| Common Core Math Standards (Wisconsin) | NCTM Standards (Advisory only) | Minnesota Standards (download from bottom of the page) |
NCTM: NCTM stands for National Council of Teachers of Mathematics. This is a professional organization of teachers, not a government agency. NCTM was the first group to write a set of standards for how mathematics should be taught. These standards are advisory and have influenced the other standards.
Wisconsin (Common Core): In 2009 several states got together to write a common set of standards that all of the states would agree on as the core of their curriculum. Wisconsin has adopted the Common Core standards (though this seems to be pretty controversial )
Minnesota: Up until a few years ago, each state had a separate set of standards. Minnesota still has different standards from the other states. There are a lot of similarities among different state standards, but there are details that are different.
In all of the Common Core (Wisconsin) and NCTM standards, the goals are split into two groups. One group is called content and the other group may be called practice (CCSS) or process (NCTM).
The content standards tell what children should be learning in which grades within content areas. A content area is something like arithmetic or geometry.
The process/practice standards tell what sorts of ways children should build and demonstrate their understanding of math concepts. The key goal is for children to understand math, and the process and practice standards are attempts to define what understanding looks like.
One thing that understanding looks like is being able to "do" math: be able to add, subtract, multiply, divide and so on. You'll find that in the standards as "fluency": statements like: "be able to add 2-digit numbers fluently". Fluently usually means being able to do something well, and without stumbling and stopping. This is sometimes considered the baseline for understanding--you can't really say you can understand math if you can't do it, but sometimes you can do math without really understanding very well what you're doing.
Another thing that understanding looks like is being able to explain what you're doing and why you're doing it (why it makes sense to do it that way). We ask children to explain their thinking when they solve problems, so we can find out what they are thinking and how well they understand what's going on. The thinking of why the math makes sense is often referred to as the "reasoning" part of the process, while "communicating" often refers to explaining one's thinking.
Having a better understanding of math also means being able to solve problems with it: taking the math you can "do" in one context and see how it can be used in a different context. This is understanding goal in the several math standards that gets the most attention. Standards that talk about "problem solving" and "inquiry" are referring to this ability to figure out how to use math in new contexts.
In the Common Core and NCTM standards, the practice/process standards have a single goal that gets reinterpreted at different grade levels, but the statement of the standards stay the same across all of the grade levels.
The Content Standards are organized by strands (NCTM, Minnesota) or domains (Common Core). An example of a strand or domain is something like "Operations and Algebraic Thinking" or "Number and Operations". Each strand contains a lot of specific standards that are different for different grade levels. In the NCTM standard, the same 5 strands appear at each grade level, but the interpretation and specific standards are different. In the Common Core standards, the domains are a little more specific, and will often appear for some grades and not others.
Lessons often will teach one of the content standards within the context of one of the practice/process standards. For example, a lesson on finding patterns in square numbers might be teaching 1-digit multiplication (finding square numbers) in a context of problem solving (finding a pattern).
The Minnesota standards are organized somewhat differently in that the practice/process standards aren't broken out as separate standards, but rather problem solving expectations are built in to specific content standards.
You'll see more of the details of how the standards are organized when you do the assignment.