Twelfth grade math concepts have a very broad range of mathematics topics. This due to whatever course a twelfth grade student is enrolled, there is no standard of what math subject should be taught in the twelfth grade. However, these are the math concepts that students should understand by the end of the twelfth grade based on the National Council of Teachers of Mathematics Standards.

When it comes to **Numbers and Operations** concepts these are
the concepts that students study. Students use rational and irrational
numbers to solve complex mathematical problems. They also use the
quadratic equation to solve real world problems, providing sound solutions.
They develop and understanding of vectors and matrices in real number
systems to solve problems. They use vectors and matrices to explain
the properties and representations that involve addition and multiplication
as they continue using real numbers. They learn to apply these concepts
using mental math and pencil - paper solutions.

In the area of **Geometry** concepts twelfth grade students develop
an understanding of two and three dimensional objects, such as: squares,
rectangles, cones, spheres, cylinders, etc. They explore relationships
that including congruence and similarity to solve the problems. They
use Cartesian coordinates to find two and three dimensional objects.

Twelfth grade students use and understand geometric translations, reflections, rotations, 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.

Students develop an understanding of **Algebra** in the relation
to functions as they investigate rates of change. In addition, they
learn to use the variables of intercepts, zeros, and behaviors. They
learn to use more commonly used algebraic functions using technology,
such as graphing calculators, to represent equations.

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

The concept area of **Measurement** is focused on the using standard
and non-standard 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. They learn how to measure all aspects of circles,
prisms, and pyramids. They use measurements to make drawings and models
of equations to explain a solution to a problem.

In the concept area of **Data Analysis and Probability**, students
use appropriate language to explain their findings in experiments
and simulations. They learn how to develop questions that will help
them find the differences between several samples in a population.
They develop studies that 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 will be used
to develop scatter plots, regression coefficients, and regression
equations using technological tools.

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

When it comes to **Problem Solving**, students develop problem
solving strategies to help them develop a fundamental understanding
of mathematics.

In the concept are of **Representation**, students learn to collect
and organize data. Then use the data to solve problems. Answers will
be presented as models that are physical and social. They are able
to draw graphs, charts, tables, and other forms to explain how they
solved a problem.

For **Connection** concepts students learn to make connections
to real world applications and other subject content areas. This includes
making connections with other concepts in mathematics.

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

Students use logical **Reasoning and Proof** to explain their
mathematical findings and problem solving techniques.

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 in college.