Math 3-6

Multiple Representations: Manipulatives


Providing physical and virtual representations of numbers and math concepts helps activate mental processes. Learners understand more deeply through hands-on experimentation and exploration with manipulatives.

Use It in the Classroom

Starting at 1:16, watch how these students use manipulatives to build their mathematical reasoning and problem solving. By using algebra tiles, snap cubes, and colored rods, students develop their conceptual understanding of abstract concepts and can more easily demonstrate their Algebraic Thinking.

  • While it is important for teachers to choose the best manipulative for a specific learning objective, such as counters for Operations or fraction strips for Proportional Reasoning, they should also let students explore in an open-ended way, developing their Mathematical Flexibility as they generate multiple solutions to problems. Teachers can also use manipulatives to launch rich discussions and to clarify students' misconceptions of content.
  • Design It into Your Product

    Videos are chosen as examples of strategies in action. These choices are not endorsements of the products or evidence of use of research to develop the feature.

    Learn how products such as DragonBox Numbers allow learners to playfully explore digital manipulatives to strengthen their Number Sense. Through various games using the manipulatives, learners can build Geometric Reasoning and enhance Algebraic Thinking.

  • Research has shown that virtual manipulatives are as effective for students as physical ones. Through interacting with virtual manipulatives by resizing, sliding, flipping, color coding, and even turning them into 3D objects, students practice their Geometric Reasoning.
  • Factors Supported by this Strategy