The document describes the Spanish mathematics curriculum for secondary school students aged 12-16. It is divided into four years (ESO 1-4). The curriculum covers topics in numbers, algebra, geometry, functions/graphs, statistics, and probability. In the later years (ESO 3-4), students can choose between Option A (terminal math) or Option B (preparing for further math study). Both options cover the same core topics in greater depth and complexity each year.

1. THE SPANISH MATHS
CURRICULUM OF E.S.O
12-16-year-old students

2. E.S.O. 12-16 years old students
(Obligatory secondary Education)
1st ESO
2nd ESO Common Maths curriculum
3rd ESO
Maths option A.- Terminal (For those
that will not need further knowledge of
4th ESO Maths)
Maths option B.- (Preparing for further
studies needing Maths knowledge)

3. First year of ESO
Numbers  The Naturals
 Divisibility.
 Fractions and decimals
 The Integers. Operations
 Combined operations
 Powers of natural indices
 Magnitudes. DMS
Currency units. €, $, converting currency units
 Percentages
 Ratios and proportions.
 Directly proportional magnitudes
 Mental calculation strategies

4. First year of ESO
Algebra Use of variables to represent numbers in
formulae
Translating word problems into an
algebraic form
Identifying regularities in sequences of
numbers

5. First year of ESO
Geometry Plane geometry elements: lines, angles and segments
Drawing parallel and perpendicular lines, angle and
segment bisectors.
Measuring angles
Triangles and quadrilaterals: elements, classification, area,
perimeter, relations
Construction of regular polygonals
Circle, circumference, arc and circular sectors
Axial symmetry

6. First year of ESO
Functions  The Cartesian axis
and graphs
 Graphing and identifying points
 Tables and graphs
 Interpreting graphs
Statistics and Data collection
Probability
Tables. Frequencies
Graphics: construction an reading
Making a guess about simple random events and
checking it by iterative experiences

7. Second year of ESO
Numbers  Divisibility: Prime factorization
 The L.C.F. and the G.C.M
 Equivalent fractions. The Lowest terms form. Reducing
to common denominator
 Operations with fractions, decimals and Integers
 Order of operations. Brackets.
 Powers. Laws of powers. The standard form
 Rounding
 Time and angles measuring. º; ; .
 Percentages, decimals and fractions
 Percent increase and decrease
 Direct and inverse proportionality

8. Second year of ESO
Algebra  Describing relations and laws through algebraic
language
 Obtaining formulae and n-terms by identifying
patterns
 Evaluating algebraic expressions
 Linear binomials
 Linear equations
 Solving problems through lineal equations
 Identifying regularities in sequences of numbers

9. Second year of ESO
Geometry  Right triangles. The Pythagorean Theorem
 Similarity. Similar plane figures.
 Similarity ratio Enlargements and reductions.
Scales
 Basic elements on 3D geometry: points, lines,
planes
 Parallel and perpendicular lines and planes
 Polyhedrons. Elements and types
 Regular polyhedrons. Laws
 The sphere. Description and laws

10. Second year of ESO
Functions  Graphing data from a table
and graphs  Describing phenomena given by a table
 Interpreting monotony, continuity and extremes
in graphs
Statistics and  Discrete variables
Probability  Absolute, relative and cumulative frecuencies
 Graphics: bars and pie charts
 Mean, median and mode for a few discrete data

11. Third year of ESO
Numbers  Rational numbers. Comparing, ordering and graphing on
a number line
 Decimals and fractions. Exact and periodic decimals
 Operations with fractions and decimals
 Order of operations. Brackets.
 Integers exponents powers. Laws. Operating in
standard form. Using the calculator
 Rounding and errors
 Time and angles measuring. The sexagesimal system.
 Word problems involving direct and inverse
proportionality. Proportional distributions
 Simple interest. Composed percentages

12. Third year of ESO
Algebra  Sequences of Integers and Rational numbers.
Recurring sequences. Identifying patterns
 Arithmetic and geometric sequences
 Translating word problems into algebraic language.
 Polynomials. Evaluating polynomials. Operations.
 Linear equations and systems of equations
 Quadratic equations
 Solving problems through equations and systems

13. Third year of ESO
Geometry  Revising plane geometry
 Loci
 Theorem of Thales. Dividing a segment in proportional
pieces
 Solving problems by the Pythagorean and Thales
theorems
 Translations, rotations and reflections on the plane
 Revising 3d geometry
 Polyhedrons symmetry planes
 Spheres. Plane sections
 The Earth. Coordinates. Maps reading
 Volume and areas calculation

