Download departamento didáctico de matemáticas. programación: para los

INSTITUTO DE ENSEÑANZA SECUNDARIA
"MIGUEL DE CERVANTES".
DEPARTAMENTO DIDÁCTICO DE MATEMÁTICAS.
PROGRAMACIÓN: PARA LOS CURSOS DE 1º Y 3º DE
E. S. O. BILINGÜE PARA
PADRES Y MADRES
CURSO ACADÉMICO 2015-2016
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Programación didáctica del Área de Matemáticas. Curso 2015-2016
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MATHEMATICS 1
UNIT 1: Natural Numbers
Evaluation Criteria
1.1. To establish equivalences among the different orders of units of the DNS.
1.2. To read and write numbers of any size.
1.3. To approximate numbers, by rounding, to different orders of units.
2.1. To add, subtract, multiply and divide natural numbers.
2.2. To resolve expressions with brackets and combined operations.
3.1. To resolve arithmetic problems with natural numbers that require one or more
operations.
3.2. To resolve arithmetic problems with natural numbers that require three or more
operations.
4.1. To interpret a reiterated multiplication as a power.
4.2. To calculate the value of simple powers.
4.3. To calculate the value of arithmetic expressions involving powers.
5.1. To mentally calculate the full square root of a number under 100 using the first ten
perfect squares.
5.2. To calculate square roots of numbers over 100 using the calculator.
Contents
NATURAL NUMBERS
• The Decimal Numeral System.
– Orders of units and equivalences.
– Reading and writing natural numbers.
– The number line. Representation of natural numbers on the line.
– Order in the series N.
• Approximations. Rounding of a given order of units.
OPERATIONS WITH NATURAL NUMBERS
• Adding and subtracting. Relations.
• Multiplication. Division: algorithm and relations with multiplication.
• Resolving expressions with brackets and combined operations. Application of the
order of operations.
• Mental calculation. Using personal strategies.
• Use of the four-operations calculator.
RESOLVING PROBLEMS
• Resolving arithmetic problems with natural numbers.
POWERS OF NATURAL NUMBERS
• Powers with natural base and exponent. Expression and nomenclature.
– Translation of products of equal factors to power format and vice versa.
• The square and the cube.
– Geometric meaning.
– Perfect squares. Memorising the squares of the first natural numbers.
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• Calculation of powers with natural exponents.
SQUARE ROOT
• Concept. Exact and approximate roots.
• Calculation of square roots. Calculation by trial and error. Approximations
• The square root on the calculator.
UNIT 2: Divisibility
Evaluation Criteria
1.1. To recognise whether there is a relation of divisibility between two numbers.
1.2. To recognise whether a number is a multiple or a divisor of another one.
2.1. To obtain all the divisors of a number.
2.2. To obtain the series of the first multiples of a number.
3.1. To identify the prime numbers under 30.
4.1. To resolve problems in which it is necessary to apply the concepts of multiple and
divisor.
Contents
THE RELATION OF DIVISBILITY
• Identifying the relation of divisibility between numbers.
• Determination of the existence (or non-existence) of the relation of divisibility between
two given numbers.
MULTIPLES AND DIVISORS OF A NUMBER
• To find out whether a number is a multiple or divisor of another.
• Obtaining the series of divisors of a number. Matching of elements.
• Obtaining the ordered series of multiples of a number.
• Prime numbers.
– Identifying-memorising the first prime numbers.
RESOLVING PROBLEMS
• Resolving problems of divisibility.
UNIT 3: Fractions
Evaluation Criteria
1.1. To graphically represent a fraction on a circular or rectangular surface.
1.2. To determine the fraction that corresponds to each part of a quantity.
1.3. To identify a fraction with the indicated quotient of two numbers. To convert from
fractions to decimals and vice versa (in very simple cases).
1.4. To calculate the fraction of a number.
2.1. To mentally compare fractions in simple cases (fraction larger or smaller than the
unit, or 1/2; fractions with the same numerator, etc.) and be capable of justifying their
answers.
2.2. To compare two fractions, converting them into decimal format.
3.1. To calculate fractions equivalent to a given one.
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3.2. To recognise whether two fractions are equivalent (using the equality of crossed
products).
3.3. To simplify fractions. To obtain the irreducible fraction of a given one.
4.1. To add and subtract fractions with the same denominator.
4.2. To reduce simple fractions to a common denominator.
4.3. To add and subtract fractions with different denominators (first reducing to a
common denominator).
5.1. To multiply fractions.
5.2. To divide fractions.
6.1. To resolve some problems based on the different concepts of fraction (calculation
of the fractions, calculation of the part, calculation of the total, etc.).
6.2. To resolve problems of fractions with addition operations.
6.3. To resolve problems of fractions with multiplication operations.
6.4. To resolve problems in which the fraction of another fraction appears.
Contents
THE MEANINGS OF A FRACTION
• The fraction as part of the unit: representation, quantification of the different parts of a
whole, comparison of fractions with the unit.
• The fraction as an indicated quotient.
– Transformation of a fraction into a decimal number.
– Transformation of a decimal into a fraction (only in simple cases).
– Comparison of fractions, after converting into decimal format.
• The fraction as an operator.
– Fraction of a quantity. Concept.
– Mechanisation of the calculation of the fraction of a number.
EQUIVALENCE OF FRACTIONS
• Identification and production of equivalent fractions.
– Identification from the graphic representation.
– Relation between the terms of two equivalent fractions (equality of crossed products).
• Simplification of fractions.
ADDING AND SUBTRACTING FRACTIONS
• Adding and subtracting fractions with the same denominator.
• Adding and subtracting fractions with different denominators.
– Adding and subtracting with the unit.
