Supporting Procedural Fluency for All
Building automaticity, strategic thinking, and fluency in basic facts — with tools for classroom, intervention, and home extension.
At CTL we know that procedural fluency isn’t simply going fast — it’s having efficient, accurate, flexible use of basic facts, bolstered by strong strategy and conceptual understanding. Our Procedural Fluency Model combines explicit strategy instruction, game-based practice, and a formative assessment system, so teachers and students can see growth, adapt instruction, and build confidence.
For extended support at home or through your MTSS framework, our companion solution PF on the Go lets families engage in short, meaningful practice anytime.
Why Procedural Fluency Matters
Fluency with basic facts supports everything from efficient problem-solving to deeper math reasoning. When students rely on strategy rather than rote recall alone, they free up cognitive space to engage with new content, make sense of operations, and apply their learning flexibly. Our model ensures students build:
-
Accuracy — correct responses
-
Efficiency — responses in a reasonable timeframe
-
Flexibility & Strategy Use — choosing and adapting strategies rather than defaulting automatically
With traditional approaches and pandemic-era learning loss, strong fact fluency has become even more critical. CTL’s model is designed to help students recover and build for the future.
How the Program Works: Three-Part Design
Explicit Strategy Instruction
Students first explore and internalize strategies for addition/subtraction and multiplication/division. Our research-informed model follows the framework of Bay-Williams and Kling (2019), outlined in Math Fact Fluency. Lessons begin with developing mastery with the foundational fact sets and progress to the selection and use of the derived fact strategies for unknown facts.
We use multiple representations (dot-patterns, pictures, tens-frames, number lines, standard and word form) so students understand why facts work, not just memorize them. Our teacher guide walk-throughs support you in launching and modelling strategies, encouraging discourse: “What’s your thinking? Why did you choose that strategy?”
game-based practice
Once strategic understanding is launched, students engage in carefully-designed games that focus on strategy application, accuracy and positive math disposition — not simply timed fact drills. The games are adaptable for all learners, encourage peer conversation and strategy sharing, and promote engagement and equity.
formative assessment system
During game-based practice, teachers observe individual students on three dimensions:
- accuracy (are responses correct),
- efficiency (are they reasonably fast and efficient), and
- strategy/flexibility (are they selecting and adapting the right strategy).
Checklists and question-routines support teachers in tracking progress. Our embedded system also includes a teacher-facing web-based app for differentiated grouping and reporting, allowing you to easily assign small groups, monitor progress, and make instructional decisions in real-time.
What’s Included in the Kits
The Procedural Fluency Model comes in two primary kits: Addition & Subtraction, and Multiplication & Division. Each kit includes durable, classroom-friendly materials (cards, dice, two-color counters, work mats, books for literacy connections, teacher guide, intervention/OST guide). Cards are colour-coded and made accessible for learners with colour‐difficulties.
PF on the Go
Whether you’re looking to strengthen fact fluency across your whole school, embed games into your math block, or launch a home-practice system for stronger family connections, CTL is ready to partner.
Contact us today:
Phone: (502) 895-9500 | Toll-Free: (800) 995-3965 | Email: info@ctlonline.org
