IKASKUNTZA BALIABIDEAK
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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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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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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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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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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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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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