Mathematics year 1–10 (MAT01‑05)
Competence aims and assessment
Competence aims after year 5
The pupil is expected to be able to
- explore and explain relationships between fractions, decimal numbers and percentages, and use these in mental arithmetic
Reasoning in mathematics means the ability to follow, evaluate and understand mathematical chains of thought. It means that the pupils shall understand that mathematical rules and results are not random, but have clear reasons. The pupils shall formulate their own reasoning in order to both understand and solve problems. Argumentation in mathematics means that the pupils give reasons for their approaches, reasonings and solutions, and prove that these are valid.
Abstraction in mathematics means gradually developing formalisation of thoughts, strategies and mathematical language. The development goes from concrete descriptions to formal symbol language and formal reasoning. Generalisation in mathematics refers to the pupils discovering relationships and structures without being presented a finished solution. This means that the pupils can explore numbers, calculations and figures to find relationships, and then formalise by using algebra and suitable representations.
- describe fractions as parts of the whole, as parts of a set and as numbers on the number line, and evaluate and name the quantities
Representations in mathematics are ways of expressing mathematical concepts, relationships and problems. Representations can be concrete, contextual, visual, verbal and symbolic. Communication in mathematics means that the pupils use mathematical language in conversations, argumentation and reasoning. The pupils shall have the opportunity to use mathematical representations in different contexts through their own experiences and in mathematical conversations. The pupils shall have the opportunity to explain and give reasons for the choice of form of representation. The pupils must be able to switch between mathematical representations and everyday language and to switch between different representations.
- represent fractions in different ways and switch between the different representations
Representations in mathematics are ways of expressing mathematical concepts, relationships and problems. Representations can be concrete, contextual, visual, verbal and symbolic. Communication in mathematics means that the pupils use mathematical language in conversations, argumentation and reasoning. The pupils shall have the opportunity to use mathematical representations in different contexts through their own experiences and in mathematical conversations. The pupils shall have the opportunity to explain and give reasons for the choice of form of representation. The pupils must be able to switch between mathematical representations and everyday language and to switch between different representations.
- develop and use different strategies for calculations with positive numbers and fractions, and explain one’s own thought processes
A model in mathematics is a description of reality using mathematical language. The pupils shall gain insight into how mathematical models are used to describe everyday life, working life and society in general. Modelling in mathematics means creating such models. It also means to critically evaluate whether the models are valid and what limitations the models have, evaluate the models in view of the original situations, and evaluate whether they can be used in other situations. Applications in mathematics means giving the pupils insight into how to use mathematics in different situations within and outside of the subject.
- formulate and solve problems from one’s own everyday life that are related to fractions
Exploration in mathematics means that the pupils search for patterns, find relationships and discuss their way to a shared understanding. The pupils shall place more emphasis on strategies and approaches than on solutions. Problem solving in mathematics means that the pupils develop a method for solving a problem not previously encountered. Computational thinking is important in the process of developing strategies and approaches to solve problems, and means breaking a problem down into sub-problems that can be solved systematically. This also includes evaluating whether sub-problems can be solved best with or without digital tools. Problem solving also means analysing and reformulating known and unknown problems, solving them and evaluating whether the solutions are valid.
- discuss randomness and probability in games and practical situations and relate this to fractions
Exploration in mathematics means that the pupils search for patterns, find relationships and discuss their way to a shared understanding. The pupils shall place more emphasis on strategies and approaches than on solutions. Problem solving in mathematics means that the pupils develop a method for solving a problem not previously encountered. Computational thinking is important in the process of developing strategies and approaches to solve problems, and means breaking a problem down into sub-problems that can be solved systematically. This also includes evaluating whether sub-problems can be solved best with or without digital tools. Problem solving also means analysing and reformulating known and unknown problems, solving them and evaluating whether the solutions are valid.
Reasoning in mathematics means the ability to follow, evaluate and understand mathematical chains of thought. It means that the pupils shall understand that mathematical rules and results are not random, but have clear reasons. The pupils shall formulate their own reasoning in order to both understand and solve problems. Argumentation in mathematics means that the pupils give reasons for their approaches, reasonings and solutions, and prove that these are valid.
- solve equations and inequalities through logical reasoning and explain what it means that a number is a solution to an equation
Exploration in mathematics means that the pupils search for patterns, find relationships and discuss their way to a shared understanding. The pupils shall place more emphasis on strategies and approaches than on solutions. Problem solving in mathematics means that the pupils develop a method for solving a problem not previously encountered. Computational thinking is important in the process of developing strategies and approaches to solve problems, and means breaking a problem down into sub-problems that can be solved systematically. This also includes evaluating whether sub-problems can be solved best with or without digital tools. Problem solving also means analysing and reformulating known and unknown problems, solving them and evaluating whether the solutions are valid.
Reasoning in mathematics means the ability to follow, evaluate and understand mathematical chains of thought. It means that the pupils shall understand that mathematical rules and results are not random, but have clear reasons. The pupils shall formulate their own reasoning in order to both understand and solve problems. Argumentation in mathematics means that the pupils give reasons for their approaches, reasonings and solutions, and prove that these are valid.
- create and solve tasks in a spreadsheet related to personal finance
A model in mathematics is a description of reality using mathematical language. The pupils shall gain insight into how mathematical models are used to describe everyday life, working life and society in general. Modelling in mathematics means creating such models. It also means to critically evaluate whether the models are valid and what limitations the models have, evaluate the models in view of the original situations, and evaluate whether they can be used in other situations. Applications in mathematics means giving the pupils insight into how to use mathematics in different situations within and outside of the subject.
Representations in mathematics are ways of expressing mathematical concepts, relationships and problems. Representations can be concrete, contextual, visual, verbal and symbolic. Communication in mathematics means that the pupils use mathematical language in conversations, argumentation and reasoning. The pupils shall have the opportunity to use mathematical representations in different contexts through their own experiences and in mathematical conversations. The pupils shall have the opportunity to explain and give reasons for the choice of form of representation. The pupils must be able to switch between mathematical representations and everyday language and to switch between different representations.
- formulate and solve problems from one’s own everyday life that are related to time
A model in mathematics is a description of reality using mathematical language. The pupils shall gain insight into how mathematical models are used to describe everyday life, working life and society in general. Modelling in mathematics means creating such models. It also means to critically evaluate whether the models are valid and what limitations the models have, evaluate the models in view of the original situations, and evaluate whether they can be used in other situations. Applications in mathematics means giving the pupils insight into how to use mathematics in different situations within and outside of the subject.
- create and programme algorithms with the use of variables, conditions and loops
Exploration in mathematics means that the pupils search for patterns, find relationships and discuss their way to a shared understanding. The pupils shall place more emphasis on strategies and approaches than on solutions. Problem solving in mathematics means that the pupils develop a method for solving a problem not previously encountered. Computational thinking is important in the process of developing strategies and approaches to solve problems, and means breaking a problem down into sub-problems that can be solved systematically. This also includes evaluating whether sub-problems can be solved best with or without digital tools. Problem solving also means analysing and reformulating known and unknown problems, solving them and evaluating whether the solutions are valid.
Abstraction in mathematics means gradually developing formalisation of thoughts, strategies and mathematical language. The development goes from concrete descriptions to formal symbol language and formal reasoning. Generalisation in mathematics refers to the pupils discovering relationships and structures without being presented a finished solution. This means that the pupils can explore numbers, calculations and figures to find relationships, and then formalise by using algebra and suitable representations.
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.