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

Examples of connections

Explanation

Competence aims after year 8

The pupil is expected to be able to

  • work with powers and square roots, and explain their approach and results

  • 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.

     commutative, associative and distributive properties to

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

     and communicate strategies for written and mental arithmetic

    Explanation of competence aims

    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). Commutativity in multiplication means that the order of the numbers does not change the product, meaning that 2 x 3 = 3 x 2. Associativity means that the way you group numbers in multiplication does not change the result, meaning that 2 x (3 x 4) = (2 x 3) x 4. Distributivity shows a relationship between multiplication and addition, for example 2 x (3 + 4) = 2 x 3 + 2 x 4.

  • 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.

     factorisation and prime factorisation, and 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.

     this in fractional arithmetic

  • 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 generalise geometric patterns and numerical patterns in their own words and algebraically

    Explanation of competence aims

    Didactic support: Working with patterns involves pupils describing relationships in geometric and numerical patterns, both in their own words, using drawings, and with algebraic symbols. Generalisation can be done recursively by explaining how the pattern develops from one step to the next, and explicitly, by formulating a direct rule that applies to a specific step or link in the pattern.

  • create and explain mathematical expressions with numbers, variables and constants related to practical situations
  • create and solve equations related to practical situations 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.

     solutions

    Explanation of competence aims

    Didactic support: Work can involve formulating and solving equations as mathematical models for practical situations, where the equations show how the quantities in the given situation are related. The situations themselves can be drawn from example in everyday life, wider society, and real datasets. Critical assessment involves checking solutions upon insertion and assessing whether the results are reasonable in light of the context and assumptions in the model. This work emphasises reasoning, argumentation, and the comparison of different solution methods.

  • 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 to solve inequalities 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.

     whether those solutions are valid

    Explanation of competence aims

    Didactic support: Working with inequalities is about finding a set of values that fulfils a comparison between expressions, such as greater than or less than. Find a solution involves the use of systematic strategies to determine which values belong, and this is often supported by a number line and testing of values. Assessing whether or not solutions are valid entails an examination and justification of whether certain values fulfil the inequality, and why others do not.

  • 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.

    ,

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

     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.

     functions related to practical situations

    Explanation of competence aims

    Didactic support: Working with functions involves exploring the relationship between quantities when the value of one quantity is conditional upon the value of another. A key understanding is that a function describes a rule that links each value of one variable to a specific value of the other. Exploration should be based on practical and visual activities in which these relationships are examined through situations drawn from daily life. The use of function machines, tables, coordinate systems and digital tools affords pupils the opportunity to identify patterns and changes, and to explore what varies and what stays the same. Functions are thus worked with as structured relationships rather than merely as graphs or 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.

     situations, tables, graphs and expressions to represent functions and show relationships between the representations

    Explanation of competence aims

    Didactic support: Working with representations of functions can entail showing that the same mathematical relationship can be expressed in different ways, including through practical situations, tables, graphs, and algebraic expressions. By working with transitions between these representations, it is possible to see what they have in common and what remains unchanged in the context – even if the form of presentation varies. Being able to justify what is the most appropriate representation in a given situation is an important part of the work.

  • 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.

     how algorithms can be created, tested and improved using programming

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 8 when they can describe, use and explore the order of operations, functions, equations, inequalities, and geometric and numerical patterns and 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 concepts and strategies for solving mathematical expressions, equations and inequalities, and in relation to the flexible use of representations in functions and the exploration of patterns and algorithms in 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 algebra, functions and modelling, and communication with mathematical concepts and the use of appropriate representations both orally and in writing.