Mathematics year 1-10 (MAT01‑06)
Competence aims and assessment

Didactic support: Working with appropriate strategies for addition and subtraction can involve the development of flexible and understanding-based approaches to arithmetic that are adapted to the context of a game or an everyday problem. It is not about pinpointing one ‘correct’ method, but rather about choosing strategies that provide meaning, are effective, and support mathematical understanding. For example, this could entail counting on rather than starting to count from 1, using partitioning (8 + 6 → 8 + 2 + 4) or the base ten structure, inverse operations and empty number lines for an ever-expanding number range.

Didactic support: In early work on multiplication, it is important that work relating to counting and grouping is not kept in isolation. Instead it should interact closely. This may involve counting at fixed intervals, understanding that each step represents a group of equal size, and connecting this counting to tangible or visual structures. Understanding the difference between the number of groups and the number of elements in each group is the key pillar. Counting and grouping are fundamental strategies for understanding the nature of multiplication as a mathematical structure.

Didactic support: Working with multiple representations provides pupils with experience that multiplication can be expressed and understood in different ways, and that the same multiplicative structure can be presented in different ways without the value itself changing. Using tangible objects to support counting and grouping (such as building blocks, counting sticks, counters, stones, beads or egg cartons) enables the exploration of multiplication as equal groups and repeated counting.

Concept explanation: Commutativity in multiplication means that the order of the numbers does not change the product, meaning that 2 x 3 = 3 x 2. Associativity means that the way you group numbers in multiplication does not change the result, meaning that 2 x (3 x 4) = (2 x 3) x 4. Distributivity shows a relationship between multiplication and addition, for example 2 x (3 + 4) = 2 x 3 + 2 x 4.

Concept explanation / didactic support: Relational symbols are signs such as the equals sign, the greater than sign and the less than sign which express a relationship between expressions. Working with the equals sign as a relational symbol entails understanding that the values to the left and the right of the symbol are equal, even if the expressions themselves may differ, e.g. 3 + 4 = 2 + 5. It is a common misconception that the equals sign is synonymous with ‘the answer is’ rather than an expression of equal value. Likewise, working with inequality signs (greater than and less than) relates to the understanding that the symbols express a relationship between the values in question. This entails an examination of which side has the greatest or smallest value, regardless of how the expressions are structured – for example, 8 > 5 + 2, or 4 + 3 < 10. A common challenge is that the inequality signs are interpreted as expressions of directionality rather than a comparison of values. As such, didactic work should focus on the comparison and the use of different representations to enhance pupils’ understanding of difference as a relationship.

Didactic support: Working with multiple representations provides pupils with experience that equivalence can be expressed and explored in different ways, and that the value can remain the same even if the expressions take different forms. Using tangible objects that support equivalence and comparison, such as building blocks or counters divided onto two sides or balancing scales, allows pupils to explore the concept of equivalence through action. When specific situations involving equivalence are translated into drawings and then into numerals, this clarifies the relationship between action, visual representation, and symbolic expression.

Didactic support: Working with areas measured using non-standardised units of measurement provides pupils with a tangible basis to understand area as the coverage of surfaces and the counting of area units. When surfaces are covered with something like squares, counters, or building blocks, it makes it clear that area relates to how many equal units can fit in. At the same time, this work highlights that different units can lead to different results, even if the surface itself is the same. This gives rise to a natural need for fixed, standardised units of measurement so that areas can be measured precisely and compared across different situations.