Homework: Week
beginning 17th November 2014
This homework is all due by Friday,
21st November.
Spellings
Mathletics
Please let us know if your child
cannot access Mathletics.
Literacy
This week we are continuing to
develop our persuasive writing skills. Your task this week is to write a
persuasive response to this question:
Is it a good thing to ever try and persuade
somebody to do something?
Science
Our science topic this half term is
‘living things’. This week we will be focusing on birds and migration. Can you find out
which birds migrate? Where do they go from and where do they go to? Write a
factfile for one of these birds to present to the class.
Topic- to be done on the blog.
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The Pythagoras Theorem
ReplyDeleteIn mathematics, the Pythagorean Theorem (also known as Pythagoras's theorem), is a relation in Euclidean geometry which teaches about the three sides of a right-angled triangle. It states that the square of the hypotenuse (the side opposite to the right angle) is equal to the sum of the squares of the other two sides.
The theorem can be written as an equation where the lengths of the sides a, b and c, often called the "Pythagorean equation."
This is an example of his equation for the Pythagorean Theorem:
A2 + B2 = C2
A is the height of a right-angled triangle
B is the base of a right-angled triangle
C is the hypotenuse of a right-angled triangle
Pythagoras was a very great and famous mathematician in the Ancient Greek times. His knowledge of mathematics was so outstanding that he was known as the world’s renowned mathematician in Ancient Greek times.
The amazing Pythagoras found out that when the two sides that meet a right angle in a right angle triangle are added, they equal the length of the side opposite the right angle.
ReplyDeleteIf the vertical line is 'A', the horizontal line is 'B' and the diagonal line is 'C' the sum would be: A+B=C.
PYTHAGORAS THEOREM
ReplyDeleteWhen the triangle has a right angle (90°) and squares are made on each of the
three sides, then the biggest square has the exact same area as the other two squares put together!
Pythagoras Theorem
It is called "Pythagoras' Theorem" and can be written in one short equation:
a2 + b2 = c2
•c is the longest side of the triangle
•a and b are the other two sides
The longest side of the triangle is called the "hypotenuse", so the formal definition is:
In a right angled triangle:
The square of the hypotenuse is equal to the sum of the squares of the other two sides.
Let's see if it really works using an example.
Example: A "3,4,5" triangle has a right angle in it.
Pythagoras Theorem
Let's check if the areas are the same:
32 + 42 = 52
Calculating this becomes:
9 + 16 = 25
It works ... like Magic!
Why Is This Useful?
If we know the lengths of two sides of a right angled triangle, we can find the length of the third side. (But remember it only works on right angled triangles!)
How Do I Use it?
Write it down as an equation:
ABC triangle a2 + b2 = c2
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)
ReplyDeleteSo for any right-angled triangle the square on the hypotenuse is equal to the sum of the squares on the other two sides.
In this triangle a2 = b2 + c2 and angle A is a right angle.
Pythagoras' Theorem only works for right-angled triangles, so you can use it to test whether a triangle has a right angle.
I tested this out on a triangle that had the following:
13cm squared = 5cm squared + 12cm squared
I found this was a right angle as 169 = 25 + 144
Pythagoras discovered a rule over 2000 years ago. The rule was that the combined length of the two short sides of a right angle triangle equal the length of the longer side.
ReplyDeleteThe Pythagoras theorem is used to find out the length of the sides of a triangle. It is written in short equation as a2 + b2 = c2. C is the longest of the triangle.A and B are the other sides of the triangle.Now you can use algebra to find any missing value.The longest side is called the "hypotenuse."Over 2000 years ago there was an amazing discovery about triangles:When the triangle has a right angle (90°) ...
ReplyDelete... and squares are made on each of the three sides, then ...
... the biggest square has the exact same area as the other two squares put together!
In mathematics, the Pythagorean Theorem, also known as Pythagoras's theorem, is a relationship among the three sides of a right triangle. It states that the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. The theorem can be written as an equation relating the lengths of the sides a, b and c, often called the "Pythagorean equation"
ReplyDeletea2 + b2 = c2
Where c represents the length of the hypotenuse and a and b the lengths of the triangle's other two sides.
Although it is often said that knowledge of the theorem predates him, the theorem is named after the ancient Greek mathematician Pythagoras (c. 570 – c. 495 BC) as it is he who, by tradition, is credited with its first recorded proof. There is some evidence that Babylonian mathematicians understood the formula. Mesopotamian, Indian and Chinese mathematicians are all known to have discovered the theorem independently and, in some cases, provide proofs for special cases.
