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La Unión Europea ha propuesto un nuevo paquete de sanciones contra Rusia que incluye un embargo al petróleo. El embargo prohibiría la importación de petróleo ruso a la UE y también impediría el acceso de buques rusos a puertos europeos. Sin embargo, Hungría se opone firmemente al embargo al petróleo, argumentando que su economía depende en gran medida de las importaciones de energía rusa.
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AIMSterdam
The document summarizes Arina and Isabella's trip to Amsterdam for a math camp. Some key details:
- Arina and Isabella arrived in Amsterdam and were excited to meet their hosts, Zorana and Asli.
- They participated in welcome activities at their school including watching music videos from different countries and learning about each other.
- Over the next few days, they went on a treasure hunt, visited science museums, went bowling, and made an unsuccessful attempt at baking an apple pie.
- The trip concluded with a math competition, souvenir shopping, and a final visit to the Van Gogh museum before sadly having to leave Amsterdam.
Triangular numbers
Triangular numbers represent the number of points within an equilateral triangle that is filled uniformly with points. The formula for a triangular number "n" is equal to the number of points in a triangle with "n" points on each side. Triangular numbers have links to other figurate numbers, such as the sum of two consecutive triangular numbers equalling a perfect square, which is the difference between the numbers.
Triangular numbers
Triangular numbers represent the number of dots or points in an equilateral triangle, with each additional row adding the next positive integer of dots. The n-th triangular number is calculated by adding all the integers from 1 to n, representing the total number of handshakes if n people greet each other or nodes connected in a fully meshed network. Triangular numbers model connectivity in situations that can be arranged in an triangular format.
Polygonal and square numbers
This document discusses polygonal numbers and square numbers. It defines polygonal numbers as numbers that can be represented by points in polygonal shapes, with the first number being 1 and subsequent numbers determined by adding points. Some examples of polygonal numbers given are triangles, squares, pentagons, and hexagons. It then defines square numbers as natural numbers that are the square of another natural number, providing the formula k2. It notes some properties of square numbers like their placement in the multiplication table and that the last digits of square numbers are limited to 0, 1, 4, 5, 6, or 9.
Pentagonal numbers
Pentagonal numbers are numbers that form a pentagon shape. The nth pentagonal number can be calculated using the formula n(3n-1)/2. Some properties of pentagonal numbers include:
1) The difference between successive pentagonal numbers is 3n-2.
2) Adding successive pentagonal numbers gives the formula 3n^2 - 4n + 2.
3) Examples are provided to demonstrate calculating individual pentagonal numbers and using the properties above.
Pentagonal numbers
This document discusses pentagonal numbers, which are numbers that can be represented as a pentagonal pattern of dots. It provides a general formula for calculating pentagonal numbers and cites two websites as sources for more information on pentagonal numbers, including their definitions and properties.
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AIMSterdam
The document summarizes Arina and Isabella's trip to Amsterdam for a math camp. Some key details:
- Arina and Isabella arrived in Amsterdam and were excited to meet their hosts, Zorana and Asli.
- They participated in welcome activities at their school including watching music videos from different countries and learning about each other.
- Over the next few days, they went on a treasure hunt, visited science museums, went bowling, and made an unsuccessful attempt at baking an apple pie.
- The trip concluded with a math competition, souvenir shopping, and a final visit to the Van Gogh museum before sadly having to leave Amsterdam.
Triangular numbers
Triangular numbers represent the number of points within an equilateral triangle that is filled uniformly with points. The formula for a triangular number "n" is equal to the number of points in a triangle with "n" points on each side. Triangular numbers have links to other figurate numbers, such as the sum of two consecutive triangular numbers equalling a perfect square, which is the difference between the numbers.
Triangular numbers
Triangular numbers represent the number of dots or points in an equilateral triangle, with each additional row adding the next positive integer of dots. The n-th triangular number is calculated by adding all the integers from 1 to n, representing the total number of handshakes if n people greet each other or nodes connected in a fully meshed network. Triangular numbers model connectivity in situations that can be arranged in an triangular format.
