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Fundamental Idea

Dr Yeap talks about one of the fundamental ideas in mathematics: that items can only be counted, added, and subtracted if they have the same nouns. He uses a simple example with concrete objects, chocolates and glue sticks to illustrate the point and then shows how it relates to column addition and the addition of fractions.


Number Bonds

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.



Dr. Yeap explains how standard column subtraction can be taught meaningfully by using children's knowledge of number bonds. Once children can explain how numbers can be split into their component parts, they can adapt their understanding to the conventional column subtraction method.


Mental Calculations

Dr. Yeap discusses how children can develop an ability to calculate the four operations (addition, subtraction, multiplication and division) in their heads without the use of paper and pencil or calculators.



Dr. Yeap discusses how children can learn their times tables meaningfully by using visualisation and other strategies.


Long Division

Dr Yeap discusses how children can learn to do long division meaningfully by first using concrete apparatus, such as base-10 materials, to perform the operations. They can then explore how this idea is represented in the long division algorithm.


Bar Model 1

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.


Bar Model 2

Dr. Yeap gives another example of the bar model: how diagrams can be used to represent situations in a problem.


Tardebigge C.E. First School Vision for Maths


We want all children to be able to:

  • believe that they can achieve well at mathematics and welcome the challenge to do so
  • develop a fascination and love of numbers and spacial awareness
  • become fluent and confident mathematicians
  • explain their mathematical thinking clearly
  • solve problems by reasoning
  • apply their mathematical skills in a wide range of situations
  • transfer to the next stage of their education having achieved age related goals so that they can be successful in their future lives

The Maths Mastery Approach


At Tardebigge C.E. First School, we use a Maths Mastery Approach and Maths No Problem. Children are encouraged to develop fluency, reasoning and problem solving skills through a concrete pictorial approach. In lessons, children use Maths No Problem textbooks and workbooks. They also use concrete resources to ensure a depth of understanding. We make use of the NRICH Mathematics website resources for develop problem solving.


We believe that all children, when introduced to a key new concept, should have the opportunity to build competency in this topic by using the CPA approach (Concrete, Pictorial, and Abstract).


Concrete – students should have the opportunity to use concrete objects and manipulatives to help them understand what they are doing.

Pictorial – students should then build on this concrete approach by using pictorial representations. These representations can then be used to reason and solve problems. 

Abstract – with the foundations firmly laid, students should be able to move to an abstract approach using numbers and key concepts with confidence.

The use of mathematics resources is integral to the CPA approach and thus planned into our learning and teaching. Resources such as number lines, Numicon, multi-link cubes, dienes, hundred squares, shapes, etc. are used.

Mathematics is a tool for everyday life.  It is a network of concepts and relationships and is used to analyse and communicate information and ideas in practical tasks and problems. By making links to other subjects we aim to provide real context in which to apply skills taught during the maths lessons.