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

Didactic support: Numbers can be grouped in various ways – for instance, based on whether they are odd or even, or single-digit or double-digit numbers. Sets can be grouped on the basis of whether they contain more, fewer or the same numbers of objects, or according to criteria such as the size, shape or colour of the objects. Working with sets that lack visible means of organisation and those that are organised according to recognisable patterns (such as containing fives and tens) is central to the progression of number sense. Working with unstructured sets develops one-to-one correspondence and an understanding that number words and numerals represent the number of elements in a sets. Working with structured sets allows pupils to see numbers as complex measures and subsequently develop efficient and flexible numeracy strategies.

Representations in mathematics er ways to express mathematical concepts, relationships and problems. Representations can be concrete, contextual, visual, verbal and symbolic.

Didactic support: Working with multiple representations provides pupils with experience that numbers can be expressed in different ways, and that the same numbers can be presented differently without their value changing. Working on translating between representations (for example, from building blocks to drawings and then on to number words and numerals) develops the understanding of the relationship between actions, language, and symbols. Tangible objects could include fingers, counting sticks, building blocks, stones, counters, dice or Cuisenaire rods.

Didactic support: For example, different intervals could be counting two at a time, five at a time, or ten at a time. By counting in different ways and explaining what is happening, counting becomes a tool for thought rather than merely an automatic skill.

Didactic support: Describing and exploring the properties of odd and even numbers relates to exploring what characterises these numbers, what sets them apart from others, and the rules that always apply regardless of how big the numbers are. For example, this could include patterns in counting, divisibility, and the results you get when adding or subtracting.

Didactic support: Working with multiple representations provides pupils with experience that the value of a figure is contingent on its position in the number (ones, tens, hundreds, etc.). When working with the positional system, it is particularly important that tangible objects clearly distinguish between ones, tens and hundreds, that there is the opportunity to regroup (10 ones -> 1 ten) and that it invites pupils to understand patterns rather than simply counting. Tangible objects can include sticks, beads on a string, or any other type of material that can be grouped into ten. Money is also tangible, but it is not based on a purely decimal system (e.g. the next denomination available after a 20-kroner coin is a 50-kroner note) and should thus only be used afterwards or in parallel with materials that clearly demonstrate values based on place.

Didactic support: Working with the number line can contribute to an understanding of numbers in terms of size, distance and relationship, and supports the development of flexible numeracy strategies. One approach can be to use empty number lines and number lines using varying scales. Empty number lines (with no markings), onto which pupils place numbers and meaningful intervals and reference points in order to count and explain mathematical relationships, help to visualise pupils’ thinking.

Didactic support: Playing shop, other role play, collecting tasks and practical activities can be used as the basis for work in which number bonds (especially the pairs of numbers that add up to 10) are used actively to support understanding and development of appropriate numeracy strategies.

Concept explanation: Commutativity in addition means that the order of the numbers does not change the sum, meaning that 2 + 3 = 3 + 2. Associativity means that the way you group numbers in addition does not change the result, meaning that (2 + 3) + 4 = 2 + (3 + 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.

Didactic support: Working with length and mass measured in non-standardised units of measurement can provide a tangible basis for understanding measurement as both a comparison and a quantity. When measuring in a unit such as footsteps, sticks, or stones, you use addition when adding up the measurements, and subtraction when taking them away or finding out the difference between measurements. Working with non-standardised units of measurement can make it clear why there is a need for fixed, standardised units when measurements need to be precise and comparable between different situations.