Work program of the elective “Mathematical mosaic”. /3rd grade/

Mathematical mosaic

Bibliographic description:

Shmeleva, S. P. Mathematical mosaic / S. P. Shmeleva. — Text: direct // School pedagogy. — 2020. — No. 2.1 (9.1). — P. 72-75. — URL: https://moluch.ru/th/2/archive/60/2422/ (access date: 10.10.2020).


Type of activity: educational

Shape: circle

Direction of education: education of social responsibility and competence; nurturing hard work, a conscious, creative attitude to education, work and life, preparation for a conscious choice of profession.

Direction of personality development: general intellectual

Explanatory note

The program of extracurricular activities is designed for 6th grade students and is designed taking into account their age characteristics. Individual - group lessons of the course "Mathematical Mosaic" are included in extracurricular activities in the direction of general intellectual development of the individual.

The program takes into account the age characteristics of schoolchildren and therefore provides for the organization of mobile activities of students that do not interfere with mental work. For this purpose, active mathematical games are included. There is a sequential change of “centers” of activity by one student during one lesson; moving around the classroom while completing math assignments. During classes, it is important to maintain direct communication between children (the opportunity to approach each other, talk, exchange thoughts). Some math games and tasks can take the form of competitions between teams.

The novelty of this course lies in the fact that during the classes students are introduced to categories of mathematical problems that are not directly related to the school curriculum, and to new methods of reasoning, which are so necessary for successfully solving educational and life problems.

The relevance of the course “Mathematical Mosaic” is the need to implement individual educational requests and satisfy cognitive needs.

The main goal of the program is to develop creative abilities, logical thinking, deepen the knowledge gained in the lesson, and expand the child’s general horizons in the process of considering practical problems and issues solved using arithmetic or initial knowledge of geometry.

Achieving this goal is ensured by solving the following tasks :

– deepening and expanding students’ knowledge in mathematics;

– development of mathematical outlook, thinking, research skills of students;

– development of practical skills in the field of geometry;

– formation of ideas about mathematics as part of universal human culture; instilling students' interest in mathematics;

– development of spatial imagination, logical and visual thinking;

– education of hard work, patience, perseverance, initiative;

– practical application of cooperation in collective information activities.

A non-evaluative form of training organization is being implemented. To assess the effectiveness of classes, the following indicators are used: the degree of independence of students in completing tasks; cognitive activity in class: interest; results of test tasks and olympiad tasks; the ability to plan the answer and progress in solving problems; originality of the answer. Classes are held in a mathematics classroom using multimedia equipment (projector, computer), video materials, and computer programs.

Forms of summing up: participation in olympiads, subject weeks, project activities, quizzes.

Table 1

Educational and thematic planning

Contents of topics

Topic 1. Divisibility of numbers.

From the history of interesting numbers. Ancient number writing systems. Ancient mass measures and ancient Russian money. Interesting properties of numbers. Signs of divisibility. Euclid's algorithm. GCD, LCM and calculator. Dirichlet's principle. Using the Dirichlet principle in solving divisibility problems.

Topic 2. Solving non-standard problems.

How to learn to solve problems. Search for patterns. Solving problems for joint work. Solving motion problems. Solving problems in reverse. An ancient way to solve problems involving mixing substances. Percentage calculations in life situations. Cash payments. How to equalize two expressions. Solving equations. Arithmetic puzzles. Time watch. The history of the calendar.

Topic 3. Geometric mosaic.

Geometry on checkered paper. Geometric puzzles. Problems involving cutting and folding shapes. Space and dimension. Interesting placements and permutations. Dots and broken lines. Parallelism of lines on a plane and in space. Perpendicularity of lines on a plane and in space. Visual representations of spatial bodies. Development of a rectangular parallelepiped.

Topic 4. Descriptive statistics.

Statistical characteristics of the data set: arithmetic mean, mode, median, largest and smallest value. Practical application of statistics. Constructing pie charts.

Test materials

Control is carried out mainly during tests at the end of the course, mathematical games, mathematical holidays, and creative works.