– Using intuitive methods in very simple cases (graphic support).
– Reducing to a common denominator.
MULTIPLICATION AND DIVISION OF FRACTIONS
• Product of fractions: product of an integer and a fraction, product of two fractions,
fraction of a fraction.
• Quotient of fractions: quotient of two fractions, quotient of whole numbers and
fractions.
RESOLVING PROBLEMS
• Resolving problems with fractions.
UNIT 4: Decimal numbers
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Evaluation Criteria
1.1. To read and write decimal numbers.
1.2. To know the equivalences between the different orders of units.
2.1. To order series of decimal numbers.
2.2. To associate decimal numbers with the corresponding points on the number line.
2.3. Given two decimal numbers, to write another one between them.
3.1. To add and subtract decimal numbers.
3.2. To multiply decimal numbers.
3.3. To divide decimal numbers (with decimal figures in the dividend, in the divisor or in
both).
3.4. To multiply and divide by the unit followed by zeros.
4.1. To resolve decimal arithmetic problems which require one or two operations.
Contents
THE DECIMAL NUMERAL SYSTEM
• Orders of decimal units.
– Equivalences between the different orders of units.
• Reading and writing decimal units.
DECIMALS ON THE NUMBER LINE
• Representation of decimals on the number line.
• Ordering decimal numbers.
• Interpolation of a decimal between two others.
OPERATIONS WITH DECIMAL NUMBERS
• Addition and subtraction.
• Multiplication.
• Division.
– Decimal approximation of a quotient between integers.
– Dividing a decimal by an integer.
– Division with decimal divisor.
• Mental calculation with decimal numbers. Estimations.
RESOLVING PROBLEMS
• Resolving arithmetic problems with decimal numbers.
UNIT 5: Integers
Evaluation Criteria
1.1. To use integers to quantify and transmit information related to everyday situations.
1.2. In a series of integers, to distinguish natural numbers from those which are not.
2.1. To associate integers with the corresponding points on the number line.
2.2. To order series of integers.
3.1. To carry out additions and subtractions with integers and correctly express
processes and results.
3.2. To know the rule of signs and correctly apply it in multiplications and divisions of
integers.
3.3. To correctly apply the order of operations in expressions with combined
operations.
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3.4. To resolve expressions with combined operations.
Contents
POSITIVE AND NEGATIVE NUMBERS
• Identification of situations which make negative numbers necessary.
• The series of integers.
– Differentiating between integer and natural number.
– Identification of the series of integers.
• Integers on the number line. Representation.
• Ordering a series of integers.
ADDITION AND SUBTRACTION OF INTEGERS
• Addition (subtraction) of two positive numbers, two negative numbers and one
positive and one negative number.
• Using strategies for the calculation of additions and subtractions with more than two
positive and negative numbers.
PRODUCT AND QUOTIENT OF INTEGERS
• Multiplication and division of two integers.
– Rule of signs.
• Combined operations with integers.
– Order of priority of operations.
– Resolving expressions with combined operations.
UNIT 6 : Initiation to Algebra
Evaluation Criteria
1.1. To translate statements in natural language into algebraic language, related to
unknown or indeterminate quantities.
1.2. To express numerical relations or properties by means of algebraic language.
2.1. To identify the degree, the coefficient and the literal part of a monomial.
2.2. To calculate the numerical value of an algebraic expression for given values of the
letters.
3.1. Addition and subtraction of monomials.
4.1. To differentiate members, terms and unknowns.
4.2. To recognise whether or not a given value is the solution to an equation.
5.1. To transpose terms in an equation (immediate cases: a + x = b; a – x = b; x– a = b;
ax = b; x/a = b).
5.2. To solve equations with first-level polynomial expressions (without denominators).
6.1. To solve problems of numerical relations.
6.2. To solve simple arithmetic problems (ages, budgets...).
6.3. To solve geometry problems.
Contents
ALGEBRAIC EXPRESSIONS
• Algebraic language.
– Use of algebra.
– Translation of statements in natural language into algebraic language.
• Interpreting expressions in algebraic language.
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• Numerical value of an algebraic expression when the values of the letters are
specified.
• Codification, in algebraic language, of relations, properties, generalisations, etc.
• Monomials. Concept and elements.
– Coefficient, literal part, degree.
– Similar monomials.
OPERATIONS WITH ALGEBRAIC EXPRESSIONS
• Addition and subtraction of monomials.
• Reduction of algebraic expressions.
– Elimination of brackets in expressions with additions and subtractions.
• Product of a number and a monomial.
• Product of a number and an addition or subtraction of monomials.
EQUATIONS AND THEIR ELEMENTS
• Equations. Concept and elements.
– Terms, members, unknowns.
– Equivalent equations.
– Solutions to an equation.
• First-level equations.
• Solving simple equations by intuitive methods: mental calculation, trial and error, etc.
• Verification of the solutions to an equation (verification of equality).
SOLVING FIRST-LEVEL EQUATIONS WITH AN UNKNOWN
• First techniques.
– Transposition of terms.
• Solving equations with first-level polynomial expressions.
SOLVING PROBLEMS WITH THE HELP OF EQUATIONS
• Use of equations as a tool to solve problems.
– Assigning the unknown.
– Codification of the elements of the problem depending on the unknown chosen.
– Construction of the equation.
– Resolution. Interpretation and explanation of the solution.
UNIT 7: The Decimal Metric System
Evaluation Criteria
1.1. To know the equivalences between the different multiples and submultiples of the
metre, the litre and the gram.
1.2. To change the unit of quantities of length, capacity and weight.
1.3. To transform quantities of length, capacity and weight from complex to noncomplex form, and vice versa.
1.4. To operate with quantities in complex form.
2.1. To know the equivalences between the different multiples and sub-multiples of the
square metre.
