MA.PA.1: Understand numbers, ways of representing numbers, relationships among numbers, and number systems

MA.PA.1.2: Compare and order rational numbers and square roots

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

MA.PA.2: Understand the meaning of operations and how they relate to each other

MA.PA.2.2: Demonstrate the inverse relationship between square numbers and square roots, and cubes and cubed roots

Square Roots

MA.PA.4: Understand attributes, units, and systems of units in measurement; and develop and use techniques, tools, and formulas for measuring

MA.PA.4.1: Select and use appropriate units to measure the surface area and volume of solids

Surface and Lateral Areas of Prisms and Cylinders

MA.PA.4.3: Use ratios and proportions to solve measurement problems

Beam to Moon (Ratios and Proportions)
Estimating Population Size
Part-to-part and Part-to-whole Ratios

MA.PA.4.4: Use formulas to determine the surface area and volume of selected prisms, cylinders, and pyramids

Prisms and Cylinders
Pyramids and Cones
Surface and Lateral Areas of Prisms and Cylinders
Surface and Lateral Areas of Pyramids and Cones

MA.PA.4.5: Use the right triangle relationships (e.g., trigonometric ratios: cosine, sine, and tangent) to solve problems

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

MA.PA.5: Analyze properties of objects and relationships among the properties

MA.PA.5.1: Apply the Pythagorean theorem to solve problems involving right triangles

Cosine Function
Distance Formula
Pythagorean Theorem
Pythagorean Theorem with a Geoboard
Sine Function
Tangent Function

MA.PA.6: Use transformations and symmetry to analyze mathematical situations

MA.PA.6.1: Perform a transformation (reflection, rotation, translation) when given a figure and necessary parameters

Absolute Value with Linear Functions
Circles
Dilations
Holiday Snowflake Designer
Reflections
Rotations, Reflections, and Translations
Similar Figures
Translations

MA.PA.6.2: Describe the size, position, and orientation of shapes under transformations and compositions of transformations

Dilations
Reflections
Rotations, Reflections, and Translations
Translations

MA.PA.7: Use visualization and spatial reasoning to solve problems both within and outside of mathematics

MA.PA.7.1: Use two-dimensional representations of pyramids, prisms, and cylinders to solve problems involving these figures

Surface and Lateral Areas of Prisms and Cylinders

MA.PA.8: Select and use different representational systems, including coordinate geometry

MA.PA.8.1: Use coordinate geometry to represent transformations in the coordinate plane

Dilations

MA.PA.9: Understand various types of patterns and functional relationships

MA.PA.9.1: Represent a variety of patterns (including recursive patterns) with tables, graphs (including graphing technology when available), words, and when possible, symbolic rules

Arithmetic Sequences
Geometric Sequences
Introduction to Functions
Points, Lines, and Equations

MA.PA.9.2: Use linear relationships with two variables to solve problems

Absolute Value with Linear Functions
Arithmetic Sequences
Compound Interest
Linear Functions
Slope-Intercept Form of a Line

MA.PA.9.3: Identify functions as linear or nonlinear and contrast their properties from tables, graphs (including graphing technology when available), or equations

Absolute Value with Linear Functions
Linear Functions

MA.PA.10: Use symbolic forms to represent, model, and analyze mathematical situations

MA.PA.10.1: Translate among tables, graphs (including graphing technology when available), and equations involving linear relationships

Geometric Sequences
Introduction to Functions
Linear Functions
Points, Lines, and Equations
Slope-Intercept Form of a Line

MA.PA.10.2: Solve linear equations and inequalities with two variables using algebraic methods, manipulatives, or models

Absolute Value with Linear Functions
Compound Inequalities
Exploring Linear Inequalities in One Variable
Linear Inequalities in Two Variables
Modeling One-Step Equations
Modeling and Solving Two-Step Equations
Solving Algebraic Equations II
Solving Equations by Graphing Each Side
Solving Linear Inequalities in One Variable
Solving Two-Step Equations
Standard Form of a Line
Systems of Linear Inequalities (Slope-intercept form)

MA.PA.10.3: Use tables and graphs to represent and compare linear relationships

Absolute Value with Linear Functions
Arithmetic Sequences
Compound Interest
Introduction to Functions
Linear Functions
Point-Slope Form of a Line
Points, Lines, and Equations
Slope-Intercept Form of a Line
Standard Form of a Line

MA.PA.10.4: Use the slope of a line to describe a constant rate of change

Cat and Mouse (Modeling with Linear Systems)
Compound Interest
Direct and Inverse Variation

MA.PA.11: Pose questions and collect, organize, and represent data to answer those questions

MA.PA.11.1: Design a study that compares two samples, collect data, and select the appropriate representation (double bar graph, back-to-back stem and leaf plot, parallel box and whisker plots, scatter plot) to compare the sets of data

Box-and-Whisker Plots
Correlation
Describing Data Using Statistics
Least-Squares Best Fit Lines
Reaction Time 1 (Graphs and Statistics)
Real-Time Histogram
Solving Using Trend Lines
Stem-and-Leaf Plots
Trends in Scatter Plots

MA.PA.11.2: Judge the validity of data based on the data collection method

Describing Data Using Statistics
Polling: City
Polling: Neighborhood
Populations and Samples

MA.PA.12: Interpret data using methods of exploratory data analysis

MA.PA.12.2: Analyze different representations of the same data to describe how representations can be used to skew a person's interpretation of the data

Box-and-Whisker Plots
Correlation
Stem-and-Leaf Plots

MA.PA.14: Understand and apply basic notions of chance and probability

MA.PA.14.2: Calculate probabilities for simple events under different relationships (e.g., inclusion, disjoint, complementary, independent, dependent, with replacement, without replacement)

Independent and Dependent Events
Theoretical and Experimental Probability

MA.PA.14.3: Use the Fundamental Counting Principle to calculate combinations and permutations

Binomial Probabilities
Permutations and Combinations