Hello, my dear pupils!

Do you want a higher mark in Social Sciences? Well, in case you get bored this long weekend, you can do this optional task about population pyramids and send your Power Point presentation to my e-mail: arcihistoria@gmail.com

Optional task



In the Social Science class, our pupils from the 2nd year of ESO have been working on population pyramids. Here you have a powerpoint presentation that will help you to deepen on what we have been doing in class. I hope you will like it.

En la clase de Ciencias Sociales, nuestros alumnos de 2 ESO han estado trabajando las pirámides de población. Aquí tenéis una presentación de diapositivas que os ayudará a profundizar en lo que hemos estado haciendo. Espero que os guste.

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Family tree and powers

Here you have the best family trees in 1ºESO DE:

Valentina López:

Laura Patricia Baldera:
María B. Castillejo:

Marina Liñán:

We studied the relationship between powers and ancestors, I write here a brief summary:








2*2 =4













Take care,



Square roots

The opposite of squaring a number is called finding the square root.

See some examples here.

A square root of a number is a value that can be multiplied by itself to give the original number.

A square root of 9 is 3, because when 3 is multiplied by itself you get 9.

It is like asking:

What can I multiply by itself to get this?

To help you remember think of the root of a tree:

"I know the tree, but what is the root that produced it?"

In this case the tree is "9", and the root is "3"

Here are some more squares and square roots:







These are the first perfect squares:

It is easy to work out the square root of a perfect square, but it is really hard to work out other square roots.

Example: what is √10?

Well, 3 × 3 = 9 and 4 × 4 = 16, so we can guess the answer is between 3 and 4.

  • Let's try 3.5: 3.5 × 3.5 = 12.25
  • Let's try 3.2: 3.2 × 3.2 = 10.24
  • Let's try 3.1: 3.1 × 3.1 = 9.61
  • ...

Getting closer to 10, but it will take a long time to get a good answer!

At this point, I get out my calculator and it says:


But the digits just go on and on, without any pattern.

So even the calculator's answer is only an approximation !

The Easiest Way to Calculate a Square Root

Use your calculator's square root button!

(And also use your common sense to make sure you have the right answer)



Among the earliest notated secular poems are Goliard songs -verses in Latin with subjects ranging from tender love lyrics to obscene drinking songs. A famous 13th-century manuscript known as Carmina burana (Songs of Beur) has been immortalized through its adaptation by 20th-century composer Carl Orff.

SEARCH ONLINE FOR PICTURES OF THIS MANUSCRIPT AND RECORDINGS OF SONGS FROM IT. You may recognize one of the songs, "O, Fortuna", from its use in numerous popular films and television commercials.

We will be commenting on your findings in our first class right after the bank holiday.
Take care


Halloween cakes contest

Do you want to participate?

Click here



Hello everybody!

If you need to have a check on the videos that we´ve been watching today in class, in order to do your composition about consequences of migration, you can find them in this website:

National Geographic videos
  • From Sudan to the United States

  • Responsibility and leadership

  • Cultural Differences

  • Sense of place and community
You can also have a look at your Spanish book (page 220). But remember: write your composition in English and add a final paragraph with your opinion. You have to hand them in next Wednesday.

I hope everything help you! Bye!




Mathematicians have powers

We usually say that witches, wizards and fairies have powers. What is a Power in Maths? We have three words for the same concept: power, exponents and indices. But, what is that?

In a power, we have two main parts:

1. The exponent of a number says how many times to use the number in a multiplication (2 in the example)

2. The base, that says what number is multiplied by itself (8 in the example)


Try on the following website to multiply any number by itself as many times as you want using exponents: See website

If you want to learn what is the meaning of cubed, squared or index form go to the next link: Click here

Once you know everything about powers, you only have to go over the index laws.

To finish with powers, have a little practice by doing these exercises.


