Marvellous Maths

We love maths at Hillside. In fact, we think that it is marvellous!

We are determined at Hillside to help all children become confident in all areas of mathematics. To achieve this, we are teaching a Maths Mastery approach.

Some parents must scratch their heads when their children show them their maths homework, with methods of teaching and learning mathematics going through more changes than any other subject. The following information on this page is to help you make sense of this approach.

What is Maths Mastery?

Maths Mastery is a new way of thinking and teaching.


When teaching maths for mastery at Hillside, the whole class now moves through topics at broadly the same pace. Each topic is studied in depth and the teacher does not move to the next stage until all children demonstrate that they have a secure understanding of mathematical concepts.


Students at Hillside are given time to think deeply about the maths so that they can understand concepts at a relational level rather than as a set of rules or procedures. This slower pace leads to greater progress because it ensures that students at Hillside are secure in their understanding and the teachers don’t need to revisit topics once they’ve been covered in depth.


In a traditional primary school maths lesson, children were put in different groups and given different content based on their anticipated ability. This means that from an early age children are classed as those who can and can’t “do maths”. Teaching maths for mastery is different because it offers all pupils access to the full maths curriculum. This inclusive approach, and its emphasis on promoting multiple methods of solving a problem, builds self-confidence and resilience, which help to build the growth mindset that we are striving to achieve at Hillside.


Though the whole class goes through the same content at the same pace, there is still plenty of opportunity for differentiation. Unlike the old model, where advanced learners are accelerated through new content, those pupils who grasp concepts quickly are challenged with rich and sophisticated problems within the topic to deepen their understanding. Those children who are not sufficiently fluent are provided additional support to consolidate their understanding before moving on. This maybe immediate feedback during the lesson from either the teacher or the teaching-assistant, or if children need extra practice, teachers will offer the opportunity for extra time on maths later in the day. This is a positive opportunity to consolidate their understanding.


Within mastery the idea is to focus on one small step at a time in a lesson, with an emphasis on the mathematical structures involved and the best way to represent these through models (equipment).  To support our mastery approach at Hillside, we are building our lessons using the Concrete, Pictorial and Abstract approach (CPA). 

CONCRETE is the “doing” stage, using concrete objects to model problems. Instead of the traditional method of maths teaching, where a teacher demonstrates how to solve a problem, the CPA approach brings concepts at Hillside to life by allowing children to experience and handle physical objects themselves.

Every new concept is learned first with a “concrete” or physical experience, e.g. if a problem is about adding up groups of children, the children might first count each other or models before progressing to handling counters or cubes which are used to represent the children.

PICTORIAL is the “seeing” stage, using representations of the objects to model problems. This stage at Hillside encourages children to make a mental connection between the physical object and abstract levels of understanding by drawing or looking at pictures, circles, diagrams or models which represent the objects in the problem. Building or drawing a model makes it easier for children to grasp concepts they traditionally find more difficult, such as fractions, as it helps them visualise the problem and make it more accessible.

ABSTRACT is the “symbolic” stage, where children are able to use abstract symbols to model problems. At Hillside, once a child has demonstrated that they have a solid understanding of the “concrete” and “pictorial” representations of the problem, the teacher will introduce the more “abstract” concept, such as mathematical symbols. Children are introduced to the concept at a symbolic level, using only numbers, notation, and mathematical symbols, for example +, –, x, / to indicate addition, multiplication, or division.Even though there are three distinct stages, the skilled teachers at Hillside will go back and forth between each representation to reinforce different concepts.

Different ways of thinking and representing a problem is the key to success at Hillside. Our teachers may vary the apparatus the children use in class, for example, one day they might use counters, another day they might use a ten frame or a part whole model. Likewise, children are encouraged to represent their maths problem in a variety of ways, for example, drawing an array, a number bond diagram or a bar model. By systematically varying the apparatus and methods they use to solve a problem, we help children to make quicker mental connections between the concrete, pictorial and abstract phases.


Below is a video from a maths specialist. Here, Dr. Yeap explains how young children can use concrete materials and later use pictorial representations as number bonds. Number bonds represent how numbers can be split up into their component parts. Children can explore number bonds using a variety of concrete materials, such as counters with containers and ten frames or with symbols.

Now Dr. Yeap discusses how diagrams can be used to represent a situation in a problem: such as rectangles representing (unknown) quantities. This method of visualising problems is known as the bar model.

What can I do to support this at home?
We would love to see children carrying out activities such as times table practice, counting out money, helping to weigh out ingredients whilst cooking at home, telling the time or even just counting items with the younger children. Plus, supporting your child with homework.

We also have parent workshops coming up, so if you would like to see mastery in action, please sign up and come to one of our events. There are also many websites and apps that your child can go on at home such as Sumdog, Times Table Rockstars and j2e. Click on the images to be taken to the sites.


Examples of apps and websites to support your child’s maths at home:

’10 Minutes a Day Times Tables’ (app)

Squeeble (times table app)

‘Hit the Button’ (webpage)

KS1 BBC Bitesize

KS2 BBC Bitesize

Topmarks (webpage)