Ninth grade math concepts can cover several topics. However ninth grade math typically focuses on general math, algebra, or geometry. This is due to whatever course a ninth grade student is enrolled; there is no standard of what math subject should be taught in the ninth grade. These are the math concepts that students should understand by the end of the ninth grade based their course they are enrolled and the National Mathematics Standards.

**Numbers and Operations** concepts focus on rational and irrational
numbers to solve complex mathematical problems. They also use the
quadratic equations to solve real world problems, providing sound
solutions. They develop an understanding vectors and real number systems
to solve problems. They use vectors and matrices to explain the properties
and representations that involve basic math computations through the
use of fractions, percents, decimals, and whole numbers. They also
learn to apply these concepts using mental math and pencil - paper
solutions.

**Geometry **concepts for ninth grade students' focus on developing
an understanding of two and three dimensional objects, such as: prisms,
pyramids, cubes, cones, spheres, cylinders, etc. They explore relationships
of shapes including congruence and similarity to solve the geometric
problems. They also use Cartesian coordinates to find the relationships
of two and three dimensional objects.

Ninth grade students use and understand geometric translations, reflections, rotations, symmetry, and dilations of objects through the use of sketches and matrices. Students construct two and three dimensional objects using various tools to explain geometric situations. They use drawings, models, and graphs to make connections of geometric situations in other subject content areas and real world objects.

**Algebra** concepts students study are the relationships to functions
such as rates of change. In addition, they learn to use the multiple
variables for intercepts, zeros, and behaviors. They learn to use
more commonly used algebraic functions through the use of technology,
such as: graphing calculators and computer programs to solve and represent
equations.

Students learn to write and solve equations and inequalities using mental processes, along with traditional paper and pencil. Students' studies include the applications of manipulation of equations which are logical and symbolic. They draw reasonable conclusions based on their solutions, along with making connections with other mathematical concept areas.

**Measurement** concepts focus on the use of standard and non-standard
(customary) units of measurement to determine the relationships between
different objects. This is also connected with geometry as they learn
how to measure the area, volume, and mass of different geometric shapes
using various tools. They learn how to measure all aspects of spheres,
prisms, pyramids, etc.. They use measurements to make drawings and
models of equations to explain a solution to a problem in both mathematical
and real world terms.

**Data Analysis and Probability**, students use appropriate language
to explain their findings in experiments and simulations. They learn
how to develop questions to help them find the differences between
several samples in a population. They develop studies of situations
to include the role of random and experimental surveys. They learn
to use and explain the univariate and bivariate in measurement and
categorical data. This information is used to develop scatter plots,
regression coefficients, and regression equations using technological
tools.

Students also study the application of sample statistics for developing explanations using appropriate data analysis. This is used to develop patterns of randomness for the probability that certain events may be independent of other events. They learn to use simulations to explain randomness of events.

**Problem Solving** for ninth grade students focuses on the development
of problem solving strategies to help them develop a fundamental understanding
of mathematics. Students use word problems and other real world simulations
in problems solving situations.

**Representation** concepts focus on students learning to collect
and organize data, then using the data to solve problems. Answers
are presented as models that are numerical, written, physical, and
social. They are able to draw graphs, charts, tables, and other forms
to explain how they solved a problem.

**Connection** concepts are designed for ninth grade students
to demonstrate how to make connections to real world applications
and other subject content areas. This includes making connections
with other concepts in mathematics.

**Communicate** their mathematics ideas in the form of sentences,
drawings, posters, and multimedia applications is another concept
that students need to master. This is used to ascertain their level
of understanding as they explain mathematical concepts to other students
and teachers.

**Reasoning and Proof **concepts are used to explain mathematical
findings and problem solving techniques. This is necessary so that
they develop skills on how to present logical arguments to math situations.

All of these mathematical concepts are used to develop a well rounded base knowledge of mathematical ideas and language as students' progress to higher levels of mathematics.