RECURSOS DE APRENDIZAJE
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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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Polynomials
This unit focuses on algebraic expressions in general and then specifically on monomials and polynomials. We take a close look at operations with monomials and polynomials, particularly at the division of polynomials by the binomial (x - a), Ruffini's rule and factorizing polynomials.
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Polygon measurements
In this unit we are going to focus on polygons and their properties. We are going to find out about their angles, area and how they relate to the circumference of a circle in an active way.
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Interpreting graphs
Through language we are able to communicate with each other. The most common forms of language are: oral, written and graphical. Nowadays, graphics represent one way of expressing and transmitting information. The media often express information by means of tables and graphs as they offer a fast, visual interpretation as well as showing how certain variables depend on others. Newton (1642-1727) was first to deal with the concept of a function. he used the term "fluents" or "flowing quantities...
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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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Geometry and a game of billiards
Geometry is an essential parts of the game of billiards. Every shot in a pool game is based on forming perfect angles. This unit is purely theoretical. It probably won't turn you into a billiards champion but you will see the game in a different light.
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Graphical representation derivative
The activities which follow are designed to familiarise the student with the concepts of the secant and tangent to a curve, to observe how the former approaches the latter and to understand the limit as a process which can be observed and checked.
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Geometric shapes on the plane
This unit deals with the most important geometric shapes on the plane: the triangle, the square, the rectangle, the parallelogram, the rhombus and the trapezium, and focuses on their area. As they are all two-dimensional we can say that they "live on the plane", unlike a matchbox (rectangular parallelepiped) which is three-dimensional and therefore "lives in three-dimensional space". Polygons are other kinds of plane shapes which you can find out about in the unit on Measuring Polygons.
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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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Percentages and indices
In this unit we shall look at the area of percentages and see how to use them in different exercises. We shall also look at examples of how percentages are used in the world around us such as Value Added Tax (VAT), simple interest and the Retail Price Index (RPI).
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Representing numbers graphically
This unit explains the steps we can take in order represent whole, rational and irrational numbers on a straight line. The first part of the unit is similar to one we saw previously, which explains how whole numbers are represented on a straight line. The second part shows the geometric process we need to follow in order to represent rational numbers graphically. Finally, the third part illustrates a method which can be used to represent some irrational numbers.
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