N: Number Sense, Properties, and Operations

N.1: The complex number system includes real numbers and imaginary numbers

N.1.a: Show that between any two rational numbers there are an infinite number of rational numbers, and that between any two irrational numbers there are also an infinite number of irrational numbers

Rational Numbers, Opposites, and Absolute Values

N.2: Formulate, represent, and use algorithms with real numbers flexibly, accurately, and efficiently

N.2.b: Use technology to perform operations (addition, subtraction, multiplication, and division) on numbers written in scientific notation

Unit Conversions

N.3: Systematic counting techniques are used to describe and solve problems

N.3.a: Use combinatorics (Fundamental Counting Principle, permutations and combinations) to solve problems in real-world contexts

Binomial Probabilities
Permutations and Combinations

P: Patterns, Functions, and Algebraic Structures

P.1: Functions model situations where one quantity determines another and can be represented algebraically, graphically, and using tables

P.1.a: Determine when a relation is a function using a table, a graph, or an equation

Introduction to Functions
Linear Functions

P.1.b: Demonstrate the relationship between all representations of linear functions using point-slope, slope-intercept, and standard form of a line

Points, Lines, and Equations
Slope-Intercept Form of a Line

P.1.c: Represent linear, quadratic, absolute value, power, exponential, logarithmic, rational, trigonometric (sine and cosine), and step functions in a table, graph, and equation and convert from one representation to another

Compound Interest
Exponential Functions
General Form of a Rational Function
Introduction to Exponential Functions
Linear Functions
Logarithmic Functions
Points, Lines, and Equations
Quadratics in Factored Form
Quadratics in Polynomial Form
Quadratics in Vertex Form
Rational Functions
Slope-Intercept Form of a Line
Translating and Scaling Functions

P.1.d: Determine the inverse (expressed graphically or in tabular form) of a function from a graph or table

Logarithmic Functions

P.1.e: Categorize sequences as arithmetic, geometric, or neither and develop formulas for the general terms related to arithmetic and geometric sequences

Arithmetic Sequences
Geometric Sequences

P.2: Graphs and tables are used to describe the qualitative behavior of common types of functions

P.2.a: Evaluate a function at a given point in its domain given an equation (including function notation), a table, and a graph

Logarithmic Functions

P.2.b: Identify the domain and range of a function given an equation (including function notation), a table, and a graph

Exponential Functions
Introduction to Functions
Logarithmic Functions
Radical Functions

P.2.c: Identify intercepts, zeros (or roots), maxima, minima, and intervals of increase and decrease, and asymptotes of a function given an equation (including function notation), a table, and a graph

Absolute Value with Linear Functions
Cat and Mouse (Modeling with Linear Systems)
Exponential Functions
General Form of a Rational Function
Introduction to Exponential Functions
Linear Functions
Logarithmic Functions
Points, Lines, and Equations
Quadratics in Factored Form
Quadratics in Polynomial Form
Quadratics in Vertex Form
Roots of a Quadratic
Slope-Intercept Form of a Line

P.2.d: Make qualitative statements about the rate of change of a function, based on its graph or table

Cat and Mouse (Modeling with Linear Systems)
Translating and Scaling Functions

P.3: Parameters influence the shape of the graphs of functions

P.3.a: Apply transformations (translation, reflection, dilation) to a parent function, f(x)

Absolute Value with Linear Functions
Exponential Functions
Translating and Scaling Functions
Translating and Scaling Sine and Cosine Functions

P.3.b: Interpret the results of these transformations verbally, graphically, and symbolically

Solving Equations on the Number Line
Using Algebraic Expressions

P.4: Expressions, equations, and inequalities can be expressed in multiple, equivalent forms

P.4.a: Perform and justify steps in generating equivalent expressions by identifying properties used including the commutative, associative, inverse, identity, and distributive properties

Equivalent Algebraic Expressions I
Equivalent Algebraic Expressions II
Simplifying Algebraic Expressions I
Simplifying Algebraic Expressions II

P.4.c: Solve equations for one variable in terms of the others

Solving Formulas for any Variable

P.5: Solutions to equations, inequalities and systems of equations are found using a variety of tools

P.5.a: Find solutions to quadratic and cubic equations and inequalities by using appropriate algebraic methods such as factoring, completing the square, graphing or using the quadratic formula

Modeling the Factorization of x²+bx+c
Quadratic Inequalities
Quadratics in Factored Form
Quadratics in Polynomial Form
Quadratics in Vertex Form
Roots of a Quadratic

P.5.b: Find solutions to equations involving power, exponential, rational and radical functions

Compound Interest
Exponential Functions
Radical Functions

P.5.c: Solve systems of linear equations and inequalities with two variables

Cat and Mouse (Modeling with Linear Systems)
Linear Programming
Solving Equations by Graphing Each Side
Solving Linear Systems (Matrices and Special Solutions)
Solving Linear Systems (Slope-Intercept Form)
Solving Linear Systems (Standard Form)
Systems of Linear Inequalities (Slope-intercept form)

P.6: Quantitative relationships in the real world can be modeled and solved using functions

P.6.a: Represent, solve, and interpret problems in various contexts using linear, quadratic, and exponential function

