Buenos Aires, Argentina

The Mathematics Curriculum in Primary and Lower Secondary Grades

In 2004, the Secretary of Education of the City of Buenos Aires approved the current primary mathematics curriculum, an adaptation of the 1986 curriculum for primary education (Resolution No. 365/SED/2004).⁶

At the secondary level, different types of schools share a core mathematics curriculum, which was established in 2009.⁷ The main types of secondary schools are: bachiller, liberal arts schools that offer the option of specializing in the upper grades in social science, science, physics and mathematics, arts, sports, graphic arts, and pedagogy; comercial, schools that focus on accounting, finance, business, and economics; and technical-professional schools that offer vocational training in areas such as agriculture, electricity, mechanics, and construction. In the lower secondary grades, the curriculum is similar for each type of school with variations depending on each school’s field of specialization.

Exhibit 2 summarizes the mathematics content objectives for Grade 4, and Exhibit 3 summarizes the mathematics content objectives for Grade 8 (first year of secondary school).

Exhibit 2: City of Buenos Aires Fourth Grade Mathematics Content Objectives

Subject Domains		Content Objectives
Numbers	Number systems	Reading and writing numbers as reference units using thousands, millions, or billions Solving problems that require deeper analysis of place value Locating numbers on a number line Knowing the rules of the Roman numeral system
Operations	Addition and subtraction of natural numbers	Solving problems involving an amount that is modified successively; comparison of debts between people; diverse operations; and information presented in charts and graphs
	Multiplication problems with natural numbers	Solving problems involving direct proportionality; multiplication using rectangular arrays; combining the four arithmetic operations; and combination strategies
	Integer division	Solving problems involving distribution; analysis of the remainder; iteration of a process of addition or subtraction; finding the remainder using a calculator; constructing division algorithms
	Divisibility	Solving problems involving multiples and factors of natural numbers Defining multiples, divisors, common multiples, and common divisors
	Exact and approximate calculations	Performing mental addition and subtraction Estimating solutions of multiplication and division operations and quotients
Geometry	Exploring polygons through construction	Constructing polygonal figures with straight angles Identifying the elements of polygons (e.g., sides, diagonals, vertices)
	Circumference and circles	Reproducing figures with a circumference or arc using a ruler, square, and compass Constructing squares and rectangles using an ungraded square and compass Solving problems by defining and using circumference as a set of points equidistant from the center of a circle
	Properties of triangles	Knowing the conditions for constructing a triangle Recognizing the properties of triangles (e.g., one side is less than the sum of the other two) Reproducing open and closed polygons Recognizing acute, right, and obtuse angles Working with angle bisectors
	Measurement	Measuring length, capacity, weight, and time (e.g., using meters and centimeters, clocks and calendars); and estimating measurements through comparison Measuring perimeter, area, and volume; calculating the perimeter of polygons using rulers and other tools made ad hoc; and estimating perimeter

Exhibit 3: City of Buenos Aires Eighth Grade Mathematics Content Objectives (Lower Secondary Level)

Subject Domains		Content Objectives
Numbers and Algebra	Natural numbers	Writing formulas that calculate the nth step of a process that meets a certain pattern Writing formulas for the transformation between two equivalent forms of a mathematical expression Validating solutions using the distributive property and common factors
	Integers	Calculating integers by subtracting natural numbers Representing integers on the number line Ordering, adding, subtracting, and multiplying integers Using the number line to study relationships among addition, multiplication, and ordering Determining the validity of ordering relationships, using the properties of operations, and interpreting algebraic expressions Analyzing how different calculators work
	Positive rational numbers	Working with fractions in different contexts (e.g., measurement, proportions, and commensurable segments) Understanding the ordering of rational numbers Understanding the relationship between fractions and decimals Calculating with fractions (e.g., multiplication in areas and proportionality) Understanding powers and roots of rational numbers Understanding powers with natural- and whole-number exponents Understanding exponentiation and order Using the √ (square root) key on the calculator
Functions and Algebra	Graphic representations of functions	Interpreting and producing graphs in the Cartesian plane, representing different situational contexts with Cartesian graphs Reading charts and making inferences Understanding the limitations of graphs in representing phenomena Identifying related variables and understanding the differences among them Generating the reverse image of a point in the Cartesian plane Identifying functions using tables of values Understanding the relationship between tables and Cartesian graphs for functions with continuous and discrete domains Understanding the advantages of different forms of graphic representations Understanding the limitations of graphic representations
	Introduction to linear functions	Analyzing processes that grow or shrink at a constant rate Understanding discrete and linear processes Understanding and using formulas to depict continuous processes Understanding linear functions as they depict uniform growth Calculating slope and intercept on graphs of linear functions Differentiating between direct proportional growth and linear, but not proportional, growth Analyzing tables of functions of proportion Finding slope and the constant of proportionality in a table of values Creating algebraic linear models Solving linear equations with one variable graphically
Geometry and Measurement	Construction of triangles	Constructing figures, including circumferences and circles Using a compass and computer to construct different figures Constructing triangles with two or three given elements, from the definition of circumference Discussing feasibility and uniqueness of constructions Developing criteria to determine congruence of triangles, and exploring, developing, and validating hypotheses based on these criteria Constructing special triangles (e.g., right, isosceles, equilateral)
	Constructions with unscaled ruler and compass	Understanding properties of segment bisectors Understanding parallel and perpendicular lines Constructing congruent angles and angle bisectors
	Construction of quadrilaterals	Constructing parallelograms given different measurements (e.g., sides, angles, diagonals, and height) Understanding the properties of quadrilaterals underlying their construction Understanding congruence between pairs of angles Understanding properties of parallelograms Discussing possible criteria for determining congruence of quadrilaterals and comparing with criteria developed for determining congruence of triangles Constructing quadrilaterals Understanding whether multiple constructions are possible given one set of measurements
Statistics and Probability		Interpreting graphs that appear in the media Comparing and analyzing different graphic representations, identifying their advantages and disadvantages Understanding the definitions of population and sample Identifying variables