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

Examples of connections

Explanation

Competence aims after year 4

The pupil is expected to be able 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.

     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.

     grouping and sharing division in practical situations

    Explanation of competence aims

    Concept explanation / didactic support: In the case of sharing division, the total quantity and the number of groups are known quantities, and the question is how much you have in each part – for example, if a 12-metre length of rope is cut into 4 equally-sized lengths (12 ÷ 4 = 3). Grouping division, however, assumes that the total quantity and the size of each group are known quantities, and the question is how many parts you end up with – for example, if a 12-metre length of rope is cut into lengths of 3 metres (12 ÷ 3 = 4). Working on both types of division strengthens the grasp of division.

  • 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.

     numbers, text, drawings, and tangible objects 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.

     division in different ways and translate between the different representations

    Explanation of competence aims

    Didactic support: Working with multiple representations provides pupils with experience that division can be expressed and understood in different ways, and that the same value can be presented in different ways depending on the situation and representation. The use of tangible objects to support work around division and grouping (such as building blocks or counting sticks) makes it possible to explore division both into equal parts and as fixed-unit groups. When tangible actions are translated to drawings, text and numerals, this clarifies the relationship between actions, language, and symbols. Work of this kind supports an understanding of division as a way to describe relationships between quantities, rather than simply a method for calculating an answer.

  • 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 explain different division strategies

    Explanation of competence aims

    Didactic support: Working with different division strategies can provide pupils with a basis for a flexible understanding of division. Examples of strategies include halving numbers, dividing place-value units such as 10, 100 and 1000, breaking down numbers into small components that can be more easily divided, using fixed-step counting or tangible division and grouping, and the use of inverse multiplication. Working on multiple strategies is important because division can express different situations and questions, and because pupils thus learn to choose and explain the most appropriate approach to any given situation.

  • 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.

     written and mental arithmetic 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.

     and explain the relationships between the four arithmetic operations

  • To assess means to consider different aspects of an issue or point of view. It may also include judging the quality of a product or process. An assessment often results in a decision, a judgement or a conclusion.

    , estimate, explain their reasoning, and critically

    To assess means to consider different aspects of an issue or point of view. It may also include judging the quality of a product or process. An assessment often results in a decision, a judgement or a conclusion.

     their own and others’ models and solutions when working in practical situations

    Explanation of competence aims

    Didactic support: Modelling is about being able to critically move back and forth between reality and mathematics while determining what is relevant, creating a mathematical model, interpreting the results, and assessing how well a proposed model describes a given situation in reality. The aim is to understand and simplify the situation, formulate and solve the problem mathematically, and then interpret and validate the answer against reality. When working with modelling, assessing and estimation are important factors in developing pupils’ understanding of how reasonable their calculations are. By estimating the quantities and results before or after the arithmetic is carried out, pupils’ flexible number sense is improved.

  • create mathematical expressions for practical situations and identify practical situations that fit a given mathematical expression

  • 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 by using angles, edges, corners, and faces

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

     volume in practical situations using both non-standardised and standardised units of measurement, and to discuss the results

    Explanation of competence aims

    Didactic support: Working with volume measured in non-standardised units of measurement can provide a tangible basis for understanding volume as being how much space something occupies. By measuring volume using measures such as cups, bowls, or other vessels, it makes it clear to pupils that volume relates to how many equal units can be fitted into one container. Volume can also be built using building blocks or centicubes. This work highlights that different units can lead to different measurements, even if the volume is the same, which gives rise to a need for fixed, standardised units of measurement. In the transition between standardised units, pupils can explore the relationship between litres and cubic decimetres.

  • 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.

     structures and patterns in games and play

    Explanation of competence aims

    Didactic support: Exploring structures and patterns in games and play can involve describing repetitions, regularities, and connections in activities. Working with rhymes and chants, figurate numbers and the development of patterns provides pupils with experience in formulating rules and generalising, and lays the foundation for early algebraic thinking.

  • create algorithms and express them using variables, conditions and loops

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 4 when they can describe, use and explore grouping and sharing division, appropriate strategies and representations in their work with the four arithmetic operations, and the properties of two- and three-dimensional shapes in play, problem solving and practical situations. Pupils also demonstrate and develop competence in mathematics when they switch between different representations, pose mathematical questions, 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 strategies pertaining to division, their understanding of the interrelationships between the four arithmetic operations, and their strategies for creating mathematical expressions for practical situations and finding practical situations that fit the given mathematical expression. 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 numeracy strategies, units of measurement, the modelling and critical assessment of their own and others’ solutions, and communication with mathematical concepts and the use of appropriate representations both orally and in writing.