14. Third year of ESO
Functions  Diferent forms of presenting a function
and graphs  Graphing functions defined algebraically, through tables
or by statements
 Graphs.- Monotony, continuity, extremes, symmetry and
periodicity
 Linear functions. Solving problems by linear functions
Statistics  Discrete and continuous variables
and  Interpreting tables of frequencies and charts
Probability  Grouped data. Histograms, line and pie charts
 Graphics: bars and pie charts
 Mean, median, mode , quartiles, range and standard
deviation
 Variation coefficient. Comparing distributions
 Random events. Frequencies
 Probability (Laplace)

15. Fourth year of ESO - Option A
Numbers  Operating with Integers, fractions and decimals
 Irrationals
 Standard form. Decimals and fractions. Exact and periodic
decimals
 Powers with fractions as exponent. Operating with
radicals
 Direct and inverse proportionality
 Percent increase and decrease
 Simple interest. Composed percentages
 Using the spread sheet to organize and solve common
and financial problems
 Intervals. Graphing numbers on the Real line

16. Fourth year of ESO - Option A
Algebra  Evaluating algebraic expressions
 Sum, subtraction and product of polynomials
 Polynomial identities
 Simultaneous linear equations
 Solving word problems through equations
 Solving equations by succeeding approximations

17. Fourth year of ESO - Option A
Geometry  Solving problems by the Pythagorean and Thales theorems
 Solving common problems by calculating lengths, areas
or volumes
 Cartesian coordinates. Distances between points
Functions  Functions. Studying function graphs
and graphs  Graphs characteristics.- Monotony, continuity, extremes,
symmetry and periodicity
 Interpreting phenomena given by statements, formulae,
tables or graphs
 Using TIC to study functions

18. Fourth year of ESO - Option A
Statistics  Design of statistical surveys on simple situations
and  Determining whether a sample is representative or not
Probability  Elaborating and interpreting tables of frequencies and
charts on discrete variables. Spread sheet
 Mean, median, mode , quartiles, range and standard
deviation
 Grouped data. Classes. Histograms, line and pie charts
 Random experiments. Random events. Frequency and
probability
 Composed experiments.- Tree diagrams and
contingence charts

19. Fourth year of ESO - Option B
Numbers  Non periodic decimals. Irrational numbers
 The Reals. Representation on the number line. Intervals
 Rounding.
 Powers with fractions as exponent. Operating and
reducing radicals
 Combined operations with Real numbers
 Operating with percentages. Composed interest
 Using the calculator to operate with all kind of real
numbers

20. Fourth year of ESO - Option B
Algebra  Roots of a polynomial. Integers roots.
 Factoring polynomials
 The synthetic division. Polynomial identities
 Linear and quadratic equations
 Solving higher than 2 degree polynomial equations
 Reducing algebraic fractions
 Simultaneous linear equations
 Solving word problems through equations
 One- unknown inequalities and simultaneous
inequalities.

21. Fourth year of ESO - Option B
Geometry  Similarity and scales. Rate of similarity for lengths,
areas or volumes
 The Theorem of Thales. Indirect measures
 Trigonometric ratios of acute angles. Relations.
 Solving right triangles. Solving problems
 Cartesian coordinates. Distances between points.
Graphing lines

22. Fourth year of ESO - Option B
Functions  Functions. Algebraic expression. Domain and graphs
and graphs  Graphs characteristics.- Monotony, continuity,
extremes, symmetry and periodicity
 Study of linear, quadratic, inverse, exponential and
logarithmic functions
 Piece-wise functions
 Variation rate
 Interpreting phenomena given by statements,
formulae, tables or graphs
 Using TIC to study functions

23. Fourth year of ESO - Option B
Statistics  Design of statistical surveys on simple situations
and  Determining whether a sample is representative or not
Probability  Elaborating and interpreting tables of frequencies and charts
on discrete variables. Spread sheet
 Mean, median, mode , quartiles, range and standard deviation
 Grouped data. Classes. Histograms, line and pie charts
 Random experiments. Random events. Frequency and
probability
 Counting techniques. Combinatory
 Composed experiments.- Tree diagrams and contingence
charts
 Conditioned probability