2.2. To change the unit of surface areas.
2.3. To transform complex and non-complex quantities of surface area and vice versa.
2.4. To operate with quantities in complex form.
Contents
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THE DECIMAL METRIC SYSTEM
• The fundamental magnitudes: length, mass and capacity.
– Units and equivalences.
– Complex and non-complex expressions.
• Operations with quantities of the same magnitude.
– Changes of unit.
– Change from complex to non-complex form and vice versa.
– Operations with complex and non-complex quantities.
• Recognition of some traditional units of measurement.
SURFACE AREA
• Measurement of surface areas by the direct counting of squared units.
• Units and equivalences.
• Differentiating between length and surface area.
• Units of surface area of the DMS and their equivalences.
– Changes of unit.
– Complex and non-complex expressions. Change from complex to non-complex and
vice versa.
• Recognition of some traditional measurements of surface area.
UNIT 8: Proportionality
Evaluation Criteria
1.1. To recognise whether there is a relation of proportionality between two
magnitudes, differentiating direct and inverse proportionality.
2.1. To complete tables of directly proportional values and obtain pairs of equivalent
fractions from them.
2.2. To obtain the unknown term in a pair of equivalent fractions, from the other three
known ones.
3.1. To resolve problems of direct proportionality using the reduction to the unit method
and the rule of three.
4.1. To identify each percentage with a fraction.
4.2. To calculate the indicated percentage of a given quantity.
5.1. To resolve problems of direct percentages.
Contents
RELATIONS BETWEEN MAGNTITUDES
• Identification and differentiation of directly and inversely proportional magnitudes.
• The relation of direct proportionality.
– Tables of directly and inversely proportional values.
– Equivalent fractions in tables of directly proportional values.
– Application of the properties of equivalent fractions to complete pairs of values in
tables of direct proportionality.
PROBLEMS OF DIRECT PROPORTIONALITY
• Reduction to the unit method.
• Rule of three.
PERCENTAGES
• The percentage as a fraction.
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• Relation between percentages and decimal numbers.
• The percentage as a proportion.
CALCULATION OF PERCENTAGES
• Mechanisation of the calculation. Different methods.
• Rapid calculation of simple percentages.
UNIT 9: Angles
Evaluation Criteria
1.1. To classify and name angles according to their openness and relative positions.
1.2. To name the different types of angles determined by a straight line which cuts two
parallels and identify relations of equality among them.
1.3. To correctly use the protractor to measure and draw angles.
2.1. To know the value of the sum of the angles of a polygon and use it to make direct
measurements of angles.
Contents
ANGLES
• Elements. Nomenclature. Classification. Measurement.
– Construction of complementary, supplementary, consecutive and adjacent angles,
etc.
– Construction of angles of a given amplitude.
• Given angles when a straight line cuts through a system of parallels.
– Identification and classification of different, equal angles, determined by a straight
line which cuts through a system of parallels.
ANGLES IN POLYGONS
• Sum of the angles of a triangle. Justification.
• Sum of the angles of a polygon of n sides.
• Interior, exterior and central angle in a polygon
• Application of the angular relations in polygons to obtain indirect measurements of
angles in different figures.
UNIT 10: Polygons and circumference
Evaluation Criteria
1.1. Given a triangle, to recognise the class it belongs to, depending on its sides and its
angles, and explain why.
1.2. To draw a triangle of a given class (for example obtuse or isosceles).
1.3. To identify bisectors, medians and heights of a triangle and know some of their
properties.
1.4 To know the four center of a triangle: incenter, circumcenter, barycenter,
orthocenter
2.1. To recognise parallelograms from their basic properties (parallelism of opposite
sides, equality of opposite sides, diagonals that intersect at the mid-point, etc.).
2.2. To identify each type of parallelogram and its characteristic properties.
2.3. To describe a given quadrilateral, naming properties that characterise it.
3.1. To distinguish regular polygons from non-regular ones and explain why they are
one or the other.
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3.1. To recognise the relative position of a straight line and a circumference from the
radius and the distance from its centre to the straight line, and draw them.
Contents
TRIANGLES
• Classification.
• Construction.
• Relations between sides and angles.
• Medians: barycenter.
• Heights: orthocenter.
• Angle bisectors: incenter
•Perpendicular bisectors : circumcenter
QUADRILATERALS
• Classification.
• Parallelograms. Properties.
• Trapeziums.
• Trapezoids.
REGULAR POLYGONS
• Elements and relations between them.
CIRCUMFERENCE
• Elements and relations .
• Relative positions of straight line and circumference
UNIT 11: The area of plane figures
Evaluation Criteria
1.1. To calculate the area and the perimeter of a plane figure (drawn) giving it all the
elements it needs.
– A triangle, with the three sides and a height.
– A parallelogram, with the two sides and the height.
– A rectangle, with its two sides.
– A rhombus, with the sides and the diagonals.
– A trapezium, with its sides and the height.
– A circle, with its radius.
– A regular polygon, with the side and the apothem.
1.2. To calculate the area and the perimeter of a circular sector, giving it the radius and
the angle.
1.3. To calculate the area of figures which must be broken down and recomposed to
identify another known figure.
.
2.1 To understand the relationship between the three sides of a right triangle.
2.2 To use the theorem to solve problems involving right triangles and other shapes
that have right triangles within the shape:
-when one side of a triangle is missing, use theorem to find missing side
-when given the length of one side of a hexagon, use theorem to calculate the area
Contents
AREAS AND PERIMETERS OF QUADRILATERALS
• Square. Rectangle.
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• Any parallelogram. Reasoning and obtaining the formula. Application.
