Mathematical Fluency in IM Math K-6

“Procedural fluency refers to knowledge of procedures, knowledge of when and how to use them appropriately, and skill in performing them flexibly, accurately, and efficiently,” as defined in Adding It Up: Helping Children Learn Mathematics from the National Research Council (2001).

IM K–5 Math is designed so that students build procedural fluency and conceptual understanding simultaneously. The representations, strategies, and algorithms that are used and highlighted are purposefully designed for coherence. Fluency is embedded throughout the lessons, rather than isolated as a separate skill.

Culturally responsive teachers can use their knowledge about their students’ cultural ways of meaning-making to provide opportunities for students to develop and practice fluency. For example, the instructional routines and centers in our curricular materials offer communal and collaborative ways to learn and practice math facts. Our lesson activities and centers also include opportunities for students to reflect on their progress by stating the facts they know and the facts they are learning. This practice allows students to engage in goal-setting and advocate for their learning by making informed decisions about their fluency development.

Students are given opportunities throughout the year to name the facts they know, the facts they are still learning, and identify strategies to learn these facts. Warm-up routines, such as Number Talks and True or False, plus centers and games during lessons support students in becoming more fluent throughout the year. 

The centers, which are usually activities or games, are designed in stages. The stages are often broken down by ranges of numbers that students are operating with so teachers can systematically support students with stages based on the facts they need to practice. 

Centers are meant for extra practice in school or outside of school and are designed to build fluency (or any skill that develops over time) across a year.

Centers:

• are aligned to grade levels and units.

• consist of states with the same general structure

• can be repeated with different results each time

• primarily focus on the major work of grade

Illustrative Mathematics does not take a position on timed tests for assessing students’ knowledge of math. Assessment can be conducted in various ways and is not limited to timed tests. For example, assessment also includes a teacher engaging with students and observing students while walking around the classroom. 

A student who is fluent in mathematics can flexibly, efficiently, and accurately use computational methods. For example, a student fluent in addition computation can mentally use 10 + 5 = 15 to know that 9 + 6 = 15.

• National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston, VA: NCTM.

• Kilpatrick, J., Swafford, J., & Findell, B. (2001). Adding It Up: Helping Children Learn Mathematics. Washington, DC: National Academy Press.