Procedural Fluency: The Core Of Every Math Lesson

When you hear someone say memorization, knowing your facts, following the steps, and procedural fluency, do each of these terms have the same meaning?

When when it comes to describing procedural fluency, we often hear educators (and parents) using these terms interchangeably.

However, this is definitely NOT the case.

Being fluent in any area of mathematics means being:

    • efficient;
    • flexible; and,
    • accurate.

(Kilpatrick et al., 2001; National Council of Teachers of Mathematics (NCTM), 2014). 

Moreover, last week NCTM released a clarifying statement about their position on procedural fluency. 

“Procedural fluency is the ability to apply procedures efficiently, flexibly, and accurately; to transfer procedures to different problems and contexts; to build or modify procedures from other procedures; and to recognize when one strategy or procedure is more appropriate to apply than another.”

(NCTM 2014, 2020; National Research Council 2001, 2005, 2012; Star 2005).

NCTM has included four (4) declarations that are necessary so that every student has access to developing procedural fluency: 

  • Conceptual understanding must precede and coincide with instruction on procedures;
  • Procedural fluency requires having a repertoire of strategies;
  • Basic facts should be taught using number relationships and reasoning strategies, not memorization; and,
  • Assessing must attend to fluency components and the learner. Assessments often assess accuracy, neglecting efficiency and flexibility.

Procedural fluency is much more than just knowing basic facts and algorithms and…

…teaching to develop true procedural fluency is so much harder to teach!

Here’s a question we’ve been asking ourselves more and more here at Make Math Moments:

“How can we help our students become more fluent and flexible in ______________________?”

At Make Math Moments, we believe that your mathematics classroom must be cultivated and fostered like a strong, healthy and balanced tree. To grow our own tree we must care and strengthen six (6) key areas:

    • The Trunk: Our Classroom Culture & Norms;
    • The Roots: Educator Mathematics Content Knowledge & Proficiency;
    • Soil, Water, Sunlight: Our Mindsets & Beliefs;
    • The Limbs: Educator (and District) Professional Learning Plans;
    • The Branches: Our Pedagogical Content Knowledge; and,
    • The Leaves: The Tools and Resources We Use as well as Our Classroom Environment.

Strengthening how we teach for the development of procedural fluency from conceptual understanding (as shared in NCTM’s guidelines above) means we will need to strengthen  all key areas of our tree, but in particular, the Roots, Branches and Leaves.


In order to develop the root system of our mathematics program, we must strengthen our own conceptual understanding in order to better scaffold our instruction to ensure we meet students where they are and push them along their developmental continuum.

As we continue to develop our own root system of mathematical content knowledge, we must also be strengthening the branches of our mathematics program. Only when we have the teacher moves and pedagogical strategies that promote learning will the work we do with students have the effect on fluency and flexibility we are striving for.

Of course, as our mathematical content knowledge and pedagogical practice evolve, we must also work towards growing the leaves of our tree by seeking out the lessons and resources that are most appropriate to bring out the big ideas, strategies and models we must highlight as we push each student further down the path towards procedural fluency.

Lessons With Fluency At The Core

Here are lesson examples that help you develop and strengthen your Roots, Branches, and Leaves. Each of these examples shows you how you can teach your standards while building procedural fluency as described by NCTM:

The way in which fluency is taught either supports equitable learning or prevents it.” ~ NCTM

If you’re interested in learning where your own mathematics program tree is flourishing and where you might focus your attention next, be sure to complete our Mathematics Program Assessment Screener.

With it, you’ll receive a customized report highlighting some immediate actions you can take to strengthen the area of your mathematics program you’ll see the most benefit from.

If you’re a mathematics leader in your district/organization, you can hop to the version designed specifically for your role as a mathematics decision-maker.

Let’s aim to put fluency at the core of our lessons each and every day.

Your Customized Improvement Plan For Your Math Classroom.

Take the 12 minute assessment and you’ll get a free, customized plan to shape and grow the 6 parts of any strong mathematics classroom program.

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Each lesson consists of:

Each Make Math Moments Problem Based Lesson consists of a Teacher Guide to lead you step-by-step through the planning process to ensure your lesson runs without a hitch!

Each Teacher Guide consists of:

  • Intentionality of the lesson;
  • A step-by-step walk through of each phase of the lesson;
  • Visuals, animations, and videos unpacking big ideas, strategies, and models we intend to emerge during the lesson;
  • Sample student approaches to assist in anticipating what your students might do;
  • Resources and downloads including Keynote, Powerpoint, Media Files, and Teacher Guide printable PDF; and,
  • Much more!

Each Make Math Moments Problem Based Lesson begins with a story, visual, video, or other method to Spark Curiosity through context.

Students will often Notice and Wonder before making an estimate to draw them in and invest in the problem.

After student voice has been heard and acknowledged, we will set students off on a Productive Struggle via a prompt related to the Spark context.

These prompts are given each lesson with the following conditions:

  • No calculators are to be used; and,
  • Students are to focus on how they can convince their math community that their solution is valid.

Students are left to engage in a productive struggle as the facilitator circulates to observe and engage in conversation as a means of assessing formatively.

The facilitator is instructed through the Teacher Guide on what specific strategies and models could be used to make connections and consolidate the learning from the lesson.

Often times, animations and walk through videos are provided in the Teacher Guide to assist with planning and delivering the consolidation.

A review image, video, or animation is provided as a conclusion to the task from the lesson.

While this might feel like a natural ending to the context students have been exploring, it is just the beginning as we look to leverage this context via extensions and additional lessons to dig deeper.

At the end of each lesson, consolidation prompts and/or extensions are crafted for students to purposefully practice and demonstrate their current understanding. 

Facilitators are encouraged to collect these consolidation prompts as a means to engage in the assessment process and inform next moves for instruction.

In multi-day units of study, Math Talks are crafted to help build on the thinking from the previous day and build towards the next step in the developmental progression of the concept(s) we are exploring.

Each Math Talk is constructed as a string of related problems that build with intentionality to emerge specific big ideas, strategies, and mathematical models. 

Make Math Moments Problem Based Lessons and Day 1 Teacher Guides are openly available for you to leverage and use with your students without becoming a Make Math Moments Academy Member.

Use our OPEN ACCESS multi-day problem based units!

Make Math Moments Problem Based Lessons and Day 1 Teacher Guides are openly available for you to leverage and use with your students without becoming a Make Math Moments Academy Member.

MMM Unit - Snack Time Fractions Unit


Partitive Division Resulting in a Fraction

Shot Put Multi Day Problem Based Unit - Algebraic Substitution


Equivalence and Algebraic Substitution

Wooly Worm Race - Representing and Adding Fractions


Fractions and Metric Units


Scavenger Hunt - Data Management and Finding The Mean


Represent Categorical Data & Explore Mean

Downloadable resources including blackline mastershandouts, printable Tips Sheetsslide shows, and media files do require a Make Math Moments Academy Membership.

Use our OPEN ACCESS multi-day problem based units!