• Rhombus. Explanation of the formula. Application.
• Trapezium. Explanation of the formula. Application.
AREA AND PERIMETER OF THE TRIANGLE
• The triangle as half a parallelogram.
• The right-angled triangle as a special case.
AREAS OF POLYGONS
• Area of a polygon by means of triangulation.
• Area of a regular polygon.
MEASUREMENTS OF CIRCLES AND ASSOCIATED FIGURES
• Perimeter and area of the circle.
• Area of a circular sector.
• Area of an annulus.
PYTHAGOREAN THEOREM
• Calculate the hypotenuse when we know the catheti.
• Calculate one cathetus when we know the two other sides in a right triangle.
UNIT 12: Tables and Graphs
Evaluation Criteria
1.1. To represent given points by their coordinates.
1.2. To assign coordinates to points given graphically.
2.1. To interpret points within a context.
3.1. To prepare a table of frequencies form a series of data.
3.2. To interpret simple tables of frequencies and double-entry tables.
4.1. To represent the data in a table of frequencies by means of a bar chart.
Contents
CARTESIAN COORDINATES. FUNCTIONAL RELATIONS
• Negative and fractional coordinates.
• Representation of points on the plane. Identification of points by means of its
coordinates.
• Interpretation of functional graphs of situations related to the student’s world.
STATISTICAL DISTRIBUTIONS
• Tables of frequencies. Construction. Interpretation.
• Statistical graphs. Interpretation. Construction of some very simple ones.
– Bar charts.
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MATHEMATICS 3
UNIT 1: Fractions and decimals
Evaluation Criteria
1.1. To identify whether two fractions are equivalent.
1.2. To obtain various fractions equivalent to one which is given.
1.3. To calculate the unknown term in two equivalent fractions, knowing the other three.
1.4. To simplify fractions until the irreducible fraction is obtained.
1.5. To reduce fractions to a common denominator.
2.1. To add and subtract fractions.
2.2. To multiply and divide fractions.
3.1. To solve expressions with additions, subtractions, multiplications, division and
brackets.
4.1. To associate a fraction with a part of a whole.
5.1. To express a fraction in decimal form.
6.1. To calculate the fraction of a number.
7.1. To solve problems in which the fraction of a number is calculated.
7.2. To solve problems of additions and subtractions of fractions.
7.3. To solve problems of multiplication and/or division of fractions.
7.4. To solve problems in which the concept of a fraction of a fraction is used.
Contents
THE MEANINGS OF A FRACTION
• The fraction as the indicated quotient.
– Transformation of a fraction into a decimal number.
• The fraction as an operator.
– Calculation of the fraction of a quantity.
EQUIVALENT FRACTIONS
• Identification and production of equivalent fractions.
– Equality of cross products.
• Simplification of fractions.
• Reduction of fractions to a common denominator.
ADDITION AND SUBTRACTION OF FRACTIONS
• Addition and subtraction of fractions with the same denominator.
• Addition and subtraction of a whole number and a fraction.
• Addition and subtraction of fractions with different denominators.
– Development of personal strategies (in very simple cases).
– Reduction of fractions to the lowest common denominator.
– Application of the different methods and algorithms for the addition and subtraction of
fractions, after reduction to a common denominator.
MULTIPLICATION AND DIVISION OF FRACTIONS
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• Product of two fractions. Product of a whole number and a fraction.
• Fraction of a fraction.
• Quotient of two fractions.
• Quotient of fractions and whole numbers.
SOLVING PROBLEMS WITH FRACTIONS
• Problems involving the fraction of a quantity.
• Problems of the addition and subtraction of fractions.
• Problems of the product and quotient of fractions.
• Problems in which the fraction of another fraction appears.
UNIT 2: Powers and roots
Evaluation Criteria
1.1. To interpret a reiterated multiplication as a power.
1.2. To reduce powers using the properties of powers
2.1 To raise to a negative power or to zero
3.1. To mentally calculate the full square root of a number under 100 using the first ten
perfect squares.
3.2. To operate with radicals
Contents
POWERS OF INTEGER NUMBERS
• Powers with natural base and exponent. Expression and nomenclature.
– Translation of products of equal factors to power format and vice versa.
• Calculation of powers with natural exponents.
• Calculation of powers with negative exponents.
SQUARE AND CUBE ROOT
• Concept. Exact and approximate roots.
• Calculation of roots. Calculation by trial and error. Approximations
RADICALS
• Concept.
• Add, products and powers of radicals
SETS OF NUMBERS
• Rational numbers
• Irrationals numbers
UNIT 3: Algebraic expressions
Evaluation Criteria
1.1. To identify the degree, the coefficient and the literal part of a monomial.
1.2. To calculate the numerical value of an algebraic expression for given values of the
letters.
2.1. Addition and subtraction of monomials or polynomials
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2.2. To multiply a number by a monomial or by a polynomial
2.3 To multiply two polynomials
2.4 To divide two polynomials
2.3. To simplify simple algebraic fractions.
Contents
ALGEBRAIC EXPRESSIONS
• Numerical value of an algebraic expression when the values of the letters are
specified.
• Polynomials. Concept and elements.
– Coefficient, literal part, degree.
– Similar monomials.
OPERATIONS WITH ALGEBRAIC EXPRESSIONS
• Addition and subtraction of monomials.
• Multiplication and division of monomials.
• Addition and subtraction of polynomials.
• Multiplication and division of polynomials.
• Reduction of algebraic expressions.
– Elimination of brackets in expressions with additions and subtractions.
