mastery Comprehensive knowledge or skill in a particular subject or activity.

 Teachers reinforce an expectation that all pupils are capable of achieving high standards in mathematics.  The large majority of pupils progress through the curriculum content at the same pace. Differentiation is achieved by emphasising deep knowledge and through individual support and intervention.  Teaching is underpinned by methodical curriculum design and supported by carefully crafted lessons and resources to foster deep conceptual and procedural knowledge.  Practice and consolidation play a central role. Carefully designed variation within this builds fluency and understanding of underlying mathematical concepts in tandem.  Teachers use precise questioning in class to test conceptual and procedural knowledge, and assess pupils regularly to identify those requiring intervention so that all pupils keep up. The intention of these approaches is to provide all children with full access to the curriculum, enabling them to achieve confidence and competence – ‘mastery’ – in mathematics, rather than many failing to develop the maths skills they need for the future.

MATHS

 The use of real objects for mathematical representation.

 The use of pictures or equipment to represent real objects.

 Mathematical concepts represented in an abstract way without the use of equipment.

 For each key concept the children will need to move through the sequence.  There is no set pace for the sequence and children may need to move back to concrete if a misconception is discovered.  The concrete is always there and the others are added, it is not replaced. Concrete Concrete & pictorial Concrete, Pictorial Abstract

7 + 6 =

=

7 + 6 = =

=

 The key to differentiation is carefully planned questioning to clarify, reason and explain.  All children should have access to physical equipment either at the concrete or pictorial stage irrespective of ability. › LA pupils will use it to find the answers › HA pupils will use it to support their reasoning skills.

 Why?  Are you sure?  How do you know?  Do you agree?  Can you prove it?  Can you say it in a sentence?

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 Tom has 2 cupcakes. Jill has 3 cupcakes. How many cupcakes do Tom and Jill have altogether? › Initially cupcakes are used to illustrate the problem. › Subsequently, generic concrete materials such as cubes are used to represent the cupcakes. › Later pictorial representations of the number of cupcakes are used. › The pictorial representation becomes more abstract.

2+3=5. Jill and Tom have 5 cupcakes altogether The method helps students visualise the situations involved so that they are able to construct relevant number sentences.

Instead of relying on keywords and superficial features of a word problem, the bar model helps students see the relationships between and among the variables of the problem.

 “Europe is the whole and Germany is part of the whole.”  “_______ is the whole and ______ is part of the whole”

 “_________ is the whole and __________ is part of the whole.”

A fish head measures 9cm. The length of the tail is equal to the size of the head and half of the body. The length of the body is equal to the length of the head and the length of the tail. How long is the fish?