In this tutorial, we'll examine the structure and organization of the Common Core math standards. We'll look at the clusters, domains, and practice standards that make up the standards. And then we'll look at some specific examples that will help you to successfully navigate the Common Core math standards. Let's get started.
Clusters are groups of individual standards that are related to each other by topic. There are three different types of clusters. Major clusters are the clusters of standards that should receive the most focus at the particular grade level. Minor clusters may receive some degree of focus at the indicated grade level, but they may be more relevant at other grade levels. And supporting clusters are those that complement the major clusters. Teachers need to make decisions about how much time and attention to spend on various clusters, based on the complexity of the clusters, how much time they're going to take to cover and for students to master, and to the degree to which each of the topics connects to later grade levels, or to college and career readiness concepts.
Though these labels of major, minor, and supporting clusters do assign varying levels of importance or urgency to different standards, it's important to note that all of the standards do need to be addressed, so that students don't have gaps that form in their understanding. Let's look at a specific example in the grade three Common Core math standards. Each cluster of standards is denoted with a boldfaced heading. For example, represent and solve problems involving multiplication and division. The four standards listed under that bold heading are a single cluster of standards. It's clear that all of the standards within a cluster are related. For example, finding the product of two whole numbers, finding the quotient of whole numbers, and using multiplication and division to solve word problems and to employ algebraic reasoning, are skills that are all related to the topic of representing and solving problems involving multiplication and division.
While a cluster is a group of related standards at a single grade level, a domain is a larger group of related standards spanning multiple grade levels. To be more specific, clusters exist within the various domains in the Common Core math standards. You may find that standards from varying domains may still sometimes be closely related to one another. The domains in grades K-8 include counting and cardinality, operations and algebraic thinking, numbers and operations in base 10, numbers and operations with fractions, measurement and data, geometry, ratio and proportional relationships, the number system, expressions and equations, statistics and probability, and functions.
The high school domains, or conceptual categories, include number and quantity, algebra, functions, modeling, geometry, and statistics and probability.
Back on the Common Core State Standards website, let's take a closer look at one of the domains. Within the measurement and data domain, we can see that the various clusters of standards are organized by grade level. For example, in kindergarten, under the measurement and data domain, students are asked to describe measurable attributes of objects such as length or weight, and to directly compare two objects that share a measurable attribute.
In grade two within the measurement and data domain, students will be asked to measure the length of an object by selecting and using appropriate tools, and to estimate the lengths of objects using appropriate units. By grade five, students will be converting among different measurement units and making line plots to display measurement data. You can see how all of these standards exist in a progression by grade level under the single domain of measurement and data.
Finally, the practice standards that exist within the Common Core State Standards apply to all of the grade levels. These standards describe how students should be interacting with mathematical content. The practice standards include making sense of problems and persevering in solving them, reasoning abstractly and quantitatively, constructing viable arguments and critiquing the reasoning of others, modeling with mathematics, using appropriate tools strategically, attending to precision, looking for and making use of structure, and looking for and expressing regularity in repeated reasoning.
For example, when I ask my geometry students to draw an accurate diagram of a three dimensional figure and then find the volume of that figure, I might choose to emphasize a few of the practice standards, including modeling with mathematics and attending to precision, as I encourage students to create accurate diagrams. This type of problem also requires perseverance, as it involves multiple, possibly lengthy steps.
We can see how these math practice standards can be applied at any grade level throughout all of the Common Core mathematics standards.
Let's take an even closer look at a few of the standards, in order to help you decipher the alphanumeric codes that identify the standards. This standard includes key words such as data and random sample that point to this being a statistics and probability standard. It turns out that the letters SP in the identification code verify that this is indeed a statistics and probability standard. More specifically, this standard is from grade seven. When covering this standard, teachers may want to focus on the practice standards of reasoning abstractly and quantitatively, and perhaps modeling with mathematics, especially if students are using a simulation to generate samples.
Here's another example standard, this one from grade three. The letters OA indicate that this is a standard from the operations and algebraic thinking domain. The concept of interpreting the product of two whole numbers definitely fits under the umbrella of both operations and the foundations of algebraic thinking. One of the math practice standards that would be a great fit with covering this particular content standard is constructing viable arguments and critiquing the reasoning of others. Students could be asked to explain and justify their interpretations, and perhaps even give feedback on their classmates' interpretations.
When looking at a cluster of Common Core math standards, look for the bold-faced type in order to help you identify the overall topic covered in the cluster. Use the alphanumeric codes to help you identify the grade level and the domain covered in each of the standards. And note that the final letter and number at the end of each alphanumeric code help you identify each individual standard within the cluster.
In this tutorial, we examined the clusters, domains, and practice standards that make up the structure and organization of the Common Core math standards. We also looked at several specific examples that helped us interpret the alphanumeric codes that identify the standards and to navigate through the standards themselves.
So here's a chance for you to stop and reflect. Do you now feel more comfortable in your ability to navigate the Common Core State Standards in math? Can you use a standard alphanumeric label in order to identify the grade level and the domain covered in the standard?
As you reflect on how this new information can be applied, you may want to explore the additional resources section that accompanies this video presentation. This is where you'll find links to resources chosen to help you deepen your learning and explore ways to apply your newly acquired skill set.
Thanks for joining me today. Have a great day.
(00:00 - 00:20) Introduction
(00:21 - 01:59) Clusters
(02:00 - 03:54) Domains
(03:55 - 05:12) Practice Standards
(05:13 - 07:00) Examples
(07:01 - 07:20) Review
(07:21 - 07:58) Stop and Reflect
Common Core State Standards Application
This is a free teacher application from Mastery Connect that is aligned to the state and CCSS standards. This is a useful resource to have at your fingertips when designing lessons. Each state application provides teachers with clickable links to each standard by grade, making this an easy to use reference tool.
Mathematics Assessment Project
This site from University of California, Berkeley offers math tasks aligned to the standards for middle school and high school students. Teachers can click on a standard to find an aligned math task. The tasks include guidance and resources for teachers to use as they facilitate student learning using the tasks. These tasks are valuable tools as teachers begin to build their curriculum resources in alignment to CCSS with a focus on critical thinking skills.
EQuIP Quality Review Rubric for Lessons & Units: Mathematics
There are currently many resources available with a CCSS sticker attached, yet very few of these resources are actually aligned. As an educator it can be difficult to know if a resource is aligned. The EQuIP rubric provides an easy to use rubric for educators when selecting and developing resources and lessons aligned to the CCSS. Below is a link to the rubric as well as a how-to video on using the rubric.
Video: http://www.achieve.org/EQuIP (Scroll to the center of page and click on the tab labeled "EQuIp Training Materials.")