· A sum squared, difference squared, sum times difference
UNIT 4: Equations
Evaluation Criteria
1.1. To differentiate members, terms and unknowns.
1.2. To recognise whether or not a given value is the solution to an equation.
1.3. To write an equation whose solution is a given value.
2.1. To transpose terms in an equation (immediate cases: a + x = b; a – x = b; x– a = b;
ax = b; x/a = b).
2.2. To solve equations with first-level polynomial expressions with denominators.
3.1. To solve complete second degree equations.
3.2. To solve incomplete second degree equations.
3.2. To know how many solutions an equation has without solving it.
4.1. To solve problems of numerical relations.
4.2. To solve simple arithmetic problems (ages, budgets...).
4.3. To solve geometry problems.
Contents
EQUATIONS AND THEIR ELEMENTS
• Equations. Concept and elements.
– Terms, members, unknowns.
– Equivalent equations.
– Solutions to an equation.
• First-level equations.
• Solving simple equations by intuitive methods: mental calculation, trial and error, etc.
• Verification of the solutions to an equation (verification of equality).
SOLVING FIRST-LEVEL EQUATIONS WITH AN UNKNOWN
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• First techniques.
– Transposition of terms.
• Solving equations with first-level polynomial expressions with denominators
SOLVING SECOND DEGREE EQUATIONS
• Solving complete second degree equations
• Solving incomplete second degree equations.
SOLVING PROBLEMS WITH THE HELP OF EQUATIONS
• Use of equations as a tool to solve problems.
– Assigning the unknown.
– Codification of the elements of the problem depending on the unknown chosen.
– Construction of the equation.
– Resolution. Interpretation and explanation of the solution.
UNIT 5: Systems of linear equations
Evaluation Criteria
1.1. To differentiate members, terms and unknowns.
1.2. To recognise whether or not a given value is the solution to an equation.
2.1. To solve system of equations by substitution method.
3.1. To solve system of equations by elimination method.
4.1. To solve problems of numerical relations.
4.2. To solve simple arithmetic problems (ages, budgets...).
4.3. To solve geometry problems.
Contents
SOLVING SYSTEM OF EQUATIONS WITH TWO UNKNOWNS
• Method of substitution
• Method of elimination or reduction
SOLVING PROBLEMS WITH THE HELP OF SYSTEM OF LINEAR EQUATIONS
• Use of equations as a tool to solve problems.
– Assigning the unknowns.
– Codification of the elements of the problem depending on the unknown chosen.
– Construction of the equations.
– Resolution. Interpretation and explanation of the solution.
UNIT 6: Proportionality
Evaluation Criteria
1.1. To differentiate directly proportional magnitudes from those that are not.
1.2. To construct tables of values, related to directly proportional magnitudes.
2.1. To identify whether two fractions form a proportion.
2.2. To construct proportions from a table of directly proportional values.
2.3. To calculate the unknown term of a proportion.
3.1. To resolve simple problems of direct proportionality using the unitary method.
3.2. To apply the rule of three to solve problems of direct proportionality.
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4.1. To resolve simple problems of inverse proportionality using the unitary method.
4.2. To apply the rule f three to solve problems of inverse proportionality.
7.1. To prepare and interpret information in the form of percentages.
7.2. To identify certain percentages with simple fractions.
8.1. To mentally calculate simple percentages.
8.2. To use automated procedures and resources for the calculation of percentages.
9.1. To solve problems of direct percentages (calculation of the part, knowing the total
and the percentage).
9.2. To solve inverse percentage problems (calculation of the total, calculation of the
percentage).
9.3. To solve problems of percentage increases and decreases.
10.1. To know and apply the bank interest formula.
10.2. To solve problems of proportional distributions.
10.3. To solve problems of blends.
Contents
DIRECTLY PROPORTIONAL MAGNITUDES
• Identification of the relations of proportionality between different magnitudes.
• Tables of values. Relations.
CONCEPT OF PROPORTION
• Construction of proportions from the values of a table of direct proportionality.
• Calculating the unknown term of a proportion.
SOLVING PROBLEMS OF DIRECT PROPORTIONALITY
• Unitary method.
• Rule of three.
SOLVING PROBLEMS OF INVERSE PROPORTIONALITY
• Unitary method.
• Rule of three.
SOLVING PROBLEMS OF COMPOUND PROPORTIONALITY
• Unitary method.
• Rule of three.
PERCENTAGES
• The concept of the percentage.
• Calculation of percentages.
– Automation of the calculation of percentages.
– Rapid calculation of some percentages (50%, 25%, 10%).
– Mental calculation of simple percentages.
SOLVING PROBLEMS WITH PERCENTAGES
• Direct percentage problems (calculation of the part, knowing the total).
• Inverse percentage problems.
– Calculation of the total, knowing the part.
– Calculation of the percentage, knowing the total and the part.
• Problems of percentage increases and decreases.
BANK INTEREST
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• Concept of simple interest.
• Solving bank interest problems with the help proportionality procedures (reiteration of
the unitary method).
• Simple interest formula.
– Solving bank interest problems, applying the formula.
OTHER ARITHMETIC PROBLEMS
• Procedure for the resolution of proportional distribution problems.
• Procedure for the resolution of problems of blends.
UNIT 7: Progressions
Evaluation Criteria
1.1. To find the pattern in a set of numbers.
1.2. To write the “n” first terms in a sequence.
2.1. To write the Nth term of the sequence
3.1. To identify if a sequence is arithmetic.
3.1. To calculate the difference and determine the first term
4.1. To calculate the Nth term of an arithmetic term.
5.1 To add several terms in an arithmetic sequence.
6.1. To identify if a sequence is geometric.
7.1. To calculate the ratio and determine the first term
7.1. To calculate the Nth term of an geometric term.
8.1. To add several terms in a geometric sequence.
Contents
SEQUENCE
• Identification of sequences
• Calculating more terms of a sequence
·Calculating the Nth terms of a sequence
ARITHMETIC SEQUENCE
• Identification of arithmetic sequences
• Determining the first term, the difference and more terms
·Calculating the Nth terms of an arithmetic sequence.
