San Marino Scuola Elementare (Fifth Year) Curriculum - Mathematics

The San Marino elementary school mathematics curriculum for fifth year emphasizes a practical approach to mathematics, integrating it with student experiences and real-world applications. The curriculum aims to equip students with the necessary tools to interpret and interact with the world around them. Learning is structured around problem-solving, encouraging students to explore situations, identify key issues, and develop conceptual and operational understanding. Language plays a crucial role, with a focus on connecting natural language with mathematical language and fostering clear and coherent explanations of mathematical processes.

The curriculum is organized around four core content areas: Numbers and Calculations, Space and Figures, Data and Predictions, and Relationships and Functions. These areas are revisited throughout the elementary school years, building upon prior knowledge and deepening understanding in a spiral progression. The curriculum also emphasizes the interconnectedness of these areas, highlighting how different learning components contribute to a robust and enduring understanding of mathematics.

Numbers and Calculations:

• Competencies: Students are expected to read, write, and perform calculations with natural and rational numbers, including fractions, decimals, and percentages. They should be able to estimate and accurately determine calculation results using mental math, written algorithms, or tools. Students are also expected to understand the properties of operations and apply them in various contexts.
• Learning Objectives:
• Read and write whole numbers and decimals based on place value.
• Recognize tenths, hundredths, thousandths, etc., in a decimal number.
• Read and write fractions.
• Recognize, in simple cases, the equivalence between two fractions and between a fraction and a decimal.
• Perform the four operations with whole numbers and decimals.
• Perform approximate calculations.
• Estimate the result of an operation, including with decimals.
• Understand the properties of operations.
• Perform simple operations with fractions.
• Compare ratios expressed as percentages, fractions, etc.
• Recognize and use simple percentages in real-world contexts.
• Recognize multiples and divisors of a natural number.
• Use the properties of multiples and divisors.
• Understand notation systems and calculation methods used in other eras or cultures.

Space and Figures:

• Competencies: Students should recognize and use the properties of plane and spatial figures to describe, classify, and reproduce simple shapes, objects, and movements. They should be able to determine measurements using tools, calculations, or other strategies. Students are also expected to use geometric drawing and measurement tools effectively.
• Learning Objectives:
• Describe and classify geometric figures in the plane and space.
• Recognize the elements and significant characteristics of a figure (angles, diagonals, heights, parallel or perpendicular elements, symmetries, etc.).
• Draw geometric figures using various tools (ruler, set square, compass).
• Use a Cartesian coordinate system to locate points and describe positions.
• Reproduce a figure to scale on a grid.
• Recognize the result of a rigid motion in the plane (rotation, translation, reflection).
• Recognize and draw parallel or perpendicular segments.
• Draw angles of a given amplitude using a protractor.
• Determine the perimeter of a figure, explaining the procedure followed.
• Determine the area of simple figures (triangles, rectangles, etc.) using formulas or other procedures (decomposition, difference).
• Understand the fundamental characteristics of circles.

Data and Predictions:

• Competencies: Students should collect, represent, and interpret data to extract information. They should begin to recognize situations of uncertainty.
• Learning Objectives:
• Use units and subunits of measurement for length, angle amplitude, area, capacity, time, weight (mass), temperature, and estimate these quantities in concrete cases.
• Recognize and perform simple measurement equivalences.
• Identify the appropriate unit of measurement in a given situation.
• Conduct simple surveys to collect data.
• Discuss, organize, and classify the data collected in a survey.
• Represent relationships and data with tables, graphs, diagrams, and pie charts.
• Represent time sequences of data.
• Read and interpret data represented in different forms.
• Interpret and use the information contained in a graph.
• Understand and determine the mode and arithmetic mean of a data set.
• Compare, in simple cases, the probability of two events.

Relationships and Functions:

• Competencies: Students should solve problems in different mathematical areas, explain the process followed, and justify their procedures.
• Learning Objectives:
• Use tables, graphs, diagrams, or symbols to express relationships.
• Represent a procedure/relationship with a diagram or flowchart.
• Interpret and use symbols to express relationships, for example, between the measurements of a geometric figure.