Mathematics year 1-10 (MAT01‑06)
Competence aims and assessment
Explanation
Competence aims after year 7
The pupil is expected to be able to
- numbers, text, tables, drawings, and tangible objects to represent percentages, and to translate between fractions, decimals, and percentages
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.
- appropriate strategies in written and mental arithmetic relating to fractions, decimals, and percentages, and to be able to explain these strategies
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
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.
negative numbers in both practical and theoretical termsTo 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.
Explanation of competence aims
Didactic support: Work on negative numbers can include an exploration of where we find negative numbers in daily life, the placing of negative numbers on a number line, and an examination of the order of operations. Working with the number line can contribute to an understanding of negative numbers in terms of size, distance and relationship, and facilitate the development of flexible numeracy strategies. The use of blank number lines and number lines with different scales allows pupils to place and compare negative numbers.
- apply the rules for the order of operations in problem solving and to create and solve multi-step numerical expressions
Explanation of competence aims
Concept explanation: Multi-step numerical expressions can involve understanding and using numerical expressions that contain several types of arithmetic. This entails the formulation of expressions for multi-step problems and demonstrating how the calculations are connected, and that they must be carried out in the correct order.
- different strategies to solve equations 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.
whether those solutions are validTo 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.
Explanation of competence aims
Didactic support: Work can involve building on previous experiences of solving equations using numbers, text, drawings and tangible objects, and working with more structured and abstract strategies where equations are solved through systematic procedures. For instance, this can include performing the same operation on both sides of the equation or working step-by-step to find out the unknown. The assessment of whether solutions are valid can be further developed from testing solutions (using things such as drawings or tangible objects) to checking solutions by inputting them into the given equation.
- formulate and solve problems related to equations
Explanation of competence aims
Didactic support: Problems can be both purely mathematical and related to everyday life. For instance, they may be pertain to unknown quantities, the relationships between numbers, or missing values. The problems are formulated by setting up equations that represent the situation and which are supported by tangible objects, drawings or symbols. Working on equation-related problems entails reasoning around relationships, explaining choices of approach, and assessing solutions rather than simply performing calculations.
- numbers, text, drawings and tangible objects to solve inequalities and test and explain solutions
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.
Explanation of competence aims
Didactic support: Working on inequalities can entail the exploration of comparisons and relationships between numbers and expressions, where one side is greater than or smaller than the other. The use of tangible objects, number lines, and drawings makes it possible to test solutions and highlights which values fulfil the inequality. By explaining why certain values result in a true or false inequality, pupils can enhance their understanding of the inequality signs.
- calculate averages from their own and others’ datasets, and to choose which average it is appropriate to use
Explanation of competence aims
Concept explanation: In this context, averages are mean, mode, and median.
- log, sort, read anddata in tables and diagrams, and explain the choice of presentation
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.
- , 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 in relation to practical situations when working on financeTo 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.
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. Work pertaining to finances can relate to everyday situations such as buying and selling, budgeting, and basic accounting. Situations such as this afford pupils the opportunity to work with estimates, percentages, and averages, while also having to explain their calculations and assessments. The use of spreadsheets allows pupils to create and assess budgets and accounts using cell references and formulas, and to explore how changes to their assumptions affect the solutions in place.
- programming 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.
data contained in tables and datasetsTo 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.
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 7 when they can describe, use and explore the relationship between fractions, decimals and percentages, the rules for the order of operations, averages and equations and inequalities 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 pertaining to the comparison of fractions, decimals and percentages, and of their grasp of equations and inequalities, diagrams, averages, programming, and finance. 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 the relationship between fractions, decimals and percentages, statistics and modelling, and communication with mathematical concepts and the use of appropriate representations both orally and in writing.