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'This School continues to be Good' -Ofsted November 2017

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What a Millfield Maths lesson looks like

Mastery Lesson Structure – Six parts



1. Recap/fluency starter:


- This is a quick task to recap prior learning. All pupils should be able to access the activity without any teacher input.

Flashback 4 and Mathsbot are both good resources to use. Ensure that children are being given opportunities to think about what they have learnt previously and not just given a list of the same operation. 


2. New learning:


- This section introduces the main mathematical concepts of the lesson. You can use the White Rose resources for guidance or NCETM resources for smaller steps. You may need to recap previous year groups learning to ensure that new concepts are understood. Imagine trying to follow a set of directions without any points of reference to begin from. Make sure that pupils know where the new learning fits into their mental map.


3. Talk task – Making talk count


- The focus of this activity is to practice new learning through talk using key mathematical vocabulary. Children should work in mixed ability pairs or table groups. Teachers should model the reasoning skills. Talking about a problem or question using a mathematical representation e.g. part whole model, number line or bar model helps to focus the talk.


4. Develop understanding


-This segment builds on the new learning and helps children to deepen their understanding by using manipulatives, representations and questioning. What is the same? What is different? Can you describe what you did? Can you draw it for me? Can you show me using a resource? How do you know? Can you prove it? Are you convinced? Why? Explain how you did it.


5. Independent task


- This enables the pupils to practice the learning independently. All pupils should be given access to concrete and pictorial resources to enable them to fully understand the learning. Once they are secure with the concepts, they can move on to more abstract methods. All children should be given opportunities to be stretched.


6. Plenary


- The final part of the lesson should be used to check understanding and celebrate success. Self and peer assessment can be used to give instant feedback and allow a chance to talk through mistakes and prove why they think that they are correct.

What does a Millfield maths lesson look like?
We follow the five CANDO essentials in each unit of work:



  • Teachers should use the appropriate age related mathematical vocabulary for the unit of work and ensure that children are also using the words in their mathematical talk when discussing their work. It is vital that pupils are exposed to the words in a mathematical context and are able to use them themselves to embed understanding.


  • To underpin the children’s understanding, each lesson should have the concrete and pictorial representations of what is being learnt at their core. Children should not be only given abstract representations of the skill in number form. Children should be able to show their understanding of a mathematical idea in a number or ways. E.g whole-part model, bar model, cubes, Cuisenaire rods, dienes, place value counters, number lines, bead strings etc. The concrete and pictorial resources should support the children in their learning and be used as a tool not a crutch. This applies to all phases.


  • When giving examples to children in class variation (both conceptual and procedural) should be used to prompt reasoning to enable deeper understanding, through for example; what is the same and what is different,  and guiding children to see patterns in their work. The choice of questions chosen by the teacher has an important role to play here. Children should also be given opportunities to talk to their peers about what they think.


  • Reasoning and Problem Solving questions should also be used throughout a unit of work. Teachers need to build in talk time and model how to talk about the problems and explain their thinking in a number of ways. Children should be given opportunities to explain, justify and prove their thinking to their peers and teacher verbally and by using concrete or pictorial representations.


  • Children should be given the chance to investigate the different areas of maths to allow them to deepen their understanding. Through investigation they are able to reason themselves which helps to embed the learning concepts. They are also able to create criteria to explain what something is and what it is not (when exploring shape for example by giving definitions of a square) which again aids deeper understanding. Investigation skills, strategies and vocabulary need to be modeled to allow children to do this. An environment where children feel safe to get things wrong (as this leads to getting things right) is vital. 
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