PA.N: Number & Operations

PA.N.1: Read, write, compare, classify, and represent real numbers and use them to solve problems in various contexts.

PA.N.1.1: Develop and apply the properties of integer exponents, including a⁰ = 1 (with a ≠ 0), to generate equivalent numerical and algebraic expressions.

Dividing Exponential Expressions
Exponents and Power Rules
Multiplying Exponential Expressions
Simplifying Algebraic Expressions II

PA.N.1.3: Multiply and divide numbers expressed in scientific notation, express the answer in scientific notation.

Unit Conversions

PA.N.1.4: Classify real numbers as rational or irrational. Explain why the rational number system is closed under addition and multiplication and why the irrational system is not. Explain why the sum of a rational number and an irrational number is irrational; and the product of a non-zero rational number and an irrational number is irrational.

Rational Numbers, Opposites, and Absolute Values

PA.N.1.5: Compare real numbers; locate real numbers on a number line. Identify the square root of a perfect square to 400 or, if it is not a perfect square root, locate it as an irrational number between two consecutive positive integers.

Comparing and Ordering Decimals
Integers, Opposites, and Absolute Values
Operations with Radical Expressions
Rational Numbers, Opposites, and Absolute Values
Simplifying Radical Expressions
Square Roots

PA.A: Algebraic Reasoning & Algebra

PA.A.1: Understand the concept of function in real-world and mathematical situations, and distinguish between linear and nonlinear functions.

PA.A.1.2: Use linear functions to represent and explain real-world and mathematical situations.

Arithmetic Sequences
Compound Interest
Function Machines 2 (Functions, Tables, and Graphs)
Function Machines 3 (Functions and Problem Solving)
Linear Functions
Slope-Intercept Form of a Line

PA.A.1.3: Identify a function as linear if it can be expressed in the form y = mx + b or if its graph is a straight line.

Function Machines 2 (Functions, Tables, and Graphs)
Function Machines 3 (Functions and Problem Solving)
Point-Slope Form of a Line
Points, Lines, and Equations
Slope-Intercept Form of a Line
Standard Form of a Line

PA.A.2: Recognize linear functions in real-world and mathematical situations; represent linear functions and other functions with tables, verbal descriptions, symbols, and graphs; solve problems involving linear functions and interpret results in the original context.

PA.A.2.1: Represent linear functions with tables, verbal descriptions, symbols, and graphs; translate from one representation to another.

Arithmetic Sequences
Function Machines 1 (Functions and Tables)
Function Machines 2 (Functions, Tables, and Graphs)
Function Machines 3 (Functions and Problem Solving)
Geometric Sequences
Linear Functions
Points, Lines, and Equations
Slope-Intercept Form of a Line

PA.A.2.2: Identify, describe, and analyze linear relationships between two variables.

Slope-Intercept Form of a Line

PA.A.2.3: Identify graphical properties of linear functions including slope and intercepts. Know that the slope equals the rate of change, and that the y-intercept is zero when the function represents a proportional relationship.

Absolute Value with Linear Functions
Cat and Mouse (Modeling with Linear Systems)
Compound Interest
Exponential Functions
Function Machines 2 (Functions, Tables, and Graphs)
Function Machines 3 (Functions and Problem Solving)
Graphs of Polynomial Functions
Linear Functions
Point-Slope Form of a Line
Points, Lines, and Equations
Slope-Intercept Form of a Line
Standard Form of a Line

PA.A.2.5: Solve problems involving linear functions and interpret results in the original context.

Absolute Value with Linear Functions
Arithmetic Sequences
Compound Interest
Function Machines 2 (Functions, Tables, and Graphs)
Function Machines 3 (Functions and Problem Solving)
Linear Functions
Slope-Intercept Form of a Line

PA.A.3: Generate equivalent numerical and algebraic expressions and use algebraic properties to evaluate expressions.

PA.A.3.1: Use substitution to simplify and evaluate algebraic expressions.

Equivalent Algebraic Expressions I
Equivalent Algebraic Expressions II

PA.A.3.2: Justify steps in generating equivalent expressions by identifying the properties used, including the properties of operations (associative, commutative, and distributive laws) and the order of operations, including grouping symbols.

Equivalent Algebraic Expressions I
Equivalent Algebraic Expressions II
Order of Operations
Simplifying Algebraic Expressions I
Simplifying Algebraic Expressions II
Solving Algebraic Equations II

PA.A.4: Represent real-world and mathematical problems using equations and inequalities involving linear expressions. Solve and graph equations and inequalities symbolically and graphically. Interpret solutions in the original context.

PA.A.4.1: Illustrate, write, and solve mathematical and real-world problems using linear equations with one variable with one solution, infinitely many solutions, or no solutions. Interpret solutions in the original context.

Modeling One-Step Equations
Modeling and Solving Two-Step Equations
Solving Algebraic Equations II
Solving Two-Step Equations

PA.A.4.3: Represent real-world situations using equations and inequalities involving one variable.

Arithmetic Sequences
Geometric Sequences
Solving Two-Step Equations

PA.GM: Geometry & Measurement

PA.GM.1: Solve problems involving right triangles using the Pythagorean Theorem.

PA.GM.1.2: Use the Pythagorean Theorem to find the distance between any two points in a coordinate plane.

Distance Formula

PA.GM.2: Calculate surface area and volume of three-dimensional figures.

PA.GM.2.1: Calculate the surface area of a rectangular prism using decomposition or nets. Use appropriate measurements such as cm².

Surface and Lateral Areas of Prisms and Cylinders

PA.GM.2.2: Calculate the surface area of a cylinder, in terms of π and using approximations for π, using decomposition or nets. Use appropriate measurements such as cm².

Surface and Lateral Areas of Prisms and Cylinders

PA.D: Data & Probability

PA.D.1: Display and interpret data in a variety of ways, including using scatterplots and approximate lines of best fit. Use line of best fit and average rate of change to make predictions and draw conclusions about data.

PA.D.1.1: Describe the impact that inserting or deleting a data point has on the mean and the median of a data set. Know how to create data displays using a spreadsheet and use a calculator to examine this impact.

Correlation

PA.D.1.2: Explain how outliers affect measures of central tendency.

Describing Data Using Statistics
Mean, Median, and Mode
Movie Reviewer (Mean and Median)

PA.D.1.3: Collect, display and interpret data using scatterplots. Use the shape of the scatterplot to informally estimate a line of best fit, make statements about average rate of change, and make predictions about values not in the original data set. Use appropriate titles, labels and units.

Correlation
Least-Squares Best Fit Lines
Solving Using Trend Lines
Trends in Scatter Plots

PA.D.2: Calculate experimental probabilities and reason about probabilities to solve real-world and mathematical problems.

PA.D.2.1: Calculate experimental probabilities and represent them as percents, fractions and decimals between 0 and 1 inclusive. Use experimental probabilities to make predictions when actual probabilities are unknown.

Geometric Probability
Independent and Dependent Events
Probability Simulations
Theoretical and Experimental Probability

PA.D.2.2: Determine how samples are chosen (random, limited, biased) to draw and support conclusions about generalizing a sample to a population.

Polling: City

PA.D.2.3: Compare and contrast dependent and independent events.

Independent and Dependent Events