Please see the document below (CPA in Action – Data) that demonstrates how the CPA model in action. Once we believe our pupils have mastered maths concepts through using concrete and pictorial resources we move into the abstract.Įven when working abstractly in maths our pupils always have access to concrete and pictorial resources to support them. It includes pictures and diagrams of resources that our pupils are familiar with and are sometimes included in the Fact Files that we provide as part of Additional Learning. The pictorial aspect of this model is a vital step for enabling all our pupils to move from concrete maths to abstract maths. Please see the document below (Concrete Resources) that details some of the resources we use as part of our everyday teaching of mathematics at Stony Dean.Īs our pupils gain understanding of a concept through using concrete materials they move into using pictorial resources to support them moving away from using concrete resources. We use a range of concrete resources in teaching all areas of mathematics but specifically with reference to number work. In her latest Instagram picture, Donna looked like a Victoria’s Secret Model. This is to make the concepts being taught real to our pupils so they can make sense of the maths rather than dealing with ideas that are abstract. The stunning 54-year-old posed in her underwear Sunday morning, looking confident as ever. When starting a new concept whatever the year group or ability of our pupils we use concrete apparatus. For example, even when a pupil has worked out the answer using an abstract method, we may ask them to use concrete manipulatives to convince others that they are correct. This study deals with the definition of shape, relations on shares, and the generation of shapes by shape. This model is not linear, we use a cyclical approach. Shape and Shape Grammars: A Pictorial Model Abstract. We believe if our pupils fully understand the concept they are learning and keep revisiting it, then they will be able to apply the maths independently in the future. Mapped to CCSS Section K.CC.A.3, K.CC.B.4b, K.NBT.A.1 Write numbers from 0 to 20. It is about giving our pupils the tools to understand the maths that they are focusing on. Algebra 1 Statistics Pictorial Models Learning to count upto 20 by using ones and tens Understanding that a set can be arranged horizontally or vertically for counting. This approach is not about getting the answer quickly or teaching quick fix ‘tricks’. We use this approach to enable our pupils to fully understand and master the maths concepts that we are teaching. When you’re satisfied, select Insert to convert the ink equation into a document equation.The Concrete, Pictorial and Abstract (CPA) Model of learning is one that fully encompasses the way we teach mathematics at Stony Dean. To write a math equation by hand, use a stylus or your finger. Symbol Symbol Name Example = equals sign 5 = 2 3 5 is equal to 2 3 not equal sign 5 4 5 is not equal to 4 x equal sin(0.01) 0.01, x y means x is roughly equal to y > strict inequality 5 What is the best place to write math equations?Ĭhoose Draw > Ink to Math Convert, then click Ink Equation at the bottom of the built-in gallery to write equations with ink. Students can use a fact from the inverse operation when multiplying or dividing. This stage encourages children to make a mental connection between the physical object they just handled and the abstract pictures, diagrams or models that represent the objects from the problem. The same three numbers are used.ĭivision “undoes” multiplication and multiplication “undoes” division are shown in the model. Here, visual representations of concrete objects are used to model problems. You divide to find the number of counters in each group in the array division model. 6 / 7 = 13, 12 / 6 = 72, and 24 / 3 = 8 are number models expressed in number form. Addition, subtraction, division, and multiplication are all possible options for the equation, which can be expressed in words or numbers. In math, a number model is a sentence that explains how the various parts of a number story relate.
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