RECURSOS DE APRENDIZAJE
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Movements on the plane
In this unit we will focus on transformations on the plane in a very intuitive and practical way. The idea is to try and "visualise" the movements before conceptualising them. In the last section, Symmetry, we shall look at how the three types of transformation relate to each other. The first section about vectors is an introduction to them and is necessary in order to fully understand the notion of translation.
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The golden number
The Greeks were very interested in measuring things by comparing them to a set unit. They found that there was a relation between pairs of measurements such as the ratio or the quotient. They were also interested in proportion e.g. when two ratios are equal. They were also interested in "beauty". They referred to the most beautiful proportion as golden ratio (from gold) and the number represented by the symbol F is the golden number. It appears in nature and the Greeks were the first to apply...
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Linear function
Before beginning this unit we assume that students have already worked with some functions, in particular functions which deal with proportion. Through the activities in this unit we expect the students to build on their existing knowledge to find out more about functions and learn how to interpret graphs of functions. The activities focus on plotting points from coordinates and reading straight line graphs, i.e. being able to identify different types of graphs depending on their gradient and...
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Metres, litres, kilograms
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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Operations with integers - I
In this unit, we revise the basic ideas of integers and we use them to practise the following operations: sums and subtractions. Before starting this unit, students should have studied integers in class in the traditional way. These activities can be used as a complement to reinforce and understand the concepts and the operations better. 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. Num...
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The cartesian plane
Students are expected to have already worked with this kind of representation on paper: tables of values, battleships etc. If this isn't the case then it could be introduced by getting students to match a pair of numbers to a member of a set to represent something such as seats in a cinema or where the students themselves are seated in the classroom. This unit introduces students to the Cartesian plane through activities which encourage them to understand concepts related to cartesian coordin...
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Areas of planes figures
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. There are two pages for each geometrical figure. On the first page students have to do the equation of the area of this figure themselves. Therefore, the equation is not given. The next page is ...
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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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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 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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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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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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