National Guidelines for the Curriculum in kindergarten and the first cycle of' Education (2012 September) Mathematics contributes to the cultural formation of individuals and communities, developing the ability to put in close relationship "thinking " and "doing" and offering tools to perceive, interpret, and linking natural phenomena, concepts and artifacts built by man, everyday events. In particular, mathematics gives tools for the scientific description of the world and for a useful application in everyday life; it helps to develop the ability to communicate and discuss, to argue properly, to understand the views and arguments of others.

Students move with confidence in written and mental calculations with whole numbers and they are able to evaluate the opportunity to use a calculator. Students recognize the forms in space, relationships and structures found in nature or created by man. They describe, they denominate and classify figures based on geometric characteristics, they determine measures, they design and manufacture concrete models of various types. They use tools for geometric design (line, compass...) and the most common measuring instruments (meters, protractor...). They are able to research data to obtain informations and to construct representations (tables and graphs). They also extract informations from data presented in charts and graphs. They recognize and quantify, in simple cases, situations of uncertainty. The National Guidelines for the Curriculum : Successes for the Development of Skills at the end of primary school

They read and comprehend texts that involve logical and mathematical aspects. They are able to solve difficult problems in all areas of content while maintaining control on both the solution process and the results. They describe the procedure followed and recognizes solution strategies than their own. They build reasoning with assumptions, supporting their ideas and confronting the views of others. They recognize and use different representations of mathematical objects ( decimals, fractions, percentages, scale reduction...). They develop a positive attitude to mathematics, through meaningful experiences, that let them understand how the mathematical tools - that they learned to use - are useful to operate in reality.

Learning goals at the end of third class of primary school (9 years old) Numbers Counting objects or events, verbally and mentally, in the sense progressive and regressive, for jumps of two, three... Reading and write natural numbers in decimal notation, having awareness of positional notation; compare and order them, even representing them on the line. Carrying out mentally simple operations with natural numbers and verbalize calculation procedures. Knowing with certainty the tables of multiplication of numbers up to 10. Performing operations with natural numbers with the usual algorithms written. Reading, writing, comparing decimal numbers and representing them on the straight; performing simple additions and subtractions, also with reference to the coins or the result of simple measures.

Space and figures Perceiving their position in space and to estimate distances and volumes from their bodies. Communicating the position of objects in physical space, both compared to the subject and both compared to other people or objects, using appropriate terms (up/down, front/back, left/right, in/out). Running a simple path from the verbal description or by a drawing, describing a path that you are doing and giving instructions to someone because he performs a desired path. Recognizing, denominating and describing geometrical figures. Drawing geometric shapes and materials to build models in space. Reports, data and forecasts Sorting numbers, figures, objects based on one or more properties, using appropriate rappresentations, depending on the contexts and purposes. Arguing on the criteria that were used to create classifications and regulations assigned. Reading and representing data and reports with charts, diagrams and tables. Measuring sizes (lengths, time, etc.), using arbitrary units and conventional units and instruments (meter, clock, etc.).

Learning goals at the end of the fifth class of primary school Numbers Reading, writing, comparing decimal numbers. Perform the four operations with security, considering if resorting to the mental or written calculation or to the calculator, depending on the situation. Carrying out division with remainder of natural numbers; identifying multiple and partitions of a number. Estimating the result of an operation. Operating with fractions and recognizing equivalent fractions. Use decimals, fractions and percentages to describe everyday situations. Interpreting negative integers in concrete contexts. Representing the numbers known on line and use scales in meaningful contexts for science and technology. Knowing notation systems of the numbers that are or have been in use in places, times and other cultures.

Space and figures Describing, denominating and classifying geometric figures, identifying significant elements and symmetry, also in order to reproduce them by themselves. Playing a figure based on a description, using the appropriate instruments (squared paper, ruler and compass, teams, geometry software). Using the Cartesian plane to locate points. Building materials and using models in space and plan in order to support a first display capabilities. Recognizing figures rotated, translated and reflected. Relations, data and forecasts Representing public relations and data and, in important situations, using representations to obtain information to formulate an opinion and to take decisions. Using notions of frequency, trend and arithmetic means, if appropriate to the type of data given. Representing problems with tables and charts that express their structure. Using the Main Unit for lengths, angles, areas, volumes/capacity, time intervals, masse, to make weights and measures estimates. Switching from one unit to another one, limited to common units more used, also in the context of Monetary System. In concrete situations, of a pair of events guessing and beginning to argue what is more likely, giving a first quantification in more simple cases, or recognizing if they are events equally likely. Recognizing and describing regularity in a sequence of code numbers or figure.

Comparing and measuring angles using properties and tools. Using and distinguishing between the concepts of squareness, parallelism, horizontality, verticality. Playing in scale a figure assigned (using, for example, the squared paper). Determining the perimeter of a figure using the most common formulas or other proceedings. Determining the area of rectangles and triangles and other shapes for breakdown or using the most common formulas. Recognizing flat representations of three-dimensional objects, identifying points of several view of the same object (top, front, etc).