Learn about the meaning of maths mastery and how it is key for children to develop deep and sustainable learning.

The term ‘teaching for mastery' is often heard in the primary classroom. Achieving ‘maths mastery’ means that pupils have a deep, secure knowledge of the subject which they can apply to different contexts and other areas of learning.

Teaching for mastery encourages all pupils to believe that by working hard they can achieve mathematical success.

Pupils develop a solid understanding of maths topics being taught before they move on to more difficult tasks. A longer time is often spent on key topics in order for children to develop deep and sustainable learning.

How to Teach Maths Mastery

Maths mastery is based on the Shanghai teaching method where whole classes are taught the same content through interactive teaching methods, ensuring that all children master concepts before moving on to the next part of the teaching sequence.

Early intervention identifies pupils who may need more support, allowing them to move on at the same pace as the rest of the class.

Maths lessons are broken down into small connected steps that help children to understand mathematical concepts and apply them. When teaching a particular area of maths pupils are exposed to different representations to allow them to make connections and explain their reasoning.

There is great emphasis placed on pupil discussion where children work together to share ideas and develop a deep understanding.

Quick and efficient recall of facts and procedures is also essential for children to master difficult mathematical concepts. Key knowledge such as multiplication tables and addition facts are learnt so that children can recall them automatically, this enables pupils to focus on new concepts.

A ‘maths mastery’ approach seeks to develop active learners and mathematical thinkers. Most importantly we want our pupils to be excited about learning maths, to build resilience and develop their own self-confidence in the subject.

The outdoor environment presents many opportunities for pupils to develop maths mastery. An outdoor space is perfectly suited to the use of concrete resources which help children to explore their mathematical thinking.

Maths Mastery Resources

Numicon shapes are a useful concrete resource which help children to see connections between numbers. Numicon’s visual and tactile properties allow pupils to easily see one more/less and odd/even numbers.

Children can physically move and manipulate the pieces when learning number bonds by placing pieces on top of each other which greatly benefits visual and kinaesthetic learners.

Acorns, seeds, shells or twigs can be collected in the outdoor environment and can be counted by placing them inside the Numicon shapes. Questions can be asked such as: How many would you have if you had double the number of seeds? How many more shells would you need to make 10?

Pupils enjoy taking part in active number hunts in the outdoor environment. Different visuals can be written on log slices or stones such as numerals, picture representations and pips on dice faces. Children can work together to find, match and order the items.

A five or ten frame is another useful, practical resource which is ideally suited for use in the outdoor environment. Pupils can place natural items inside the frame when learning how to count and subitise. Children will learn that there are different ways to represent the same number and they will begin to develop their understanding of place value.

Ten frames can be useful for supporting mental addition methods. A useful strategy is to emphasise ‘Magic 10.’ If children were asked to calculate 9 + 7  number bond knowledge would be needed to know 9+7 = 9+1+6 =10+6 = 16.

A part-part-whole ‘cherry’ diagram is a fantastic tool to aid maths mastery when studying number, addition and subtraction and inverse operations. The diagram shows pupils that a whole object can be split into two or more parts in many different ways.

The parts might look different, each part will be smaller than the whole and the parts can be combined to make the whole. Part-part whole diagrams can be made using hoops in the outdoor area, where children can physically see and move concrete items or they can be drawn on Pentagon’s Scribble Boards.

Number Fact Fluency

It is important for children to develop accurate and rapid recall of multiplication and division facts and number bonds to 20.

Spending a short time each day in the outdoor classroom chanting and learning these facts can lead to improvements in speed, accuracy and understanding when calculating.

A playground multiplication square, that is readily accessible for the children to chant and explore daily will help pupils to make connections between numbers such as the relationship between the 2, 4 and 8 times table.

Weigh the Ingredients!

Pentagon’s Weighing Scales are an invaluable resource that can be used alongside a Mud Kitchen and Sand Box.

The use of balance scales is essential for children to form an understanding of comparing mass. Through free exploration pupils will begin to understand which objects are heavier and which are lighter.

Children will begin to realise that objects smaller in size can be heavier than large objects and they will begin to predict what will happen when objects are placed on to the scale. Pupils will begin to understand equality when using non-standard units to weigh an object e.g. How many cubes are the same weight as the apple?

When discussing balanced scales, pupils are beginning to understand ‘equals to.’ Through play and exploration learners will begin to understand mathematical concepts and abstract symbols.

