**Background**

Olympics Recreational Mathematics was founded in the city of Loja, by the Particular Educational Unit “San Gerardo” in the school year 2007 – 2008, and since then has organized five meetings between schools in this city for the eighth, ninth and tenth years of education basic

On Friday, March 4, 2005, an interschool mathematics contest was held, which consisted of mental calculation and mathematical games, which was created by Dr. Violeta Pilco Correa and executed by Dr. Astrid Reich.

As of the academic year 2012 – 2013, the invitation was made to all the educational establishments of the Province of Loja. It involved students from schools, public and private, both the sierra and the coast.

In the academic year 2013 – 2014, the invitation was also made to students of sixth and seventh years of basic education, and of high school students of the different public and private educational establishments of Southern Ecuador and Northern Peru.

It is expected that from this event will emerge the participants who will represent the province of Loja and Ecuador, inside and outside the country.

Acquiring the commitment to establish a regular contest and with the standards of international level competitions.

Organized Olympics are not strictly curricular competencies. In them, it is sought, above all, to encourage creativity, inventiveness, critical spirit through a playful approach to mathematics and, at higher levels, the capacity for abstraction and deduction, core characteristics of mathematical activity, applicable and necessary in everyday life, university studies, and professional life.

**General Objective:**

Perform the SG Recreational Mathematics Olympiad at the Binational level, with the fifth, sixth, seventh, eighth, ninth, and tenth grade levels of basic education; First, Second and Third Baccalaureate Ecuador – Third, Fourth, Fifth, Sixth Grade of Primary; First, Second, Third, Fourth and Fifth Secondary Peru.

**Specific objectives:**

- Cultivate enthusiasm and curiosity in children and young people of our region, the study of mathematics.
- To consolidate participation in events related to mathematical work in the educational institutions of southern Ecuador and northern Peru, such as the recreational mathematics Olympiad.
- Stimulate the resolution of mathematical problems in an atmosphere of friendship and companionship.
- Encourage in society the recognition of mathematics as a tool that is part of their culture and that promotes the freedom of the individual by providing them with reasoning and deduction skills.
- Collaborate with the institutions of basic education and baccalaureate in the mathematical formation of children and young people.
- Highlight and recognize the mathematical talent of children and young people.
- Obtain the knowledge and recognition of our work in the Olympics by the Educational Institutions at the International level.
- Promote the participation of the most outstanding competitors, representing the Province and the Country in national and international competitions.

**Levels and Categories:**

Category |
Level |
Ecuador |
Perú |

Group | Level 7 | 1st, 2nd and 3rd Baccalaureate | 3rd, 4th and 5th Grade Secondary School |

Individual | Level 6 | 10th Grade General Basic Education | 2nd Grade Secondary School |

Individual | Level 5 | 9th Grade General Basic Education | 1st Grade Secondary School |

Individual | Level 4 | 8th Grade General Basic Education | 6th Grade Primary School |

Individual | Level 3 | 7th Grade General Basic Education | 5th Grade Primary School |

Individual | Level 2 | 6th Grade General Basic Education | 4th Grade Primary School |

Individual | Level 1 | 5th Grade General Basic Education | 3rd Grade Primary School |

**Tests contents by level**

The tests consist of 10 questions related to the following topics for each level:

**Level 1: 5th Grade of Basic Ecuador – 3rd Grade of Primary Peru**

- Decreasing numerical patterns.
- Natural numbers of up to 9 figures.
- Positional value of natural numbers.
- Sequence and order.
- Operations: addition, subtraction, multiplication, and division of natural numbers
- Calculate the product of natural numbers by 10, 100 and 1000.
- Basic operations with decimal numbers.
- Fractions and operations with fractions.
- Statistics.

**Level 2: 6th Grade of Basic Ecuador – 4th Grade of Primary Peru**

- Numerical successions: increasing and decreasing-combined with the four basic operations.
- Divisibility criteria: prime and composite numbers ..
- MCM and MCD of natural numbers. Exercises and problems.
- Operations: addition, subtraction, multiplication, and division of fractions.
- Decimal expressions and Rounding.
- Percentages
- Areas and Classification of parallelograms, triangles, and trapezoids.
- Statistical study: Representation and interpretation of data, polygonal and circular diagrams.

**Level 3: 7th Grade of Basic Ecuador – 5th Grade of Primary Peru**

- Sets, union, intersection, and difference.
- Divisibility:: MCM and MCD. Exercises and Problems
- Operations combined with fractions (addition, subtraction, multiplication, potentiation, root, and division).
- Problems with fractions.
- Potentiation and exact radication with natural numbers.
- Cartesian plane.
- Volume measurements (Reductions).
- Multiples and divisors.
- Reasoning.

