SIII.MP: Mathematical Practices

SIII.MP.1: Make sense of problems and persevere in solving them.

Biconditional Statements
Conditional Statements
Estimating Population Size
Pattern Flip (Patterns)

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
Fraction, Decimal, Percent (Area and Grid Models)
Improper Fractions and Mixed Numbers
Linear Inequalities in Two Variables
Modeling One-Step Equations
Multiplying with Decimals
Pattern Flip (Patterns)
Polling: City
Solving Equations on the Number Line
Using Algebraic Equations
Using Algebraic Expressions

SIII.MP.2: Reason abstractly and quantitatively.

Conditional Statements
Estimating Population Size

SIII.MP.3: Construct viable arguments and critique the reasoning of others.

Biconditional Statements

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.

Biconditional Statements
Conditional Statements

SIII.MP.4: Model with mathematics.

Estimating Sums and Differences

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.5: Use appropriate tools strategically.

Elapsed Time

SIII.MP.5.a: Consider the available tools and be sufficiently familiar with them to make sound decisions about when each tool might be helpful, recognizing both the insight to be gained as well as the limitations. Identify relevant external mathematical resources and use them to pose or solve problems. Use tools to explore and deepen their understanding of concepts.

Segment and Angle Bisectors

SIII.MP.6: Attend to precision.

Biconditional Statements
Fraction, Decimal, Percent (Area and Grid Models)
Using Algebraic Expressions

SIII.MP.6.a: Communicate precisely to others. Use explicit definitions in discussion with others and in their own reasoning. They state the meaning of the symbols they choose. Specify units of measure and label axes to clarify the correspondence with quantities in a problem. Calculate accurately and efficiently, express numerical answers with a degree of precision appropriate for the problem context.

Arithmetic Sequences
Finding Patterns
Fraction, Decimal, Percent (Area and Grid Models)
Function Machines 2 (Functions, Tables, and Graphs)
Geometric Sequences
Pattern Flip (Patterns)

SIII.MP.7: Look for and make use of structure.

Pattern Flip (Patterns)

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
Function Machines 2 (Functions, Tables, and Graphs)
Geometric Sequences
Pattern Flip (Patterns)

SIII.MP.8: Look for and express regularity in repeated reasoning.

Arithmetic Sequences
Arithmetic and Geometric Sequences
Finding Patterns
Geometric Sequences
Pattern Finder
Pattern Flip (Patterns)

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

A: Algebra

A.SSE: Seeing Structures in Expressions

(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
Translating and Scaling Functions
Using Algebraic Expressions

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
Factoring Special Products
Modeling the Factorization of ax²+bx+c
Modeling the Factorization of x²+bx+c
Multiplying Exponential Expressions
Simplifying Algebraic Expressions I
Simplifying Algebraic Expressions II
Simplifying Trigonometric Expressions
Solving Algebraic Equations II
Using Algebraic Expressions

A.APR: Arithmetic With Polynomials and Rational 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 x²+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
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

(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.

Binomial Probabilities

A.CED: Creating Equations

(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
Quadratic Inequalities
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.

Linear Programming

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

Solving Formulas for any Variable

A.REI: Reasoning with Equations and Inequalities

(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.

Radical Functions

(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)
Point-Slope Form of a Line
Solving Equations by Graphing Each Side
Solving Linear Systems (Matrices and Special Solutions)
Solving Linear Systems (Slope-Intercept Form)
Standard Form of a Line

F: Functions

F.IF: Interpreting Functions

(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
Function Machines 3 (Functions and Problem Solving)
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
Exponential Functions
Introduction to Exponential Functions
Logarithmic Functions
Logarithmic Functions: Translating and Scaling
Sine Function
Tangent Function
Translating and Scaling Sine and Cosine Functions

F.BF: Building 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
Logarithmic Functions
Logarithmic Functions: Translating and Scaling
Quadratics in Vertex Form
Radical Functions
Rational Functions
Translating and Scaling Functions
Translating and Scaling Sine and Cosine Functions
Translations
Zap It! Game

F.LE: Linear, Quadratic, and Exponential Models

(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.

Compound Interest
Logarithmic Functions

(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
Exponential Growth and Decay
Introduction to Exponential Functions

F.TF: Trigonometric 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.

Sound Beats and Sine Waves

S: Statistics

S.IC: Making Inferences and Justifying Conclusions

(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