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
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
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
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
