# Skills in mathematics

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This is a nice way to learn it.
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Through out the year you might get different grades in school. Some grades could be excellent some not so good. At the end of the semester you might want to calculate your average grade. How can you do this? If we would like to find a middle between two number values le'ts say 5 and 3 all we need to do is to find mean or average. In order to do that we should add up the numbers and devide the sum with 2. (5 + 3) ÷ 2 = 8 ÷ 2 = 4 Now 4 is exactly between 5 and 3 and it is the average value, of the two numbers, equally distant from both. Finding an average of 5 and 3 was easy, you could do it even without calculation, but what if you want to calculate of average of more than two numbers? Well in the first example we added up the numbers and divied the sum with two and two is the amount of number values we added. This means if we would like to find an average for more than two numbers we would also have to add them up and devide the sum but with the value equal to the how many numbers we added. As an example we can find the average of 17,11,8. (17 + 11 + 8) ÷ 3 = 36 ÷ 3 = 12 So we first added up the numbers and because we added three numbers, we devided the sum with three and we got an average or a mean of twelve. Twelve is not equally distant from all three numbers, but if we would share the sum of all numbers equally this is the number we get which makes it kind of the "central" value for these numbers. No matter how many values we have if we want to find the mean value we only need to add them all and devide the summ with a number equal to how many values we added. To find out more you can check out these interesting videos that do more examples on average values. This interestig video shows the practicall application of calculating and understanding average:
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Here is a video in english that describes how to use short division

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A video in english that teaches multiplaying with the box or grid method

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The meter is the base unit from smaller units are dm, cm and mm. The prefixes deci, centi and mili that we put before meter come from latin idicating deci (like decimal) - tenth part, centi - (like century) one hudreth part and mile (as mille in italian which means thousand) a one thousandth part.

For easy conversion have in mind that we use decimal system meaning step of conversion is ten. If we are converting to smaller units we multiply with than for each step of conversion because we need to get a larger number if we count in smaller units. Just as if we would count the money in cents rather than in dollars we would get a larger number though value would be the same.

Picture taken from https://www.uzinggo.com/conversion-volume-measures/proportions-measurement/math-foundations-grade-6 where you can check out for more examples

If we convert from larger to a smaller unit we would multiply with ten for each step of conversion.
The exception is when we convert from meter to kilometer we devide with a thousand but that is only beacuse in between we actually have two units that we rarely use - dekameter and hectometar.

For example if we would convert 15 m to mm we would multiply with 10 to get the value in dm (150 dm) than again with 10 to get a value in cm (1500 cm) than once more with 10 to get a value in mm (15000). So for each step of conversion we multiplied with ten and since there were three steps in between we multiplied with one thousand effectively which is exactly how many milimiters there is in one meter so if we have 15 m there is 15 000 mm in it.

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## What is Fraction?

Fractions represent equal parts of a whole or a collection.

Fraction of a whole: When we divide a whole into equal parts, each part is a fraction of the whole.

For example

Powerd by splashlearn.com
https://www.splashlearn.com/math-vocabulary/fractions/fraction

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Mellan två linjer som möter varandra finns alltid en vinkel. Vi skiljer på tre olika sorters vinklar:

Tänk på att linjernas längd inte spelar någon roll, bara hur de möter varandra. Linjerna kallas vinkelben. Den punkt de möts på kallas vinkelspets.
Vi mäter vinklar i grader. Ett helt varv är 360 grader. Ett halvt varv är 180 grader.

Ett fjärdedels varv är:

Thanks to Matteboken

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A perimeter of a geometric shape would be the path we would have to travel if we would walk around the shape on its edges.
Simply speaking in order to figure out a perimeter of a geometric shape we need to know the lenght of all of its edges and sum these lengths together.

Irregular geometric shapes make it difficult as we have to know each and every edge in order to make the calculation. So if have a irregular geometric shape with four diffrent egdes : a,b,c,d... The perimetire would simply be:

P = a + b + c + d

A good example of this you can find on this link

With regular geometric shapes it is a little bit easier as they follow some rules. For example if we take rectangle, it is a geometric shape that is by definition made of four egdes, out of two and two are equal.

Image sourced: https://www.splashlearn.com/math-vocabulary/geometry/rectangle

Taking that into account, we would write that perimeter of a rectangle is a sum of its four egdes:

P = a + a + b + b

or simpified

P = 2 x a + 2 x b

Which makes it a lot easier.

Let's try it on an examle.
Let's try and find a perimeter of some rectangles.

Here we can se we have edge a= 32 m and edge b= 20 m (here we also use units which doesn't change things a lot).

So our perimeter should be the sum of all edges.

P = 2 x a + 2 x b
P = 2 x 32m + 2 x 20m = 64m + 40m
P = 104m

So our perimeter is 104 m and this is the procudere we will use whenever we have to calculate perimiter of a rectangle.

To find out more about calculating perimeter check out this interesting video:

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Estimating the weight of different objects can be successfully done if we compare them to an object of the same type, or a similar type made of the same materials.

Milk is an interesting example.
Milk is a liquid and like most everyday liquids it consists almost entirely of water - 87%, the rest is protein, milk fat, lactose, micronutrients like calcium etc. So we will estimate that milk is a little bit heavier than water. One liter of water is exactly one kilogram in weight, that is the density of water -  1 kg/l. So we can say that a liter of milk has slightly the same density (weight per kilogram), maybe a little above but close.

Image source: https://www.inchcalculator.com/water-weight-calculator/

If we check it out it turns out one liter of milk is 1 kilogram and 30 grams, so for smaller amounts we can even approximate the weight of milk with a weight of water.
In fact we can approximate the weight of any liquid this way as long as it has similar density as water, we can estimate the density by examining the thickness of the substance though this is not entirely correct but for an estimation it is ok.

