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

Examples of connections

Explanation

Competence aims after year 6

The pupil is expected to be able to

  • To describe means to portray or recount an experience, situation, work process or a topic. To describe something may also refer to using relevant terminology to systematise knowledge of a topic.

     and place decimal numbers on the number line and

    To compare means to examine the character or qualities to discover resemblances or differences between two or more issues.

     numbers with different numbers of decimals as part of the positional system

    Explanation of competence aims

    Didactic support: Working with the number line can contribute to an understanding of decimal numbers in terms of size, distance and relationship, and facilitate the development of flexible numeracy strategies. The use of blank number lines and number lines with markings allows pupils to place and compare decimal numbers. This highlights key relationships in the positional system, including the role of zero as a placeholder, decimals as part of a whole, and that there are an infinite number of decimal numbers between any two given numbers.

  • To develop means to design, create, model or shape a new method, a product or a service.

     and

    To use means to apply something or to carry out a task to reach a goal. To use, which is closely related to apply, is understood as to utilise or to employ, for example, a method or a tool.

     different strategies for arithmetic using decimals and be able to

    To compare means to examine the character or qualities to discover resemblances or differences between two or more issues.

     these to numeracy strategies used for whole numbers

    Explanation of competence aims

    Didactic support: Work 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 also encompasses exploring and discussing how these strategies can be transferred and adapted when working with decimal numbers. The use of different representations (such as tangible objects, drawings, empty number lines and numerals) makes it possible to visualise and explain strategies both orally and in writing.

  • create and solve problems featuring decimal numbers, fractions, and percentages, and to provide reasoning for their own solutions

  • To describe means to portray or recount an experience, situation, work process or a topic. To describe something may also refer to using relevant terminology to systematise knowledge of a topic.

     and

    To explore refers to experiencing and experimenting, often encouraging curiosity and sense of wonder. To explore may mean to sense, seek, discover, observe and examine. In some cases, to explore means to investigate different aspects of an issue through open and critical discussion. To explore may also mean testing or trying out and evaluating work methods, products or equipment.

     the properties of two- and three-dimensional shapes and explain which properties the shapes share in common, and which properties distinguish the shapes from each other

    Explanation of competence aims

    Didactic support: Working with shapes can entail the exploration and description of properties such as the length of the shape’s sides, its angles, parallel sides, faces, and corners. One approach when comparing shapes can be to discuss the minimum definitions – ergo the properties that must be present in order for a shape to be regarded as that particular shape. Working on descriptions of this kind provides pupils with an opportunity to explore what shapes have in common, what distinguishes them from one another, and how they can be sorted and grouped based on their characteristics. Such practice can support the development of conceptual understanding and the ability to explain and assess mathematical claims.

  • To explore refers to experiencing and experimenting, often encouraging curiosity and sense of wonder. To explore may mean to sense, seek, discover, observe and examine. In some cases, to explore means to investigate different aspects of an issue through open and critical discussion. To explore may also mean testing or trying out and evaluating work methods, products or equipment.

     and

    To describe means to portray or recount an experience, situation, work process or a topic. To describe something may also refer to using relevant terminology to systematise knowledge of a topic.

     symmetry in patterns
  • perform congruence transformations with and without a coordinate system

    Explanation of competence aims

    Concept explanation / didactic support: The point of departure for work on congruence transformations can be practical and exploratory work relating to mirroring, rotation, and parallel displacement, as well as combinations of these. This facilitates reasoning and justification around why shapes are congruent both visually and with the help of coordinates.

  • To measure a quantity or a property means to compare it to another quantity or property of the same kind.

     the radius, diameter and circumference of circles, and

    To explore refers to experiencing and experimenting, often encouraging curiosity and sense of wonder. To explore may mean to sense, seek, discover, observe and examine. In some cases, to explore means to investigate different aspects of an issue through open and critical discussion. To explore may also mean testing or trying out and evaluating work methods, products or equipment.

     and explain the relationship between pi and the diameter of a circle

    Explanation of competence aims

    Didactic support: Exploration can entail pupils measuring the radius, diameter and circumference of various circles and then comparing these and discussing what they find out. The work can provide pupils with an understanding of pi as a fixed ratio and furthermore elucidate how mathematical relationships can be identified through measurement and comparison.

