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The Greville Primary School

Inspire, nurture, achieve

Welcome to The Greville! Junior Sports day is postponed until June 21st.

Teaching for Mastery

What does Teaching for Mastery mean?

Since the introduction of Mastery in Mathematics, there has been a lot of confusion over what this actually means. Below we have detailed out the basics for you, to help you understand this concept.

Teaching for Mastery means acquiring a deep, long-term, secure and adaptable understanding of the subject. This will allow children to represent a concept in multiple ways, have the mathematical language to explain and be able to apply the concept to new problems and unfamiliar situations. This is achieved through carefully designed lessons which include the ‘5 big ideas’ that underpin TfM.

Some people confuse mastery with Greater Depth. This is not the case, they are two very different things. All lessons allow all pupils to deepen their knowledge and master their learning. Greater Depth refers to pupils who show a greater level of understanding for an area or aspect of learning and are able to challenge themselves further in how they apply and represent the concept.

The 5 Big Ideas


•Small connected steps to reach the bigger picture- the generalisation
•Each lesson has one l key point
•Careful sequencing of ideas, procedures, images and learning points throughout the lesson.

Representation and Structure- include mathematical resources

•Using concrete, pictorial and abstract representations (a CPA approach)
•manipulatives and images are well chosen to reveal the underlying structure of the concept being taught
•Developing an understanding of why pattern occur
•Using stem sentence to provide a linguistic representation/structure to enable pupil to develop the language they need to explain their thinking.

Mathematical Thinking

•This is central to deep and sustainable learning throughout a pupils education.
•Ideas not just ‘received’ passively but worked on by the pupils. They are thought about, reasoned with and  discussed.
•Maths is not just ‘done’, it is understood at a deeper level
•Children are encouraged to look for patterns and link ideas through reasoning logically (what’s the same / difference?)
•Children are expected to explain, convince, draw diagrams to illustrate an idea or strategy
•Stem sentences: to provide a platform for precise mathematical language using full sentences


•The quick and efficient recall to enable children to access learning in maths lessons and reduces cognitive load. This enables them to reason and solve problems
•Fluency is more than memorising procedures and facts. Pupils need to build and internal visual imagery to support their fluency in recalling and applying number facts.
•Pupils develop an ability to fluently make links, generalise, recognise relationships, move between contexts


Conceptual variation

When introducing concepts to children,  examples will be carefully selected to include the following:

1. standard representations (a common representation-a and d)

2. non standards representation (an irregular representation which is less common and may challenge the children’s understanding of a concept-c and e)

3. non-concept (A true/false question which pre-empts possible misconceptions-f)

It is important to see concepts in arrange of different representations. This will help them to explain, make connections and see patterns. Some children can find it difficult to visualise concepts. This gives all children an opportunity to use visuals to support their understanding.

Procedural Variation

Within teaching inputs and children’s independent work, numbers and representations will be carefully chosen to draw children’s attention to the learning point.

The Greville Primary School

Inspire, nurture, achieve

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Location: Stonny Croft, Ashtead, Surrey, KT21 1SH
Tel: 01372 274 872