In the abstract phase, students are solving multiplication problems without the use of manipulatives or drawings. In this phase, they benefit from multiplication practice that involves drawing pictures or diagrams. In the representational phase, students understand what it means to multiply and now they're learning to apply more strategic ways of solving multiplication problems, such as using drawing arrays and skip counting to find the answer. In this phase, they benefit from multiplication practice with hands-on manipulatives, such as counters and unifix cubes.
In the concrete phase, students are learning the conceptual meaning of multiplication. In this post, we talked about different phases of multiplicative thinking that students progress through on the way towards multiplication mastery. Math games for each phase of math learning
