# 1.1 Mathematical practices

The Standards for Mathematical Practice describe ways in which developing student practitioners of the discipline of mathematics increasingly ought to engage with the subject matter as they grow in mathematical maturity and expertise throughout the elementary, middle and high school years.

—Common Core State Standards for Mathematics, page eight

**The eight Standards for Mathematical Practice are:**

- Make sense of problems and persevere in solving them
- Reason abstractly and quantitatively
- Construct viable arguments and critique the reasoning of others
- Model with mathematics
- Use appropriate tools strategically
- Attend to precision
- Look for and make use of structure
- Look for and express regularity in repeated reasoning

What does all this mean? And what do the Standards for Mathematical Practice look like *in practice*? These resources are intended to help you begin to answer these and other questions.

### Resources

- Think Math — CCSS Mathematical Practices
- This site is set up much like Wikipedia. This page briefly describes the Standards for Mathematical Practice that are part of the Common Core State Standards for Mathematics. At the bottom of the page are links to pages, which describe each of the Standards for Mathematical Practice in greater detail and provide an example of what each might look like at the elementary level.
- Differences between, and connections between, Content and Practice Standards
- This page explains ways in which the Mathematical Practices and the Content Standards are intended to work collaboratively in the Common Core State Standards for Mathematics.
- Inside Mathematics
- This site includes resources and videos illustrating the Standards of Mathematical Practice. Scroll down to the bottom of the page to find the table that will link you to these resources, which include descriptions of what each practice might look like in the classroom and videos illustrating that practice at different grade levels.
- Dan Meyer: Math Class Needs a Makeover
- In this TEDx talk, Dan Meyer says, “I teach high school math. I sell a product to a market that doesn’t want it but is forced by law to buy it.” He goes on to demonstrate how he has adapted curriculum materials and created learning opportunities for students that immerse them in becoming what he terms “patient problem solvers.” He ends the talk with five ways teachers can assist in this process, including, “Be less helpful.”
Questions to consider while viewing this video:

- How do you see the Standards for Mathematical Practice at work in Mr. Meyer’s approach?
- How might Mr. Meyer’s approach assist you in examining your own process of engaging students in mathematics?

- Hunt Institute Common Core State Standards Videos
- These videos were developed to help teachers, policymakers, and parents understand the Common Core State Standards and the ways in which they will impact teaching and learning. There is a group of general videos introducing the Common Core State Standards and a more detailed group of videos focused specifically on the Mathematics Standards. The video
*The Importance of Mathematical Practices*introduces the Standards for Mathematical Practice and their importance in the Common Core State Standards for Mathematics. - Illustrative Mathematics
- This site contains sample tasks and problems, referred to as “illustrations,” for the Common Core State Standards in Mathematics. If you click on the K-8 Standards link on the left you will be able to browse the database by grade level or by domain. This site also includes a section on the Standards for Mathematical Practice. Though not as extensive as other sites, this is a nice presentation of information.