Spain 1º ESO School Syllabus - Mathematics

This entry details the topics covered in a 1º ESO Mathematics course based on a textbook from I.E.S. Andres de Vandelvira, designed for a bilingual program.

Unit 1: Numbers

• Number Systems: Cardinal numbers (one, two, three...), ordinal numbers (first, second, third...), and Roman numerals. Includes reading and writing large numbers, place value, and the use of "and," "a," and "one." Covers special cases for zero: "nought," "zero," "O," "nil," and "love" in different contexts.
• Decimals: Introduction to decimal fractions, place value, and reading decimals.
• Fractions and Percentages: Basic concepts of fractions and percentages.

Unit 2: Powers

• Powers and Exponents: Definition of powers, bases, and exponents (indices). Includes special cases for squares and cubes. Covers operations with powers: multiplication, division, and power of a power. Introduces the concept of square roots and estimating square roots.
• Standard Form: Expressing large numbers using powers of 10.

Unit 3: Multiples and Factors

• Multiples: Definition and examples of multiples.
• Factors: Definition and examples of factors.
• Prime Numbers: Definition of prime numbers and the Sieve of Eratosthenes.
• Divisibility Rules: Rules for divisibility by 2, 3, 4, 5, 6, 8, 9, and 11.
• Common Multiples and Factors: Finding common multiples and factors, including the lowest common multiple (LCM) and highest common factor (HCF). Includes prime factorization.

Unit 4: Fractions

• Fractions: Definition of fractions, numerators, and denominators. Includes reading fractions, equivalent fractions, comparing and ordering fractions, and simplifying fractions to their simplest form.
• Operations with Fractions: Adding, subtracting, multiplying, and dividing fractions. Covers multiplying fractions by whole numbers and calculating fractions of a quantity.
• Improper Fractions and Mixed Numbers: Converting between improper fractions and mixed numbers.

Unit 5: Decimal Numbers

• Decimals: Place value and reading decimal numbers.
• Operations with Decimals: Adding, subtracting, multiplying, and dividing decimals.
• Rounding Decimals: Rounding decimal numbers to different place values.
• Converting Fractions to Decimals: Converting fractions to decimals, including repeating decimals and irrational numbers.

Unit 6: Integers

• Integers: Introduction to positive and negative integers and the number line. Includes comparing integers and absolute value.
• Operations with Integers: Adding, subtracting, multiplying, and dividing integers. Covers the order of operations (BEDMAS).

Unit 7: Measurements

• Metric System: Introduction to the metric system and its units: meter, square meter, cubic meter, liter, and gram. Includes metric prefixes (deca, hecto, kilo, deci, centi, milli, mega, giga, tera, micro, nano, pico) and converting between units.
• Imperial Units: Introduction to imperial units (mile, yard, foot, inch, acre, gallon, pint, quart, ton, stone, pound, ounce) and converting between imperial and metric units.
• Temperature: Introduction to Celsius and Fahrenheit scales and converting between them.

Unit 8: Ratio and Percentages

• Ratios: Definition of ratios and comparing ratios. Includes simplifying ratios and expressing ratios in the form 1:n or n:1.
• Proportionality: Direct and inverse proportionality. Includes solving proportions.
• Ratios with Multiple Parts: Ratios with three or more parts.
• Percentages: Definition of percentages and converting between percentages, decimals, and fractions. Includes calculating percentages of quantities, calculating the number when the percentage is known, expressing ratios/fractions as percentages, estimating percentages, and percentage increase/decrease.

Unit 9: Algebra and Equations

• Variables: Introduction to variables and algebraic expressions.
• Expressions: Evaluating expressions and expanding brackets.
• Monomials: Definition of monomials, coefficients, and literal parts. Includes operations with monomials: addition, subtraction, and multiplication.
• Factoring: Factoring algebraic expressions by finding common factors.
• Equations: Definition of equations, unknowns, and solutions. Includes solving equations using basic rules (expanding expressions, moving terms, combining like terms, dividing/multiplying).

Unit 10: Geometry, Angles

• Basic Terms: Points, lines, rays, line segments, intersection, and parallel lines.
• Angles: Definition of angles, vertices, and sides. Includes naming angles, angle bisectors, measuring angles in degrees, types of angles (acute, obtuse, right, straight, complete turn), related angles (complementary, supplementary, vertical), operations with angles (addition, subtraction, multiplication, division), angles in polygons (triangles, quadrilaterals, n-sided polygons, regular polygons), angles in a circle (central, inscribed), and symmetric shapes.

Unit 11: Polygons and 3-D Shapes

• Triangles: Classifying triangles by sides (equilateral, isosceles, scalene) and angles (acute, obtuse, right). Includes triangle equality, points and lines associated with triangles (perpendicular bisectors, circumcentre, altitudes, orthocentre, angle bisectors, incentre, medians, barycentre), and the Pythagorean theorem.
• Quadrilaterals: Properties of special quadrilaterals (rectangle, square, rhombus, parallelogram, trapezium/trapezoid, kite).
• Regular Polygons: Definition and properties of regular polygons, including circumcircle, circumcenter, radius, apothem, and central angle.
• Circles and Circumferences: Definitions and lines in a circle (radius, diameter, chord, arc, sector, segment, tangent, secant). Includes positions of circles (concentric, eccentric, interior, exterior, tangent, secant).
• Polyhedrons: Definition and components of polyhedrons (faces, edges, vertices, diagonals, dihedral angles). Includes regular polyhedrons (tetrahedron, cube, octahedron, dodecahedron, icosahedron), cuboids, prisms, pyramids, and Euler's formula.
• Solids of Revolution: Cylinders, cones, and spheres.

Unit 13: Graphs

• Coordinate Plane: Plotting points on a coordinate plane (x-axis, y-axis, origin, ordered pairs, coordinates).
• Graphs of Functions: Independent and dependent variables, formulas, and conversion graphs.
• Handling Data: Categorical and numerical data (discrete, continuous), frequency tables, bar charts, pie charts, and pictograms.