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Project Details


112318-CP-1-2003-1 -IT-COMENIUS-C21


Project span

Project Coordinator

CAFRE Centro di Ateneo di Formazione e Ricerca Educativa
Università di Pisa

Contact person
Prof. Franco FAVILLI


Project Partners
(CZ) Univerzita Karlova v Praze

(DK) Skårup Seminarium

(FR) Institut Universitaire de Formation des Maîtres de Créteil

(IT) Università degli Studi di Firenze

(IT) Università degli Studi di Siena

(SK) Univerzita Mateja Bela

National Standards
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Danish Lower Secondary School Mathematics Standards

Numbers and algebra



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


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.





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




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




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



Whole numbers

Decimal numbers




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






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




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



 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


Franco Favilli and Giuseppe Fiorentino, eds.

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