PA.1: Apply concepts and perform basic operations using real numbers in real-world contexts.

PA.1.a: Define, classify, and order rational and irrational numbers and their subsets.

Comparing and Ordering Decimals
Integers, Opposites, and Absolute Values
Rational Numbers, Opposites, and Absolute Values

PA.1.b: Formulate and solve standard and real-life problems involving addition, subtraction, multiplication, and division of rational numbers.

Adding on the Number Line
Dividing Fractions
Dividing Mixed Numbers
Estimating Sums and Differences
Improper Fractions and Mixed Numbers
Multiplying Fractions
Multiplying Mixed Numbers
Multiplying with Decimals
Sums and Differences with Decimals

PA.1.d: Simplify and evaluate expressions using order of operations and use real number properties to justify solutions.

Order of Operations
Simplifying Algebraic Expressions I
Simplifying Algebraic Expressions II
Solving Equations on the Number Line

PA.1.e: Explain the rules of exponents related to multiplication and division of terms with exponents.

Dividing Exponential Expressions
Multiplying Exponential Expressions

PA.1.f: Recognize and appropriately use exponential and scientific notation.

Unit Conversions
Unit Conversions 2 - Scientific Notation and Significant Digits

PA.1.g: Explain and use the inverse relationship between square roots and squares.

Square Roots

PA.2: Apply properties to simplify algebraic expressions, solve linear equations and inequalities, and apply principles of graphing.

PA.2.a: Simplify and evaluate numerical and algebraic expressions.

Dividing Exponential Expressions
Equivalent Algebraic Expressions I
Equivalent Algebraic Expressions II
Multiplying Exponential Expressions
Operations with Radical Expressions
Order of Operations
Simplifying Algebraic Expressions I
Simplifying Algebraic Expressions II
Solving Equations by Graphing Each Side
Solving Equations on the Number Line

PA.2.b: Apply properties of real numbers with an emphasis on the distributive properties of multiplication over addition and subtraction.

Equivalent Algebraic Expressions II
Square Roots

PA.2.c: Solve and check equations and inequalities using one variable.

Compound Inequalities
Modeling and Solving Two-Step Equations
Solving Algebraic Equations II
Solving Equations on the Number Line
Solving Linear Inequalities in One Variable

PA.2.d: Model inequalities (and their solutions) on a number line.

Absolute Value Equations and Inequalities
Compound Inequalities
Exploring Linear Inequalities in One Variable
Solving Linear Inequalities in One Variable

PA.2.e: Graph linear equations and non-linear equations (y = x²) using multiple methods including t-tables and slope-intercept.

Absolute Value with Linear Functions
Linear Functions
Linear Inequalities in Two Variables
Point-Slope Form of a Line
Points, Lines, and Equations
Slope-Intercept Form of a Line
Solving Equations by Graphing Each Side
Standard Form of a Line

PA.2.f: Given a linear graph, identify its slope as positive, negative, undefined, or zero, and interpret slope as rate of change.

Cat and Mouse (Modeling with Linear Systems)
Point-Slope Form of a Line
Slope-Intercept Form of a Line

PA.2.g: Determine slope, x-intercept, and y-intercept from a graph and/or equation in slope-intercept or standard form.

Cat and Mouse (Modeling with Linear Systems)
Linear Inequalities in Two Variables
Point-Slope Form of a Line
Points, Lines, and Equations
Roots of a Quadratic
Slope-Intercept Form of a Line
Standard Form of a Line

PA.2.h: Add, subtract, and multiply monomials and binomials.

Addition of Polynomials
Modeling the Factorization of x²+bx+c

PA.2.i: Predict characteristics of a graph given an equation or t-table.

Function Machines 1 (Functions and Tables)
Introduction to Functions
Points, Lines, and Equations

PA.3: Identify and apply geometric principles to polygons, angles, and two- and three-dimensional figures.

PA.3.a: Locate and identify angles formed by parallel lines cut by a transversal(s) (e.g., adjacent, vertical, complementary, supplementary, corresponding, alternate interior, and alternate exterior).

Triangle Angle Sum

PA.3.d: Solve real-world and non-routine problems involving congruent and similar figures.

Circles
Similar Figures

PA.4: Understand measurable attributes of objects and apply various formulas in problem solving situations.

PA.4.a: Solve real-world application problems that include length, area, perimeter, and circumference using standard measurements.

Fido's Flower Bed (Perimeter and Area)
Measuring Trees

PA.4.b: Develop, analyze, and explain methods for solving problems involving proportions, such as scaling and finding equivalent ratios.

Estimating Population Size

PA.4.c: Use formulas and/or appropriate measuring tools to find length and angle measures (to appropriate levels of precision), perimeter, area, volume, and surface area of polygons, circles, spheres, cones, pyramids, and composite or irregular figures.

Area of Parallelograms
Measuring Trees
Perimeter and Area of Rectangles
Prisms and Cylinders
Surface and Lateral Areas of Pyramids and Cones

PA.5: Interpret, organize, and make predictions about a variety of data using concepts of probability.

PA.5.a: Use a given mean, mode, median, and range to summarize and compare data sets including investigation of the different effects that change in data values have on these measures.

Box-and-Whisker Plots
Describing Data Using Statistics
Mean, Median, and Mode
Movie Reviewer (Mean and Median)
Populations and Samples
Reaction Time 1 (Graphs and Statistics)
Reaction Time 2 (Graphs and Statistics)
Sight vs. Sound Reactions
Stem-and-Leaf Plots

PA.5.b: Select the appropriate measures of central tendency for a particular purpose.

Box-and-Whisker Plots
Describing Data Using Statistics
Mean, Median, and Mode
Movie Reviewer (Mean and Median)
Reaction Time 1 (Graphs and Statistics)
Reaction Time 2 (Graphs and Statistics)
Stem-and-Leaf Plots

PA.5.c: Make and list conjectures by calculating probability for experimental or simulated contexts.

Independent and Dependent Events
Spin the Big Wheel! (Probability)

PA.5.d: Construct and interpret scatter plots to generalize trends from given data sets.

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