Mathematics subject curriculum (MAT1-03)

Competence aims after Year 10

Number and algebra

The aims of the training are to enable the apprentice to

• compare and convert between integers, decimal numbers, fractions, percentages, per mil (per thousands) and numbers in standard form, and represent such numbers in varied ways
• calculate with fractions, carry out division of fractions and simplify fractions
• use factors, powers, square roots and prime numbers in calculations
• develop, use and justify the rationale for methods of mental computation, rough estimations and written calculations with regards to the four arithmetic operations
• process and factor simple algebraic expressions, and carry out calculations with formulas, brackets and fractions with single term denominator
• solve first order equations and inequalities and simple systems of equations with two unknowns
• compose simple budgets and perform calculations related to personal finances
• use, with and without digital aids, numbers and variables in inquiry, experimentation, practical and theoretical problem solving and technology and design projects

Geometry

The aims of the training are to enable the apprentice to

• analyse characteristics of two- and three-dimensional figures, both digitally and by hand, and use them in constructions and calculations
• perform and explain geometric constructions and representations with ruler and compass and other aids
• use similarity and the Pythagorean theorem to calculate unknown sizes/quantities
• interpret and compose working drawings and perspective drawings with several vanishing points by using various aids
• use coordinates to represent figures and find characteristics of geometric forms
• 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

Measurement

The aims of the training are to enable the apprentice to

• estimate and calculate length, perimeter, angle, area, surface area, 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, mean and variance, and display data with and without digital tools
• determine probabilities in everyday contexts and games by experimenting, simulating and calculating
• describe sample space and represent probability as fraction, percentage and decimal number
• demonstrate, using examples, and find the possible solutions to simple combinatorics problems

Functions

The aims of the training are to enable the apprentice to

• compose, on paper and digitally, functions that describe numerical relationships and practical contexts, interpret them and convert between varied representations of functions, such as graphs, tables, formulas and text
• identify and make use of characteristics of proportional, inversely proportional, linear and elementary quadratic functions, and provide examples of situations that may be described by these functions