The Pythagorean Theorem was one of the earliest theorems known to ancient civilizations. This famous theorem is named for the Greek mathematician and philosopher, Pythagoras. Pythagoras founded the Pythagorean School of Mathematics in Cortona, a Greek seaport in Southern Italy. He is credited with many contributions to mathematics although some of them may have actually been the work of his students.
ReplyDeleteThe Pythagorean Theorem is Pythagoras' most famous mathematical contribution. According to legend, Pythagoras was so happy when he discovered the theorem that he offered a sacrifice of oxen. The later discovery that the square root of 2 is irrational and therefore, cannot be expressed as a ratio of two integers, greatly troubled Pythagoras and his followers. They were devout in their belief that any two lengths were integral multiples of some unit length. Many attempts were made to suppress the knowledge that the square root of 2 is irrational. It is even said that the man who divulged the secret was drowned at sea.
The Pythagorean Theorem is a statement about triangles containing a right angle. The Pythagorean Theorem states that:
"The area of the square built upon the hypotenuse of a right triangle is equal to the sum of the areas of the squares upon the remaining sides."
According to the Pythagorean Theorem, the sum of the areas of the two red squares, squares A and B, is equal to the area of the blue square, square C.
Thus, the Pythagorean Theorem stated algebraically is:
for a right triangle with sides of lengths a, b, and c, where c is the length of the hypotenuse.
Although Pythagoras is credited with the famous theorem, it is likely that the Babylonians knew the result for certain specific triangles at least a millennium earlier than Pythagoras. It is not known how the Greeks originally demonstrated the proof of the Pythagorean Theorem. If the methods of Book II of Euclid's Elements were used, it is likely that it was a dissection type of proof similar to the following:
"A large square of side a+b is divided into two smaller squares of sides a and b respectively, and two equal rectangles with sides a and b; each of these two rectangles can be split into two equal right triangles by drawing the diagonal c. The four triangles can be arranged within another square of side a+b as shown in the figures.
The area of the square can be shown in two different ways:
1. As the sum of the area of the two rectangles and the squares:
2. As the sum of the areas of a square and the four triangles:
Now, setting the two right hand side expressions in these equations equal, gives
CROSSBILL
ReplyDeleteA chunky finch with a large head and bill which is crossed over at the tips. Most often encountered in noisy family groups or larger flocks, usually flying close to treetop height. It feeds acrobatically, fluttering from cone to cone. Adult males are a distinctive brick-red and females greenish-brown.
Latin name
Loxia curvirostra
Family
Finches (Fringillidae)
Where to see them
They are an irruptive species and may be numerous and widespread in some years, less so in others. Established breeding areas include the Scottish Highlands, the North Norfolk coast, Breckland, the New Forest and the Forest of Dean. It regularly comes down to pools to drink.
When to see them
All year round. In irruption years, birds will arrive from the Continent from late summer, often staying to breed.
What they eat
Seeds from conifers.
Population
Europe UK breeding * UK wintering* UK passage*
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40,000 pairs -
It is surely an awful idea to persuade somebody to do something!
ReplyDeleteIf people don't want to do something you must'nt persuade them
to do it because they don't like it!!!!!
Everybody knows that, don't you agree?
Unless, a person desperately wants to get or buy something
You must persuade them. E.G. Do not delay get it today!
If they are scared to ask or do something, do not do it for
Them persuade them to do it by their selves!
Pythagoras was a Greek Mathematician from around 2500 BC,and developed a rule for L-shaped Right Angled Triangles.
ReplyDeleteEgypt was the most famous country where Pythagoras found out that they were using the Right Angled Rule.
Over 2000 years ago there was an amazing discovery about triangles:
Pythagoras proved that,for a right triangle the some of the squares of the two sides that join at a right angle equals the square of the third side. The third side is the side opposite the right angle is called hypotenuse of the right angle triangle. The two shorter sides are called legs.
This formula is called the Pythagorean Theorem in honor of Pythagoras:
A2 + B2 = C2
A and B are the measures of the legs of the triangle and C equals the measure of the hypotenuse.
by Tanraj
Syberian Crane
ReplyDeleteMigration: arctic tundra of Russia to the western population along the Ob Yakutia and western Siberia
Food: These cranes feed mainly on plants although they are omnivores.
Breeding Area: The breeding area of the Siberian crane formerly extended between the Urals and Ob river
Kingdom: Animalia
Phylum: Chordata
Class: Aves
Order: Gruiformes
Family: Gruidae
Genus: Grus
Species: Grus leucogeranus
Time of life: Critically almost extinct