Common Core Math: Domains and Standards Explained

Video Transcription

Hello, ladies and gentlemen. I hope you're having a great day today. Today, we're going to focus in on the Common Core Math standards and specifically explaining those domains and standards that are a part of Common Core Math. For today's lesson, I've chosen a quote by Rene Descartes, which states, "but in my opinion, all things in nature occur mathematically." By the end of today's lesson, you are going to be able to analyze the structure of Common Core Math standards, the domains, and the practice standards that are involved.

First, let's take a look and break down the different parts of the standards. First, we have the content standards. What these do is these help to define for teachers what students should understand and be able to do. We then break down the Common Core Math standards into what are called clusters. These clusters summarize groups of related standards. They look at major, minor, and supporting standards.

Some clusters tend to be given more attention over others based on the complexity or the time it takes to master or the connection to topics covered in later grades or to college and career readiness. And although they are not all critical, all standards should be addressed to help avoid those knowledge gaps that students can sometimes fall into in their understanding of the material. You'll get the opportunity to see an example of clusters later on and to see how they really relate back to those standards.

Finally, let's focus in on the domains. Domains are larger groups of related standards. It's important to note that standards from different domains may sometimes be closely related. So you could see something that looks a little bit like an overlap here.

Let's focus in and really explain those domains. First, we can look at those high school in conceptual categories. You'll notice here these are the major groups of related standards that high school students are going to focus in on. You'll notice that some of them look very similar to actual class names of high school math classes.

When we get into the K-8 domains, we're looking at a larger group since we're looking at eight grades-- technically nine if you consider kindergarten-- as opposed to just four and a lot more different base information that these students are going to need to hone in on.

What I'd like to do really quickly is to give you an example of one of these domains and talk about some of the relevant skills for it across a few grade levels, just so you can see how it progresses forward. The domain we're going to look at in this case is The Number System. And I'm going to focus in on that junior high or middle school age. So when we look at The Number System within grade 6, some of the relevant skills would be for students to be able to compute fluently with multi-digit numbers and then also to be able to find common factors and multipliers. That's a pretty basic element for grade 6.

You'll notice as we move onto grade 7, there is an increased ability to be able to apply and extend their previous understanding of those fractions. So again, building on what was learned before. And then in grade 8, you see an even greater, more in-depth look at The Number System as students are to know that there are numbers that are not rational and then to be able to approximate them by rational numbers. So you can see how, as we go from 6 to 7 to 8, our influenced within the domain of The Number System continues to get progressively more challenging for the students.

Finally, let's take a look at the eight math practice standards. These are the major standards developed by the Common Core Standards Initiative finalized in 2012. The first is to make sense of problems and persevere in solving them. These are the standards put in place when we are practicing math. We should be able to reason abstractly and quantitatively when looking at math, to construct viable arguments and critique the reasoning of others for why we've solved something the way we have, model with mathematics, use appropriate tools strategically, attend to precision-- really making sure we're getting into the nitty gritty of each element-- looking for and making use of structure within mathematics, and finally, looking for and expressing regularity in repeated reasoning, really tying together all of those math elements that are being learned.

Now I would like to go ahead and take a look at a couple of the math standards and really walk through how to read these standards. We're going to look at a few samples, discuss the domains that they belong to and why, and look at how you can identify the domain, the standard, and the cluster.

So this first one we're using is from grade 2. And you'll notice that it represents three different standards that we can see here. The three standards that we're working with within this area are that students are going to be able to represent and solve problems involving addition and subtraction. They'll be able to add and subtract within 20. And students should be able to work with equal groups of objects to gain foundations for multiplication.

Now, within each of those standards, you'll notice that they're broken down even more into clusters. These elements underneath each standard really help to show each individual student what they should be able to do by the end of the year. And these are the parts that you're going to take and break down into those I-can statements.

So for example, with add and subtract within 20, it breaks it down stating that students should fluently add and subtract within 20 using mental strategies, by the end of grade 2 know from memory all sums of two one-digit numbers. So it really breaks down even more specifically what needs to be done there.

Now, you'll notice that up at the top is where you're able to identify the domain that they belong to. So these various standards belong to the domain of operations and algebraic thinking. You'll notice over off to the side you see a 2.0A. That's the really quick way to remind you that it's Operations and Algebraic Thinking for Grade 2. Now it makes sense that all of these represent the elements for Operations in Algebraic thinking, because it's asking students within the area of algebra to really identify and work within the various operations such as problem solving, adding and subtracting, working within groups, gaining foundations for multiplication really within that specific area.

Now let's take a look at another math standard for an older age group. You'll notice that within here the standard is the same. It is bolded so that it's easily seen. And it's worth asking that students know that there are numbers that are not rational and approximate them by rational numbers.

Now, this is broken down even more and even includes a couple of examples within the cluster. So it really focuses on the two major parts of that standard and even gives you an example that, as a teacher, you can use as you work through those I-can statements and achieving these standards with your students. Again, at the top, you notice that this standard is for eighth grade as noted by the 8 off to the right there. And this falls under the domain of The Number System. Now, it clearly falls under that domain as we are looking at the various types of numbers.

As you can imagine, the number system and the standards for that in first or second or third grade are very different than the ones in eighth grade. This is a little more advanced. We're talking about rational and irrational numbers as we begin to focus in on how students can develop all of the various elements within The Numbers System.

Now that we've reached the end of the lesson, you should be able to analyze the structure of the Common Core Math standards, the domains, and the practice standards. Now I want to take a little time for reflection. As you look back on all that we've learned here in this unit, I'm wondering, what do you think will be the most difficult part of getting students to really adopt those eight Math Practice standards that we discussed?

Now, to dive a little deeper and learn how to apply this information, be sure that you check out the Additional Resources section associated with this video. This is where you'll find the links targeted toward helping you discover more ways to apply this course material.