Sixth grade math students will focus on more advanced numbers, such as negative numbers, square roots and exponents. They are also taught orders of operation in order to move into solving more complex numbers. Decimals, fractions and other non-whole numbers are also focused on, as these are necessary for most high-level math problems. It is no longer acceptable to solve a division problem and leave a remainder--rather, children need to learn how to solve division problems with decimals or fractions.
Measurement is taught to sixth graders as well, although it tends more toward a geometric perspective. Rather than just measure objects, sixth grade math students are taught how to measure objects and then use the results of their measurements to draw conclusions. Sixth grade math students are taught how to find perimeter and area in order to apply math skills to the world around them and move into higher-level geometry.
Sixth grade math teachers also show students how to draw conclusions from data by doing things like finding the mean, median and more, drawing graphs and carrying out other basic analyzes. Like the geometry mentioned above, this helps students apply math to real-life situations and use it to their advantage. It brings math from a matter of looking at and working on numbers to figuring out what those numbers mean, which is substantially more important.
Sixth grade students study basic algebra too. This is just a foundation-level course, where they learn how to substitute variables and solve basic problems, such as "x-5=2." Algebra is taught more in terms of a a firm foundation rather than teaching kids advanced things like quadratic equations. These more complicated things can come later in a child's academic career, but they will be easier if the child has a firm foundation, which is taught in sixth grade.