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Review 100 basic addition and subtraction facts: Revision, backed by a pre-test, ensures whether pupils are ready to progress to Lesson 1, or would benefit from more practice by playing the games at the beginning of Unit 1 first. This is particularly important for those pupils new to Structural Arithmetic.

Review regrouping in addition and subtraction facts: Pupils consolidate regrouping, starting in Unit 1. Regrouping, also known as exchanging, borrowing, carrying and similar terms, is used when it necessary to exchange 1 ten for 10 ones (in addition), and 10 ones for 1 ten (in subtraction). Pupils become familiar with the use of vocabulary, which can be confusing. The aim is to give a proper understanding of the important concepts represented by the words, so the approach is unhurried and thorough. A test, in the form of games, at the end of Unit 1 shows readiness to apply these concepts to problem-solving in Unit 2; these applications include Roman numerals, the calendar and months of the year, finding the rest, finding the difference and conclude with a test.

Study 3-, and 4-, place numbers: Concepts learned so far are extended further to 3-, and 4-place numbers. In keeping with Structural Arithmetic’s multi-sensory approach, pupils practise, for example, with a specially constructed ‘carrying machine’ (see resources shield in Structural Arithmetic  Book 2) holding 10 cubes, and a 1000 cube.  After a series of lessons involving games and activities, pupils apply their knowledge to problems including money and time. As in Structural Arithmetic Book 3, money exercises are presented in three separate currencies: Pounds sterling, US Dollars, and Euros This section also explores rounding numbers to the nearest ten, hundred or thousand.

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.