Sixth grade math concepts have a very broad range of mathematics topics. However, these are the math concepts that students should understand by the end of the sixth 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 in sixth grade. Students study fractions,
decimals, and percents. They use these concepts to solve problems,
word problems, and be able to properly place them on a number line.
They learn how to apply and use percents that are greater than 100
and less than 1. The understanding of fractions is critical to their
ability to take higher levels of math in upper middle school.

Another area of numbers and operations they study is the use of factors, multiples, prime numbers to solve problems and word problems. They continue their preparation in elementary algebra by using and apply the distributive property and commutative property in addition and multiplication. Then they apply the associative property in addition and multiplication. Their studies continue in the area of square roots of numbers as they apply to the inverse relationships of addition and subtraction.

In the area of **Geometry** concepts sixth grade students develop
an understanding of two and three dimensional objects, such as: squares,
rectangles, cones, spheres, cylinders, etc. They also study polygons
as they relate to lines that are parallel and perpendicular. Additional
areas of geometry and shapes are the focus on transformations and
symmetry of shapes as they are flipped, rotated, and turned.

Students also learn how to find the area and volume of objects, using mathematical formulas. These include squares, prisms, rectangles, cones, circles, spheres, cylinders, etc. They also spend time learning how to apply geometric shapes to real world applications, along with connections to of content subject 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.

In the concept area of **Data Analysis and Probability**, students
use appropriate language to explain findings of experiments and simulations.
They learn how to develop questions that will help them find the differences
between tow samples in a population.

When it comes to **Problem Solving**, students develop 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.

In the concept are of **Representation**, students learn to collect
and organize data. Then use the data to solve problems. Answers are
presented as models that are physical and social. They use the data
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. This concept
is also used to as method for students' to defend the answers they
arrive at during calculations. This concept is used to improve mental
math skills and connections with other math concepts areas.

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.