Polygonal and square numbers
This document discusses polygonal numbers and square numbers. It defines polygonal numbers as numbers that can be represented by points in polygonal shapes, with the first number being 1 and subsequent numbers determined by adding points. Some examples of polygonal numbers given are triangles, squares, pentagons, and hexagons. It then defines square numbers as natural numbers that are the square of another natural number, providing the formula k2. It notes some properties of square numbers like their placement in the multiplication table and that the last digits of square numbers are limited to 0, 1, 4, 5, 6, or 9.
Pentagonal numbers
Pentagonal numbers are numbers that form a pentagon shape. The nth pentagonal number can be calculated using the formula n(3n-1)/2. Some properties of pentagonal numbers include:
1) The difference between successive pentagonal numbers is 3n-2.
2) Adding successive pentagonal numbers gives the formula 3n^2 - 4n + 2.
3) Examples are provided to demonstrate calculating individual pentagonal numbers and using the properties above.
Pentagonal numbers
This document discusses pentagonal numbers, which are numbers that can be represented as a pentagonal pattern of dots. It provides a general formula for calculating pentagonal numbers and cites two websites as sources for more information on pentagonal numbers, including their definitions and properties.
Fibonacci numbers
This document discusses the Fibonacci sequence and numbers. It notes that each Fibonacci number is the sum of the two previous ones, starting with 1 and 1. Nature often displays the Fibonacci sequence, like pineapple spirals. The mathematician Leonardo Fibonacci invented these numbers and the sequence is named after him. Sources used include Wikipedia pages on Fibonacci numbers.
Factorial numbers
Factorial numbers are calculated by multiplying all natural numbers from 1 up to and including a given number. For example, 4! = 1 x 2 x 3 x 4. In general, n! is calculated as n x (n-1) x (n-2) x ... x 2 x 1. Factorial numbers were originally denoted with an exclamation point rather than the modern notation. They are used in various mathematical exercises and calculations.
Cube numbers
The document discusses cubic numbers, which are numbers multiplied by themselves three times. It provides examples such as 3 cubed equaling 27 and 4 cubed equaling 64. The cubic root of a number is the value that when cubed produces the original number. Perfect cubes are the results of cubing whole numbers, with examples including 8 from 2 cubed and 1331 from 11 cubed. Cubic numbers can also have roots that are not whole numbers, such as the cubic root of 40 being between 3.4 and 3.5.
Amicable numbers
Amicable numbers are pairs of numbers where the sum of the divisors of each number (excluding the number itself) is equal to the other number. The document provides examples of amicable number pairs such as 220 and 284, where the sum of divisors of 220 is 284 and the sum of divisors of 284 is 220. The document also explains how to find if two numbers are an amicable pair by listing the divisors of each number and comparing the sums. Amicable numbers were first discovered in antiquity by Pythagoras and later, in 1636, Fermat discovered another pair.
Magic squares
This document provides information about magic squares. It defines a magic square as a grid of numbers where the sums of each row, column and diagonal are always the same number, called the constant. A 3x3 magic square's constant is 15 if it contains the numbers 1-9 without repetition. The document explains how to construct a 3x3 magic square by placing 5 in the center and arranging the remaining numbers such that the row/column/diagonal sums equal 15. It provides examples and tasks for creating different types of magic squares.
Dressing Mr. Cube- How we worked
The document describes a classroom activity where students were tasked with creating net patterns to dress a cube-shaped character named Mr. Cube. Students worked in groups to find all possible net patterns using six squares. They were challenged to consider symmetrical patterns, "zippers" to connect the squares, and coloring the nets attractively. The teacher observed that students engaged well with the constructive metaphorical task, with some groups working efficiently through teamwork and sharing roles.
Tessellations instructions
This document provides instructions for creating Escher-type tessellations in 4 steps: starting with a square and cutting curves into the top and side, then translating and rotating the side pieces to the other sides and taping together to form a pattern; cutting out the pattern and using it to tessellate a large piece of paper by tracing the shape and sliding it to fit into the previous tracing until the paper is filled, then adding details and color.
Hexagonal figures fractals
The document describes creating an ornament for Christmas using hexagonal fractal figures with different color combinations. It states that each hexagon side can be one of 6 colors, no hexagon will have the same color in two parts, and rotations and reflections are not differences. It then asks what the colors are of the missing 20th hexagon to complete the set of all combinations using the 6 colors without repetition, and which hexagon will not be used to join the 19 in the provided figure so that touching sides are the same color.
