[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

[4eso] UD1: Álgebra: polinomios, factores y raíces

Los enlaces que aquí puedes encontrar contienen los materiales que, junto con el libro de texto, vamos a utilizar los próximos días en clase.
En el primero está el material que os pasé en clase; el segundo es el pdf con las soluciones de las actividades del tema.

4ESO_ud1_alumno                4ESO_ud1_soluciones

Contenidos tratados:
operaciones con polinomios, regla de Ruffini, raíces y factores de un polinomio, fracciones algebraicas

[2eso] UD1: Estadística (intro)

Comenzamos el curso con el tema sobre Estadística (volumen 3, unidad 14 del libro de texto). En el enlace está el pdf con la actividad que presenta los contenidos del tema.

2ESO_estadistica_intro

[2eso] Actividad de introducción

En el siguiente enlace puedes encontrar el texto y los ejercicios de la actividad con la que hemos comenzado este curso.

La actividad consiste en la lectura de un extracto del artículo de Bernardo Marín titulado El 'anumerismo' también es incultura y publicado en el diario El País el 6 de abril de 2011. Además de la lectura, se plantean cuatro preguntas relacionadas con el contenido del artículo. Tres de ellas son más sencillas y la cuarta puede dar lugar a plantear una interesante investigación para el alumnado.

2ESO_actividad_intro

The doctor who didn´t know (enough) math

Follow the links below to get the handouts and the solutions to this activity on functions

Topics worked:
comprehensive reading, linear functions, piecewise functions, graph functions, proportions, algebraic language, solve equations, real-life context problems

handouts         solutions

En los siguientes enlaces puedes encontrar esta misma actividad en castellano

enunciado      soluciones

Primer encuentro astur-cántabro GeoGebra en el aula

Aquí puedes encontrar los materiales para desarrollar las sesiones presentadas en la comunicación Números reales y polinomios con GeoGebra, dentro del primer encuentro astur-cántabro GeoGebra en el aula, Castro Urdiales 27 de abril de 2013.

números reales y polinomios con GeoGebra

[4eso] Assessment exercise 6: Maths & Arts

Follow the link below to get the text and the activities of this assessment exercise.

Closing date 20/V/2013

Topics worked:  

comprehensive reading, history of mathematics, mathematical proof, prime and composite numbers, Pythagoras' theorem.

Thank you very much Haylee Ryan Yale, our language assistant, for your help with the translation

4ESOassessExercise_geometry

En los siguientes enlaces puedes encontrar el texto de la actividad en castellano

matematicas&arte_alumno            matematicas&arte_profe

[4eso] Assessment exercise 5: functions

Look here for the pdf file with the text of assessment exercise 5 on functions.
Closing date: 2/V/2013

Topics worked:  
definition of function.
characteristics of a function: domain, range, intercepting points, monotony, extrema, curvature, boundedness, asymptotes and continuity.
types of functions: quadratic and rational (degree 1) functions.
use of GeoGebra: graph funtions, export as image, intersection tool, object properties


4ESOassessExercise_functions

[4eso] Functions

Here you can find the materials to develop a unit on functions.

Topics worked:  
definition of function.
characteristics of a function: domain, range, intercepting points, monotony, extrema, curvature, boundedness, symmetry and periodicity.
types of functions: linear, affine, quadratic and rational (degree 1) functions, piecewise functions
straight lines: equations and relative position
real-life context problems with functions.

theory             activities             solutions

off topic: problemas con los comentarios

No sé cuántos de los que os pasáis por aquí habéis tenido problemas para publicar comentarios. Yo hace tiempo que me di cuenta del problema porque no podía responder a los que aparecían. Desde entonces he intentado resolverlo: primero consultando el problema a los de blogger (sin respuesta), luego consultando en multitud de foros (sin respuesta satisfactoria) y finalmente consultando a mi propia intuición ayudada del sofisticado método de ensayo-error.
Al final creo que lo conseguí, cambiando el modo en el que aparece la ventana de comentarios de debajo de la entrada a ventana emergente.
Espero que de ahora en adelante no haya problemas para que podáis dejar vuestros comentarios (que siempre son bienvenidos y agradecidos).
Un saludo desde la Casa a todos sus visitantes.

