RECURSOS DE APRENDIZAJE
-
Pythagoras' Theorem
This unit focuses on Pythagoras' theorem and how to prove it is true.
Área de conocimientoContexto educativoTipo de recursoColecciones -
Operations with integers - II
In this unit, we revise the basic ideas of integers and we use them to practise the following operations: sum, multiplication, division and powers. Before starting this unit, students should have studied integers in class in the traditional way. These activities are suitable as a complement to get a better understanding of the concepts and the operations. The numbers that appear in each window are generated at random. This allows you to use the window indefinitely and practise a lot of differ...
Área de conocimientoContexto educativoTipo de recursoColecciones -
Simultaneous equations and inequations
Solving equations, simultaneous equations and inequations belongs to the branch of mathematics called Algebra. These equations are often used in the field of science to assist with their most important task: that of solving problems. Throughout the history of mathematics numerous mathematicians have dedicated many years of study to the procedures needed to solve equations and simultaneous equations. In this unit we focus on quadratic or higher degree equations, linear and quadratic simultaneo...
Área de conocimientoContexto educativoTipo de recursoColecciones -
Analytical Geometry
In this unit we will approach the study of the straight line in a plane considering thoroughly the necessary concepts to do so. We will be working with numerical and geometric elements to find algebraically the concepts associated with the study in a plane. In some places geometry will be contemplated where it can be shown how an analytical method can be used to simplify geometric concepts.
Área de conocimientoContexto educativoTipo de recursoColecciones -
Continuity and discontinuities
This unit deals with the concept of continuity of functions. It carries on from previous units which dealt with limits of functions and the properties of these limits. Firstly, we take an intuitive approach to introduce the concept of continuity through different examples. The unit then follows on with a detailed analysis of the concept of continuity and ends by focusing on the different types discontinuities.
Área de conocimientoContexto educativoTipo de recursoColecciones -
Chance and probability
This unit introduces the concepts of probability and chance. The basic concept of theoretical probability is also introduced (events, frequency etc.). Practical examples are used to illustrate different concepts and the basic laws and rules governing probability are outlined (e.g. Laplace's rule and the law of large numbers). The unit ends with an introduction to the probability of compound events and focuses on examples of the union and intersection of events.
Área de conocimientoContexto educativoTipo de recursoColecciones -
Escher's_tessellations
The Dutch artist Mauritis Cornelis Escher (1898-1972) is, perhaps, one of the most highly respected artists in the world of mathematics. He is, without a doubt, one of the most successful contemporary "mathematical artists". His work reflects a deep understanding of geometry. However, the mathematical content of his work is much closer to you than you think. Just look around you, perhaps with a slightly different perspective to normal, and you will start to recognise different areas of maths ...
Área de conocimientoContexto educativoTipo de recursoColecciones -
A history of Mathematics
These pages aim to present some of the most important mathematical problems in chronological order. It is not intended to be an exhaustive explanation of each problem but to simply show the evolution of mathematical thought throughout history. In each section there is an outline of the most relevant historical events of the era and the maps indicate the area of interest, both from a mathematical point of view.
Área de conocimientoContexto educativoTipo de recursoColecciones -
Measuring angles
This unit focuses on how to measure angles as well as carrying out operations with these angles. It also looks at how these special pairs of angles relate to each other: complementary and supplementary.
Área de conocimientoContexto educativoTipo de recursoColecciones -
Logarithmic function
The Logarithmic function is of great importance in the world of mathematics. It constitutes a very useful way of making certain numerical calculations. It represents the inverse of an exponential function which is one of the most commonly found functions in the world around us. Certain examples where it can be found include a colony of bacteria reproducing, the disintegration of a radioactive substance, some examples of population growth, inflation, capitalising money invested with compound i...
Área de conocimientoContexto educativoTipo de recursoColecciones -
Math in an envelope
An envelope is an object which is used a lot in everyday life. We have all used envelopes to put letters or important documents into and as students we have often had to use them. However, as well as being very useful objects, envelopes are also interesting to analyse from a mathematical point of view. Their geometrical shape is of interest firstly to people who have to make them and secondly to maths students who can use them to review a few interesting concepts such as line symmetry and sim...
