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Allergies are an overreaction by the body. Harmless substances are seen as enemies and attacked. An allergic reaction occurs. The immune system reacts to these substances, known as allergens, in the same way as it would to germs, and forms antibodies. At the end of the film is a glossary with a summary of the contents.
Limited growth is characterized by the fact that it does not exceed a certain limit or bound. The film explains limited growth using several catchy examples from the economy, nature and everyday life, explains the recursive function equation and finally illustrates limited growth with an exponential function.
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This film explains linear equations and their graphical representation. A linear equation, in which there is exactly one y-value for each x-value, is a linear function. The general functional rule for a linear function is y = m * x + b, the corresponding graph is a straight line with the gradient m and the y-axis section b.
The subject of this film is linear equations. Equations are made up of a series of mathematical symbols with logical connections that are linked by an equals sign. An equation is always linear if the variables do not occur in any power higher than the 1st. Linear equations are solved using equivalence transformations.
The basics of interest calculation are presented using practical examples. Credit, capital, interest rate and term are explained. Clear calculation examples explain how the interest rate affects the amount of money that has to be paid back. The different terms of loans and per annum interest are also introduced.
This film uses an example from everyday school life to demonstrate the intercept theorems when scaling a triangle centrally. The first and second intercept theorems are explained and shown in detail using specific problems. The benefit in daily life is then also shown when calculating a difficult to measure length.
The subject of this film is improper fractions. In top-heavy fractions the numerator is a multiple of the denominator. Top-heavy fractions can therefore be converted into whole numbers using reduction. The film uses clear examples to explain what top-heavy fractions are and how to calculate with them.
We are familiar with the term growth from everyday life. Children grow, the state´s mountain of debt grows, the number of computer users worldwide too. Generally we can say: if any size increases with time, we refer to growth. This film explains the term growth in detail, including positive and negative growth.
In logistic growth, exponential and bounded growth are combined. The curve of a logistic growth starts exponential. In the middle it becomes approximately linear, and it finally ends at a limit which cannot be exceeded. The video explains the formula and gives some illustrative examples from everyday life.
The audience learns what exponential growth is through the legend of Buddhiram, the inventor of chess. The video explains the recursive and explicit functional equations and shows how both positive and negative exponential growth work. Exponential, linear and quadratic growth are compared with each other.
This film introduces the mathematical expression "term" and sets out the arithmetical rules for terms. Variables are also introduced as substitutes for numbers and we explain how they can usefully be used in various formulas. The difference between dependent and independent variables is also clearly shown.
Using examples from everyday life as well as animations and real models, we show you how the surfaces of different geometric figures can be understood using grids. Clear examples of the grids of tetrahedrons, square pyramids, cuboids, and prisms as well as complicated shapes such as cylinders and cones are shown.
The subject of this film is the graphical representation of percentage calculations. The principle of visualizing parts and their proportions in histograms or pie charts is explained. The various criteria that have to be taken into account to reach a reliable and accurate graphical representation are looked at.
This film introduces the construction and the daily use of circles. Easy-to-understand practical examples show how circles can be made with the help of a compass or using string, and how important these geometric shapes are in navigation and shipping. The uses of the circle in art are also mentioned in this film.
When adding or reducing fractions, it is helpful to know the least common multiple and the greatest common divisor. The video shows how to find these numbers using several illustrative examples. Both denominators or both denominators and numerators must be reduced with the help of the prime factorization.
The film explains how the fraction bar, the numerator, and the denominator work: The denominator gives the fraction its name, while the numerator gives the number of parts. It is shown that fractions with the same name can easily be added. The fraction calculation is illustrated with everyday examples.
For comparison and calculation, fractions can be expanded until they have the same denominator. To do this, the numerator and denominator are multiplied by the same number, whereby the valence does not change. If the numerator and denominator have a common divisor, you can reduce the fraction by this number.
Fractions can easily be divided by multiplying the first fraction by the reciprocal of the second fraction. The film shows the individual steps necessary for this with the help of an illustrative example and explains the rules that apply here. The reduction advantage for mental arithmeticians is also discussed.
Three laws of arithmetic - the commutative law, the distributive law and the associative law - make arithmetic easier. The film introduces the three laws, explains their meaning and gives the corresponding formulae. The content of each law is summarized in an understandable way in a short and catchy mnemonic.
You multiply fractions with integers by keeping the denominator and multiplying the numerator by the number, and using the reduction advantage. If you have parent fractions, you multiply the denominators together. If you have different fractions, you multiply numerators by numerators and denominators by denominators.
This film is about which numbers are divisible by which other numbers. The video explains the divisibility rules and how to check them: Depending on whether a remainder is left after division or not, a number is divisible by another number. Illustrative examples explain the rules of the last digit and the checksum.
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This film uses catchy examples to explain what a power is and how to calculate with powers. Among other things, the multiplication and division of powers with the same exponent or with the same base, as well as the exponentiation of powers, are explained. In addition, special cases such as negative exponents are considered.
Rounding means making numbers less precise and as a result easier to calculate with. But in such a way that they are still precise enough for their purpose. This film introduces the rounding rule according to DIN 1333 using clear everyday examples. We also look at rounding errors and rounding already rounded numbers.
Roman numerals are still used relatively often today. Therefore, the film explains how to read them correctly and transfer them to our number system. It explains the history of the numbers from the beginning, describes the expansion of the system, and points out the special features of the numbers 4 and 9.
This film shows the relationship between lines and points. It explains how a set square can be used to measure the vertical distance between a point and a straight line. Two straight lines can either be parallel to one another or intersect each other. In three-dimensional space, straight lines can also be crooked to one another.
This film first gives several examples of reflections in the Cartesian coordinate system and then develops generally applicable rules from them. First, individual points are mirrored on the y-axis, the x-axis and the zero point. Then it is shown that and why mirroring also works with geometric figures.
This video looks at the basics of probability calculation. First of all, the term probability is explained. Using ideal random trials, disjoint and non-dijoint events are defined amongst others, simple probabilities for disjoint events are calculated, and the respective arithmetic rules are presented.
Prime numbers are only divisible by themselves and by one. All other numbers consist of products of prime numbers. In the video, examples are used to show how a number can be identified as a prime number, both through the application of divisibility rules and through the helpful sieve of Eratosthenes.