Competence aims after Year 10

Numbers and algebra in practice

The aims of the training are to enable the apprentice to
  • compare and convert whole numbers, decimal numbers, fractions, percentages, per thousandths and express such figures in various ways, and evaluate situations where the different representations are suitable
  • calculate with fractions, carry out division of fractions and simplify fractions
  • use factors, powers, square roots and prime numbers in calculations
  • develop, use and elaborate on methods for counting in one’s head, make estimation calculations and written calculations with the four arithmetic operations
  • process, factor and simplify algebraic expressions, tie expressions to practical situations, calculate using formulas, brackets and fraction expressions and use square expressions
  • solve equations and inequalities of the first order and simple equation systems with two unknowns and use this to solve practical and theoretical problems
  • do calculations on consumption, use of credit cards, income, loans and savings, set up budgets and accounts using a spreadsheet, explain the calculations and present the results
  • analyse complex problems, identify fixed and variable quantities, connect complex problems to known solution methods, carry out calculations and present the results in a suitable manner
  • use numbers and variables in exploration, experimentation, practical and theoretical problem solving and technology and design projects


The aims of the training are to enable the apprentice to
  • investigate and describe the characteristics of two- and three-dimensional figures and use them for constructions and calculations
  • perform, describe and provide rationale for geometric constructions using a compass and ruler and dynamic geometry programs
  • use congruence and the Pythagorean theorem to calculate unknown lengths and angles and provide rationale for one’s choices
  • interpret and make working drawings and perspective drawings with several vanishing points, with and without digital tools
  • use coordinates to represent figures and find characteristics of geometric forms with and without the use of digital tools
  • explore, experiment with and formulate logical reasoning by means of geometric ideas, and elaborate on geometric relations that are particularly important in technology, art and architecture


The aims of the training are to enable the apprentice to
  • make estimates of and calculate length, circumference, angle, area, surface, volume and time, and use and change scales
  • choose appropriate measurement units, explain relationships and convert between different measurement units, use and assess measuring instruments and measuring methods for practical measuring, and discuss and elaborate on precision and measuring uncertainty
  • elaborate on the number π and use it for calculating circumference, area and volume

Statistics, probability and combinatorics

The aims of the training are to enable the apprentice to
  • carry out investigations and use databases to search for and analyse statistical data and critically assess sources
  • order and group data, find and discuss and elaborate on the median, mode, average and spread, and present data with and without digital tools, and discuss and elaborate on different ways of presenting data and what impressions these can give
  • find and discuss probability by experimenting, simulating and calculating in day-to-day contexts and games
  • describe sample space and represent probability as fraction, percentage and decimal number
  • discuss and elaborate on and solve simple combinatorics problems


The aims of the training are to enable the apprentice to
  • prepare functions that describe numerical relationships and practical situations, on paper and digitally, describe and interpret them and convert between various representations of functions, such as graphs, tables, formulas and text
  • identify and exploit characteristics of proportional, inversely proportional, linear and simple square functions, and provide examples of situations that may be described using these functions

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