Mathematics year 1–10 (MAT01‑05)
Competence aims and assessment
Competence aims after year 10
The pupil is expected to be able to
- explore and generalise multiplication of polynomials algebraically and geometrically
Writing in mathematics refers to describing and explaining relationships, discoveries and ideas using suitable representations. Writing in mathematics is a tool for developing one’s own thoughts and learning. This means the ability to solve problems and to present solutions that are adapted to the receiver and the situation. The development of writing skills in mathematics goes from using an everyday language to gradually using a more precise mathematical language.
Numeracy in mathematics refers to using mathematical representations, concepts and approaches to do calculations and evaluate whether solutions are valid. This means recognising concrete problems that can be solved using numeracy skills and formulating questions about these. Mathematics has a particular responsibility for teaching numeracy. Development of numeracy skills in mathematics means analysing and solving a range of increasingly more complex problems with effective and suitable concepts, symbols, methods and strategies.
- explore and compare the properties of different functions using digital tools
Oral skills in mathematics refers to creating meaning through dialogue in and about mathematics. This means communicating ideas and discussing mathematical problems, strategies and solutions with others. The development of oral skills in mathematics goes from using an everyday language to gradually using a more precise mathematical language.
Digital skills in mathematics refers to the ability to use graphing tools, spreadsheets, CAS, dynamic geometry software and programming to explore and solve mathematical problems. It also means finding, analysing, processing and presenting information using digital tools. The development of digital skills refers to increasingly being able to choose and use suitable digital tools as aids for exploring, solving and presenting mathematical problems.
- create, solve and explain equation sets related to practical situations
Oral skills in mathematics refers to creating meaning through dialogue in and about mathematics. This means communicating ideas and discussing mathematical problems, strategies and solutions with others. The development of oral skills in mathematics goes from using an everyday language to gradually using a more precise mathematical language.
Writing in mathematics refers to describing and explaining relationships, discoveries and ideas using suitable representations. Writing in mathematics is a tool for developing one’s own thoughts and learning. This means the ability to solve problems and to present solutions that are adapted to the receiver and the situation. The development of writing skills in mathematics goes from using an everyday language to gradually using a more precise mathematical language.
Numeracy in mathematics refers to using mathematical representations, concepts and approaches to do calculations and evaluate whether solutions are valid. This means recognising concrete problems that can be solved using numeracy skills and formulating questions about these. Mathematics has a particular responsibility for teaching numeracy. Development of numeracy skills in mathematics means analysing and solving a range of increasingly more complex problems with effective and suitable concepts, symbols, methods and strategies.
- calculate the slope of a linear function, and use it to explain the concepts change per unit and average speed
Oral skills in mathematics refers to creating meaning through dialogue in and about mathematics. This means communicating ideas and discussing mathematical problems, strategies and solutions with others. The development of oral skills in mathematics goes from using an everyday language to gradually using a more precise mathematical language.
Numeracy in mathematics refers to using mathematical representations, concepts and approaches to do calculations and evaluate whether solutions are valid. This means recognising concrete problems that can be solved using numeracy skills and formulating questions about these. Mathematics has a particular responsibility for teaching numeracy. Development of numeracy skills in mathematics means analysing and solving a range of increasingly more complex problems with effective and suitable concepts, symbols, methods and strategies.
- explore the relationship between constant change by percentage, growth factors and exponential functions
Oral skills in mathematics refers to creating meaning through dialogue in and about mathematics. This means communicating ideas and discussing mathematical problems, strategies and solutions with others. The development of oral skills in mathematics goes from using an everyday language to gradually using a more precise mathematical language.
Digital skills in mathematics refers to the ability to use graphing tools, spreadsheets, CAS, dynamic geometry software and programming to explore and solve mathematical problems. It also means finding, analysing, processing and presenting information using digital tools. The development of digital skills refers to increasingly being able to choose and use suitable digital tools as aids for exploring, solving and presenting mathematical problems.
- extract and interpret relevant information from texts related to purchases, sales and different types of loans, and use this to formulate and solve problems
Reading in mathematics refers to creating meaning in texts from everyday life, society and the field of mathematics. Reading in mathematics means being able to sort information, analyse and evaluate its form and content, and summarise information in multimodal texts. The development of reading skills in mathematics refers to finding and using information in increasingly complex texts with advanced symbolic language and use of concepts.
Numeracy in mathematics refers to using mathematical representations, concepts and approaches to do calculations and evaluate whether solutions are valid. This means recognising concrete problems that can be solved using numeracy skills and formulating questions about these. Mathematics has a particular responsibility for teaching numeracy. Development of numeracy skills in mathematics means analysing and solving a range of increasingly more complex problems with effective and suitable concepts, symbols, methods and strategies.
