RECURSOS DE APRENDIZAJE
-
Quadratic functions. Parabola curves
This unit deals with graphs of second degree polynomial (quadratic) functions. It starts by looking at the simplest graph, y = x2, and focuses on different types of quadratic functions, relating them back to this initial example by using translations.
Área de conocimientoContexto educativoTipo de recursoColecciones -
Quadratic equations
This unit deals with quadratic equations. It looks at how to interpret them geometrically and focuses on a formula that can be used to solve them. At the end of the unit there are some different exercises and problems that can be solved by using these equations.
Área de conocimientoContexto educativoTipo de recursoColecciones -
The Bolzano and Weierstrass Theorems
Assumptions are carefully analyzed and the thesis of the theorems of Bolzano and Weierstrass on continuous functions. We study some of its most important applications.
Área de conocimientoContexto educativoTipo de recursoColecciones -
Applications of the derivative
Using the concept of the derivative we are going to study some of the local properties of functions. Drawing their graphs will be made much easier through the study of these characteristics. This unit also aims to obtain information about functions from their derivatives.
Área de conocimientoContexto educativoTipo de recursoColecciones -
Grid measurements
In this unit there are different practical activities to do, some of which focus particularly on Pythagoras' theorem, which are based on a grid of points that cover the plane.
Área de conocimientoContexto educativoTipo de recursoColecciones -
Geometric ratio
This unit deals with some formulae connected to Thales' theorem. Rather than giving rigorous, step-by-step demonstrations, this unit offers the advantage of verifying conclusions and properties in a straightforward manner. To conclude, 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 theorem of the sides adjacent to the right angle and the perp...
Área de conocimientoContexto educativoTipo de recursoColecciones -
Geometric construction of conic sections
In this unit you will learn how to construct different conic sections (the parabola, the hyperbola and the ellipse) geometrically using basic geometric elements such as segments, their midpoints, perpendicular lines and circles. You will be able to draw these shapes in the windows as if you were drawing on a sheet of paper, the only difference being that the computer will save you having to draw several straight lines by hand.
Área de conocimientoContexto educativoTipo de recursoColecciones -
Exponential function
Exponential functions are of great importance in mathematics. These functions are the ones which are most commonly found in the world around us. The following represent examples of exponential behaviour: a colony of bacteria reproducing, the disintegration of a radioactive substance, some examples of population growth, inflation, capitalising money invested with compound interest etc.
Área de conocimientoContexto educativoTipo de recursoColecciones -
Bounded sequences
This unit introduces the concepts of upper bound, lower bound, supreme, lowest, highest and lowest of a sequence of real numbers for the sequences calsificar as lower bound bounded bounded above bounded not
Área de conocimientoContexto educativoTipo de recursoColecciones -
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...
Área de conocimientoContexto educativoTipo de recursoColecciones -
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
Área de conocimientoContexto educativoTipo de recursoColecciones -
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.
Área de conocimientoContexto educativoTipo de recursoColecciones -
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...
Área de conocimientoContexto educativoTipo de recursoColecciones -
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...
Área de conocimientoContexto educativoTipo de recursoColecciones -
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...
Área de conocimientoContexto educativoTipo de recursoColecciones -
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...
Área de conocimientoContexto educativoTipo de recursoColecciones -
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.
Área de conocimientoContexto educativoTipo de recursoColecciones -
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...
Área de conocimientoContexto educativoTipo de recursoColecciones -
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...
Área de conocimientoContexto educativoTipo de recursoColecciones -
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.
Área de conocimientoContexto educativoTipo de recursoColecciones