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

Didactic support: Exploring fractions, decimals and percentages relates to expressing the same part of a whole in different ways. Through the use of tangible objects, models, drawings, and numerals, pupils are able to experience that one half, 0.5 and 50% show exactly the same share of the whole as they encounter it in daily life. Working on translating between representations lays the foundations for more systematic work around comparisons and arithmetic.

Didactic support: Working with multiple representations provides pupils with experience that fractions can be expressed and understood through numbers, drawings, tangible objects, and practical situations, and that the same value can be presented in different ways. The use of tangible objects (such as papers that can be folded, counters or building blocks that can be distributed, measuring cups or food that can be shared out) provides an experiential basis for the exploration of fractions in everyday situations. These experiences can be visualised through drawings and further expressed using numerals and text. When pupils work to translate between the different representations, this clarifies the relationships between action, visual representation and symbolic expression, thereby forming the basis for further exploration and understanding of the concept of fractions.

Didactic support: This can involve building upon known strategies applicable to arithmetic using whole numbers, such as dividing numbers, counting using familiar units, or halving and doubling. It may also extend to exploring and discussing how these strategies can be transferred and adapted when working with fractions. The use of different representations (such as tangible objects, drawings, empty number lines and numerals) makes it possible to visualise and explain strategies and communicate solutions both orally and in writing.

Didactic support: Problems can be both purely mathematical and related to everyday life. For instance, they may be pertain to the relationships between numbers, division or missing parts. Problems can be formulated by representing situations using tangible objects, symbols, drawings or text. Solving fraction-related problems calls for pupils to engage in reasoning and to explain their approach, rather than merely their calculation.

Didactic support: Working with equations can be based on exploring similarity as an equivalence and a relationship, rather than as a purely calculation-based procedure. For example, the use of scales and tangible objects (such as building blocks or other objects that can be placed on two sides) makes it possible to explore whether two expressions have the same value. Testing of this kind can help support an understanding of the equals sign as an expression of the fact that both sides are of equal value, rather than serving as punctuation that suggests ‘the answer is coming’. The work to translate between tangible actions, drawings, and numerals highlights and justifies the strategies used.

Didactic support: Work relating to time should include both analogue and digital clocks so that pupils can read, compare and translate between different expressions of time in practical situations.