Notre Dame School

The earliest documentation of the existence of Léonin and Pérotin occurred in a treatise from ca 1275. The author is unknown to us but is referred to as "Anonymous IV". He praises the skills and accomplishments of the two master composers with reference to specific works and techniques. Today, the four-voice female ensemble aptly named Anonymous 4 specializes in Medieval music.

Listen to a recording by this group to enrich your experience with the music of this era.

Have fun while learning



Pythagoras Theorem

Years ago, a man named Pythagoras found an amazing fact about triangles:

"if the triangle had a right angle (90º)... and you made a square on the three sides, then... the biggest square had the exact same area as the other two squares put together!

It is called Pythagoras Theorem, and can be written in a short equation: a2 + b2 = c2

  • c is the longest side called Hypothenuse
  • a and b are the other sides, named cathetus or legs

Then, the Theorem says: In a right angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

More on Pythagoras Theorem
More on Pythagoras

If you don't believe me, here you can see a demo using water:


Take care,


Welcome to the Section!!!!

We hope you enjoy (and learn) a lot this year.


Rounding and estimating

Estimating i
s an important part of mathematics and a very handy tool for everyday life. It is not always necessary to give the exact number. Get in the habit of estimating amounts of money, lengths of time, distances, and many other physical quantities. For example, if there were 54 785 inhabitants in a town, you could say that its population was approximately 55 000. By doing this, what we have done is to round to the nearest thousand.

Rounding off is a kind of estimating.

To round off decimals
  1. Find the place value you want (the "rounding digit") and look at the digit just to the right of it.
  2. If that digit is less than 5, do not change the rounding digit but drop all digits to the right of it.
  3. If that digit is greater than or equal to five, add one to the rounding digit and drop all digits to the right of it.

To round off whole numbers:

  1. Find the place value you want (the "rounding digit") and look to the digit just to the right of it.
  2. If that digit is less than 5, do not change the "rounding digit" but change all digits to the right of the "rounding digit" to zero.
  3. If that digit is greater than or equal to 5, add one to the rounding digit and change all digits to the right of the rounding digit to zero.
Depending on the study, we may need to round to the nearest ten, hundred, thousand, ten thousand...

I give you some links to practice here,

Round to the nearest thousand, ten thousand, hundred thousand.

Have fun

Statistics Review: Mean, mode, median, range, quartiles

Statistics is the study of data: how to collect, summarize and present it. We commonly use some parameters to support our statistic studies, these are the following I sum up here for you:

The statistical mean is commonly called the average:

To find the mean of a group of numbers:

  • Add the numbers together
  • Divide by how many numbers were added together

Mean 1

Mean 2

The statistical mode is the number that occurs most frequently in a set of numbers.

To find the mode of a group of numbers:

  • Arrange the numbers in order by size.
  • Determine the number of instances of each numerical value.
  • The numerical value that has the most instances is the mode.
  • There may be more than one mode when two or more numbers have an equal number of instances and this is also the maximum instances
  • A mode does not exist if no number has more than one instance.

Example: The mode of 2, 4, 5, 5, 5, 7, 8, 8, 9, 12 is 5.


The statistical median is middle number of a group of numbers that have been arranged in order by size. If there is an even number of terms, the median is the mean of the two middle numbers:

To find the median of a group of numbers:

  • Arrange the numbers in order by size
  • If there is an odd number of terms, the median is the center term.
  • If there is an even number of terms, add the two middle terms and divide by 2.

Median 1

Median 2

The statistical range is the difference between the lowest and highest valued numbers in a set of numbers.

To find the range of a group of numbers:

  • Arrange the numbers in order by size
  • Subtract the smallest number from the largest number.

Range 1

Range 2

Quartiles are the values that divide a list of numbers into quarters.

  • First put the list of numbers in order
  • Then cut the list into four equal parts
  • The Quartiles are at the "cuts"

Quartiles 1

Quartiles 2

Quartiles 3

Quartiles 4