Math PK-2

Multiple Representations: Manipulatives


Providing physical representations of numbers and math concepts helps activate mental processes. Learners understand more deeply through hands-on exploration, which requires but also develops fine motor skills. Manipulatives that have minimal visual distractions are most effective, supporting students' Attention and Inhibition as they practice the target math skills. Research has also found that manipulatives are effective when students are able to understand that concrete objects can represent abstract ideas, a developmental milestone often achieved by second grade.

Use It in the Classroom

  • Math manipulatives can be used to build understanding of Symbolic Number and Cardinality through the tactile manipulation of quantity. Learners can also work on their Counting and Operations skills by combining and separating manipulatives.
  • 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 can allow learners to playfully explore digital manipulatives to strengthen their number sense. Through various games with the manipulatives, learners can build their understanding of Estimation, Cardinality, and Operations.

  • Products with digital manipulatives have increased requirements for fine motor skills, so developers need to provide extra support for these challenging motor demands for their younger users. Also, considering additional design choices, like using color-coding and allowing learners to resize or combine objects, can support Place Value and Estimation.
  • Factors Supported by this Strategy