  • To explore refers to experiencing and experimenting, often encouraging curiosity and sense of wonder. To explore may mean to sense, seek, discover, observe and examine. In some cases, to explore means to investigate different aspects of an issue through open and critical discussion. To explore may also mean testing or trying out and evaluating work methods, products or equipment.

     areas and volumes in practical situations and

    To use means to apply something or to carry out a task to reach a goal. To use, which is closely related to apply, is understood as to utilise or to employ, for example, a method or a tool.

     appropriate units of measurement

  • To explore refers to experiencing and experimenting, often encouraging curiosity and sense of wonder. To explore may mean to sense, seek, discover, observe and examine. In some cases, to explore means to investigate different aspects of an issue through open and critical discussion. To explore may also mean testing or trying out and evaluating work methods, products or equipment.

     practical issues relating to area through the

    To use means to apply something or to carry out a task to reach a goal. To use, which is closely related to apply, is understood as to utilise or to employ, for example, a method or a tool.

     of partitioning and distributivity

    Explanation of competence aims

    Concept explanation / didactic support: Exploring areas using partitioning and distributivity pertains to solving practical area-related problems by dividing complex shapes into simpler parts, calculating the area of each part separately and then combining those areas into one total area. This approach highlights the distributive nature of how the area of a complex shape can be understood as the sum of the areas of its parts. By choosing different ways to divide the area, it is possible to compare strategies, justify choices of approach, and to see the relationships between geometric division and mathematical expressions.

  • To use means to apply something or to carry out a task to reach a goal. To use, which is closely related to apply, is understood as to utilise or to employ, for example, a method or a tool.

     and

    To explore refers to experiencing and experimenting, often encouraging curiosity and sense of wonder. To explore may mean to sense, seek, discover, observe and examine. In some cases, to explore means to investigate different aspects of an issue through open and critical discussion. To explore may also mean testing or trying out and evaluating work methods, products or equipment.

     strategies for measuring and calculating area and perimeter

    Explanation of competence aims

    Didactic support: Exploration involves measuring and calculating the area and perimeter of different shapes and comparing the results. This work demonstrates that shapes can have the same area but different perimeters, and the same perimeter but different areas. Practical activities (such as the use of ropes or measuring tapes) provide a basis for reasoning about area and perimeter and can help to explain why some shapes have a bigger area for a given perimeter and vice versa.

  • To use means to apply something or to carry out a task to reach a goal. To use, which is closely related to apply, is understood as to utilise or to employ, for example, a method or a tool.

     variables, loops, conditions and functions in programming to

    To explore refers to experiencing and experimenting, often encouraging curiosity and sense of wonder. To explore may mean to sense, seek, discover, observe and examine. In some cases, to explore means to investigate different aspects of an issue through open and critical discussion. To explore may also mean testing or trying out and evaluating work methods, products or equipment.

     geometric shapes and patterns

Formative assessment

The formative assessment should help promote learning and the development of competence in mathematics. Pupils demonstrate and develop competence in mathematics during year 6 when they can describe, use and explore numeracy strategies pertaining to whole and decimal numbers, the properties of geometric shapes, and appropriate units of measurement relating to area and volume in problem solving and practical situations. Pupils also demonstrate and develop competence in mathematics when they switch between different representations, pose mathematical questions, explain mathematical relationships, and are able to explain and argue their own and others’ solutions. Furthermore, they demonstrate and develop competence in mathematics by using appropriate strategies and mathematical concepts both orally and in writing.

The teacher shall facilitate pupil participation and encourage the desire to learn by having the pupils describe, use and explore mathematics through movement, play, fascination and practical work. The teacher shall engage in dialogue with the pupils about their development of numeracy strategies pertaining to whole and decimal numbers, and their grasp of the properties of geometric shapes and programming. Pupils are encouraged to work through trial and error. Based on the competence demonstrated by the pupils, they are given the opportunity to express what they believe they have accomplished and how they have improved their skills. The teacher shall provide guidance on further learning and adapt the teaching to enable the pupils to use the guidance provided to develop their numeracy skills and their exploratory and problem-solving competences in relation to decimal numbers, the properties of geometric shapes, and communication with mathematical concepts and the use of appropriate representations both orally and in writing.