Creating Potions in the Mud Kitchen

A Mud Kitchen is a fantastic resource for introducing children to volume and capacity. As children fill different containers, they will describe them using mathematical vocabulary such as ‘full, nearly full, empty or nearly empty.’

Pupils can investigate how many smaller containers are needed to fill a large container and they will begin to notice patterns. A mud kitchen is a great space to promote mathematic talk as teachers question pupils e.g. Which container do you think will hold more? Shall we check?

Tell a Mathematical Story

An outdoor storytelling area can also be a great space for groups of children to consolidate mathematical skills. When learning about addition and subtraction it can be really useful for learners to create a mathematical story.

For example, ‘There are 12 people in the rocket. When it returns to Earth 3 people get off and on the Moon 6 more people get on. How many people are on the rocket now? By providing a context to the mathematics children will develop their understanding of the concepts of addition and subtraction.

Practitioners can use toys/blocks or images and ask children to write their own number sentences to match the story.

A circular seating arrangement can be really useful for group Maths lessons.

To develop ‘maths mastery’ children are expected to use correct mathematical terminology and to be able to explain their mathematical thinking. When seated in a circle, all pupils can see the teacher and the ‘I say, you say, you say, you say, we all say.’ technique can be practised.

The teacher models a sentence e.g. If 12 beanbags are the whole, half of the whole is 6 beanbags. Having modelled the sentence, the teacher asks individual children to repeat it before asking the whole class to chant the sentence. Repetition helps to embed key conceptual knowledge.

Use Role Play Areas to Aid Mathematical Understanding

Pentagon’s Giant Playhouse can be transformed into a variety of different role play areas with a mathematical theme.

A shop provides a useful context where items can be priced as single-digit numbers, multiples of ten, teen numbers and two-digit numbers. Teacher questions will focus on mental addition where pupils apply several skills within a single calculation. Children should be able to explain what known facts or mental strategies they use to calculate their answers.

Pupils will start to compare items in their shop, noticing for example there are more yellow cars than red cars or the blue ribbon is shorter than the green ribbon. Your pupil will then begin to make quantitative comparisons such as, ‘there are two fewer red cars than yellow cars.’

A café role play area provides the perfect environment for introducing fractions to children. Children will begin to use the language ‘a half’ and ‘a quarter’ Pupils will be able to practise serving half of a piece of toast or an apple, they can then use sweets to divide a group of items into equal parts.

Early Multiplication and Division

A Sorting Table is a useful resource when working with groups of children to introduce the concepts of multiplication and division. Pupils have plenty of space to look at collections of concrete objects and begin to identify equal and unequal groups.

Paper plates or hoops help to clearly demarcate the groups. Children could be set challenges which require them to work together such as, ‘How many different ways can you find to arrange ten cubes into equal groups?’

Beat the Clock!

Pupils can begin to read, say and write decimal numbers with Pentagon’s Solar Powered Stopwatch. Children will be able to clearly see how many ones/tenths and hundredths are in a number.

Groups of pupils can work together to time each other to complete a trim trail/obstacle course and gather their results. Times can then be ordered and rounded to the nearest whole numbers and to one decimal place. When children see how maths is used in ‘real-life scenarios’ motivation, enthusiasm and confidence increases.

Finding our Voices in the Outdoor Classroom!

A key component of ‘maths mastery’ is that children learn to effectively communicate their mathematical ideas. In doing so, they show an understanding of mathematical concepts and the ability to reason. Some pupils may be more willing to share their thoughts more freely when working in the outdoor classroom.

Teacher modelling is a useful tool to demonstrate expectations. The class teacher firstly models the answer to a question before asking a pupil to answer a similar problem using the same structure. This helps to set expectations and build pupils confidence.

Think, Pair, Share is a great strategy to use in the outdoor classroom which allows pupils to try out their ideas with a partner before sharing with the class.

Asking children if they agree/disagree with an answer or if a problem can be solved in another way or more efficiently helps to create a classroom culture where mathematics is discussed and unpicked. Asking pupils to talk about what they notice ‘What’s the same? What’s different?’ promotes classroom talk where children are looking for patterns and making connections.

The use of an outdoor environment can offer plenty of opportunities to develop ‘maths mastery,’ Large, tactile resources can be used in the outdoor classroom to help children to understand different problems, scenarios and relationships. Being outdoors encourages pupils to explore, wonder, try things out and discuss.

When mathematics relates to real-life situations and their own environment children are particularly engaged and will rise to the challenge of mathematical reasoning.