THE SPANISH MATHSCURRICULUM OF E.S.O 12-16-year-old students
E.S.O. 12-16 years old students(Obligatory secondary Education)   1st ESO   2nd ESO         Common Maths curriculum   3rd ...
First year of ESONumbers    The Naturals           Divisibility.           Fractions and decimals           The Intege...
First year of ESOAlgebra   Use of variables to represent numbers in           formulae          Translating word problem...
First year of ESOGeometry   Plane geometry elements: lines, angles and segments           Drawing parallel and perpendic...
First year of ESOFunctions       The Cartesian axisand graphs                Graphing and identifying points            ...
Second year of ESONumbers    Divisibility: Prime factorization           The L.C.F. and the G.C.M           Equivalent ...
Second year of ESOAlgebra    Describing relations and laws through algebraic            language           Obtaining for...
Second year of ESOGeometry    Right triangles. The Pythagorean Theorem            Similarity. Similar plane figures.    ...
Second year of ESOFunctions        Graphing data from a tableand graphs       Describing phenomena given by a table     ...
Third year of ESONumbers    Rational numbers. Comparing, ordering and graphing on            a number line           Dec...
Third year of ESOAlgebra    Sequences of Integers and Rational numbers.            Recurring sequences. Identifying patte...
Third year of ESOGeometry    Revising plane geometry            Loci            Theorem of Thales. Dividing a segment i...
Third year of ESOFunctions      Diferent forms of presenting a functionand graphs     Graphing functions defined algebra...
Fourth year of ESO - Option ANumbers    Operating with Integers, fractions and decimals           Irrationals          ...
Fourth year of ESO - Option AAlgebra    Evaluating algebraic expressions           Sum, subtraction and product of polyn...
Fourth year of ESO - Option AGeometry      Solving problems by the Pythagorean and Thales theorems              Solving ...
Fourth year of ESO - Option AStatistics     Design of statistical surveys on simple situationsand            Determining...
Fourth year of ESO - Option B Numbers    Non periodic decimals. Irrational numbers            The Reals. Representation ...
Fourth year of ESO - Option BAlgebra    Roots of a polynomial. Integers roots.           Factoring polynomials          ...
Fourth year of ESO - Option BGeometry  Similarity and scales. Rate of similarity for lengths,               areas or volu...
Fourth year of ESO - Option BFunctions  Functions. Algebraic expression. Domain and graphsand graphs  Graphs characteris...
Fourth year of ESO - Option BStatistics   Design of statistical surveys on simple situationsand          Determining whe...
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The maths curriculum ESO

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The maths curriculum ESO

  1. 1. THE SPANISH MATHSCURRICULUM OF E.S.O 12-16-year-old students
  2. 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. 3. First year of ESONumbers  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. 4. First year of ESOAlgebra Use of variables to represent numbers in formulae Translating word problems into an algebraic form Identifying regularities in sequences of numbers
  5. 5. First year of ESOGeometry 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. 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. 7. Second year of ESONumbers  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. 8. Second year of ESOAlgebra  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. 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. 10. Second year of ESOFunctions  Graphing data from a tableand graphs  Describing phenomena given by a table  Interpreting monotony, continuity and extremes in graphsStatistics and  Discrete variablesProbability  Absolute, relative and cumulative frecuencies  Graphics: bars and pie charts  Mean, median and mode for a few discrete data
  11. 11. Third year of ESONumbers  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. 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. 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. 14. Third year of ESOFunctions  Diferent forms of presenting a functionand graphs  Graphing functions defined algebraically, through tables or by statements  Graphs.- Monotony, continuity, extremes, symmetry and periodicity  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 standard deviation  Variation coefficient. Comparing distributions  Random events. Frequencies  Probability (Laplace)
  15. 15. Fourth year of ESO - Option ANumbers  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. 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. 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. 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 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. 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. 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 simultaneous inequalities.
  21. 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. 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 and logarithmic functions  Piece-wise functions  Variation rate  Interpreting phenomena given by statements, formulae, tables or graphs  Using TIC to study functions
  23. 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 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

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