• Calculating the sum of the “n” first terms in an arithmetic sequence.
GEOMETRIC SEQUENCE
• Identification of geometric sequences
• Determining the first term, the ratio and more terms
·Calculating the Nth terms of a geometric sequence.
• Calculating the sum of the “n” first terms in a geometric sequence.
UNIT 8: Plane geometry concepts
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Evaluation Criteria
1.1 To find unknown angles in polygons.
2.1. To calculate the surface area of triangles, quadrilaterals, regular and irregular
polygons, circles and associated figures, knowing the necessary data.
2.2. To calculate the surface area of triangles, quadrilaterals, regular and irregular
polygons, circles and associated figures, previously calculating the data which is
missing using Pythagoras´s theorem.
2.3. Given the lengths of the three sides of a triangle, to recognise whether or not it is
right-angled.
2.4. To calculate the unknown side of a right-angled triangle from the other two.
2.5. On a square or rectangle, to apply Pythagoras’s theorem to relate the diagonal to
the sides and calculate the unknown element.
2.6. On a rhombus, to apply Pythagoras’s theorem to relate the diagonals to the side
and calculate the unknown element.
2.7. On a right-angled or isosceles trapezium, to apply Pythagoras’s theorem to
establish a relation that makes it possible to calculate an unknown element.
2.7. On a regular polygon, to use the relation between the radius, apothem and side
and, applying Pythagoras’s theorem, to find one of these elements from the others.
2.8. To numerically relate the radius of a circumference to the length of a piece of string
and its distance to the centre.
2.9. To apply Pythagoras’s theorem in resolving simple geometry problems.
Contents
PYTHAGORAS’S THEOREM
• Relation between areas of squares.
• Applications of Pythagoras’s theorem.
– Calculation of one side of a right-angled triangle knowing the other two.
– Calculation of a segment of a plane figure from others which, with it, form a rightangled triangle.
– Identification of triangles and rectangles from the measurements of their sides.
AREAS OF PLANE FIGURES
– Quadrilaterals: rectangles, squares, rhombuses, trapeziums, etc.
– Triangles.
– Regular polygons.
– Circle and associated figures.
UNIT 9: Solids. Surface and volume of solids
Evaluation Criteria
1.1. To know and name the different components of a polyhedron (edges, apexes,
faces, side faces of prisms, bases of prisms and pyramids, etc.).
1.2. To select, among a series of figures, those which are polyhedrons and justify the
selection made.
1.3. To classify a series of polyhedrons.
1.4. To describe a polyhedron and classify it in accordance with the characteristics
outlined.
2.1. To schematically draw the development of a cuboid.
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2.2. To schematically draw the development of a prism.
2.3. To schematically draw the development of a pyramid.
3.1. Given a regular polyhedron, to explain its regularity, name it, analyse it, giving the
number of faces, edges, apexes, faces per apex, and schematically draw its
development.
3.2. To name the regular polyhedrons whose faces are a given regular polygon.
4.1. To identify, among a series of figures, those which are of revolution, name the
cylinders, cones, truncated cones and spheres and identify their elements (axis, bases,
generatrix, radius, etc.).
5.1. To draw freehand the development of a cylinder.
5.2. To draw freehand the development of a cone.
5.3. To draw freehand the development of a truncated cone.
6.1. To relate the generatrix, height and radius in a cone.
6.2. To relate the radius of a sphere, the distance from the centre to a plane and the
circumference in which they intersect.
7.1. To calculate the surface area of cuboids and cubes.
7.2. To calculate the surface area of prisms and cylinders.
8.1. To calculate the volume of prisms, cylinders, pyramids, cones and spheres, using
the corresponding formulas (the figure and the necessary data about it will be given).
8.2. To calculate the volume of a prism, having to previously calculate some of the data
to be able to apply the formula (for example, find the volume of a hexagonal prism
knowing the height and the edge of the base).
8.3. To calculate the volume of a pyramid with a regular base, knowing the side and
basic edges (or similar).
8.4. To calculate the volume of a cone knowing the radius of the base and the
generatrix (or similar).
9.1. To calculate the volume of compound bodies.
Contents
POLYHEDRONS
• Characteristics of polyhedrons.
– Elements of polyhedrons: faces, edges and apexes.
• Prisms.
– Classification according to the polygon of the bases.
– Development of a right prism.
• Parallelepipedons. Cuboids.
– The cube as a specific case.
• Pyramids: characteristics and elements.
– Development of a regular pyramid.
REGULAR POLYHEDRONS
• Description of the five regular polyhedrons.
• Development of regular polyhedrons.
THE BODIES OF REVOLUTION
• Right and oblique cylinders.
– Identification of cylinders.
– Development of a right cylinder.
• Cones.
– Identification of cones.
– Development of a right cone.
• The sphere.
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– Flat sections of the sphere. The great circle.
– Obtaining circles as flat sections of spheres.
AREAS OF THREE-DIMENSIONAL FIGURES
– Cuboids and cubes. Development and calculation of areas.
– Prisms. Development and calculation of areas.
– Cylinders. Development and calculation of areas.
– Pyramids. Development and calculation of areas.
– Cones. Development and calculation of areas.
– Spheres and associated figures. Calculation of areas.
VOLUME OF SPATIAL BODIES
• Volume of the cuboid. Volume of the cube.
– Calculating the volume of cuboids and cubes.
• Volume of prisms and cylinders.
– Calculating the volume of prisms and cylinders.
