Building Strong Foundations in Maths
The Power of the Concrete–Representational–Abstract Model The CRA model involves three stages where teachers scaffold students understanding through moving through these three phases.
-
Concrete – using hands-on materials this could be real life materials, then moving to mathematical materials (like counters, blocks or number lines) to explore a concept.
-
Representational – drawing or using pictures, diagrams, or informal jottings to show their thinking.
-
Abstract – using numbers and symbols to solve problems and express ideas efficiently.
In the early years, for example, students learning to add numbers might start by physically combining two groups of counters (concrete), then draw the groups as dots or tally marks (representational) and finally write the number sentence 3 + 2 = 5 (abstract). This helps them develop a clear, connected understanding of what addition means.
In the middle primary years, students learning multiplication may begin by building equal groups with blocks or arrays (concrete), move on to drawing area models or number lines (representational), and then use multiplication facts and algorithms (abstract).
Together, we are working towards helping students see mathematics not as a set of rules to memorise, but as a powerful way to make sense of the world.
© Brisbane Catholic Education, Our Lady of Dolours Catholic Primary School (2025)
 © Brisbane Catholic Education, Our Lady of Dolours Catholic Primary School (2025)
|