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