CPA & BAR MODEL

Concrete, Pictorial, Abstract Approach

One of the key learning principles behind mathematics teaching at Hollywood Primary School is the concrete, pictorial, abstract approach often referred to as CPA. This is a three step instructional process to teach mathematics concepts. This model develops pupils' mathematical ability and confidence making mathematics more engaging and interesting. 



  


The "doing" stage. During this stage, students use concrete objects to model problems. This approach brings concepts to life by allowing students to experience and handle concrete objects. 

 

 

 

 

 
Pictorial is the "seeing" stage. Visual representations of concrete objects are used to model problems. This stage encourages children to make a mental connection between the physical object they handled and the abstract pictures, diagrams or models that represent the objects from the problem. 

 

 

 

 

 

 

Abstract is the symbolic stage where children use abstract symbols to model problems. Students will not progress to this stage until they have solid understanding of the concrete and pictorial stages. Children are introduced to the concept at a symbolic level using only numbers and mathematics symbols (+ - x /). 

 

 

 

 


Hollywood Primary School has a focus on explicit teaching to model mathematical thinking also known as metacognition. We have a strong focus on problem solving with an emphasis on non-routine, multi-step problems as we often experience in real world situations. 

 

We use the Bar Model as an approach to solving word problems. Some students are visual learners. The Bar model can help some students decide when they need to add, subtract, multiply or divide because they are able to draw out a model to show what information they have and what they still need. Words problems can be tricky and Bar Models are meant to serve as an aide to help your child be successful in problem solving. 

Concrete

Pictorial

Abstract

Problem Solving using the Bar Method

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Tel: (08) 9278 6400

Email: hollywood.ps@education.wa.edu.au

Address

117 Monash Avenue
NEDLANDS WA 6009