What does a student learn in StateMissouri,GradeGrade 9,SubjectMathematics?

Interpret and use structure.

Interpret the contextual meaning of individual terms or factors from a given problem that utilizes formulas or expressions.

Analyze the structure of polynomials to create equivalent expressions or equations.

Define and use logarithms.

Understand why logarithmic scales are used, and use them to solve problems.

Use complex numbers.

Know and apply the Fundamental Theorem of Algebra.

Experiment with transformations in the plane.

Demonstrate the ability to rotate, reflect or translate a figure, and determine a possible sequence of transformations between two congruent figures.

Understand congruence in terms of rigid motions.

Develop the definition of congruence in terms of rigid motions.

Prove geometric theorems.

Prove theorems about polygons.

Make geometric constructions.

Construct geometric figures using various tools and methods.

Create equations that describe linear, quadratic and exponential relationships.

Create equations and inequalities in one variable and use them to model and/or solve problems.

Solve equations and inequalities.

Create and solve equations and inequalities, including those that involve absolute value.

Solve general systems of equations and inequalities.

Create and solve systems of equations that may include non-linear equations and inequalities.

Understand solving equations as a process, and solve equations and inequalities in one variable.

Analyze different methods of solving quadratic equations.

Represent and solve linear and exponential equations and inequalities graphically.

Explain that the graph of an equation in two variables is the set of all its solutions plotted in the Cartesian coordinate plane.

Solve problems involving a system of linear inequalities.

Prove theorems involving similarity.

Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.

Define trigonometric ratios, solve problems involving right triangles.

Use trigonometric ratios and the Pythagorean Theorem to solve right triangles.

Perform operations on polynomials and rational expressions.

Understand the Remainder Theorem and use it to solve problems.

Interpret linear, quadratic and exponential functions in terms of the context.

Use and interpret functions.

Using tables, graphs and verbal descriptions, interpret key characteristics of a function that models the relationship between two quantities.

Analyze linear, quadratic and exponential functions using different representations.

Identify and interpret key characteristics of functions represented graphically, with tables and with algebraic symbolism to solve problems.

Graph functions expressed symbolically and identify and interpret key features of the graph.

Use coordinates to prove geometric theorems algebraically.

Use coordinates to prove geometric theorems algebraically.

Create new functions from existing functions.

Create new functions by applying the four arithmetic operations and composition of functions (modifying the domain and range as necessary).

Build new functions from existing functions (limited to linear, quadratic and exponential).

Describe the effects of transformations algebraically and graphically, creating vertical and horizontal translations, vertical and horizontal reflections and dilations (expansions/compressions) for linear, quadratic, cubic, square and cube root, absolute value, exponential and logarithmic functions.

Analyze the effect of translations and scale changes on functions.

Explain volume formulas and use them to solve problems.

Use volume formulas for cylinders, pyramids, cones, spheres and composite figures to solve problems.

Apply geometric concepts in modeling situations.

Apply geometric methods to solve design mathematical modeling problems.

Construct and compare linear, quadratic and exponential models and solve problems.

Construct linear, quadratic and exponential equations given graphs, verbal descriptions or tables.

Use arithmetic and geometric sequences.

Write arithmetic and geometric sequences in recursive and explicit forms, and use them to model situations and translate between the two forms.

Use functions to model real-world problems.

Create functions and use them to solve applications of quadratic and exponential function model problems.

Understand independence and conditional probability and use them to interpret data.

Understand the definition of independent events and use it to solve problems.

Recognize and explain the concepts of conditional probability and independence in a context.

Make inferences and justify conclusions.

Determine whether a specified model is consistent with a given data set.

Use data from a sample to estimate characteristics of the population and recognize the meaning of the margin of error in these estimates.

Summarize, represent and interpret data.

Fit a data set to a normal distribution.

Analyze and interpret graphical displays of data.

Know and use the characteristics of normally distributed data sets; predict what percentage of the data will be above or below a given value that is a multiple of standard deviations above or below the mean.