Digital skills in mathematics refers to the ability to use graphing tools, spreadsheets, CAS, dynamic geometry software and programming to explore and solve mathematical problems. It also means finding, analysing, processing and presenting information using digital tools. The development of digital skills refers to increasingly being able to choose and use suitable digital tools as aids for exploring, solving and presenting mathematical problems.
- plan, carry out and present an exploratory work related to one’s personal finances
Oral skills in mathematics refers to creating meaning through dialogue in and about mathematics. This means communicating ideas and discussing mathematical problems, strategies and solutions with others. The development of oral skills in mathematics goes from using an everyday language to gradually using a more precise mathematical language.
Numeracy in mathematics refers to using mathematical representations, concepts and approaches to do calculations and evaluate whether solutions are valid. This means recognising concrete problems that can be solved using numeracy skills and formulating questions about these. Mathematics has a particular responsibility for teaching numeracy. Development of numeracy skills in mathematics means analysing and solving a range of increasingly more complex problems with effective and suitable concepts, symbols, methods and strategies.
Digital skills in mathematics refers to the ability to use graphing tools, spreadsheets, CAS, dynamic geometry software and programming to explore and solve mathematical problems. It also means finding, analysing, processing and presenting information using digital tools. The development of digital skills refers to increasingly being able to choose and use suitable digital tools as aids for exploring, solving and presenting mathematical problems.
- use functions in modelling and argue for approaches and results
Oral skills in mathematics refers to creating meaning through dialogue in and about mathematics. This means communicating ideas and discussing mathematical problems, strategies and solutions with others. The development of oral skills in mathematics goes from using an everyday language to gradually using a more precise mathematical language.
Digital skills in mathematics refers to the ability to use graphing tools, spreadsheets, CAS, dynamic geometry software and programming to explore and solve mathematical problems. It also means finding, analysing, processing and presenting information using digital tools. The development of digital skills refers to increasingly being able to choose and use suitable digital tools as aids for exploring, solving and presenting mathematical problems.
- model situations related to real datasets, present the results and argue for the validity of the models
Oral skills in mathematics refers to creating meaning through dialogue in and about mathematics. This means communicating ideas and discussing mathematical problems, strategies and solutions with others. The development of oral skills in mathematics goes from using an everyday language to gradually using a more precise mathematical language.
Reading in mathematics refers to creating meaning in texts from everyday life, society and the field of mathematics. Reading in mathematics means being able to sort information, analyse and evaluate its form and content, and summarise information in multimodal texts. The development of reading skills in mathematics refers to finding and using information in increasingly complex texts with advanced symbolic language and use of concepts.
Numeracy in mathematics refers to using mathematical representations, concepts and approaches to do calculations and evaluate whether solutions are valid. This means recognising concrete problems that can be solved using numeracy skills and formulating questions about these. Mathematics has a particular responsibility for teaching numeracy. Development of numeracy skills in mathematics means analysing and solving a range of increasingly more complex problems with effective and suitable concepts, symbols, methods and strategies.
Digital skills in mathematics refers to the ability to use graphing tools, spreadsheets, CAS, dynamic geometry software and programming to explore and solve mathematical problems. It also means finding, analysing, processing and presenting information using digital tools. The development of digital skills refers to increasingly being able to choose and use suitable digital tools as aids for exploring, solving and presenting mathematical problems.
- explore mathematical properties and relationships by using programming
Digital skills in mathematics refers to the ability to use graphing tools, spreadsheets, CAS, dynamic geometry software and programming to explore and solve mathematical problems. It also means finding, analysing, processing and presenting information using digital tools. The development of digital skills refers to increasingly being able to choose and use suitable digital tools as aids for exploring, solving and presenting mathematical problems.
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 10 when they formalise thoughts and strategies using mathematical language. They also demonstrate and develop competence when they explore and generalise mathematical relationships and structures using algebra and suitable representations. Furthermore, they also demonstrate and develop competence in mathematics when they reason about and argue for their own and others’ approaches and solutions.
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, modelling and reflecting. The teacher and pupils shall engage in dialogue about their development when it comes to discovering relationships between different fields of knowledge and choosing suitable strategies. The pupils shall have the opportunity to 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 reflect on their development in the subject. 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 modelling and understanding of mathematics and how to use obtained knowledge and skills in new and unfamiliar contexts.
Assessment of coursework
The grade awarded for coursework shall express the overall competence of the pupil in mathematics after completing year 10. The teacher shall plan and facilitate for the opportunity for the pupils to demonstrate their competence in different ways, including through understanding, reflection and deliberation, and in different contexts. The teacher shall award one grade in mathematics based on the competence the pupil has demonstrated in writing, orally and digitally, by using mathematical forms of expression, problem-solving strategies and reflecting on and arguing for solutions and models.