Graphs

Graphs

What are the different graph and their uses?

Pie graph

Pie charts are best to use when you are trying to compare parts of a whole. They do not show changes over time. There are two primary use cases for a pie chart: If you want your audience to have a general sense of the part-to-whole relationship in your data and comparing the precise sizes of the slices is less important.

Bar Graph

Bar graphs are used to compare things between different groups or to track changes over time. Bar graphs are ideal for comparing two or more values, or values over time. Data is displayed either horizontally or vertically. Single bar graphs are used to convey discrete values of an item within a category.

Line Graph

Line graphs are used to track changes over short and long periods of time. When smaller changes exist, line graphs are better to use than bar graphs. Line graphs can also be used to compare changes over the same period of time for more than one group. Straight-line graphs are used in the research process and the preparation of the government budget.

Scatter Graph

Scatter graphs uses are to observe and show relationships between two numeric variables. The dots in a scatter plot report the values of individual data points and patterns when the data are taken as a whole. A scatter chart works best when comparing large numbers of data points without regard to time. This is a very powerful type of chart and good when you are trying to show the relationship between two variables

Bubble graph

A bubble chart is primarily used to depict and show relationships between numeric variables. The addition of marker size as a dimension allows for the comparison between three variables rather than just two. Bubble charts are often used to present financial data. Different bubble sizes are useful to visually emphasize specific values. 

Area Chart

Area charts are used to represent cumulated totals using numbers or percentages. Use the area chart for showing trends over time among related attributes. Area charts are commonly used to showcase data that depicts a time-series relationship. Information in an area chart is plotted on the x- and y-axis; data values are plotted using data points that are connected using line segments.

Triangle, Pythagoras Theorem, Square

   Triangle 

Triangle Facts

• The sum of all the internal angles of a triangle is always 180o no matter how the triangle is constructed.

• The length of any side of a triangle is shorter than the sum of the other two sides.

• A triangle can always be split into two right triangles no matter how the triangle is constructed.

• All triangles add up to 180°.

Right angle triangle

The right Triangle angle has one angle that is 90 degrees. The other two angles always add up to 90 degrees but can be different sizes. The longest side of a right-angle triangle is the hypotenuse.

Acute Angle

An acute angle is a triangle that has 3 acute ( less than 90 degrees) angles.

Obtuse Angle

An obtuse angle is a triangle that has one obtuse (greater than 90 degrees) angle. An obtuse angle is a type of angle that is always larger than 90° but less than 180°. In other words, it lies between 90° and 180°.

Equilateral Triangle 

Equilateral triangles have all angles, some measure 60 degrees. All angles are acute angles. An equilateral triangle is a triangle in which all three sides have the same length.

Isosceles Triangle

A triangle with two sides of equal length is an isosceles triangle. The two equal sides of an isosceles triangle are known as 'legs' whereas the third or unequal side is known as the 'base'.

 

 

Scalene Triangle 

A scalene triangle is a triangle in which all three sides are in different lengths, and all three angles are of different measures. However, the sum of all the interior angles is always equal to 180 degrees.

 

Pythagoras's Theorem

what is Pythagoras theorem? a theorem in geometry: the square of the length of the hypotenuse of a right triangle equals the sum of the squares of the lengths of the other two sides.

 

Who is Pythagoras theorem? There is concrete evidence that the Pythagorean Theorem was discovered and proven by Babylonian mathematicians 1000 years before Pythagoras was born. The purpose of this article is to plot a fascinating story in the history of mathematics. Nevertheless, the theorem came to be credited to Pythagoras. It is also proposition number 47 from Book I of Euclid's Elements. According to the Syrian historian Iamblichus (c. 250–330 ce), Pythagoras was introduced to mathematics by Thales of Miletus and his pupil Anaximander.

 

 

When was Pythagoras theorem invented?  The Pythagorean theorem was first known in ancient Babylon and Egypt (beginning about 1900 B.C.). The relationship was shown on a 4000-year-old Babylonian tablet now known as Plimpton 322. However, the relationship was not widely publicized until Pythagoras stated it explicitly.

 

Where was Pythagoras theorem invented?  First was known in ancient Babylon and Egypt.

 

How does Pythagoras theorem work? Pythagoras theorem states that for all right-angled triangles, 'The square on the hypotenuse is equal to the sum of the squares on the other two sides. The hypotenuse is the longest side and it's always opposite the right angle.

 

 

 

Square

What is square? Square, in geometry, a plane figure with four equal sides and four right (90 degrees) angles. A square is a special kind of rectangle ( an equilateral one) and a special kind of parallelogram ( an equilateral and equiangular one).    

What is a square root? a number that produces a specified quantity when multiplied by itself. Square root, in mathematics, a factor of a number that, when multiplied by itself, gives the original number. For example, both 3 and –3 are square roots of 9.

What is a prime number in the square? All square numbers have an odd number of factors. A prime number by definition has exactly 2 factors - 1 and itself. Therefore no prime number is a square and no square number is prime.

What are square numbers?  A square number is a result when a number has been multiplied by itself.

