Danish Lower Secondary School Mathematics Standards
Numbers and algebra
Knowledge 
Abilities 
Rational numbers and the expansion to real numbers 
Working investigating, especially with systematic counting and with the numbers mutual size as a part of forming a general understanding of numbers 
Culturalhistorical meaning of numbers as a means of description. 
Using mental arithmetic and estimate 

Using pocket calculator and computer in problem solving 

Understand and using formulas for example in calculation of interest and volume 

Understand and using expressions containing variables 
Percent 
Using percent 

Calculating with fractions including solving of equalities and algebraic problems. 

Investigate and describe "changes" and structures for example in series of numbers, series of figures, and patterns 
Conception of functions 
Using graphical methods in solving equalities and systems of equalities 

Solving simple equalities and solving inequalities by inspection. 
Geometry
Knowledge 
Abilities 
Properties of different geometric figures 
Using the properties of different geometric figures 

Drawing pictures after given preconditions 

Using basic geometric conceptions including ratio of size and the mutual position of lines 

Understand and produce:
 Workshop drawings
 Isometric drawings
 Perspective drawings
In description of the surroundings
Investigate, describe and estimate connections between a drawing and the object drew 
The conception of measurement 
Using the conception of measurement, including measuring and calculation of circumference, surface and volume 
Scale, similarity and congruence 
Using scale, similarity and congruence 

Execute simple geometric calculations for example using Pythagoras` theorem 

Working with simple geometric proofs 

Using computers in drawing, investigations and calculations concerning geometric figures 
Applied mathematics
Knowledge 
Abilities 

Choose arithmetical operations
Use percent
Calculate with proportion in various connections 

Handle examples of problems in societal development with respect to:
Economy, technology and environment 

Make economic considerations regarding daily purchase, transport, housing conditions, salary and calculation of tax 

Working with interest and making calculation of interest especially regarding saving up, borrowing, buying on credit 

Work with and investigate formulas and functions entering mathematic models 
Possibilities and limitations in using mathematics as a description and a basis for decisions 
Working with statistical description of a collection of data, with the emphasis on method and interpretation 

Execute simulations for example by the computer 
Statistical probability 
Using computers for calculations, simulations, investigations and descriptions included societal conditions 

Using mathematics as a tool in solving practical and theoretical problems in a comprehensive way 
Communication and problem solving
Knowledge 
Abilities 

Understand and take a position on information's, with mathematic expressions 

Formulate problems, describe procedure and give solutions in a understandable manner, both in writing and oral 

Using experimenting and investigating in working and formulating results of the professional knowledge, which is obtained 

Choose suitable professional methods, working and tool by solution of transverse problems 

Cooperation with others in mathematic problem solving 

Using systematizing and mathematic argumentation 

Using variables and symbols, when rules and connections are going to be proofed 

Using geometric drawings in formulating hypotheses and argumentation 

Understand that choosing a specific mathematic model can mirror a specific norm of value 

Alternate between practical and theoretical considerations in solutions of mathematic problems 
Denmark's Input Situation summary of mathematics taught at the primary level
Numbers and algebra
Knowledge 
Abilities 
Whole numbers
Decimal numbers
Fractions 


Using experiences from everyday life in connection with working with numbers in school 
System of numbers
Number line
Position systems
The four basic arithmetical operations 
Use mental arithmetic and estimate 

Using pocket calculator and computer in problem solving 

Working with counting's and examples on connections and rules for the four basic arithmetical operations 
Examples of how to use variables, including formulas, simple equalities and functions 

Percent and the use of percent in everyday life 
Calculation with decimal numbers and using fractions linked to percent and concrete connections 
Coordinate system including the connection between number and drawing 
Working with "changes" and structures for example in series of numbers, series of figures, and patterns 
Geometry
Knowledge 
Abilities 

Using geometry in the description of object from everyday life including figures and patterns 

Investigate and describe simple figures in plane 
Basic geometric conceptions like angles and parallelism 


Working with real models and simple drawing of these 
The method of different cultures to give depth in a picture 
Investigate the application of drawing methods 

Measure and calculate perimeter, area and volume in concrete situations 

Draw, investigate and do experimentation in relation to geometric figures, including using computers 
Applied mathematics
Knowledge 
Abilities 

Choose and use arithmetical operations
in various connections 

Using professional tools included numbers, graphical representation and statistics in the solution of mathematical problems concerning everyday life, family life and the nearest societal 

Working with simple percent calculations including discount price 

Describe and interpret data in tables and diagrams 

Collect and treat data and make simulations for example with a computer 

Experimentation with chance 
Communication and problem solving
Knowledge 
Abilities 
Working with experiment and investigation 
Make hypotheses and using " try and error" in constructing professional concepts 

Formulate, solve and describe problems and in this connection choose different methods 

Cooperate with others in applying mathematics in problem solving 

In relation to mathematics investigate, systematize, and argue using concrete materials 

