As of July 2013, 45 of the 50 states, as well as the District of Columbia, had adopted the Common Core State Standards Initiative. The Common Core, as it is generally known, lays out for schools units of study and the standards that schoolchildren in the United States should be meeting in grades kindergarten through 12 in English language arts and mathematics. According to the Common Core, the units of study for ninth grade math are number and quantity, algebra, functions, geometry and statistics and probability.

### Number and Quantity

The Number and Quantity unit of ninth-grade mathematics focuses on numbers and number systems. This unit of study is broken up into four smaller areas of study. In studying the real number system, students continue the work they have done with exponents in the lower grades and focus on extending the properties of exponents to rational exponents. Students also examine the properties of rational and irrational numbers. The next section, quantities, allows students to practice using quantitative reasoning and units to solve problems. Ninth grade students will also study the complex number system. During this portion of the unit, students perform arithmetic operations with complex numbers, represent complex numbers and their operations on a complex plane, and use complex numbers in polynomial identities and equations. Finally, students' studies turn to vector and matrix quantities. Here, students are expected to represent and model with vector quantities, perform operations on vectors, perform operations on matrices and use matrices in applications.

### Algebra

The second unit of study for ninth-grade mathematics is algebra. During this unit, students focus specifically on expressions, equations and inequalities. Like the first unit, algebra is also broken up into several smaller units of study including seeing structure in expressions, arithmetic with polynomials and rational expressions, creating equalities and reasoning with equations, and, finally, inequalities. At the conclusion of this unit, students' skills should include the ability to interpret the structure of equations, write equations in equivalent forms to solve problems, use polynomial identities to solve problems, create equations that describe numbers and relationships, solve equalities and inequalities in one variable, and represent and solve equations and inequalities graphically.

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### Functions

Functions, according to the Common Core website, describe situations where one quantity determines another. The focus in this unit is on understanding connections to expressions, equations, modeling and coordinates. Students study this topic by breaking it down into the study of interpreting and building functions; linear, quadratic and exponential models; and trigonometric functions. In the first part of this unit, the ability to understand, interpret, analyze and build functions is key. Students then move on to construct and compare linear and exponential models. In the final part of this unit, trigonometric functions, students learn to extend the domain of trigonometric functions using the unit circle, model periodic phenomena with trigonometric functions, and prove and apply trigonometric identities.

### Geometry

Ninth-grade geometry focuses on plane Euclidean geometry through the study of a number of smaller topics. Included in the geometry unit are congruence; similarity, right triangles and trigonometry; circles; expressing geometric properties with equations; geometric measurement and dimension; and modeling with geometry. Students are introduced to the Pythagorean theorem, as well as the law of sines and the law of cosines, and have an opportunity to experiment with transformations in the plane. By the end of the unit, they are expected to be able to use geometric theorems in a variety of ways, explain the use of a variety of theorems and formulas, and apply geometric concepts in both theoretical and concrete ways.

### Statistics and Probability

The use, interpretation, manipulation and presentation of data is at the heart of the ninth-grade unit on statistics and probability. Within this unit, students study how to interpret categorical and quantitative data; practice making inferences and justifying their conclusions; conditional probability and the rules of probability; and how to use probability to make decisions. Technology plays an important role in the study of statistics and probability, and students use it to generate plots and simulate outcomes. Students in this unit frequently summarize, represent and interpret a variety of forms of data and then use their own work to calculate and evaluate possible outcomes. Applying these skills to real-world scenarios encourages students to think critically about their own decision-making processes.

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