Maths

Mean: The mean is the average of the numbers. It is easy to calculate: add up all the numbers, then divide by how many numbers there are. In other words, it is the sum divided by the count. E.g 10 + 10 + 10 + 10 +10 = 50  50 ÷ 5= 10. 10 is the mean.

Who invented Mean?

The Belgian statistician Quetelet (1796-1874), famous as the inventor of l'homme moyen, the average man, was one of the first scientists to use the mean as tyhe representative value for an aspect of a population.

Mode: The mode is the number that occurs most often in a data set. To find the mode or modal value, it is best to put the numbers in order. Then count how many of each number. A number that appears most often is the mode.

Who Invented Mode?

Early use of the statistical concept of the mode was by English mathematician Karl Pearson (1857-1936) in 1895 

Median: The middle number; found by ordering all data points and picking out the one in the middle (or if there are two middle numbers, taking the mean of those two numbers). Example: The median of 4, 1, and 7 is 4 because when the numbers are put in order (1 , 4, 7) , the number 4 is in the middle.

Who invented Median?

An early use in English of the statistical concept of median was Francis Galton's (1822-1911) 

Video

Mean, Mode and Median

Volume

What Do We Mean By Volume

What do we mean by volume?

- the amount of space that a substance or object occupies or that is enclosed within a container.

How do we measure it?

- In math, the volume is the amount of space in a certain 3D object. For example, a fish tank has 3 feet in length, 1 foot in width, and two feet in height. To find the volume, you multiply length times width times height, which is 3x1x2, which equals six. So the volume of the fish tank is 6 cubic feet.

Is there a conversion to liters?

- A liter is a cubic decimetre, which is the volume of a cube 10 centimeters × 10 centimeters × 10 centimeters (1 L ≡ 1 dm3 ≡ 1000 cm3). Hence 1 L ≡ 0.001 m3 ≡ 1000 cm3 and 1 m3 (i.e. a cubic meter, which is the SI unit for volume) is exactly 1000 L.

The volume of a rectangle

- To find the volume of a rectangle, multiply its 3 dimensions: length x width x height. The volume is expressed in cubic units.

The volume of a cylinder

- A cylinder's volume is π r² h, and its surface area is 2π r h + 2π r²

The volume of a prism 

-Volume of a rectangular prism = (length x width x height) cubic units. V = (l x w x h) cubic units

The volume of a barrel

- Formula. Barrel Volume = πh12 (2D² + d²

The volume of a cone

There is a kiddy pool in the back garden it is 3 meters wide 8 meters long and we can only fill it 1.2m high.

- How much water does it take to full?

to calculate I use 

lxbxh

3 x 8 x l.2 = 28.8

I know that 1m3 = 1 liter = 1000cm3

28.8 x 1000 = 28800 liter

-the pool is on a deck how heavy is it?

3m x 8m x 1.2m = 28.8M3

1l = 1kg

28.8 x 1000 = 28800kg

There is a trailer of barrels 

Each barrel is 1.5m high with a diameter of 0.75m

how much weight is on the trailer

0.75/2 = 0.375

3.142 x 0.375 x 2 = 2.3565m2

2.3565 x 1000 - 2356.5

2356.5 x 6 = 14139L

M3

Cm3

Mm3

Circle

 Perimeter

Circle

𝛑=22/7 or 3.14

How I do calculate the circumference of a circle?

Formule based= using radius

                            circumference = 2𝛑r

                            Using diameter= 

Diameter: The diameter is the length of the line through the center that touches two points on the edge of the circle.

Radius: The Radius is the distance from the center outwards.

The Circumference is the distance once around the circle.

Radius = 26000mm

Diameter = 520000

PI = 22/7 or 3.141

To convert the radius from cm to M I am going to divide it by 100

26000/100 = 260 m

Cir 2 x PI x 260

=1633.62817987

Convert MM To KM

MM	CM	M	KM
12,000MM	1,200CM	12M	0.012KM
5,000MM	500CM	5M	0.005KM
12,000,000MM	120,000CM	1,200M	1.2KM
326MM	32.6CM	0.326M	0.000326KM
1,200MM	120CM	1.2M	0.0012KM

Cm to MM- we multiply by 10 we move the decimals point 1 place to the right. 

M to CM- we multiply by 100 move decimals point 2 places to the right.

MM to CM - we divided by 10 we move the decimals point 1 place to the left.

Cm to M - we divided by 100 we move the decimals point 2 places to the left.

Maths ( Measuring Obiject in CM, MM and M)

 Objects

Grey Circle Table =100mm x 72.3mm

                              =10cm x 7.23cm

                              =1m x 0.0723m

Second Measurement 

Door=73.2mm x 199.5mm

        =7.32cm x 19.95cm

        =0.0732m x 0.1995m

Third Measurement

Tv= 146mm x 84.1mm

    =14.6cm x 8.41cm

    =1.46m x 0.841m

Math

 How To Convert MM To M

Today in maths we learned how to convert mm into m, I will show you how to do it. To convert mm into m, I move the decimal point 3 places left. Today we worked on moving the decimal and dividing, tomorrow for maths we will be working on multiplying.

E.g

3800mm is 3.8metres 

47200mm is 4.720metres

12700mm is 127metres

720mm is 0.720metres

12/02/2021