Mathematics. Grades 5-11. Collection of interactive models. FGOS (CDpc)

The collection of interactive mathematics models for grades 5-11 contains more than 200 multi-leaf tasks and demonstrations equipped with detailed methodological recommendations. Models are created in the 1C: Mathematical Designer 7 "and designed to accompany the following sections of mathematics: arithmetic, algebra, functions, planimetry, stereometry, probability and statistics.
models are launched on desktop computers and mobile devices using a browser, do not require installation of additional software or plugins.
The composition of the collection was selected in such a way as to affect a wider range of topics if possible - with an emphasis on those in which the use of interactive models for educational purposes seems to be the most effective. At the same time, the developers sought to present all kinds of educational materials used at different stages of the educational process and at different types of educational activities. From the point of view of the methodology, preference was given to materials that can be used as part of the existing teaching system according to standard programs.
Many models consist of several parts (sheets) - sometimes these are logical steps of one task, sometimes independent examples or exercises. Models, methodically connected with each other, are united in training modules. In total, in the collection of 489 interactive sheets in 213 models, united in 166 training modules. All modules are equipped with detailed instructions that describe the structure of the module, the procedure for working with it, the recommended method of use (work under the guidance of a teacher, independent work in the class, independent work of the house) and methodological recommendations (up to the notes of the lessons) are given.
In models of the-submarines, it is usually possible to check a numerical response, construction, manipulation results, and demonstration models are used to explain theoretical material. But the division is quite conditional: many tasks are accompanied by demonstrations, and working with demonstrations involves answers to some questions. "Tasks with instructions", as a rule, contain either tasks for proof in which there is no automatic verification of solutions, or construction tasks presented by the version of the same problem without instructions.
Many models can be used not only for conducting lessons and setting homework, but also to organize classes of circles and options in mathematics using computer research and experiments.
The collection consists of six parts - arithmetic, algebra, functions, planimetry, stereometry, probability and statistics.
In the “Arithmetic” section, models are presented that can be used in teaching mathematics in grades 5-6:
- models illustrating a bit recording of the number,
- simulators aimed at consolidating the skills of oral account and comparison of natural numbers,
- tasks for the search for dividers and finding the NOD and NOC of several numbers,
- models illustrating the concepts of shares and ordinary fractions,
- models illustrating arithmetic operations with integers and Their properties,
- tasks for the image of numbers on the numerical axis.
In addition, the tasks available in this section allow students to introduce students to the busting method.
In the Algebra "section, models devoted to algebraic expressions (the procedure for performing operations, their properties, calculation, formulas of reduced multiplication) and linear dependence (solution of linear equations and their systems, physical meaning of linear dependence) are offered. The main purpose of these models is the development of skills in working with letter expressions and propaedeutics of studying the functional line of the school course of mathematics.
The “Functions” section includes:
- models illustrating different ways of assigning functions,
- laboratories for studying linear, quadratic, fractional and degree functions, their properties and graphs, as well as The geometric properties of parabola and hyperbola,
- exercises for converting graphs.
The largest section of the collection is dedicated to planimetry. It includes:
- demonstration models illustrating different types of polygons, including triangles and quadrangles,
- laboratories for studying quadrangles and circles,
- tasks for construction, including classical tasks on the construction of a circuit and a ruler, non-standard ways of performing protozoa constructions for the least number of operations, tasks with a limited set of tools, building geometric points of points, tasks for building using geometric transformations,
- illustrations for the tasks for proof and calculation,
- tasks for experiment and research,
- multivariate tasks that allow various configurations and several answers,
- tasks for research using geometric transformations,
the proposed tasks not only cover the entire school course of planimeters but also contain a lot of additional material, which can be studied on circles and electives by ge Ometry. They contribute to the development of geometric observation, mathematical culture, as well as the skills of solving geometric problems for building, calculating, evidence.
The stereometry materials include:
- 3D models of the simplest geometric bodies that can be used as templates to create tasks,
- entertaining tasks-heads to determine the figures for its three types,
- Tasks for building sections of polyhedra.
Stereometric tasks are aimed at the development of spatial imagination, form the ability to build and "read" drawings of spatial figures. They can be used already when meeting stereometry in the introductory course in grade 9, and tasks-heads will be interesting and available even to fifth graders.
In the section "probability and statistics", models developed specifically to study the new probabilistic and statistical line of the school course of mathematics. They allow
- to visualize the process of conducting an accidental experiment with the possibility of changing its parameters,
- to conduct a series of random tests and demonstrate the main probabilistic-statistical patterns,
- check the theoretically obtained through a statistical experiment,
- process the data obtained in the experiment using statistical functions and show them on the graphs,
- perform an independent statistical study.
Probabilized models presented in the collections can be divided into discrete, associated with a classic approach to determining probability, and continuous, based on the so -called "geometric probability". A separate class is devoted to the study of random values ​​and their distributions