Geometric Sequences

Geometric Sequences

(Framing Text): Interpret the structure of expressions. Extend to polynomial and rational expressions

A.SSE.1: Interpret polynomial and rational expressions that represent a quantity in terms of its context.

A.SSE.1.a: Interpret parts of an expression, such as terms, factors, and coefficients.

Compound Interest

Exponential Growth and Decay

Unit Conversions

A.SSE.1.b: Interpret complex expressions by viewing one or more of their parts as a single entity. For example, examine the behavior of P(1+r/n) to the nt power as n becomes large.

Compound Interest

Simplifying Algebraic Expressions I

Simplifying Algebraic Expressions II

A.SSE.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).

Dividing Exponential Expressions

Equivalent Algebraic Expressions I

Equivalent Algebraic Expressions II

Exponents and Power Rules

Multiplying Exponential Expressions

Simplifying Algebraic Expressions I

Simplifying Algebraic Expressions II

Using Algebraic Expressions

(Framing Text): Perform arithmetic operations on polynomials, extending beyond the quadratic polynomials.

A.APR.1: Understand that all 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.

Addition and Subtraction of Functions

Addition of Polynomials

Modeling the Factorization of *x*^{2}+*bx*+*c*

(Framing Text): Understand the relationship between zeros and factors of polynomials.

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

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

(Framing Text): Use polynomial identities to solve problems.

A.APR.5: Know and apply the Binomial Theorem for the expansion of (x + y)ⁿ in powers of x and y for a positive integer n, where x and y are any numbers.

(Framing Text): Create equations that describe numbers or relationships, using all available types of functions to create such equations.

A.CED.1: Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions.

Absolute Value Equations and Inequalities

Absolute Value with Linear Functions

Arithmetic Sequences

Compound Interest

Exploring Linear Inequalities in One Variable

Exponential Functions

General Form of a Rational Function

Geometric Sequences

Introduction to Exponential Functions

Linear Functions

Linear Inequalities in Two Variables

Logarithmic Functions

Modeling One-Step Equations

Modeling and Solving Two-Step Equations

Quadratics in Factored Form

Quadratics in Polynomial Form

Quadratics in Vertex Form

Rational Functions

Slope-Intercept Form of a Line

Solving Equations on the Number Line

Solving Linear Inequalities in One Variable

Solving Two-Step Equations

Translating and Scaling Functions

Using Algebraic Equations

A.CED.2: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.

2D Collisions

Air Track

Compound Interest

Determining a Spring Constant

Golf Range

Points, Lines, and Equations

Slope-Intercept Form of a Line

A.CED.3: Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or non-viable options in a modeling context.

A.CED.4: Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations.

Solving Formulas for any Variable

(Framing Text): Understand solving equations as a process of reasoning and explain the reasoning.

A.REI.2: Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise.

(Framing Text): Represent and solve equations and inequalities graphically.

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, for example, 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.

Cat and Mouse (Modeling with Linear Systems)

Solving Equations by Graphing Each Side

Solving Linear Systems (Matrices and Special Solutions)

Solving Linear Systems (Slope-Intercept Form)

(Framing Text): Interpret functions that arise in applications in terms of a context.

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. Key features include intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity.

Absolute Value with Linear Functions

Cat and Mouse (Modeling with Linear Systems)

Exponential Functions

General Form of a Rational Function

Graphs of Polynomial Functions

Logarithmic Functions

Points, Lines, and Equations

Quadratics in Factored Form

Quadratics in Polynomial Form

Quadratics in Vertex Form

Radical Functions

Roots of a Quadratic

Slope-Intercept Form of a Line

Translating and Scaling Sine and Cosine Functions

F.IF.5: Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.

General Form of a Rational Function

Introduction to Functions

Radical Functions

Rational Functions

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

(Framing Text): Analyze functions using different representations.

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.b: Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. Compare and contrast square root, cubed root, and step functions with all other functions.

Absolute Value with Linear Functions

Radical Functions

Translating and Scaling Functions

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.d: Graph rational functions, identifying zeros and asymptotes when suitable factorizations are available, and showing end behavior.

General Form of a Rational Function

Rational Functions

F.IF.7.e: Graph exponential and logarithmic functions, showing intercepts and end behavior; and trigonometric functions, showing period, midline, and amplitude.

Cosine Function

Sine Function

Tangent Function

Translating and Scaling Sine and Cosine Functions

(Framing Text): Build new functions from existing functions.

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.

Absolute Value with Linear Functions

Exponential Functions

Introduction to Exponential Functions

Rational Functions

Translating and Scaling Functions

Translating and Scaling Sine and Cosine Functions

Translations

Zap It! Game

(Framing Text): Construct and compare linear, quadratic, and exponential models and solve problems.

F.LE.3: Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quanitity increasing linearly, quadratically, or (more generally) as a polynomial function.

Compound Interest

Introduction to Exponential Functions

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. Include the relationship between properties of logarithms and properties of exponents, such as the connection between the properties of exponents and the basic logarithm property that log xy = log x + log y.

(Framing Text): Interpret expressions for functions in terms of the situation it models. Introduce f(x) = ex as a model for continuous growth

F.LE.5: Interpret the parameters in a linear, quadratic, and exponential functions in terms of a context.

Arithmetic Sequences

Compound Interest

Introduction to Exponential Functions

(Framing Text): Extend the domain of trigonometric functions using the unit circle.

F.TF.3: Use special triangles to determine geometrically the values of sine, cosine, tangent for π/3, π/4 and π6, and use the unit circle to express the values of sine, cosine, and tangent for π – x, π + x, and 2π – x in terms of their values for x, where x is any real number.

Cosine Function

Sine Function

Sum and Difference Identities for Sine and Cosine

Tangent Function

Translating and Scaling Sine and Cosine Functions

(Framing Text): Model periodic phenomena with trigonometric functions.

F.TF.5: Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline.

(Framing Text): Understand and evaluate random processes underlying statistical experiments.

S.IC.1: Understand that statistics allow inferences to be made about population parameters based on a random sample from that population.

Polling: City

Polling: Neighborhood

Populations and Samples

(Framing Text): Draw and justify conclusions from sample surveys, experiments, and observational studies. In earlier grades, students are introduced to different ways of collecting data and use graphical displays and summary statistics to make comparisons. These ideas are revisited with a focus on how the way in which data is collected determines the scope and nature of the conclusions that can be drawn from that data. The concept of statistical significance is developed informally through simulation as meaning a result that is unlikely to have occurred solely as a result of random selection in sampling or random assignment in an experiment. For S.IC.4, focus on the variability of results from experiments—that is, focus on statistics as a way of dealing with, not eliminating, inherent randomness.

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

Correlation last revised: 1/22/2020