## A - Numerical Reasoning

• solve mathematical problems involving irrational numbers and rational approximations of irrational numbers to explain realistic applications
• solve relevant, mathematical problems involving radicals and integer exponents; apply place value understanding with scientific notation and use scientific notation to explain real-life phenomena

## B - Patterning & Algebraic Reasoning

• create and interpret expressions within realistic situations; create, interpret, and solve linear equations and linear inequalities in one variable to model and explain real-life phenomena
• show and explain the connections between proportional and non-proportional relationships and linear equations; create and interpret graphical, mathematical models and use the graphical, mathematical model to explain real-life phenomena represented in the graph

## C - Functional & Graphical Reasoning

• describe the properties of functions to define, evaluate, and compare relationships; model and explain real-life phenomena using linear functions
• use bivariate quantitative data to solve relevant, linear problems
• justify and use various strategies to solve systems of linear equations to model and explain realistic phenomena

## D - Geometric & Spatial Reasoning

• solve problems involving the Pythagorean Theorem and the volume of cones, cylinders, and spheres to explain real-life phenomena

• # 8th Grade Mathematics -- Mathematics Connection

## A - Numerical Reasoning

• solve mathematical problems involving irrational numbers and rational approximations of irrational numbers to explain realistic applications
• solve relevant, mathematical problems involving radicals and integer exponents; apply place value understanding with scientific notation and use scientific notation to explain real-life phenomena

## B - Patterning & Algebraic Reasoning

• create and interpret expressions within realistic situations; create, interpret, and solve linear equations and linear inequalities in one variable to model and explain real-life phenomena
• show and explain the connections between proportional and non-proportional relationships and linear equations; create and interpret graphical, mathematical models and use the graphical, mathematical model to explain real-life phenomena represented in the graph

## C - Functional & Graphical Reasoning

• describe the properties of functions to define, evaluate, and compare relationships; model and explain real-life phenomena using linear functions
• use bivariate quantitative data to solve relevant, linear problems
• justify and use various strategies to solve systems of linear equations to model and explain realistic phenomena

## D - Geometric & Spatial Reasoning

• solve problems involving the Pythagorean Theorem and the volume of cones, cylinders, and spheres to explain real-life phenomena

• # 8th Grade Mathematics -- Enhanced Algebra: Concepts & Connections

## A - Patterning & Algebraic Reasoning

• create and interpret expressions within realistic situations; create, interpret, and solve linear equations and linear inequalities in one variable to model and explain real-life phenomena
• show and explain the connections between proportional and non-proportional relationships and linear equations; create and interpret graphical, mathematical models and use the graphical, mathematical model to explain real-life phenomena represented in the graph
• create, analyze, and solve linear inequalities in two variables and systems of linear inequalities to model real-life phenomena
• build quadratic expressions and equations to represent and model real-life phenomena; solve quadratic equations in mathematically applicable situations
• create and analyze exponential expressions and equations to represent and model real-life phenomena; solve exponential equations in mathematically applicable situations

## B - Functional & Graphical Reasoning

• describe the properties of functions to define, evaluate, and compare relationships; model and explain real-life phenomena using linear functions
• construct and interpret arithmetic sequences as functions, algebraically and graphically, to model and explain real-life phenomena; use formal notation to represent linear functions and the key characteristics of graphs of linear functions, and informally compare linear and non-linear functions using parent graphs
• justify and use various strategies to solve systems of linear equations to model and explain realistic phenomena
• construct and interpret quadratic functions from data points to model and explain real-life phenomena; describe key characteristics of the graph of a quadratic function to explain a mathematically applicable situation for which the graph serves as a model
• construct and analyze the graph of an exponential function to explain a mathematically applicable situation for which the graph serves as a model; compare exponential with linear and quadratic functions
• use bivariate quantitative data to solve relevant, linear problems

## C - Numerical Reasoning

• solve mathematical problems involving irrational numbers and rational approximations of irrational numbers to explain realistic applications
• solve relevant, mathematical problems involving radicals and integer exponents; apply place value understanding with scientific notation and use scientific notation to explain real-life phenomena
• investigate rational and irrational numbers and rewrite expressions involving square roots and cube roots

## D - Data & Statistical Reasoning

• collect, analyze, and interpret univariate quantitative data to answer statistical investigative questions that compare groups to solve real-life problems; represent bivariate data on a scatter plot and fit a function to the data to answer statistical questions and solve real-life problems

## E - Geometric & Spatial Reasoning

• solve problems involving the Pythagorean Theorem and the volume of cones, cylinders, and spheres to explain real-life phenomena
• solve problems involving distance, midpoint, slope, area, and perimeter to model and explain real-life phenomena

• # 8th Grade Mathematics -- Foundations of Algebra

## A - Numerical Reasoning

• solve relevant, mathematical problems involving operations with whole numbers, fractions, and decimal numbers
• solve relevant, mathematical problems involving the four operations with rational numbers in any form (i.e., integers, percentages, fractions, and decimal numbers), including problems that involve multiple steps
• solve mathematical problems involving irrational numbers and rational approximations of irrational numbers to explain realistic applications
• solve relevant, mathematical problems involving radicals and integer exponents; apply place value understanding with scientific notation and use scientific notation to explain real-life phenomena
• solve a variety of contextual problems involving ratios, unit rates, equivalent ratios, percentages, and conversions within measurement systems using proportional reasoning

## B - Patterning & Algebraic Reasoning

• recognize proportional relationships in relevant, mathematical problems; represent, solve, and explain these relationships with tables, graphs, verbal descriptions, and equations
• show and explain the connections between proportional and non-proportional relationships and linear equations; create and interpret graphical, mathematical models and use the graphical, mathematical model to explain real-life phenomena represented in the graph
• identify, write, evaluate, and interpret numerical and algebraic expressions as mathematical models to explain relevant, mathematical problems
• represent authentic situations using equations and inequalities with variables; solve equations and inequalities symbolically, using the properties of equality
• create and interpret expressions within realistic situations; create, interpret, and solve linear equations and linear inequalities in one variable to model and explain real-life phenomena

## C - Functional & Graphical Reasoning

• describe the properties of functions to define, evaluate, and compare relationships; model and explain real-life phenomena using linear functions

## D - Geometric & Spatial Reasoning

• solve problems involving the Pythagorean Theorem and the volume of cones, cylinders, and spheres to explain real-life phenomena