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Discover and master the multiplication facts (tables 1 up to 12): Structural Arithmetic shows that the understanding of the concept of multiplication (and of its inverse function, division) is equally as important as memorising the facts of the tables. Pupils enjoy finding out about these operations through experiments and games, making discoveries with the SA materials which stimulate their imaginations.

Understand the relationship between multiplication and division: Working with the Structural Arithmetic materials to learn multiplication, prepares pupils to understand its interrelationship with division: pupils find it is one of ‘doing’ and ‘undoing’, just as it is between addition and subtraction. Pupils also learn why they can check their answers after dividing by multiplying the quotient by the divisor. They begin to understand the meaning of new vocabulary such as ‘divide’, ‘share’, ‘go into’, ‘remainder’, and the use of new symbols: ÷ (division sign) and √ (the radical sign).

Discover division with remainders: Working with tables 2 to 10, pupils build on a firm foundation of division by learning about division with remainders. This stage combines what are often the two trickiest operations: subtraction and division. The methodical approach, with lots of practice, allows pupils to assimilate this comfortably and confidently.

Understand the reasons underlying the steps in long division: The radical sign √ introduces pupils to long division from the start of division. From a simple beginning the more complex aspects of division are approached in a systematic way which fosters understanding. Alongside this emerging understanding pupils learn to record their exercises at every step as part of the process; they practise how to set out their calculations as an integral part of their learning.

Analyse problems systematically: Problem-solving is built into the fabric of Stern teaching. Pupils become familiar with the fact that the logical, practical steps that have led to their understanding of a concept can be applied to real life. In addition, because their knowledge is based on meaningful activities with the Structural Arithmetic materials, they are more aware of what size of answer to expect.

also … Through games and activities, pupils explore simple fractions such as wholes, halves, quarters and eighths. They investigate the sizes of different fractions to learn about the structure and special characteristics of each one, before they study the operations of addition, subtraction, multiplication and division with fractions later on At the end of Stern’s Structural Arithmetic Book 4 are several mastery tests in the form of group activities and games as well as written work to consolidate learning.