**Level 4: 8th Grade of Basic Ecuador – 6th Grade of Primary Peru**

- Natural and integer numbers
- Successions with natural and integer numbers.
- Fractions and Decimals. Operations and Problems.
- Thales theorem.
- Arithmetic Polynomials and Grouping Signs.
- Simple equations
- Cartesian plane.
- Absolute and Accumulated Frequencies.

**Level 5: 9th Grade of Basic Ecuador – First of Secondary Peru**

- Sets: operations, properties, power set, problems.
- Rational Numbers: operations of addition, subtraction, multiplication, division, potentiation, and root.
- Linear Growth Patterns
- Algebra: algebraic expressions, classification, algebraic term, reduction of similar terms, operations with polynomials.
- Simple equations and inequalities of the first degree.
- Geometry: areas of regular polygons, areas of prisms and cylinders.
- Pythagorean theorem, problems.
- Statistics: measures of central tendency.
- Propositional logic

**Level 6: 10th Grade of Basic Ecuador – 2nd of Secondary Peru**

- Operations combined with real numbers.
- Scientific notation.
- Rationalization.
- Notable Products and Factoring. Algebraic Fractions
- Geometry: Segments: operations, Angles: classification, properties, angles between parallels, Triangles: basic properties.
- Trigonometry: Reasons and functions, Resolution of right triangles and obliques, Trigonometric identities.
- Systems of Linear Equations.
- Linear and quadratic equations.
- Statistics: Frequency distribution, tables, and graphs.
- Propositional logic

**Level 7: 1st, 2nd, 3rd of Baccalaureate Ecuador – 3rd, **4th**, and 5th Secondary Peru**

- Operations combined with real numbers.
- Scientific notation.
- Rationalization.
- Notable Products and Factoring. Algebraic Fractions
- Geometry: Segments: operations, Angles: classification, properties, angles between parallels, Triangles: basic properties.
- Trigonometry: Reasons and functions, Resolution of right triangles and obliques, trigonometric identities, trigonometric equations.
- Matrixes and systems of linear equations.
- Linear, quadratic, polynomial, logarithmic and exponential equations.
- Arithmetic and Geometric Progressions.
- Arc lengths, circular sectors and wheels.
- Segments, angles, circles, circles, triangles.
- Analytical geometry: lines, circles, parabolas, ellipses hyperbolas.
- Functions: domains, ranges, monotonies, symmetries, limits, derivatives, applications.
- Matrices: matrix algebra, matrix inverse, matrix equations, determinants.

**Regulation OLIMARE SG**

**The Unidad Educativa Particular “San Gerardo”**

- To create an adequate environment to perform the tests.
- Guarantee the transparency of the contest.
- Provide timely information.
- Provide the necessary tools for the development of the tests.
- Deliver medals and diplomas to the winners.
- Offer a snack during the break to the participants and representatives of each of the institutions.
- Solve the problems if presented.

**Of the participants**

- The participants are only and exclusively those students belonging to the educational institutions of the province who have made the corresponding registration, through the indicated procedure.

**From the representative of the educational institution**

Each educational institution must appoint a representative, which will have the following functions:

- It will act as the link between the participating institution and Olimare SG.
- Will inform the authorities, students, and parents about the dispositions of participation in the Olympics in a timely and adequate manner.
- Enroll the students of your institution to participate in the Olympics, on the website www.sangerardo.edu.ec, filling out each of the forms correctly.
- The data that should be entered on each participant is the following:

First name.

Year of Basic Education. - You must go to the facilities of the Unidad Educativa Particular “San Gerardo”, the day the test is given, one hour before its start, to register the participants of your institution, bearing the documentation that accredits you as the representative of the institution, as well as the identifications of the participants who will take the test and a letter from the institution’s secretariat that certifies the years in which the enrolled students are enrolled.

**Registration**

Participation in the Olympics is not particular, but institutional. For this reason, it is the institutions that must register according to the procedure indicated below:

- The number of participants: minimum 3 and maximum of 5 participants per level.
- Registration: the institution must register its participation through the forms that will be published on the website of the “San Gerardo” Individual Educational Unit: www.sangerardo.edu.ec until 3:00 pm on the last day of registration.
**INSCRIBIRSE** - For levels 1 -2- and 3 to the email olimarekids3@sangerardo.edu.ec
- For levels 4-5-6 and 7 to the email olimaresg@sangerardo.ecu.ec
- File that will be filled out completely from and with legible handwriting.
- Another way to register is online (online) at: www.sangerardo.edu.ec / option BIOLEAGE / REGISTRATION and choose the OLIMARESG event, until 3:00 pm on the last day of registration.