Addition and Subtraction of Functions
Arithmetic Sequences
Compound Interest
Exponential Functions
Introduction to Exponential Functions
Linear Functions
Logarithmic Functions
Points, Lines, and Equations
Quadratics in Factored Form
Quadratics in Polynomial Form
Quadratics in Vertex Form
Slope-Intercept Form of a Line
Translating and Scaling Functions

P.6.b: Represent, solve, and interpret problems involving direct and inverse variations and a combination of direct and inverse variation

Direct and Inverse Variation

P.6.c: Analyze the impact of interest rates on a personal financial plan

Compound Interest

D: Data Analysis, Statistics, and Probability

D.1: Statistical methods take variability into account, supporting informed decision-making through quantitative studies designed to answer specific questions

D.1.a: Formulate appropriate research questions that can be answered with statistical analysis

Describing Data Using Statistics
Real-Time Histogram

D.1.b: Determine appropriate data collection methods to answer a research question

Describing Data Using Statistics

D.1.c: Explain how data might be analyzed to provide answers to a research question

Box-and-Whisker Plots
Polling: City
Real-Time Histogram

D.2: The design of an experiment or sample survey is of critical importance to analyzing the data and drawing conclusions

D.2.a: Identify the characteristics of a well-designed and well-conducted survey

Correlation
Polling: City
Polling: Neighborhood

D.2.b: Identify the characteristics of a well-designed and well-conducted experiment

Polling: Neighborhood

D.3: Visual displays and summary statistics condense the information in data sets into usable knowledge

D.3.a: Identify and choose appropriate ways to summarize numerical or categorical data using tables, graphical displays, and numerical summary statistics (describing shape, center and spread) and accounting for outliers when appropriate

Box-and-Whisker Plots
Least-Squares Best Fit Lines
Mean, Median, and Mode
Reaction Time 1 (Graphs and Statistics)
Stem-and-Leaf Plots

D.3.b: Define and explain how sampling distributions (developed through simulation) are used to describe the sample-to-sample variability of sample statistics

Polling: City
Populations and Samples

D.3.d: When the relationship between two numerical variables is reasonably linear, apply the least-squares criterion for line fitting, use Pearson's correlation coefficient as a measure of strength, and interpret the slope and y-intercept in the context of the problem

Correlation
Least-Squares Best Fit Lines
Solving Using Trend Lines

D.4: Randomness is the foundation for using statistics to draw conclusions when testing a claim or estimating plausible values for a population characteristic

D.4.a: Define and explain the meaning of significance (both practical and statistical)

Polling: City
Polling: Neighborhood
Populations and Samples

D.4.c: Determine the margin of error associated with an estimate of a population characteristic

Polling: City
Polling: Neighborhood

D.5: Probability models outcomes for situations in which there is inherent randomness, quantifying the degree of certainty in terms of relative frequency of occurrence

D.5.b: Apply and solve problems using the concepts of independence and conditional probability

Binomial Probabilities
Independent and Dependent Events
Theoretical and Experimental Probability

D.5.d: Evaluate and interpret probabilities using a normal distribution

Polling: City

D.5.e: Find and interpret the expected value and standard deviation of a discrete random variable X

Polling: City

S: Shape, Dimension, and Geometric Relationships

S.1: Attributes of two- and three-dimensional objects are measurable and can be quantified

S.1.b: Justify, interpret, and apply the use of formulas for the surface area, and volume of cones, pyramids, and spheres including real-world situations

Pyramids and Cones
Surface and Lateral Areas of Pyramids and Cones

S.1.c: Solve for unknown quantities in relationships involving perimeter, area, surface area, and volume

Area of Parallelograms
Area of Triangles
Circumference and Area of Circles
Perimeter and Area of Rectangles
Prisms and Cylinders
Pyramids and Cones
Surface and Lateral Areas of Prisms and Cylinders
Surface and Lateral Areas of Pyramids and Cones

S.2: Objects in the plane and their parts, attributes, and measurements can be analyzed deductively

S.2.a: Classify polygons according to their similarities and differences

Classifying Quadrilaterals
Classifying Triangles
Parallelogram Conditions
Special Parallelograms

S.2.c: Know and apply properties of angles including corresponding, exterior, interior, vertical, complementary, and supplementary angles to solve problems. Justify the results using two-column proofs, paragraph proofs, flow charts, or illustrations

Investigating Angle Theorems
Triangle Angle Sum

S.3: Objects in the plane can be transformed, and those transformations can be described and analyzed mathematically

S.3.b: Represent transformations (reflection, translation, rotation, and dilation) using Cartesian coordinates

Dilations
Rotations, Reflections, and Translations
Translations

S.3.c: Develop arguments to establish what remains invariant and what changes after a transformation (reflection, translation, rotation, and dilations). Justify these conjectures using two-column proofs, paragraph proofs, flow charts, and/or illustrations

Dilations
Similar Figures

S.4: Right triangles are central to geometry and its applications

S.4.a: Apply right triangle trigonometry (sine, cosine, and tangent) to find indirect measures of lengths and angles

Cosine Function
Sine Function
Sine, Cosine, and Tangent Ratios
Tangent Function

S.4.b: Apply the Pythagorean theorem and its converse to solve real-world problems

Distance Formula
Pythagorean Theorem
Pythagorean Theorem with a Geoboard

S.4.c: Determine the midpoint of a line segment and the distance between two points in the Cartesian coordinate plane

Points in the Coordinate Plane