[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