Argentina Educación Secundaria Ciclo Básico (1er año) - Matemática

This section details the curriculum for Matemática in the first year of Ciclo Básico of Secundaria in Argentina, based on the Núcleos de Aprendizajes Prioritarios (NAP). The NAPs provide a common foundation for teaching across the country, established through agreements reached within the Consejo Federal de Educación.

General Objectives:

The curriculum aims to foster the following in students:

• Confidence in their problem-solving abilities and formulating questions.
• A conception of mathematics where results are a necessary consequence of applying specific relationships.
• Willingness to defend their viewpoints, consider and debate others' ideas, and draw conclusions, accepting errors as part of the learning process.
• Interpretation of information presented orally or in writing (texts, tables, formulas, graphs, algebraic expressions), with the ability to switch between representations as needed.
• Development of problem-solving procedures tailored to the situation.
• Interpretation and production of texts containing mathematical information, using appropriate language.
• Comparison and analysis of problem-solving approaches, assessing their validity and suitability.
• Formulation and validation of general conjectures and statements, progressing from empirical arguments to more general ones.

Specific Learning Objectives - First Year:

The following learning objectives are prioritized for the first year:

Number and Operations:

• Understanding and using rational numbers in various problem situations, including interpreting, recording, communicating, and comparing integers in different contexts (e.g., temperatures, sea level, card games).
• Comparing integers, finding distances between them, and representing them on the number line.
• Interpreting rational numbers as quotients.
• Using different representations of rational numbers (fractions, decimals, scientific notation, points on the number line) and justifying their equivalence.
• Analyzing differences and similarities between the properties of integers (Z) and rational numbers (Q) (order, discreteness, and density).
• Understanding and using operations between rational numbers in different expressions, explaining their properties, and interpreting models that give meaning to addition, subtraction, multiplication, division, and exponentiation in Z.
• Using exponentiation (with integer exponents) and roots in Q.
• Analyzing operations in Z and their properties as an extension of those in N.
• Using and analyzing calculation strategies with rational numbers, selecting the appropriate type of calculation (mental and written, exact and approximate, with and without a calculator) and the way to express the numbers involved.
• Using the hierarchy and properties of operations in calculations.
• Exploring and stating properties related to divisibility in N.

Algebra and Functions:

• Using relationships between variables in problem situations, including interpreting relationships in tables, graphs, and formulas in various contexts (numerical patterns, direct and inverse proportionality).
• Modeling uniform variations and expressing them using the most appropriate representation.
• Explaining and analyzing properties of direct proportionality functions.
• Creating and comparing formulas to analyze variations in perimeters, areas, and volumes as a function of changes in dimensions of figures and bodies.
• Creating formulas to represent numerical patterns in N and analyzing their equivalences.
• Using equations and other algebraic expressions in problem situations, including making and analyzing statements about properties of operations or divisibility criteria, progressing from oral to symbolic expression.
• Transforming algebraic expressions to obtain equivalent expressions, using different properties when solving equations of the type ax + b = cx + d.
• Using linear equations with one variable as an expression of a condition on a set of numbers and analyzing their solution set.

Geometry and Measurement:

• Analyzing and constructing figures, reasoning based on properties, in problem situations, including determining points that meet distance conditions and constructing circles, mediatrices, and bisectors as geometric loci.
• Exploring different triangle constructions and reasoning about necessary and sufficient conditions for congruence.
• Constructing polygons using a non-graduated ruler and compass, justifying the procedures used.
• Formulating conjectures about relationships between different types of angles based on parallelogram properties and providing arguments to validate them.
• Analyzing statements about figure properties and arguing their validity, recognizing the limits of empirical proofs.
• Analyzing relationships between sides of triangles whose measurements are Pythagorean triples and interpreting some proofs of the Pythagorean theorem based on area equivalence.
• Understanding the process of measuring and calculating measurements in problem situations, including estimating and calculating quantities, choosing the unit and form of expression that is most convenient based on the situation and required precision, and recognizing the inherent inaccuracy of all measurements.
• Exploring relationships between bodies with equal lateral area and different volume or with the same volume and different lateral areas.

Probability and Statistics:

• Interpreting and creating statistical information in problem situations, including organizing discrete and bounded data sets to study a phenomenon, communicate information, and/or make decisions, analyzing the data collection process.
• Identifying different variables (qualitative and quantitative), organizing data, and creating appropriate graphs.
• Interpreting the meaning of mean and mode to describe the data being studied.
• Recognizing and using probability as a way to quantify uncertainty in problem situations, including comparing probabilities of different events.
• Determining the relative frequency of an event through real or simulated experimentation and comparing it with the theoretical probability.

This information is based on publicly available information and may not represent the full scope of the curriculum. Consult official Ministry of Education resources for the most up-to-date information.