Aims Avila_Claudia si Iulia
Iulia Cisu and Claudia Stanciu document their trip to Avila, Spain for a school project over several days. On Sunday they arrived in Madrid and took a train to Avila where they were greeted by their Spanish partners and toured the town. On Monday they had classes and activities at school with other international students and went on a treasure hunt around Avila. On Tuesday they had math-focused classes and activities and toured the city in the evening. On Wednesday they took a trip to Madrid to visit the Mathematics Institute and tour the city. On Thursday they performed their "Maths Ballet" and toured Avila one last time before departing on Friday after saying goodbye to their hosts and taking a tour
Alexandra's Diary from Avila
The team took a flight from Bucharest to Madrid, then a train to their final destination of Ávila where they were greeted by their partner families. Over the next few days, they participated in various math-focused workshops, activities and tours around Ávila and Madrid. The student formed a close friendship with their Spanish partner Sara and enjoyed learning about math in new ways and Spanish culture. On the last day, they reluctantly said goodbye after a week of the best experiences.
Sierpinski carpet work proposal
Schools participate in a Sierpinski carpet project where they:
1) Receive templates and stickers to create iterations of the Sierpinski carpet pattern in small groups.
2) Upload videos of the process and final iterations to an online platform.
3) Bring their iterations to Greece to mount the larger 3rd iteration carpet, then continue the process to collaboratively create a 4th and 5th iteration carpet.
A perfect week in Poland
The document summarizes a student's perfect week visiting Poland for a school project. It describes their arrival and being paired with host families. During the week, they participated in various activities like visiting town halls, museums, and lectures. They also went on treasure hunts and solved math mysteries. The student formed strong bonds with their host family and other students. They were sad to leave Poland at the end of the week, but were grateful for the opportunity to learn about another culture and make international friends.
Visit to Poland as lived by Ioana
The student describes their experience participating in the 2014 COMENIUS AIMS project in Poland. Over the course of the week-long trip, the student and their classmates from Romania met students from Greece and the Netherlands and stayed with host families in Myslenice, Poland. Their activities included learning about the history of Myslenice, playing math games, going on a treasure hunt, horseback riding, visiting historic sites in Krakow, solving a "mathematical crime mystery", and designing pages for a magazine about the AIMS project. Although sad to leave at the end of the week, the student felt the trip provided an unforgettable experience to learn about math and culture in Poland.
Christma(th)s romania
This document provides instructions for a Christmas quiz with two riddles. Solving the first riddle of finding the square of the third prime number results in the number 9, which corresponds to the letter I. Solving the second riddle of evaluating the function f(x)=2^x-2^1 with x=2^2 results in the number 6, which corresponds to the letter F. Participants are asked to write the letters on paper and hold them to their webcams, with the intent that all letters combined from different countries will form a sentence.
Diary AIMS France2013
The document summarizes the activities during a Comenius project in France between November 17-22, 2013. Participants from several European countries engaged in icebreaker activities like introducing themselves and a treasure hunt around the city of Charleville. Teachers and students collaborated on math activities like calculating costs of pie ingredients in different countries and a puppet show. The group also took a trip to Paris where they visited educational sites and had creative math workshops. Students participated in a math quiz and farewell celebrations marked the end of the successful collaboration.
Preferences
The document summarizes the results of a survey conducted by students from class 8C. They gathered information from 7-10 year olds and 11-14 year olds on topics such as countries visited, hobbies, favorite subjects, sports, music and future careers. For example, the majority of 7-10 year olds preferred football over other sports while 11-14 year olds were more evenly split between football, basketball and tennis. The survey also found Romanian language and literature and English were the most popular school subjects overall.
Students Preferences Statistics
The document summarizes the results of a survey conducted by 8 teams of students from class 8C. The survey gathered information from 7-10 and 11-14 year old children on topics such as which countries they have visited, how they spend their spare time, favorite subjects and sports. It also includes charts showing results on favorite music types, landmarks visited in Romania, and future career wishes.
A piece of pie in Bucharest-2
This document provides information about baking a chocolate pie, including:
- Ingredients and quantities needed to make one pie and one portion. Flour, butter, sugar, cocoa, eggs, and other ingredients are listed.
