[4eso] Probability

The post contains the materials to develop 10 sessions on Probability.
Topics worked:
Random experiments, sample space, events, elementary/simple events, mutually-exclusive/incompatible events, non mutually-exclusive/compatible events, complementary events, independet events, probability definition and properties, probability function, probability assignment (equally likely events, relative frequency), conditional probability.

handouts for students
s1     s2     s3     s4     s5     s6     s7     s8     s9     s10

solutions
s1     s2     s3     s4     s5     s6     s7     s8     s9     s10

teacher guides
s1     s2     s3     s4     s5     s6     s7     s8     s9     s10

Activities in session1 are taken from BBC-GCSE Bitesize.
Session2 (theory & activities) is written in Spanish
Activities in session2 are taken from ¡Ajá! Paradojas que hacen pensar. Martin Gardner, RBA 2007

[4eso] Estadística

Materiales correspondientes a la unidad de Estadística de 4ESO, opción B. Pueden ser desarrollados en 10 sesiones.
Contenidos tratados:
Estadística descriptiva, población, muestra, variable estadística, gráficos estadísticos, parámetros de centralización, parámetros de dispersión, parámetros de posición, hoja de cálculo.

material fotocopiable
material alumnado       soluciones       material profesorado

hojas de cálculo (Excel)
enunciados       soluciones 

[4eso] Functions / Funciones

This post contains the materials to develop 14 sessions working with different types of functions.
Topics worked:
Function: definition and characteristics; types of functions: affine (straight line), quadratic (parabola) and rational (hyperbola), solving problems, use of GeoGebra.

Most of the sessions are planned to be carried out using laptops or tablets and GeoGebra. It is good for the students to draw what they are calculating.

handouts for students / material alumando
 s1   s2   s3   s4   s5   s6   s7   s8   s9   s10   s11   s12   s13   s14   [English]
 s1   s2   s3   s4   s5   s6   s7   s8   s9   s10   s11   s12   s13   s14   [Español]

solutions / soluciones
 s1   s2   s3   s4   s5   s6   s7   s8   s9   s10   s11   s12   s13   s14   [English]
 s1   s2   s3   s4   s5   s6   s7   s8   s9   s10   s11   s12   s13   s14   [Español]

teacher guide /guía profesorado
 s1   s2   s3   s4   s5   s6   s7   s8   s9   s10   s11   s12   s13   s14   [English]
 s1   s2   s3   s4   s5   s6   s7   s8   s9   s10   s11   s12   s13   s14   [Español]

Este post contiene los materiales para desarrollar 14 sesiones trabajando con diferentes tipos de funciones.
Contenidos trabajados:
Función: definición y características; tipos de funciones: afín (recta), cuadrática (parábola) y racional (hipérbola), resolución de problemas y uso de GeoGebra.

Muchas de las sesiones están pensadas para llevarse a cabo usando portátiles o tabletas y GeoGebra. Es bueno para los estudiantes visualizar lo que calculan.

unit plan / guión del tema
s1: definition, domain, range, intersecting points, symmetry and periodicity
      definición, dominio, imagen, puntos de corte, simetría y periodicidad.
s2: monotony, extrema, boundedness, solving problems
      monotonía, extremos, acotación, resolución de problemas.
s3: characteristics of a function (graphic and algebraic study), solving problems
      caracteríaticas de una función (estudio gráfico y algebraico), resolución de problemas.
s4: affine and linear functions: theory and examples
      funciones afines y lineales: teoría y ejemplos.
s5: characteristics of a function (graphic and algebraic study), quadratic functions: theory and examples
      características de una función (estudio gráfico y algebraico), funciones cuandráticas: teoría y ejemplos
s6: quadratic functions
      funciones cuadráticas
s7: characteristics of a function (graphic and algebraic study), affine and linear functions     
      características de una función (estudio gráfico y algebraico), funciones afines y lineales.
 s8: affine and quadratic functions, rational functions: theory and examples
       funciones afines y cuadráticas, funciones racionales: teoría y ejemplos.
s9: characteristics of a function (graphic study), rational functions, piecewise functions
      características de una función (estudio gráfico), funciones racionales, funciones a trozos.
s10: characteristics of a function (graphic study), quadratic and piecewise functions
        características de una función (estudio gráfico), funciones cuadráticas y a trozos
s11: quadratic and piecewise functions, solving problems
       funciones cuadráticas y a trozos, resolución de problemas.
s12: affine and piecewise functions, solving problems
        funciones afines y a trozos, resolución de problemas.
s13: characteristics of a function (algebraic study), affine and quadratic functions 
        características de una función (estudio algebraico), funciones afines y cuadráticas. 
s14: solving problems
        resolución de problemas

