RECURSOS DE APRENDIZAJE
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Triangles
This first look at triangles during the first two years of secondary education is mainly focused on the following: constructing triangles using a ruler and compass, characteristics of equal triangles, angles and area. Before studying this unit students should be familiar with how to measure angles and carry out operations with them. Although the study of special lines in a triangle usually takes place during the third and fourth years of secondary education a general introduction to this area...
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Similar triangles
This unit provides a detailed study of similarity focusing specifically on similar triangles. The criteria governing similarity are analysed and exercises are carried out to focus in these criteria
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Progressions
This unit introduces students to the concepts of arithmetic and geometric progression. It also demonstrates how to find the terms in a progression, the general or nth term and the sum of terms.
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Tessellating the plane
Throughout history geometric shapes have been used as decorative motifs. Although many objects such as containers, fabrics, doors, windows and other bits of architecture have all been decorated using regular geometric designs we are going to focus specifically on walls and floors. Walls and floors are decorated using mosaics. A mosaic is the complete covering of a plane area with pieces usually called floor tiles that fit together exactly without covering each other or leaving any gaps betwee...
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Tables and algebraic terms
This unit is intended for students in their third year of secondary education. It aims to reinforce their ability to connect algebraic terms to data, which is usually given in the form of a table. It also helps them to match tables of values to given graphs and introduces them to the basic characteristics of graphs. Furthermore, there are activities which encourage students to compare two graphs and give a detailed interpretation of them. In addition, the data used in the examples is based o...
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Numerical and geometrical patterns
This unit is designed to show students, in their third year of secondary education, how to recognise arithmetic and geometric series, how to use certain strategies to solve problems and to try and work out general rules to express these series using symbols. The activities in this unit are designed to be varied, interesting and motivating but they also lend themselves to small classroom discussions where pupils can compare their ideas and strategies used during the activities. This will hopef...
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Polyhedron
A polyhedron is a three-dimensional solid whose faces are polygons joined at their edges. A polyhedron is said to be regular if its faces are made up of regular polygons. In this unit we can see some of this polyhedrons and learn about their properties. The design of these activities allows autonomous learning, but they also raise questions for students to investigate using the windows and to do their own deductions. Therefore, students should take notes in their notebooks so that they can sh...
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Multiples and factors. Prime numbers
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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Nim game
Counting was one of the first mathematical activities that primitive man had to learn how to do. Expressing a quantity with symbols meant a great step forward as they were the first number systems. However, they were awkward to work with. The decimal system and place-value notation, which we use nowadays, was thought up in India (VI - IX Century) and the Arabs introduced it to the Western world (X century) where it started to be used in the XIII century. We use the decimal number system as we...
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Proving Pythagoras' theorem graphically
Pythagoras' Theorem is one of the most well-known statements in the world of mathematics. It has been discovered and used by different civilizations during different periods. The Egyptians and the Hindus used it to help construct buildings. The Chinese (who called it "kou ku") also used it to help with construction and later on applied it to astronomy and algebra. There are over two hundred ways of proving Pythagoras' Theorem and there are even books which are specially written to explain the...
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Powers and roots
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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Powers of rational numbers
This unit follows on from the "Powers and Square Roots" unit in the 'first and second years of secondary education' section. In this earlier unit we focused on whole base numbers raised to the power of a positive whole number and examined their properties. In this unit there was also an introduction to the concept of the square root. This unit focuses on numbers raised to whole number and fractional indices and will generalise the rules which were examined in the earlier unit.
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Polygon measurements
In this unit we are going to focus on polygons and their properties. We are going to find out about their angles, area and how they relate to the circumference of a circle in an active way.
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Interpreting graphs
Through language we are able to communicate with each other. The most common forms of language are: oral, written and graphical. Nowadays, graphics represent one way of expressing and transmitting information. The media often express information by means of tables and graphs as they offer a fast, visual interpretation as well as showing how certain variables depend on others. Newton (1642-1727) was first to deal with the concept of a function. he used the term "fluents" or "flowing quantities...
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Homothety and Similarity
This unit deals with some of the basic concepts of homothety (or enlargement) and some formulae connected to Thales' theorem. Rather than rigorous, step-by-step demonstrations, this unit offers the advantage of proving theories and properties in a straightforward manner. To conclude the unit, different examples of similarity in triangles and polygons in general is also focused on, through an interactive approach. There is an introduction to metric relations in a right-angled triangle: the the...
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Geometry and a game of billiards
Geometry is an essential parts of the game of billiards. Every shot in a pool game is based on forming perfect angles. This unit is purely theoretical. It probably won't turn you into a billiards champion but you will see the game in a different light.
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Geometric shapes on the plane
This unit deals with the most important geometric shapes on the plane: the triangle, the square, the rectangle, the parallelogram, the rhombus and the trapezium, and focuses on their area. As they are all two-dimensional we can say that they "live on the plane", unlike a matchbox (rectangular parallelepiped) which is three-dimensional and therefore "lives in three-dimensional space". Polygons are other kinds of plane shapes which you can find out about in the unit on Measuring Polygons.
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Average rate of change
The average speed of a car on a journey is a very familiar concept and can be used to illustrate a very important mathematical concept clearly. This concept is that of the rate of change of a function during an interval. Likewise, the speed at which a car travels at any particular moment is another familiar concept. This piece of information can lead us to the notion of the instantaneous rate of change of a function or a point. The examples and exercises presented in this unit have been taken...
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RECURSOS EDUCATIVOS ABIERTOS EN MATEMÁTICAS
SON REA DE MATEMÁTICAS, LOS CUALES HAN SIDO UNO DE LOS RESULTADOS DE UN PROYECTO ERASMUS+ DE ASOCIACIONES ESTRATÉGICAS ENTRE ESCUELAS, QUE ESTÁ LLEVANDO EL IES HUELIN DE MÁLAGA CON OTROS INSTITUTOS EUROPEOS.
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