[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