Mathematics year 1–10 (MAT01‑05)
Competence aims and assessment

Examples of connections

Explanation

Competence aims after year 5

The pupil is expected to be able to

  • explore

    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 relationships between fractions, decimal numbers and percentages, and
    use

    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.

    these in mental arithmetic
  • describe

    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.

    fractions as parts of the whole, as parts of a set and as numbers on the number line, and evaluate and name the quantities
  • represent fractions in different ways and switch between the different representations
  • develop

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

    and
    use

    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 calculations with positive numbers and fractions, and explain one’s own thought processes
  • formulate and solve problems from one’s own everyday life that are related to fractions
  • discuss randomness and probability in games and practical situations and relate this to fractions
  • solve equations and inequalities through logical reasoning and explain what it means that a number is a solution to an equation
  • create and solve tasks in a spreadsheet related to personal finance
  • formulate and solve problems from one’s own everyday life that are related to time
  • create and programme algorithms with the use of variables, conditions and loops

Formative assessment

Formative assessment shall help to promote learning and develop competence in the mathematics subject. The pupils demonstrate and develop competence in the subject in year 5 when they explore and reflect on different mathematical concepts, representations and strategies when working with fractions and informal solving of equations and inequalities. The pupils also demonstrate and develop competence when they use their knowledge and skills to formulate and solve problems related to everyday life and society. They also demonstrate and develop their competence in mathematics when they reason about and argue for solutions and mathematical relationships.

The teacher shall facilitate for pupil participation and stimulate the desire to learn by allowing the pupils to explore mathematics and solve mathematical problems by being creative, and by reasoning and reflecting. The teacher and pupils shall engage in dialogue about their development in programming and understanding of numbers. The pupils shall have the opportunity try and fail. With the competence the pupils have demonstrated as the starting point, they shall have the opportunity to express what they believe they have achieved 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 competence in exploring different representations and problem solving strategies and in arguing using mathematical concepts.