[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

[4eso] Algebra: polynomials (operations, roots & factors)

Here you can find the links to eight activities on algebra. Each of them can be developed in a single 55 minutes session.
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

act1_teacherGuide      act1_handouts      act1_solutions
act2_teacherGuide      act2_handouts      act2_solutions     combining like terms (video)
act3_teacherGuide      act3_handouts      act3_solutions
act4_teacherGuide      act4_handouts      act4_solutions     plotting polynomials (GeoGebra)
act5_teacherGuide      act5_handouts      act5_solutions
act5 GeoGebra applets
act5_explicitEq_degree1    act5_implicitEq_degree1    act5_degree2a    act5_degree2b

act6_teacherGuide      act6_handouts      act6_solutions
act7_teacherGuide      act7_handouts      act7_solutions
act8_teacherGuide      act8_handouts      act8_solutions
polynomial roots (GeoGebra)

[4eso] Probability

Here you have the links to three activities on probability. Each of them can be developed in a single 55 minutes session.
The two first activities may be used at the beginnig of a unit on probability; third one consists of two problems to be solved by the end of the unit.
Topics worked: probability vocabulary, random experiments, sample space, outcomes, events, conditonal probability, probability assignment.

act1_teacherGuide         act1_handouts
act2_teacherGuide         act2_handouts         act2_solutions         [en español]
act3_teacherGuide         act3_handouts         act3_solutions
theory: brief summary       [en español]  

[1eso] Rational numbers / Números racionales

The set of the rational numbers is formed by all the numbers that can be written as fractions, namely quotients of integer numbers. This quotients may yield a whole number or a decimal number, but not any kind of decimal number.

Find here the materials we are going to use in this unit on Racional numbers

Topics worked: fractions, arithmetics and aplications; decimal numbers, arithmetics, errors and approximations, aplications; relation fraction/decimal number

act_RationalNumbers


El conjunto de los números racionales está formado por todos los números que pueden escribirse en forma de fracción, es decir cociente de números enteros. Estos cocientes pueden dar un número entero o un decimal, pero no cualquier tipo de decimal.

Aquí puedes encontrar los materiales que vamos a usar en esta unidad sobre Números racionales

Temas trabajados: fracciones, aritmética y aplicaciones; números decimales, aritmética, errores y aproximaciones, aplicaciones; relación fracción/número decimal, fracción generatriz

act_NúmerosRacionales

Una breve historia de las sucesiones

En el siguiente artículo se describe brevemente la evolución histórica del concepto de sucesión dentro de las matemáticas. También se mencionan algunas de las aplicaciones que las sucesiones han tenido y tienen dentro y fuera de las matemáticas.

Sucesiones_BreveHistoria

[4eso] Statistics

Here you can find the links to three activities on statistics. Each of them can be developed in a single 55 minutes session.
Topics worked: populations, statistical variables, tables, frequencies, parameters (central tendency, location and dispersion), graphs and use of Excel.

act1_teacherGuide       act1_handouts       act1_solutions
act2_teacherGuide       act2_handouts       act2_solutions
act3a_spreadsheet       act3a_solution
act3b_spreadsheet       act3b_solution

[1eso] Assessment exercise 2: divisibility / Ejercicio de evaluación 2: divisibilidad

This is the pdf file with the text of assessment exercise 2 on divisibility:
assessment exercise 2

Aquí puedes encontrar el enunciado del ejercicio de evaluación 2 sobre divisibilidad:
ejercicio de evaluación 2

[1eso] Integer numbers / Números enteros

These are the materials we are going to use in this unit on Integer Numbers:
 integer numbers

Aquí puedes encontrar los materiales que vamos a usar en este tema sobre Números Enteros:
números enteros

[1eso] Class exercises: divisibility / Ejercicios de clase: divisibilidad

Click on these links to get the handouts of class exercises on divisibility:

Sieve of Eratosthenes                          Numbers maze
Sieve of Eratosthenes_solution            Numbers maze_solution

En los siguientes enlaces puedes encontrar las fichas con los ejercicios de clase sobre divisibilidad:

Criba de Eratóstenes                           Laberinto de números
Criba de Eratóstenes_solución            Laberinto de números_solución

[1eso] Assessment exercise 1: natural numbers / Ejercicio de evaluación 1: números naturales

Follow this link to get the activities of the assessment exercise on natural numbers

assessment exercise 1_ text                        assessEx1_solution

En el siguiente enlace puedes encontrar las actividades del ejercicio de evaluación sobre números naturales

ejercicio de evaluación 1_enunciado          ejEvaluacion1_solución