Uruguay Primary School Curriculum - Mathematics (4th/5th Grade)

The Uruguayan primary mathematics curriculum emphasizes the development of mathematical thinking through active methodologies, problem-solving, and real-world connections. The curriculum is structured around "Tramos," with Tramo 3 covering 3rd and 4th grade and Tramo 4 covering 5th and 6th grade. The core content area is "Relationships and Functions," supported by three main axes: Number, Figure, and Variable.

Tramo 3 (3rd/4th Grade):

• Number: This axis focuses on developing a deeper understanding of natural and rational numbers.
• Natural Numbers: Counting, representation, order, place value, composition, decomposition (additive and multiplicative), and divisibility (by 2, 4, 5, 8, 10, 100). In 4th grade, this extends to five and six-digit numbers, divisibility by 4, 8, and 100, and exploring multiples and divisors.
• Rational Numbers: Fractions (halves, thirds, fourths, fifths, sixths, eighths, ninths, tenths, twelfths, hundredths), decimal representation, number lines, and mixed numbers. Emphasis on understanding different representations and meanings of rational numbers (part-whole, quotient, operator, ratio, measure).
• Operations: Addition, subtraction, multiplication, and division with natural numbers, including algorithms, mental calculations, and estimation. Properties of multiplication (commutative, associative, identity, zero property, distributive). Multiplication and division with two-digit numbers in 4th grade. Introduction to operations with rational numbers in the context of problem-solving. Direct proportionality, scales, and percentages are introduced in 4th grade.
• Geometry:
• Plane Geometry: Relative positions of lines (parallel, perpendicular, intersecting), angles (concept, classification, measurement), polygons (properties, triangles, quadrilaterals, circles, circumference), and constructions using geometric tools. In 4th grade, focus on classifying triangles and quadrilaterals, exploring the sum of interior angles, and constructing figures with specific properties.
• Spatial Geometry: Polyhedra (characteristics, prisms, pyramids), non-polyhedra (sphere, cone, cylinder), and relative positions of planes in space (parallel, intersecting). In 4th grade, this includes distinguishing right parallelepipeds and exploring properties of prisms and pyramids.
• Statistics and Probability: Introduction to data collection, representation (lists, tables, graphs), and interpretation. Simple and compound events, tree diagrams, and relative frequencies are introduced. In 4th grade, students classify events as impossible, probable, or certain.
• Introduction to Algebra: Double, triple, quadruple in 3rd grade. Use of formulas and expressions for calculating values, and patterns with even and odd numbers in 4th grade.
• Magnitudes and Measurements: Angular amplitude, perimeter of triangles and polygons, the metric system (units of length, capacity, mass, and their conversions). In 4th grade, this extends to area and its calculation for quadrilaterals and triangles, and relationships between area and perimeter, and capacity and volume.

Tramo 4 (5th/6th Grade):

• Number:
• Natural Numbers: Five-digit and larger numbers, place value, composition, decomposition (additive, multiplicative, exponential), powers of 10, scientific notation, and divisibility (by 3, 6, 9, 1000). Prime and composite numbers are introduced in 5th grade.
• Rational Numbers: Decimals, fractions, mixed numbers, order, composition, decomposition, representation on the number line, quotient of natural numbers, density of rational numbers, and thousandths.
• Operations: Combined operations, properties, mental calculation with natural and rational numbers. Addition and subtraction of fractions with different denominators in 5th grade. Potentiation and its notation are introduced. Inverse proportionality is introduced in 6th grade. Percentage calculations, including VAT and other taxes, are covered in 6th grade.
• Geometry:
• Plane Geometry: Parallel lines, parallelograms (properties, classification, construction), polygons (inscribed, regular, non-regular, central angle, apothem, tessellations), convex polygons (properties, sum of interior angles), circle and circumference as geometric loci, axial symmetry, mediatrix, and construction algorithms. Tessellations with pentagons and hexagons are explored in 6th grade.
• Spatial Geometry: Prisms and pyramids (properties, nets, diagonals), relative positions of lines in space (coplanar, non-coplanar), parallel and perpendicular planes, regular polyhedra, and non-polyhedra (right cylinder and cone, sphere, nets). Relationships between vertices, edges, and bases of prisms and pyramids are explored in 6th grade.
• Statistics and Probability: Bar graphs, histograms, sample space. In 6th grade, circle graphs, measures of central tendency (mean, mode, median), and Laplace's Law are introduced.
• Introduction to Algebra: Generalizations about sums of even and odd numbers in 5th grade. Formulas for perimeter, area, and volume, and numerical value in 6th grade.
• Magnitudes and Measurements: The metric system (square meter, square centimeter, square kilometer, hectare), area (measurement, calculation, estimation), relationships between area and perimeter, capacity and volume, length of circumference and diameter, pi, calculation of lateral surface area of polyhedra and non-polyhedra, and the sexagesimal system. Volume and its relationship with mass and surface area are covered in 6th grade.

Methodological Orientations:

The curriculum emphasizes active learning methodologies, including STEAHM (Science, Technology, Engineering, Arts, Humanities, Math), problem-based learning, project-based learning, inquiry-based learning, and gamification. The focus is on student-centered learning, real-world connections, collaborative work, and the development of critical and creative thinking.

Evaluation:

Evaluation is competency-based, focusing on the student's ability to apply mathematical knowledge and skills in various contexts. It is formative, process-oriented, and global, taking into account the diversity of learners and learning styles. Reflection on errors is seen as an opportunity for learning and self-regulation. A variety of assessment tools are used, including rubrics, checklists, portfolios, and student productions.