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

Examples of connections

Explanation

Competence aims after year 10

The pupil is expected to be able to

  • 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.

     the order of operations and generalise relationships algebraically

    Explanation of competence aims

    Concept explanation / didactic support: In this case, the order of operations refers to the use of algebraic notation to show the commutative, associative and distributive laws, and to generalise the order of operations for integers, fractions, powers, and square roots.

  • 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 square theorems geometrically and algebraically 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.

     the square theorems as calculation strategies
  • create, solve and explain systems of equations related to practical situations

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

     properties of linear functions, exponential functions, fractional functions and second-degree functions 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 digital tools
  • explain the concept of change per unit and calculate the slope of linear functions

  • 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 constant percentage change, growth factor and exponential functions
  • retrieve and

    To interpret means to construct a perception or understanding of the meaning of a phenomenon, a practical situation or an artistic expression. The understanding often builds on an analysis of individual elements and how they are linked.

     relevant information and

    To reflect means to examine and consider different aspects of your own and others’ actions, attitudes and ideas. We may also reflect on a subject, practical activities or our own learning. Reflection means testing out our own thoughts and attitudes to develop better insight and understanding.

     on the possible consequences of buying and selling, interest on savings, loans and credit purchases

  • To plan means to set up a course of action to reach a goal. The plan describes how we intend to reach the goal, and may show the link between activities, implementation and the goal.

    , carry out and

    To present means to show, explain and outline a topic or a product. The way of presenting may vary, but the goal of the presentation is to make the topic or product accessible to others. To present may also mean to illustrate and to demonstrate.

     an exploratory assignment related to personal finance
  • model situations,

    To present means to show, explain and outline a topic or a product. The way of presenting may vary, but the goal of the presentation is to make the topic or product accessible to others. To present may also mean to illustrate and to demonstrate.

     the results and

    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.

     the validity of the models

    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. Working with functions is key, but modelling can also be linked to other areas, such as statistics, probability and geometry. 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.

  • 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.

     mathematical properties and relationships using programming
  • read and explain text-based programming code in Python

Formative assessment

The formative assessment should help promote learning and the development of competence in mathematics. Pupils demonstrate and develop competence in the subject in year 10 when they describe, use and explore order of operations, the algebraic identities, systems of equations, properties of functions, and issues related to statistics and personal finance. Pupils also demonstrate and develop competence in mathematics when they pose mathematical questions, explain mathematical relationships, and justify and critically evaluate their own and others’ solutions. Furthermore, they demonstrate and develop competence in mathematics by using appropriate representations, 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 competences relating to modelling, generalisation, mathematical reasoning, and algorithmic and computational thinking. 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 generalising, modelling, exploring and problem-solving competences in relation to the mathematical fields of knowledge, the interrelationships between these, and communication with mathematical concepts and the use of appropriate representations both orally and in writing.

Assessment of coursework

The mark awarded for classwork reflects the overall competence of the pupil in mathematics at the end of the education after completing year 10. The teacher shall plan and facilitate the pupils in demonstrating their competence in various ways, including understanding, reflection and critical thinking in various contexts. The teacher shall award a grade in Mathematics based on the competence shown by the pupil – orally, digitally, and in writing – in terms of using mathematical forms of expression and problem-solving strategies, as well as their ability to reflect upon and reason in relation to solutions and models.