1. THE SPANISH MATHSCURRICULUM 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 ESONumbers The Naturals Divisibility. Fractions and decimals The Integers. Operations Combined operations Powers of natural indices Magnitudes. DMSCurrency units. , $, converting currency units Percentages Ratios and proportions. Directly proportional magnitudes Mental calculation strategies 4. First year of ESOAlgebra Use of variables to represent numbers in formulaeTranslating word problems into an algebraic formIdentifying regularities in sequences of numbers 5. First year of ESOGeometry Plane geometry elements: lines, angles and segments Drawing parallel and perpendicular lines, angle andsegment 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 ESOFunctions The Cartesian axisand graphs Graphing and identifying points Tables and graphs Interpreting graphsStatistics and Data collectionProbability Tables. Frequencies Graphics: construction an reading Making a guess about simple random events and checking it by iterative experiences 7. Second year of ESONumbers Divisibility: Prime factorization The L.C.F. and the G.C.M Equivalent fractions. The Lowest terms form. Reducingto common denominator Operations with fractions, decimals and Integers Order of operations. Brackets. Powers. Laws of powers. The standard form Rounding Time and angles measuring. ; ; . Percentages, decimals and fractions Percent increase and decrease Direct and inverse proportionality 8. Second year of ESOAlgebra Describing relations and laws through algebraiclanguage Obtaining formulae and n-terms by identifyingpatterns Evaluating algebraic expressions Linear binomials Linear equations Solving problems through lineal equations Identifying regularities in sequences of numbers 9. Second year of ESOGeometry 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 ESOFunctions Graphing data from a tableand graphs Describing phenomena given by a table Interpreting monotony, continuity and extremesin graphsStatistics and Discrete variablesProbability Absolute, relative and cumulative frecuencies Graphics: bars and pie charts Mean, median and mode for a few discrete data 11. Third year of ESONumbers Rational numbers. Comparing, ordering and graphing ona number line Decimals and fractions. Exact and periodic decimals Operations with fractions and decimals Order of operations. Brackets. Integers exponents powers. Laws. Operating instandard form. Using the calculator Rounding and errors Time and angles measuring. The sexagesimal system. Word problems involving direct and inverseproportionality. Proportional distributions Simple interest. Composed percentages 12. Third year of ESOAlgebra 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 ESOGeometry 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 ESOFunctions Diferent forms of presenting a functionand graphs Graphing functions defined algebraically, through tablesor by statements Graphs.- Monotony, continuity, extremes, symmetry andperiodicity Linear functions. Solving problems by linear functionsStatistics Discrete and continuous variablesand Interpreting tables of frequencies and chartsProbability Grouped data. Histograms, line and pie charts Graphics: bars and pie charts Mean, median, mode , quartiles, range and standarddeviation Variation coefficient. Comparing distributions Random events. Frequencies Probability (Laplace) 15. Fourth year of ESO - Option ANumbers Operating with Integers, fractions and decimals Irrationals Standard form. Decimals and fractions. Exact and periodicdecimals Powers with fractions as exponent. Operating withradicals Direct and inverse proportionality Percent increase and decrease Simple interest. Composed percentages Using the spread sheet to organize and solve commonand financial problems Intervals. Graphing numbers on the Real line 16. Fourth year of ESO - Option AAlgebra 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 AGeometry Solving problems by the Pythagorean and Thales theorems Solving common problems by calculating lengths, areas or volumes Cartesian coordinates. Distances between pointsFunctions Functions. Studying function graphsand 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 AStatistics Design of statistical surveys on simple situationsand Determining whether a sample is representative or notProbability Elaborating and interpreting tables of frequencies andcharts on discrete variables. Spread sheet Mean, median, mode , quartiles, range and standarddeviation Grouped data. Classes. Histograms, line and pie charts Random experiments. Random events. Frequency andprobability Composed experiments.- Tree diagrams andcontingence 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 BAlgebra 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 simultaneousinequalities. 21. Fourth year of ESO - Option BGeometry 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 BFunctions Functions. Algebraic expression. Domain and graphsand graphs Graphs characteristics.- Monotony, continuity,extremes, symmetry and periodicity Study of linear, quadratic, inverse, exponential andlogarithmic 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 BStatistics Design of statistical surveys on simple situationsand Determining whether a sample is representative or notProbability Elaborating and interpreting tables of frequencies and chartson 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