• Volume of pyramids and cones.
– Calculating the volume of pyramids and cones.
• Volume of a sphere.
– Calculating the volume of a sphere and associated figures.
• Resolving problems involving the calculation of volumes.
UNIT 10: Transformations of a plane. Mosaics
Evaluation Criteria
1.1 To translate, rotate and reflect a point or an object.
2.1 To find the vector of translation.
3.1 To determine the centre and the angle of a rotation.
4.1. To draw the line of symmetry.
5.1. To apply a combined transformation to a point or an object.
6.1 To do a mosaics from a basic figure.
Contents
TRANSLATION
• Translation by a vector
ROTATION
• Rotation about the origin at an angle of α.
REFLECTION
• Reflection along a line of symmetry.
COMBINED TRANSFORMATIONS
MOSAICS
UNIT 11: Functions.
Evaluation Criteria
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1.1 To know if a graph is a function.
1.2 To identify the dependent and independent variable
2.1. To recognise and represent a function, from the equation or the table of values.
3.1. To find the domain of a function.
4.1. To explain whether a function is increasing or decreasing.
4.2. To mark the points that represent a maximum or a minimum.
4.3. To identify periodic functions.
4.4. To identify whether a function is continue or discontinue
Contents
FUNCIONS AND THEIR GRAPHS
• Function. Independent and dependent variable.
– Using the appropriate vocabulary to describe and quantify functional situations.
– Graph, table of values, algebraic expression, context.
CHARACTERISTIC OF A FUNCTION
• Domain of definition.
• Function variation: Increase and decrease.
• Maxima and minima.
• Trends and periodicity.
• Continuity and discontinuity.
• General study of functions
PLOTTING GRAPHS
• Graphs and word problems.
UNIT 12: Linear functions
Evaluation Criteria
1.1. To recognise and represent a proportionality function, from the equation, and
obtain the slope of the corresponding straight line.
1.2. To recognise and represent a linear function from the equation and obtain the
slope of the corresponding straight line.
1.3. To obtain the slope of a straight line from its graph.
1.4. To identify the slope of a straight line and the point of intersection with the vertical
axis from its equation, given in the form y = mx + n.
1.5. To obtain the equation of a straight line from the graph.
1.6. To recognise a constant function from its equation or graphic representation. To
represent the straight line y = k, or write the equation of a straight line parallel to the
horizontal axis.
Contents
THE PROPORTIONALITY FUNCTION y = mx
Proportionality functions of the type y = mx.
– Use of the function y = mx to represent relations of proportionality.
• Slope of a straight line.
– Deduction of the slopes of straight lines from graphic representations or from two of
its points.
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THE LINEAR FUNCTION y = mx + b
• Linear functions: y = mx + b.
– Identification of y = mx + b with a straight line.
– Identification of the role represented by the parameters a and b of the equation y = ax
+ b.
– Representation of a straight line given by an equation and obtaining the equation
from a straight line drawn on squared paper.
THE CONSTANT FUNCTION y = k
• The constant function y = k.
– Recognition of the type of graph corresponding to a linear or constant function.
UNIT 13: Statics
Evaluation Criteria
1.1. To draw up and interpret simple statistical tables (related to discrete variables).
1.2. To draw up and interpret tables of frequencies related to statistical distributions
which require the grouping of data by ranges.
2.1. To represent and interpret statistical information given in a bar chart.
2.2. To represent and interpret statistical information given by means of a histogram.
3.1. To calculate the mean of the values taken by a statistical distribution.
3.2 To calculate the standard derivation of the values taken by a statistical distribution.
Contents
FREQUENCY
• Frequency. Table of frequencies.
• Drawing up frequency tables from the data collected:
– with isolated data.
– with data grouped into ranges (giving the ranges).
STATISTICAL GRAPHS
• Graphic representation of statistics.
– Bar charts.
– Histograms.
– Frequency polygon.
– Pie charts.
STATISTICAL PARAMETERS
• Statistical parameters:
– Mean.
– Standard derivation.
UNIT 14: Probability
Evaluation Criteria
1.1. To difference correctly between random experiment and no random experiment.
2.1. To obtain the sample space and the outcomes.
3.1. To apply the law of large numbers to calculate the probability of an event
4.1 To apply the rule of succession to calculate the probability of an event.
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Contents
RANDOM EVENTS
• Random experiment:
– Outcome.
– Sample space.
– Event.
PROBABILITY
• Probability of an event:
– Law of large numbers.
– Equally likely outcomes.
– Rule of succession.
METODOLOGÍA (Aspectos metodológicos – espacios, agrupamientos, tiempos, materiales y recursos
didácticos)
We begin learning the basic vocabulary and doing simple exercises. Then, step by step, the students
do more complicated activities until they are able to solve problems where they use any of the things
they have learnt so far.
The students are usually grouped in pairs
We use a Spanish textbook, an English textbook, worksheets and web pages. We also watch videos in
English to introduce basic math concepts and we play games to practice them.
We also have the help of an English language assistant in the classroom who works with the students
in their pronunciation and comprehension.
OBJETIVOS Y CONTENIDOS MÍNIMOS
Minimum objetives and contents are the same as in the other groups ( see the Spanish
programation)
INSTRUMENTOS PARA LA EVALUACIÓN Y CRITERIOS DE CALIFICACIÓN
80 %
Exams
x%
Homework and classwork
y%
attitude
z%
Notebook
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EVALUACIÓN DE LAS COMPETENCIAS BÁSICAS: relación con los instrumentos de evaluación
Information processing
and ICTs
Learning to learn
Autonomous learning
skills
Learning to learn
Social awareness and
citizenship
Mathematical
competency
Siendo x+y+z = 20 a criterio del profesor que imparta la asignatura
CRITERIOS DE CALIFICACIÓN EN ESO:
Para los alumnos que cursan la E.S.O. el Departamento de Matemáticas acuerda
cuantificar éstos como sigue:
1.- Pruebas objetivas: Se realizarán al menos dos por evaluación, a las que se
les hará una media ponderada, el primer examen se multiplicará por 1, el
segundo por 2, el tercero por 3 y así sucesivamente, dividiendo la suma de esas
notas entre la suma de esos pesos.