Final Olympiad 6th grade

1. Several teams came to the tournament with the flags of their provinces. It turned out that all the flags are different, each consists of three horizontal stripes of the same length and width. Each stripe is painted yellow, red or blue, and adjacent stripes are necessarily different in color. What is the largest number of teams with such flags that could come to the tournament?
2. Select suitable 5 consecutive natural numbers and put a + or − sign in front of each of them so that the algebraic sum is equal to 2012.
3. Alex wants to measure the diagonal length of a brick. The only measuring tool he has is a ruler, but he can take several identical bricks. How can he do this and what is the smallest number of bricks he will have to use?
4. Find the smallest value of the product (A−B)(A−C)(B−C) provided that A, B and C are even numbers, and A>B>C>2012.
5. The school director decided to compare the results of his students’ performance at the Olympiad with their neighbors. First, he calculated what percentage of the 5th grade Olympiad participants became diploma winners. It turned out that this figure in his school is 20% higher than in the neighboring one. Exactly the same difference of 20% was obtained when comparing the same indicators in grades 6, 7 and 8. However, when the director compared the same indicators for all participants from grades 5–8 at once, the advantage of the same 20% was on the side of the neighbors. How could this happen?
6. Place different natural numbers in the cells of a 5x5 square so that the sum in each row and column is equal to 2012.

Research topics

One of the most difficult tasks in projects is choosing a topic for students' research work in mathematics. She can wear

1) historical character : “Great mathematicians”, “The emergence of geometry”, “The emergence of counting”, “The Sieve of Eratosthenes”, “The history of the development of mathematics”, “From the history of fractions”, “Historical and mathematical excursion”, “The life of zero - numbers and numbers",

2) serve as a continuation of the topic of the lesson or deepen it : “Arithmetic and geometric progressions in our lives”, “In the world of polyhedra”, “In the world of prisms”, “Dependence of the number of diagonals of a polygon on

3) number of vertices", "Study of the influence of the radius of a circle on the circumference and area of ​​a circle"

4) be of an applied nature: “Loans and interest in the life of a modern person”, “Without a measuring stick or measuring with bare hands”, “Methods of oral calculations”, “Geometry on checkered paper”, “Dividing a circle into equal parts”, “Parquets” ,

5) related to local history: “Research on the convenient location of a school in the city”, “Calculations of the costs of building an ice skating rink in the city”;

6) be creative in nature: “Author’s problems”, “Problems in drawings”, “Favorite drawings on a coordinate plane”, “Mathematical tales”;

7) have an entertaining, playful, magical character : “Variations on an Escher Theme”, “Riddles of the Pyramids”, “Theory of Probability in Gambling”, “Mathematical Tricks”, “Unusual in Ordinary Numbers”, “Magic Numbers”, “In the World” amazing numbers”, “Do numbers influence fate?”, “Study of the Möbius strip”;

logical problems: “Types of problems on logical thinking”, “Direct and inverse operations in mathematics”, “Solving logical problems”, “Mathematical sophisms”;

9) revealing the beauty of mathematics, connection with art: “Unified laws of mathematics, art and nature”, “Symmetry of crystals”, “Symmetry around us”, “Mathematics and the laws of beauty”, “Mathematics around us”, “Numbers in fairy tales”, “Use of origami in human life”, “Golden ratio around us”.

Literature:

1. B. P. Geidman. “Preparation for the Mathematical Olympiad”, M., 2012.
2. T. D. Gavrilova. "Entertaining Mathematics", ed. Teacher, 2011
3. E. V. Galkin. “Non-standard problems in mathematics, grades 5–11”, M., 1969.
4. O. S. Sheinina, G. M. Solovyova. Mathematics. School club activities. Moscow "Publishing House NC ENAS" 2007
5. FarkovA. V. Mathematical clubs in school, grades 5–8. M: Iris-press, 2012
6. I. I. Grigorieva “Mathematics. Subject week at school." Moscow, Globe 2014
7. M. A. Kalugin. “After lessons: puzzles, crosswords, puzzles” Yaroslavl, “Academy of Development”, 2014
8. I. F. Sharygin, A. V. Shevkin “Tasks for ingenuity. Grades 5–6” Moscow, “Prosveshchenie”, 2014
9. https://ru.wikipedia.org/
10. https://pedsovet.org/ - presentations, simulators, scenarios
11. https://ya-umni4ka.ru/ - competitions, olympiads

Key terms
(automatically generated)
: problem solving, task, Number, checkered paper, Mathematician, divisibility test, extracurricular activities, geometric mosaic, logical thinking, least value.