Área de conocimientoContexto educativoTipo de recursoColecciones -
Inverse functions
The origin of the concept of functions has always been closely linked to the study of the phenomena of change. The oldest written references can be found amongst the writings of Babylonian astronomers. In the Middle Ages the study of functions appeared to be linked to the concept of movement. Nicole Oresme (1323-1392), a scholar interested in this concept, gave graphical representations showing change in velocity with respect to time. Three centuries later, Galileo studied movement from a qua...
Área de conocimientoContexto educativoTipo de recursoColecciones -
Exponential equations and logarithms
Exponential and logarithmic functions are the most common types of functions which exist in the world around us. As a result there are many problems which may require the use of exponential or logarithmic equations in order to solve them. One example of this is the Richter scale, which measures the magnitude M of an earthquake according to the amplitude of its surface waves A Hence: M=log A+C where C =3.3+1.66 logD-logT is a constant which depends on the period of time that the waves are regi...
Área de conocimientoContexto educativoTipo de recursoColecciones -
Square root
After the four basic operations (addition, subtraction, multiplication and division) the square root is another mathematical operation which is traditionally studied at primary and secondary schools, because it is necessary to solve problems using the Pythagoras theorem, proportions and second grade equations. Nowadays, the calculation ease supplied by calculators and computers may lead us to think that learning mental calculation is no longer necessary. However, we also have technical means ...
Área de conocimientoContexto educativoTipo de recursoColecciones -
The game of life
This unit focuses specifically on "Simulation as a formal model". Most of the ideas and content of this unit have been taken from the last three units of Martin Gardner's book "Wheels. Life and other Mathematical Amusements".(W.H. Freeman and Company 1983), which specifically focus on the Game of Life. It uses a simple game to simulate social or biological behaviour based on a simple mathematical model Despite its simplicity, we shall look in more detail at its far reaching implications.
Área de conocimientoContexto educativoTipo de recursoColecciones -
The definite integral and the area function
In this unit we shall demonstrate this method of exhaustion with an example. We shall then apply the same idea to introduce intuitively the concept of the definite integral of a function and we shall focus on some of its properties. Finally, we shall look at the relationship between the definite integral and finding antiderivatives.
Área de conocimientoContexto educativoTipo de recursoColecciones -
Powers
The main principles and properties of powers are revised in the first pages to let students discover them intuitively when using the windows. Then students can check their knowledge of these principles through simple excercises. In the pages with calculation games students can practice mental calculation of multiplications and divisions and apply the index laws. Finally it revises one of the applications of powers, how it is the factor decomposition of a number.
Área de conocimientoContexto educativoTipo de recursoColecciones -
Representing numbers on a straight line
This short unit shows how whole numbers and decimals can be represented on a straight line. The concept of ordering numbers graphically is also introduced.
Área de conocimientoContexto educativoTipo de recursoColecciones -
Operations with natural numbers - II
In this unit, we revise the basic ideas of natural numbers and we use them to practise the following operations: addition, multiplication, division and powers. The numbers that appear in each window are generated at random. This allows you to use the window indefinitely and practise a lot of different exercises. Numbers consist of only one or two figures so the calculations can easily be done mentally. Magic squares with sums and multiplications are used in the exercises, however the main obj...
Área de conocimientoContexto educativoTipo de recursoColecciones -
Operations with natural numbers - I
In this unit, basic concepts of natural numbers are revised and the operations of addition and subtraction are practised. Numbers that appear in each window are generated at random. This allows you to use the window indefinitely and practise a lot of different exercises. Numbers consist of only one or two figures so the calculations can easily be done mentally. Magic squares are used in the exercises, however the main objective of this unit is to learn things about natural numbers.
Área de conocimientoContexto educativoTipo de recursoColecciones