 # Danish Lower Secondary School Mathematics Standards

## Numbers and algebra

### 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

Cultural-historical 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

### 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

### 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

### 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 Situationsummary of mathematics taught at the primary level

## Numbers and algebra

### 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

### 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

### 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

### 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

This page comes from the LOSSTT-IN-MATH Project website
http://losstt-in-math.dm.unipi.it