[4eso] Álgebra: ecuaciones, sistemas, inecuaciones

Materiales correspondientes a la segunda parte del bloque de álgebra de este curso.
Las referencias al libro de texto corresponden a Matemáticas 4ESOb, proyecto Los Caminos del Saber. Editorial Santillana, 2011.

álgebra II (alumnado)      álgebra 2 (soluciones)      álgebra 2 (profesorado)

Contenidos tratados:
Ecuaciones: bicuadradas, polinómicas, racionales e irracionales; sistemas de ecuaciones lineales y no lineales; resolución de problemas; inecuaciones grados 1, 2 y n>2

archivos GeoGebra
ecuación 1, ecuación 2, sistema lineal, sistema no lineal, inecuación

[4eso] Algebra: equations, systems, inequations

Follow the links below to get the materials to develop fifteen sessions on solving different types of equations, systems of equations and inequations.
Topics worked: biquadratic equations, polynomial equations, rational equations, irrational equations, systems of linear equations, systems of non-linear equations, inequations degree 1, inequations degree 2, inequations degree n>2, solving problems, use of GeoGebra.

session 1 (biquadratic equations): teacher guide, handouts, solutions
session 2 (polynomial equations): teacher guide, handouts, solutions 
session 3 (rational equations): teacher guide, handouts, solutions  
session 4 (irrational equations): teacher guide, handouts, solutions 
session 5 (irrational equations): teacher guide, handouts, solutions 
session 6 (solving equations): teacher guide, handouts, solutions 
session 7 (systems of linear equations): teacher guide, handouts, solutions
session 8 (systems of non-linear equations): teacher guide, handouts, solutions 
session 9 (systems of non-linear equations): teacher guide, handouts, solutions 
session 10 (solving problems): teacher guide, handouts, solutions 
session 11 (solving problems): teacher guide, handouts, solutions 
session 12 (inequations degree 1): teacher guide, handouts, solutions 
session 13 (inequations degree 2): teacher guide, handouts, solutions 
session 14 (inequations degree n>2): teacher guide, handouts, solutions 
session 15 (inequations degree n>2): teacher guide, handouts, solutions          

GeoGebra files
equation1, equation2, linear system, non-linear system, inequation     

[4eso] The set of the real numbers

This post contains the materials to develop nine sessions (55 minutes each) working with real numbers.
Topics worked: rational & irrational numbers, rational numbers as fractions, intervals, scientific notation, rounding numbers, approximations & errors, powers: integer & rational exponents, radicals, drawing real numbers, use of GeoGebra.

session 1 (the set of the real numbers): teacher guide, handouts, solutions
session 2 (from decimals to fractions): teacher guide, handouts, solutions 
session 3 (intervals): teacher guide, handouts, solutions  
session 4 (scientific notation): teacher guide, handouts, solutions
session 5 (errors & approximations): teacher guide, handouts, solutions 
session 6 (errors & approximations): teacher guide, handouts, solutions
session 7 (powers with integer exponents): teacher guide, handouts, solutions 
session 8 (powers with rational exponents): teacher guide, handouts, solutions 
session 9 (radicals): teacher guide, handouts, solutions       

draw real numbers
examples (GeoGebra files): ex1, ex2, ex3, ex4
assessment exercise: text, solution1, solution2, solution3, solution4

[4eso] Polynomials: operations, roots & factors

The set of the integer numbers Z, and the set of the polynomials with integer coefficients, Z[x] are  almost the same thing from an algebraic point of view. They have the same algebraic structure. In both sets you can factor their elements into the product of some simple elements (prime numbers and irreducible polynomials).

