RECURSOS DE APRENDIZAXE
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Trigonometrical ratios
As Thales' theorem tells us, trigonometrical ratios of an angle do not depend on the right-angled triangle we choose. Therefore, we can choose a right-angled triangle whose hypotenuse is the radius of a unit circle. We have drawn a set of axes and used the origin as the centre of an auxiliary circle whose radius is equal to one unit. We have drawn a right-angled triangle in the circle, which we will use to define the trigonometrical ratios. By choosing a radius of this length we have made it ...
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Trigonometrical ratios of right angles triangles
This unit offers an introduction to basic trigonometry such as trigonometrical ratios of acute angles. Students are expected to have some notion of angles and measuring angles as well as a basic understanding of complementary angles. There is also an introduction to the connection between trigonometrical ratios and the basic trigonometrical identities needed to solve right-angled triangles.
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Transformations of functions: Traslations and Dilatations
This unit focuses on the changes produced on the graph of a real function with a real variable when any of the unknown factors are altered to the same factor added to or multiplied by a constant. In the first example we will see that the result is a graph of a function which is the same shape as the original one, but which has moved from its initial position. From then we will refer to it as a translation. In the second example we get a similar result but the change is either more noticeable ...
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Similarity
This unit deals with some formulae connected to proportionality between segments and 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, using an interactive approach.
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Sequences of real numbers
This unit introduces the concept of a sequence of real numbers and shows how they can be represented on two types of graphs, one on the Cartesian plane and the other on a straight line.
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Quadrilaterals
In this unit we will look at different types of quadrilaterals and the properties of each kind. Then we will look at different ways to work out their area and perimeter.
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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.
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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.
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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.
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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.
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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.
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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...
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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.
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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.
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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
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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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