La calificación obtenida en éstas, supondrá el 80% de la calificación del alumno
en la correspondiente evaluación.
2.- Interés, participación en clase y realización de tareas encomendadas: se
asignará un 10% de la calificación.
3.- Cuaderno del alumno: se asignará un 10% de la calificación.
La calificación final del curso será la mayor de las calificaciones obtenidas entre
la media ponderada de las tres evaluaciones, asignando un peso de 1 a la 1ª, un
peso de 2 a la 2ª y un peso de 3 a la 3ª y de la obtenida en la calificación en la
3ª evaluación.
En la calificación de septiembre se tendrá únicamente en cuenta la nota obtenida
en la prueba realizada, valorándose ésta, hasta 10 puntos.
TEMPORALIZACIÓN DE LOS CONTENIDOS DEL ÁREA.
Se acuerda temporalizar los contenidos del Área de la siguiente manera:
Primero de E.S.O.:
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Primera Evaluación: Unidades 1, 2,3, 4 y 5.
Segunda Evaluación: Unidades 6, 7, 8 y 9. (sólo ángulos del tema 9)
Tercera Evaluación: Unidades 9, 10, 11, 12, 13 y 14.
Tercero de E.S.O.:
Primera Evaluación: Unidades 1, 2, 3, 4 y 5.
Segunda Evaluación: Unidades 6, 7, 8, 9 y 10.
Tercera Evaluación: Unidades 11, 12, 13 y 14.
RECUPERACION DE ALUMNOS PENDIENTES:
El Departamento ha acordado recuperar a los alumnos con la asignatura pendiente de cursos
anteriores como sigue: Se realizarán dos evaluaciones y una prueba final de recuperación para
aquellos alumnos que no hayan superado las mismas.
Para facilitar la recuperación de los alumnos, se facilitará a éstos relaciones de ejercicios. A tal
fin, se elaborará un fichero de pruebas para cada uno de los cursos. El mencionado fichero
estará en la página web del Instituto:
http://www.iesmigueldecervantes.es/index.php?option=com_content&view=article&id=236&Ite
mid=671
Las dudas que les puedan surgir en la resolución de los ejercicios se las resolverán el
profesorado del Departamento que les imparta docencia.
Los alumnos, entregarán la libreta con los ejercicios indicados resueltos, siendo esto condición
necesaria para poder aprobar la correspondiente evaluación.
Las fechas y distribución de materia en las distintas evaluaciones serán:
DISTRIBUCIÓN DE MATERIA PARA ALUMNOS PENDIENTES DE
MATEMÁTICAS DE CURSOS ANTERIORES.
CURSO ACADÉMICO 2014/15.
PRIMERO DE ESO:
1ª EVALUACIÓN: 1, 2, 3, 4, 5 y 6.
2ª EVALUACIÓN: 7, 8, 9, 10 y 11.
SEGUNDO DE ESO:
1ª EVALUACIÓN: 1, 2, 3, 4, 5 y 6.
2ª EVALUACIÓN: 7, 8, 9, 10 y 11 y 12.
TERCERO DE ESO:
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1ª EVALUACIÓN: 1, 2, 3, 4 y 5.
2ª EVALUACIÓN: 6, 7, 8 y 9.
PRIMERO DE BACHILLERATO:
CIENCIA Y TECNOLOGÍA
1ª EVALUACIÓN: 1, 2, 3, 4, 5 y 6.
2ª EVALUACIÓN: 7, 8, 9, 10 y 11.
HUMANIDADES Y CIENCIAS SOCIALES
1ª EVALUACIÓN: 1, 2, 3 y 4.
2ª EVALUACIÓN: 5, 6, 7, 8 y 11.
CALENDARIO DE RECUPERACIÓN DE ALUMNOS CON LA ASIGNATURA
DE MATEMÁTIAS PENDIENTE DE CURSOS ANTERIORES.
CURSO ACADÉMICO 2014/15.
ALUMNOS PENDIENTES DE 1º. DE ESO.
Primera prueba:
 Jueves, 22 de enero de 2015.
Segunda prueba:

Jueves, 16 de abril de 2015.
Prueba final:

Jueves, 4 de junio de 2015.
ALUMNOS PENDIENTES DE 2º. Y 3º. DE ESO.
Primera prueba:

Miércoles, 21 de enero de 2015.
Segunda prueba:
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
Miércoles, 15 de abril de 2015.
Prueba final:

Miércoles, 3 de junio de 2015.
ALUMNOS DE BACHILLERATO:
Primera prueba:

Martes, 20 de enero de 2015, a las 9,15 horas.
Segunda prueba:

Martes, 7 de abril de 2015, a las 9,15 horas.
Prueba final:

Martes, 28 de abril de 2015, a las 9,15 horas.
ACTIVIDADES EXTRAESCOLARES:
El Departamento de Matemáticas propone como actividad extraescolar realizar
una visita a la Alhambra con alumnado de 3º ESO con contenido matemático.
PLAN DE LECTURA:
En el Departamento de Matemáticas los alumnos leen los ejercicios en clase
además de las lecturas que hay en cada tema en su libro de manera comprensiva
para que sean capaces de interpretar lo que leen.
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