So a two liter bottle of juice, for example will most likely weigh around 2 kilograms as juices are almost entirely water.

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First let's see a very nice way how to practically prove that triangles always have 180° sum of angles.
Check out this video:

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A sequence is said to be known if a formula can be given for any particular term using the preceding terms or using its position in the sequence. For example, the sequence 1, 1, 2, 3, 5, 8, 13, … (the Fibonacci sequence) is formed by adding any two consecutive terms to obtain the next term.

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Learning coding nowadays is almost what learning to read and write was to people in the past. If you learn the “language of the machines” you will have a much better understanding of the world of the future and even the world you live in right now!

Here are a few excellent websites that teach you coding. They are sorted by the type of coding they are and what their difficulty level is. You should start from the right one according to your level of experience. Scratch programming is one way:

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How to calculate to get the probability of getting 11 with two dice

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Math is often ambiguous at best, especially when things get more and more complicated. However, this is also true for real life: How do you make sense of team or player statistics in sports, for example? How do the meteorologists figure out where the weather patterns are taking us? The common denominator is graphing. With visualisations we can make complicated things make sense much easier.

Let’s learn the theory about Graphing equations:

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Practical Geometry Excercices:

1. Go around your home and take pictures of things that represent the following (Google the names first if needed!):

• Cone
• Pyramid
• Rectangular prism
• Sphere
• Tetrahedron
• Cylinder
• Cuboid

2. Draw a floor plan of your dream house. Use at least the following shapes in your plan and name them in your drawing.

• Circle
• Square
• Rectangle
• Parallelogram
• Trapezoid

3. Practice using the compass by drawing these beautiful mandala shapes.

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Patterns are everywhere in the world. Maybe the most famous pattern that appears everywhere in the world from nature to fine arts is the Fibonacci sequence. Have a look at the following video to learn more. What kind of repeating patterns can you find at home?

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Quite often in life, we know some variables, but we must figure out an unknown. For example, we may want to save money for a moped, but to know how long it is going to take, we must be able to calculate it according to our weekly allowance, price of the moped and perhaps other things we are going to end up buying with the money.

Linear equation - A practical example

How long would it take for you to come up with the money if your weekly allowance was 10€, the price of the moped 1550€ and you would buy sweets with 2€ every week? What kind of calculations do you need to make to get the answer? Equations are a way of writing expressions with unknown variables that can be figured out using math. Let’s learn the theory:

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Have you ever come across the problem of understanding how warm or cold it is when the temperature is given in Fahrenheit or vice versa, if you live in the US, in Celsius? Wouldn’t it be convenient if you could have a machine that would do the conversion for you? This is what functions do: You input something, and it is given as output as something else according to a rule.

Let’s learn the theory about Functions:

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When one comes across a problem that seems like it's too hard to solve, many give up. However, when equipped with the right strategies, there's no problem in this world that is impossible. As the saying goes, an elephant is eaten one little piece at a time and the same goes for problem solving. Have a look at the steps below that are meant for solving typical school math written problems.

2. What is the QUESTION? Highlight it.
3. What is known? Circle all pieces of information there are.
4. Make a drawing of the problem.
5. How can you solve the problem?
6. Write an expression
7. Calculate

Exercises for Problem solving strategy:

A 30m long rope is used to make a rectangle that is 4m wider than its length. Calculate the width and length of the rectangle using a linear equation.

CDs were sold for a discount of 5,40€. Jane calculated that 7 CDs now cost the same as 5 CDs with the normal price. What is the price before the discount?

Jane, Rita and Howard get 51€ for plowing all the snow of their neighbours driveways. They split the money as follows: Rita gets 7€ more than Howard and Jane, who worked the most, gets twice the amount of Rita and Howard combined. How much money do they each get?

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When looking at box scores of your favourite NHL, NBA, Champions League or F1 racing team, it is important to understand what kind of descriptors are used to make sense of the big set of numbers that are collected. For example, it might be important to know how many times a point guard loses the ball in a basketball match or how fast an F1 driver drives around a certain track. But how can we compare different point guards or F1 drivers to know which one is best and gets the contract or a place in the starting five. This is when mean, median and mode come in handy.

Let’s learn the theory about Statistics: Mean, median and mode

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Easy percentages:

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Source

Let’s learn the theory:

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Prime numbers are numbers that are divisible only by themselves and 1.

Let’s dive into the theory of Prime numbers

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Some of the practical applications of the Pythagorean theorem include marine navigation, building almost anything (houses, bridges etc.) and figuring out which TV-size to choose (sizes are given as diagonals, so you don’t know the hight and width).

Let’s learn the theory about Pythagorean Theorem:

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Let’s learn the theory about Rotational Symmetry:

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Let’s learn the theory and method of Linear Differential Equations:

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Everything that you study in Math has a practical application. Here are some practical applications for average rate of change:

• Rocket science and space travel
• Chemical Engineering Calculations
• Predicting your electricity bill: If you have an idea of the average rate in which electricity is consumed in your household, then you can predict your electricity bill for a month.

Let’s learn the theory about Rate of change:

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Mathematical equations can be used to solve many everyday life situations. Calculating the average speed of an object is one of them. However, perhaps a much more useful skill is the ability to tell someone who is waiting for you to finish your journey, at what time you will arrive.

Let’s learn the theory about Calculating average speed and distance travelled:

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Once you enter adulthood, you will be faced with many responsibilities. You will have to understand new concepts that have a direct effect on your life. Understanding finances can save you a lot of money and help you make wise decisions. Buying your first house or apartment might happen sooner than you think. It’s worth getting ready to understand how to calculate interest and amortization.

Let’s learn the theory about Interest and amortization: