# Maths

The GLA Vision:

A GLA Mathematician...

• can recall prior knowledge and use suitable technical vocabulary to articulate their explanations
• is able to talk effectively about their Maths and the strategies they have used in their mathematical processes
• is able to use different resources to support their learning and show resilience in their approaches
• loves Maths and is confident with reasoning, problem solving and thinking in different ways
• is fully equipped for the mathematical challenges of everyday life, preparing them for the world of work and have economic awareness.

# Modelling - CPA

## Concrete Stage:

This stage should always be used during the learning of new concepts or when building further onto learnt concepts for every child in the classroom. It involves the physical manipulation of objects to explore structure, find commonalities and rehearse the mathematics. When pupils are acting on the mathematics with the manipulatives they are also more likely to form the language to communicate concepts and ideas. This allows teachers to gain a greater understanding of where misconceptions lie and the depth of understanding a child exhibits. It also allows pupils to develop their ability to communicate mathematically and to reason.

## Pictorial Stage:

This stage involves the use of images to represent the concrete situation enacted in the first stage. It can be pupils’ drawings of the resources they are acting on or a representation such as the bar model, number line or a graph. This stage acts as a ‘bridge’ to support pupils to make links between the concrete and the abstract and develops their ability to communicate and to represent their mathematics.

## Abstract Stage:

This is the use of words and symbols to communicate mathematically. It is difficult for pupils to get to this stage without the other two stages working alongside. This is because words and symbols are abstractions. They do not necessarily represent a direct connection to the information. For example, a number is a symbol used to describe how many of something there are, but the symbol of a number, in itself, has little meaning. Why should a ‘5’ represent five any more than the digit ‘2’ stand for five? The other stages support pupils’ understanding of this stage.

# The GLA Maths Sequence of Learning

## Elicitation

An elicitation should be conducted with all children before a unit of work is taught. The purpose of the elicitation is to determine how well prior learning has been retained and identify any misconceptions.

## Planning

Teachers will use the elicitation outcomes to inform differentiated planning, teaching strategies, resources and activities. Within each lesson, a child should review prior learning, learn new material in small steps and ask questions. The C-P-A model should be used to enable children to make links in their learning and transfer skills in to different areas of maths. They should have opportunity to practice new material in groups and independently in order to achieve mathematical fluency. They should be stretched and challenged with problem solving and reasoning tasks throughout a learning sequence.

## Delivery and Environment

Teachers should provide models to support children’s understanding of key concepts in maths. Working walls should be used to support children when working independently. The environment should be rich with mathematical vocabulary, modelled examples and concrete examples.

## Supporting Documents

The KS1 Maths Calculation Policy

The Lower KS2 Maths Calculation Policy

The Upper KS2 Maths Calculation Policy