- Calculations of the costs to make one pie and one portion based on prices of ingredients in Bucharest, Romania. The cost per portion is approximately 1.735 lei.
- Comparisons of the cost per portion in other cities involved in the project, ranging from 0.91 times to 1.66 times the Bucharest cost.
- The average cost per portion across all cities is approximately 2.37 lei.
- An indication that the pie was
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Fibonacci numbers
This document discusses the Fibonacci sequence and numbers. It notes that each Fibonacci number is the sum of the two previous ones, starting with 1 and 1. Nature often displays the Fibonacci sequence, like pineapple spirals. The mathematician Leonardo Fibonacci invented these numbers and the sequence is named after him. Sources used include Wikipedia pages on Fibonacci numbers.
Factorial numbers
Factorial numbers are calculated by multiplying all natural numbers from 1 up to and including a given number. For example, 4! = 1 x 2 x 3 x 4. In general, n! is calculated as n x (n-1) x (n-2) x ... x 2 x 1. Factorial numbers were originally denoted with an exclamation point rather than the modern notation. They are used in various mathematical exercises and calculations.
Cube numbers
The document discusses cubic numbers, which are numbers multiplied by themselves three times. It provides examples such as 3 cubed equaling 27 and 4 cubed equaling 64. The cubic root of a number is the value that when cubed produces the original number. Perfect cubes are the results of cubing whole numbers, with examples including 8 from 2 cubed and 1331 from 11 cubed. Cubic numbers can also have roots that are not whole numbers, such as the cubic root of 40 being between 3.4 and 3.5.
Amicable numbers
Amicable numbers are pairs of numbers where the sum of the divisors of each number (excluding the number itself) is equal to the other number. The document provides examples of amicable number pairs such as 220 and 284, where the sum of divisors of 220 is 284 and the sum of divisors of 284 is 220. The document also explains how to find if two numbers are an amicable pair by listing the divisors of each number and comparing the sums. Amicable numbers were first discovered in antiquity by Pythagoras and later, in 1636, Fermat discovered another pair.
Magic squares
This document provides information about magic squares. It defines a magic square as a grid of numbers where the sums of each row, column and diagonal are always the same number, called the constant. A 3x3 magic square's constant is 15 if it contains the numbers 1-9 without repetition. The document explains how to construct a 3x3 magic square by placing 5 in the center and arranging the remaining numbers such that the row/column/diagonal sums equal 15. It provides examples and tasks for creating different types of magic squares.
Dressing Mr. Cube- How we worked
The document describes a classroom activity where students were tasked with creating net patterns to dress a cube-shaped character named Mr. Cube. Students worked in groups to find all possible net patterns using six squares. They were challenged to consider symmetrical patterns, "zippers" to connect the squares, and coloring the nets attractively. The teacher observed that students engaged well with the constructive metaphorical task, with some groups working efficiently through teamwork and sharing roles.
Tessellations instructions
This document provides instructions for creating Escher-type tessellations in 4 steps: starting with a square and cutting curves into the top and side, then translating and rotating the side pieces to the other sides and taping together to form a pattern; cutting out the pattern and using it to tessellate a large piece of paper by tracing the shape and sliding it to fit into the previous tracing until the paper is filled, then adding details and color.
Hexagonal figures fractals
The document describes creating an ornament for Christmas using hexagonal fractal figures with different color combinations. It states that each hexagon side can be one of 6 colors, no hexagon will have the same color in two parts, and rotations and reflections are not differences. It then asks what the colors are of the missing 20th hexagon to complete the set of all combinations using the 6 colors without repetition, and which hexagon will not be used to join the 19 in the provided figure so that touching sides are the same color.
