The 8 Mathematical Practices: What’s the Real Value in the K–2 Classroom?

By Shannon Samulski

The Common Core State Standards are redefining how teachers teach math and how students learn math. While focus is still on core content and skill fluency, the Common Core also emphasizes such practices as reasoning, perseverance, problem-solving, and justification.

Teaching students these skills—the skills of true mathematical thinkers—does not happen without a plan. For students to meet the high level of expectations outlined in the Common Core State Standards, they must build a foundation of mathematical thinking and communicating.

The 8 Mathematical Practices are a tool teachers can use to build that foundation and transform what can be an overwhelming process into a set of comprehensible and concrete steps. Teachers cannot be expected to automatically weave these practices into their curriculum. But once they understand the 8 practices and the relationships between them, they can begin to transform their math culture and let higher-level thinking and reasoning occur naturally. In this article, we’ll look at how to understand and make these practices more manageable in the classroom.

Understanding the practices

These 8 standards are presented as separate practices. But in reality, they intermingle and blend together, and are rarely used in isolation from one another. When you pair the practices, you can better understand the relationships between them and how to use them in the classroom.

  • Practices 1 (Make sense of problems and persevere in solving them) and 6 (attend to precision) present habits of mind that apply to all mathematical thinking and problem solving.
  • Practices 2 (Reason abstractly and quantitatively) and 3 (Construct viable arguments and critique the reasoning of others) emphasize the need for students to reason and justify their thinking and the thinking of others as they establish the validity of their work.
  • Practices 4 (Model with mathematics) and 5 (Use appropriate tools strategically) pertain to students as they prepare to use mathematics in their work and, later, in real life.
  • Practices 7 (Look for and make use of structure) and 8 (Look for and express regularity in repeated reasoning) focus on the need to identify and generalize patterns and structure as students perform calculations and use mathematical objects.

Transforming math culture

The days when teachers “explained” how to solve a math problem are over. In the 21st century classroom, students are expected to “show” how they solve problems. How do teachers make that critical “shift” in their classrooms?

They allow students to make connections and discoveries, work together, ask questions, and solve problems based on their prior knowledge to make math a student-centered experience. They combine the 8 Mathematical Practices, performance tasks and activities, and numeracy development to improve math proficiency. They differentiate instruction to meet the needs of each child—including at-risk students—while addressing the 8 Mathematical Practices. Most importantly, they make math fun and exciting for young learners and demonstrate how easy it is to be successful in math.


Dive deeper into the link between the Common Core State Standards and the 8 Mathematical Practices. Check out SDE’s webinar 8 Mathematical Practices: Addressing the Higher Standards (Grades K–2) by author and intervention expert Shannon Samulski.

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