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

Examples of connections

Explanation

Competence aims after year 9

The pupil is expected to be able to

  • create and solve problems involving compound units

  • 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 different two-dimensional shapes and explain the concepts of isomorphism and congruence

    Explanation of competence aims

    Concept explanation / didactic support: Two shapes are congruent when they are the same shape and size and can be mapped onto each other by moving, rotating, or mirroring them – or through a combination of these approaches. Two shapes are isomorphic when they are the same shape but of different sizes. That is to say that they can be mirrored onto one another by enlarging or reducing one of the shapes, or by moving or rotating them, or through a combination of these. When two shapes are isomorphic, the corresponding angles are the same and the ratio between corresponding sides remains constant. This work can involve exploring and comparing the properties of two-dimensional shapes, such as side lengths, angles, parallel sides and symmetry, as well as the specific characteristics of circles, such as radius, diameter and circumference. Exploration can be supported through drawing, measurements, tangible models and digital tools where shapes change systematically and the work emphasises the development of a precise mathematical language.

  • 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.

     isomorphism and Pythagoras’ theorem to explore practical situations

    Explanation of competence aims

    Didactic support: Exploration can be supported through the use of tangible, visual and digital tools. Practical situations, such as creating stable structures, checking that a structure is right-angled, or finding heights or distances that can’t be measured directly, are examples of meaningful approaches to working with Pythagoras’ theorem. Isomorphism can be explored through work with maps, drawings, and models at different scales. By comparing shapes of different sizes, pupils can investigate how proportions and angles are maintained, even if the side lengths change. The use of varied practical examples and representations can support pupils’ understanding of the distinction between isomorphism as a general concept and Pythagoras’ theorem as a specific context for right-angled triangles, and can counteract misconceptions that these are used in the same 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.

    ,

    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 reason around the relationships between side lengths in triangles

    Explanation of competence aims

    Didactic support: Exploring the relationships between the side lengths of triangles is entails investigating the relationship between the sides when dividing a triangle into two right-angled triangles, when you have a 30-60-90 triangle, or when you have an isosceles or an equilateral triangle. Through work like this, pupils are able to make the case for fixed ratios between the side lengths, for the use of Pythagoras’ theorem, and why sides of equal lengths result in symmetry and stable structures.

  • 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 put forward the argument for how changing assumptions in geometric problems affects solutions both practically and algebraically

    Explanation of competence aims

    Didactic support: This work can involve an exploration of how changes to assumptions in geometric problems affect their solutions – for example by examining what happens when lengths, angles, or heights are changed. A key approach is the use of the ‘what if?’ question in which pupils systematically vary one variable at a time and examine the consequences. Exploration includes both hands-on investigations and algebraic reasoning, for instance by identifying the relationship between formulas and geometric changes. Being able to put forward the argument for why solutions change rather than simply describing the fact that they do is a key pillar. Digital tools afford pupils the opportunity to dynamically vary shapes and use drawings, graphs, and tables to see patterns and relationships.

  • 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 put forward the argument for formulas for the calculation of the surface area and volume of three-dimensional shapes

  • 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.

     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.

     statistical presentations found in the media and the local community
  • calculate averages and measures of dispersion in their own and others’ datasets, and then

    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 results 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.

     the data

    Explanation of competence aims

    Concept explanation: In this context, averages refer to mean, mode, and median. The measure of dispersion refers to the range of distribution.

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

     and put forward the argument for how presentations of figures and data can be used to promote different points of view
  • calculate 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.

     probability in statistics and games
  • simulate outcomes in randomised trials and calculate the probability of something occurring 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 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 9 when they can describe, use and explore isomorphism, congruence, Pythagoras’ theorem, the relationships between the lengths of the sides of triangles, formulae for calculating the surface area and volume of three-dimensional shapes, and statistical representations in problem solving and practical situations. 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 concepts, strategies and mathematical reasoning pertaining to their work on the properties of geometric shapes, the calculation of surface area, volume, probability, averages, measures of dispersion, and the critical assessment of statistics. 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 geometry, statistics and probability, and communication with mathematical concepts and the use of appropriate representations both orally and in writing.