RECURSOS D'APRENENTATGE
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Pythagoras' Theorem
This unit focuses on Pythagoras' theorem and how to prove it is true.
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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...
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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.
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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 ...
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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.
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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.
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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...
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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 ...
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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.
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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.
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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.
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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...
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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.
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Square metres, cubic metres
These activities are designed to be viewed on a 17-inch screen and with a resolution of 1024 x 768 pixels because some windows show measurements in centimetres and millimetres that, when viewed with another configuration, won't correspond with reality; and the size of some windows can even be too big. This unit only deals with a basic knowledge on length, volume and weight units, as studied in primary school. It does not deal with the other units of the International System. Moreover, the stu...
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Regular polygons and circles
This unit is based on the study of the properties of regular polygons, their basic characteristics and the concept of the circle as a regular polygon with an infinite number of sides. As this unit is aimed at students in their first and second years of secondary education the content is at a very basic, purely constructive level.
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Ratio and proportional division
This unit has been designed to introduce the concept of both direct and inverse proportional parts or quantities. We will approach the above-mentioned concepts through a series of problems and exercises and also focus on methods which will allow us to apply these concepts to similar situations.
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Star-shaped polygons and algorithms
In this unit we will learn how to construct and 'define' star-shaped polygons. The first part involves a description of how to construct them, using a ruler and compass, although we will be using the computer to draw them. The second part is somewhat more abstract as we discover which conditions we need to produce a star-shaped polygon and which properties it has. In both parts we use algorithms to give constructive explanations, i.e. we define star-shaped polygons as shapes obtained by follo...
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Solving equations graphically
This unit deals with equations and identities and focuses on solving simple equations both numerically and graphically. Finally, we show how these equations can be applied to many everyday problems.
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Simple equations with an unknown
This unit deals with the concepts of equations and identities and focuses on solving simple equations both numerically and graphically. Graphs are used to introduce the concept of affine functions. Finally, we show how this concept can be applied to many everyday problems.
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Solids of revolution
In this unit we will learn about solids of revolution. First, we define what a solid of revolution is. To get a solid of revolution we start out with some segments and a semi-circumference that they will be rotated 360º around its own axis. And so, three surfaces of revolution will form: cylindrical surface, conical surface and spherical surface. Then we will study the properties of these figures. Students should have a pencil and a piece of paper to do calculations and deductions of the fo...
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