How to teach multiplicative fluency.

Posted in
March 24, 2024

Unlock mathematical success by building multiplicative fluency. Here’s an example of what it might look like!

Multiplication fluency is fundamental for many higher-level mathematical concepts and procedures
Multiplication fluency is fundamental for many higher-level mathematical concepts and procedures

Why is multiplicative fluency so crucial? It’s more than just memorizing times tables; it’s about developing a deep understanding of the relationships between numbers, paving the way for efficient problem-solving and mathematical reasoning. Students who possess multiplicative fluency not only excel in mathematics but also develop critical thinking skills that transcend the classroom. 

Multiplication fluency is a fundamental

Multiplication is a fundamental operation that forms the basis for many higher-level mathematical concepts and procedures, including division, fractions, ratios, proportions, and algebraic equations. Fluency in multiplication lays the groundwork for understanding and mastering these advanced topics. Adding to this, students will enhance their capacity and efficiency for higher level math problems. It also is a wonderful opportunity to build confidence and self-efficacy early on in a student’s mathematical journey.

You can find out more about fluency here in or deep dive long read on the subject: What does fluency mean to you?

As you explore, keep in mind that a learning progression is rarely linear. Students will visit and re-visit different concepts depending on their understanding. It’s also important to note that building retention and flexibility needs to happen to reinforce the learning. I have given a few examples throughout.

Phase 1: Emphasize Multiplication as Repeated Addition:

  • Illustrate multiplication as repeated addition, utilizing manipulatives, visuals, and real-world examples.
  • Foster understanding through rich discussions and number talks, reinforcing vocabulary associated with multiplication.
  • Incorporate engaging games like “Addition by Heart” to solidify conceptual understanding.

Phase 2: Explore Arrays and Equal Groups:

  • Introduce arrays as visual representations of multiplication, encouraging students to analyze and create arrays.
  • Utilize games such as “Multiplication by Heart” and “How Close to 100” to reinforce concepts using dot arrays and grids.
  • Incorporate hands-on activities to deepen comprehension of multiplication concepts.

Phase 3: Introduce Properties of Commutativity and Associativity:

  • Teach commutative and associative properties of multiplication conceptually before formal language introduction.
  • Provide opportunities for exploration through problem-solving tasks and hands-on activities.
  • Engage students in discussions, problem strings, and games like “Multiplication by Heart” and “Number Hive” to reinforce understanding.

Phase 4: Teach Multiplication Strategies:

  • Equip students with various strategies like skip counting, number lines, and partial products for efficient multiplication.
  • Utilize problem strings to scaffold students’ strategy-building process and encourage flexibility in approach.
  • Foster rich discussions and problem-solving tasks to reinforce strategic thinking

Phase 5: Highlight Division as the Inverse of Multiplication:

  • Establish the relationship between multiplication and division, introducing division as the inverse operation.
  • Employ concrete examples and hands-on activities to solidify conceptual understanding.
  • Facilitate discussions, problem strings, and activities to reinforce the inverse relationship.

Phase 6: Problem-Solving with Multiplication and Division:

  • Engage students in problem-solving tasks requiring the application of multiplication and division skills.
  • Encourage the use of multiple strategies and provide opportunities for students to justify their solutions.
  • Foster solution and error analysis to promote critical thinking and metacognition.

Phase 7: Connect Multiplicative Thinking to Real-World Contexts:

  • Provide context-rich problems that necessitate the application of multiplicative thinking in practical scenarios.
  • Encourage students to articulate how multiplication and division can be utilized to solve everyday problems.
  • Foster a deeper understanding of multiplicative concepts by relating them to real-world applications.


By following this comprehensive guide, educators can effectively nurture multiplicative fluency among students, laying a robust foundation for mathematical success. Through a combination of engaging activities, strategic instruction, and real-world connections, educators can empower students with the skills and confidence needed to excel in mathematics and beyond.

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