RECURSOS DE APRENDIZAJE
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Square metres, cubic metres
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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Regular polygons and circles
This unit is based on the study of the properties of regular polygons, their basic characteristics and the concept of the circle as a regular polygon with an infinite number of sides. As this unit is aimed at students in their first and second years of secondary education the content is at a very basic, purely constructive level.
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Ratio and proportional division
This unit has been designed to introduce the concept of both direct and inverse proportional parts or quantities. We will approach the above-mentioned concepts through a series of problems and exercises and also focus on methods which will allow us to apply these concepts to similar situations.
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Star-shaped polygons and algorithms
In this unit we will learn how to construct and 'define' star-shaped polygons. The first part involves a description of how to construct them, using a ruler and compass, although we will be using the computer to draw them. The second part is somewhat more abstract as we discover which conditions we need to produce a star-shaped polygon and which properties it has. In both parts we use algorithms to give constructive explanations, i.e. we define star-shaped polygons as shapes obtained by follo...
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Solving equations graphically
This unit deals with equations and identities and focuses on solving simple equations both numerically and graphically. Finally, we show how these equations can be applied to many everyday problems.
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Simple equations with an unknown
This unit deals with the concepts of equations and identities and focuses on solving simple equations both numerically and graphically. Graphs are used to introduce the concept of affine functions. Finally, we show how this concept can be applied to many everyday problems.
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Solids of revolution
In this unit we will learn about solids of revolution. First, we define what a solid of revolution is. To get a solid of revolution we start out with some segments and a semi-circumference that they will be rotated 360º around its own axis. And so, three surfaces of revolution will form: cylindrical surface, conical surface and spherical surface. Then we will study the properties of these figures. Students should have a pencil and a piece of paper to do calculations and deductions of the fo...
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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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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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