#Pictorial models in math free#

The use of visual strategies for problem-solving, such as bar models, number lines (for whole numbers, decimal numbers and fractions), number bonds and branching, also provide a pictorial way to bridge the gap between the concrete and the abstract.

Within the RUCSAC approach to problem-solving, the stage “create to show what you know” specifically prompts the children to use concrete materials and/or pictorial representations to represent the problem.

These can be used to add variety to the resource examples and also provide the means to explore decimal numbers in a concrete way. the images of 1c, 10c and €1 coins, €10 and €100 notes.

The inclusion of base-ten money as photocopiables in the senior end TRBs i.e.

The TRBs suggest ways in which the teacher can organise concrete activities and use real objects to explore concepts, including suggestions for stations and Aistear themes in the junior end TRBs.

#Pictorial models in math free#

The free mini-white boards (MWBs) facilitate the drawing of quick jottings to represent concepts and calculations.The inclusion of free place value manipulatives with the 3rd to 6th class books which enable teachers to include explore and use these resources to demonstrate place value, addition, subtraction, multiplication and division.The inclusion of free five, ten and twenty frames with the infants to 2nd class books which enable teachers to include frames as one of the concrete activities.These are only a few small selection of examples of the CPA approach across the Operation Maths programme. The best way to fully appreciate the CPA approach in Operation Maths is to look at some examples.Īddition without renaming (Operation Maths 1)įraction pie pieces in the Discovery Book there are also blank number lines as an extra pictorial resources given on the inside cover of the Pupil’s Book Other examples of a CPA approach in Operation Maths What does CPA look like in Operation Maths? Use a written algorithm for multiplicationĮxplore operations with fractions using concrete manipulatives eg paper plates in halves, quarters, eighths Use a written algorithms for addition and subtractionĮxplore multiplication using rows of base ten blocks (area model of multiplication)ĭraw images to represent the concrete manipulatives Use or draw images to represent the concrete manipulative Use digits and/or symbols to represent the relationships established during the previous two stages eg 2 + 3 = 5Īdding and subtracting, without or with renaming using base ten materials eg straws, cubes, base-ten blocks Use counters and ten frames, cubes, blocks, cuisinere rods and/or draw images to represent the concrete Use logic bears, toys, etc to show a set of five and explore the various ways to partition and then re-combine Abstract stage: also known as the “symbolic” stage and involves using only numbers and symbols to represent and solve a computation.īelow are some examples of a how a CPA approach might look, at each of the main class levels:.Pictorial stage: also referred to as the representational stage in some literature, it can be explained as the “seeing” stage and involves using images to represent the objects previously used in the concrete stage.Concrete stage: Also known as the “doing” stage, this involves physically manipulating objects to demonstrate and explore a concept.What exactly is CPA?Ĭoncrete Pictorial Abstract (CPA) is a three step instructional approach that has been found to be highly effective in teaching math concepts.

$pictorial models in math$

This CPA approach is also the mainstay of maths teaching in Singapore. Research has consistently shown this methodology to be the most effective instructional approach to enable students to acquire a thorough understanding of the concepts required. Developed by American psychologist, Jerome Bruner, it is based on his conception of the enactive, iconic and symbolic modes of representation. As explained in previous posts, Operation Maths is built on a concrete, pictorial, abstract approach, or CPA approach.