This post contains the materials to develop thriteen sessions (55 minutes each) working with polynomials.
Topics worked: algebraic expressions, numerical value, polynomials, algebraic operations, expand and simplify expressions, perfect squares, difference of two squares, Ruffini's rule, remainder theorem, polynomial roots and factors, plotting algebraic expressions, use of GeoGebra

session 1 (algebraic language): teacher guide, handouts, solutions
session 2 (numerical value + operations): teacher guide, handouts, solutions
session 3 (operations + draw algebraic expressions): teacher guide, handouts, solutions
GeoGebra: draw algebraic expressions
session 4 (drawing algebraic expressions): teacher guide, handouts, solutions
GeoGebra: deg 1 (explicit equation), deg 1 (implicit equation), deg 2(a), deg 2(b)
session 5 (Ruffini's rule): teacher guide, handouts, solutions
session 6 (the remainder theorem): teacher guide, handouts, solutions
session 7 (roots & factors): teacher guide, handouts, solutions
session 8 (roots & factors): teacher guide, handouts, solutions
GeoGebra: polynomial roots
session 9 (find the roots): teacher guide, handouts, solutions
session 10 (find the factors): teacher guide, handouts, solutions
session 11 (roots & factors): teacher guide, handouts, solutions
session 12 (algebraic fractions): teacher guide, handouts, solutions
session 13 (algebraic fractions): teacher guide, handouts, solutions

[4eso] El conjunto de los números reales

Materiales del tema de números reales. Como en ocasiones anteriores puedes encontrar las fotocopias que os pasé en clase y las soluciones detalladas de todas las actividades planteadas.

números reales (alumnado)             números reales (soluciones)

Contenidos tratados:
conjuntos de números, fracción generatriz, notación científica, errores y aproximaciones, potencias de exponente entero y racional, racionales.

[4eso] Assessment exercise 1. Polynomials: operations, roots & factors / Ejercicio de evaluación 1. Poliomios: operaciones, raíces y factores

Follow the link to get the handout of this first assessment exercise on Algebra.

Remember you can also find it in Moodle. 

assessment exercise 1

Topics worked:

operations with polynomials, Ruffini's rule, roots and factors of a polynomial

En el enlace siguiente puedes encontrar el texto del ejercicio de evaluación sobre Álgebra.

ejercicio de evaluación 1

Contenidos tratados:

operaciones con polinomios, regla de Ruffini, raíces y factores de un polinomio.

[2eso] Natural & integer numbers / Números naturales y enteros

Look here for the materials we are going to work on in class the next two weeks. Remember you can also find this handout in Moodle.
Natural & integer numbers
Topics worked:
Natural numbers, prime and composite numbers, divisibility, factors and multiples, highest common factor, lowest common multiple, integer numbers, operations with integer numbers. 

En el siguiente enlace puedes encontrar los materiales que vamos a trabajar en clase las próximas dos semanas.
Números naturales y enteros
Contenidos tratados:
Números naturales, números primos y compuestos, divisibilidad, divisores y múltiplos, máximo común divisor, mínimo común múltiplo, números enteros, operaciones con números enteros.

[2eso] Assessment exercise 1: statistics / Ejercicio de evaluación 1: estadística

Follow the link to get the handout of this first assessment exercise on Statistics.
Remember you can also find it in Moodle. 
assessment exercise 1
Topics worked:
data collection, frequency tables, statistical graphs, measures of central tendency

En el enlace siguiente puedes encontrar el texto del ejercicio de evaluación sobre Estadística.
ejercicio de evaluación 1
Contenidos tratados:
recuentos, tablas de frecuencias, gráficos estadísticos, medidas de centralización