The evolution of ideas (an example)

This is a new version of this activity

This activity consists of a text that starts with Tartaglia, Cardano and their competition to find the solution to the third and fourth degree equations and finishes with Complex Numbers and the Mandelbrot Set. It also has some activities for the students related to the text.
In the links below you can find the handouts for the students and the teacher guide. You can also get a couple of videos from YouTube and a GeoGebra applet with interesting representations of the Mandelbrot Set.

The evolution of ideas (handouts)
The evolution of ideas (teacher guide)
Mandelbrot Set 2010 Odyssey (video)
Mandelbrot Set Zoom (video)
Mandelbrot Set (applet GeoGebra)

[1eso] Algebra: algebraic language, equations

Here you can find the materials to develop 14 sessions on algebra (55 minutes/session)
Topics worked: algebraic language, algebraic expressions, creating formulae, numerical value, operations with algebraic expressions, equivalent equations, solutions, first degree equations, solving problems.
Some exercises are taken from a selection made by J.A. Trevejo from Australian text books Mathematics for the International Student, Haese & Harris Publications, 2008.

session 1 (algebraic language): teacher guide, handouts, solutions
session 2 (algebra vs english + guess the number): teacher guide, handouts, solutions
session 3 (creating formulae + numerical value): teacher guide, handouts, solutions
session 4 (like terms + numerical value): teacher guide, handouts, solutions
session 5 (expand and simplify): teacher guide, handouts, solutions
session 6 (operate algebraic expressions): teacher guide, handouts, solutions
session 7 (operations + equations & solutions): teacher guide, handouts, solutions
session 8 (solving equations): teacher guide, handouts, solutions
session 9 (equivalent equations + solve equations): teacher guide, handouts, solutions
session 10 (solve equations): teacher guide, handouts, solutions
session 11 (problems with equations 1): teacher guide, handouts, solutions
session 12 (problems with equations 2): teacher guide, handouts, solutions
session 13 (problems with equations 3): teacher guide, handouts, solutions
session 14 (problems with equations 4): teacher guide, handouts, solutions

[1eso] Assessment exercise 6: algebra / Ejercicio de evaluación 6: álgebra

Look here for the pdf file with the text of assessment exercise 6 on algebra.
Closing date: 8/III/2013
assessment exercise 6

Aquí puedes encontrar el archivo con el enunciado del ejercicio de evaluación 6 sobre álgebra.
Fecha límite: 8/III/2013
ejercicio de evaluación 6

[1eso] Ejercicio de evaluación 5: proporcionalidad y porcentajes

En el siguiente enlace tienes el texto del quinto ejercicio de evaluación del curso. En este caso sobre proporcionalidad y porcentajes, los contenidos del último tema que hemos trabajado en clase.
Recuerda que el plazo de entrega finaliza el viernes 15 de febrero de 2013

ejercicio de evaluación 5

[4eso] Algebra: equations, inequations and systems of equations

Look here for the materials to develop 15 sessions on algebra (55 minutes/session).
Topics worked: polynomial, rational and irrational equations; linear and non-linear systems of equations; one variable inequations; problem solving; use of GeoGebra.
Some exercises are taken from the textbook Matemáticas 4ESO, opción B, proyecto Los Caminos del Saber, editorial Santillana, 2011.

Unit handouts
equations, inequations and systems

GeoGebra applets
equations 1     equations 2     linear systems     non-linear systems     inequations

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

[1eso] Assessment exercise 4: fractions / Ejercicio de evaluación 4: fracciones

Look here for the pdf file with the text of assessment exercise 4 on fractions:
assessment exercise 4

Aquí puedes encontrar el pdf con el enunciado del ejercicio de evaluación 4 sobre fracciones:
ejercicio de evaluación 4