Aims Avila_Claudia si Iulia
Iulia Cisu and Claudia Stanciu document their trip to Avila, Spain for a school project over several days. On Sunday they arrived in Madrid and took a train to Avila where they were greeted by their Spanish partners and toured the town. On Monday they had classes and activities at school with other international students and went on a treasure hunt around Avila. On Tuesday they had math-focused classes and activities and toured the city in the evening. On Wednesday they took a trip to Madrid to visit the Mathematics Institute and tour the city. On Thursday they performed their "Maths Ballet" and toured Avila one last time before departing on Friday after saying goodbye to their hosts and taking a tour
Alexandra's Diary from Avila
The team took a flight from Bucharest to Madrid, then a train to their final destination of Ávila where they were greeted by their partner families. Over the next few days, they participated in various math-focused workshops, activities and tours around Ávila and Madrid. The student formed a close friendship with their Spanish partner Sara and enjoyed learning about math in new ways and Spanish culture. On the last day, they reluctantly said goodbye after a week of the best experiences.
Sierpinski carpet work proposal
Schools participate in a Sierpinski carpet project where they:
1) Receive templates and stickers to create iterations of the Sierpinski carpet pattern in small groups.
2) Upload videos of the process and final iterations to an online platform.
3) Bring their iterations to Greece to mount the larger 3rd iteration carpet, then continue the process to collaboratively create a 4th and 5th iteration carpet.
A perfect week in Poland
The document summarizes a student's perfect week visiting Poland for a school project. It describes their arrival and being paired with host families. During the week, they participated in various activities like visiting town halls, museums, and lectures. They also went on treasure hunts and solved math mysteries. The student formed strong bonds with their host family and other students. They were sad to leave Poland at the end of the week, but were grateful for the opportunity to learn about another culture and make international friends.
Visit to Poland as lived by Ioana
The student describes their experience participating in the 2014 COMENIUS AIMS project in Poland. Over the course of the week-long trip, the student and their classmates from Romania met students from Greece and the Netherlands and stayed with host families in Myslenice, Poland. Their activities included learning about the history of Myslenice, playing math games, going on a treasure hunt, horseback riding, visiting historic sites in Krakow, solving a "mathematical crime mystery", and designing pages for a magazine about the AIMS project. Although sad to leave at the end of the week, the student felt the trip provided an unforgettable experience to learn about math and culture in Poland.
Christma(th)s romania
This document provides instructions for a Christmas quiz with two riddles. Solving the first riddle of finding the square of the third prime number results in the number 9, which corresponds to the letter I. Solving the second riddle of evaluating the function f(x)=2^x-2^1 with x=2^2 results in the number 6, which corresponds to the letter F. Participants are asked to write the letters on paper and hold them to their webcams, with the intent that all letters combined from different countries will form a sentence.
Diary AIMS France2013
The document summarizes the activities during a Comenius project in France between November 17-22, 2013. Participants from several European countries engaged in icebreaker activities like introducing themselves and a treasure hunt around the city of Charleville. Teachers and students collaborated on math activities like calculating costs of pie ingredients in different countries and a puppet show. The group also took a trip to Paris where they visited educational sites and had creative math workshops. Students participated in a math quiz and farewell celebrations marked the end of the successful collaboration.
Preferences
The document summarizes the results of a survey conducted by students from class 8C. They gathered information from 7-10 year olds and 11-14 year olds on topics such as countries visited, hobbies, favorite subjects, sports, music and future careers. For example, the majority of 7-10 year olds preferred football over other sports while 11-14 year olds were more evenly split between football, basketball and tennis. The survey also found Romanian language and literature and English were the most popular school subjects overall.
Students Preferences Statistics
The document summarizes the results of a survey conducted by 8 teams of students from class 8C. The survey gathered information from 7-10 and 11-14 year old children on topics such as which countries they have visited, how they spend their spare time, favorite subjects and sports. It also includes charts showing results on favorite music types, landmarks visited in Romania, and future career wishes.
A piece of pie in Bucharest-2
This document provides information about baking a chocolate pie, including:
- Ingredients and quantities needed to make one pie and one portion. Flour, butter, sugar, cocoa, eggs, and other ingredients are listed.
- Calculations of the costs to make one pie and one portion based on prices of ingredients in Bucharest, Romania. The cost per portion is approximately 1.735 lei.
- Comparisons of the cost per portion in other cities involved in the project, ranging from 0.91 times to 1.66 times the Bucharest cost.
- The average cost per portion across all cities is approximately 2.37 lei.
- An indication that the pie was
Más de Irina Vasilescu (20)
Notas del editor
- 06 nov 2008
- 06 nov 2008
- 06 nov 2008