**Levels and categories:**

- Olimare SG has two types of participation: Individual. This for levels 1,2, 3, 4, 5 and 6. Teams. This only for level 7. The team to be formed for this level will be three people whose members must be in the case of Ecuador a student for each year of high school (First, Second and Third) and in the case of Peru a student by every year of high school (Third, Fourth, and Fifth)
- Schools belonging to Costa regime must enroll their students at the level above the level of basic approved. In other words, the ninth grade students will participate with the eighth-grade students belonging to the Sierra regime and thus correspondingly.
- Each institution can participate with a minimum of 3 and a maximum of 5 students per level in the individual mode and 3 students in the teams’ mode.
- Each institution can participate with a minimum of 3 and a maximum of 5 students per level.

**From the competition**

- The GS Recreational Mathematics Olympics will consist of a single test, which will be given on the day established by the directors, which will contain both multiple choice and development questions for the basic education levels.
- The representative of each educational institution will register the students to participate in the event, according to the procedure indicated in the responsibilities of the representative of the educational institution.
- Additionally, Olimare SG, will publish on its website, the solutions of the test once the event is over.

**From the qualifying committee**

- The qualifying committee will be made up of members from outside the Unidad Educativa Particular “San Gerardo”, preferably teachers from Universities and/or non-participating Educational Institutions and will be in charge of the qualification of the tests.
- In addition, the committee will be responsible for issuing the results and proposing solutions to the problems taken in the tests.
- If deemed necessary, the qualifying committee may request the collaboration of qualified persons belonging to the Organizing Institution to expedite the qualification process.

**Of the exams and their qualification**

- The test for basic education levels will consist of 10 questions: 7 multiple choice and 3 development.
- Each question will have a value of 10 points.
- The duration of the tests is 90 minutes.
- The criteria for qualifying the tests are the following:
- If the answer to a multiple choice question is correct, 10 points will be awarded to the test score.
- If the answer to a multiple-choice question is incorrect, 5 points will be deducted from the test score.
- If a multiple-choice question is not answered, no score will be awarded or removed from the test score.
- The qualification of the development questions is at the discretion of the qualifying committee.
- If the answer to a development question is incorrect, there will be no penalty for the grade.
- The participants who have obtained a grade equal to or greater than 75 points will be declared the winner or winner of the Olympics for each corresponding basic education year.
- In case of a tie, priority will be given to the highest score in the logical reasoning questions.
- If there is a tie in the logical reasoning score, the jury must make a decision based on the development of the operative exercises.
- The test for the general baccalaureate level will consist of 10 development questions, which will have a different degree of complexity.
- Each question will have a value of 10 points.
- The duration of the tests is 90 minutes.
- The criteria for qualifying the tests are the following:
- The qualification of the development questions will be at the discretion of the qualifying committee.
- The participants who have obtained a grade equal to or greater than 75 points will be declared the winner or winner of the Olympiads at the general baccalaureate level.
- In case of a tie, priority will be given to the participant who answered the most questions at the most complex level.

**The results of the competition.**

- The names of the winners of the SG Recreational Mathematics Olympiad for each grade of basic and high school education will be indicated the day after the tests, in an official award ceremony.
- Olimare SG reserves the right to resolve any dispute in a board session with the qualifying committee, should there be any.

**Of the award**

- Gold, silver and bronze medals will be awarded to the winners with their respective diploma for each grade of basic and high school education.
- In addition, diplomas will be awarded with honorable mentions and participation.

**Contacts**

For more information, contact the Unidad Educativa Particular “San Gerardo”.

**Central Building** (Bernardo Valdivieso 11-71 and Mercadillo)

- Telephones: 07 2585658 / Fax 07 2587066
- Hours of operation: Monday to Friday from 7:30 a.m. to 12:30 a.m. and from 2:30 p.m. to 5:30 p.m.
- Email: olimaresg@sangerardo.edu.ec
- Website: www.sangerardo.edu.ec

**Campus Pompeya** (Km. 3.5 via Vilcabamba, Loja, Ecuador)

- Telephone: 07 2545744 / Fax 07 2545743
- Hours of operation: Monday to Friday from 07:15 to 14:00
- Email: olimaresg@sangerardo.edu.ec
- Website: www.sangerardo.edu.ec