Math. Grades 5-11. Collection of interactive models. FSES (CDpc)

The collection of interactive models in mathematics for grades 5-11 contains more than 200 multi-leaf tasks and demonstrations with detailed methodological recommendations. The models are created in the program '1C:Mathematical Designer 7' and are designed to support the following sections of mathematics: arithmetic, algebra, functions, planimetry, stereometry, probability and statistics.
Models are run on desktop computers and mobile devices using a browser and do not require installation of additional software or plug-ins.
The composition of the collection was chosen to cover as wide a range of topics as possible, with an emphasis on those in which the use of interactive models for educational purposes seems to be most effective. At the same time, the developers sought to present all the different types of learning materials used at different stages of the learning process and in different types of learning activities. From the point of view of methodology, preference was given to materials that can be used within the existing system of teaching standard programs.
Many models consist of several parts (sheets) - sometimes they are logical steps of one task, sometimes they are independent examples or exercises. The models, methodologically related to each other, are combined into teaching modules. In total, the collection contains 489 interactive sheets in 213 models organized into 166 learning modules. All modules are provided with detailed instructions, which describe the structure of the module, the order of work with it, the recommended way of use (work under the guidance of the teacher, independent work in the classroom, independent work at home) and provide methodological recommendations (up to lesson notes).
In models-tasks there is usually an opportunity to check the numerical answer, construction, manipulation results, and models-demonstrations are used when explaining theoretical material. But this division is rather conditional: many tasks are accompanied by demonstrations, and work with demonstrations implies answers to some questions. 'Tasks with instructions', as a rule, contain either proof tasks, in which no automatic checking of solutions is provided, or construction tasks, presented as a version of the same task without instructions.
Many models can be used not only for conducting lessons and setting homework, but also for organizing classes of circles and elective courses in mathematics with the use of computer research and experiments.
The collection consists of six parts - arithmetic, algebra, functions, planimetry, stereometry, probability and statistics.
The 'Arithmetic' section includes models that can be used in teaching math in grades 5-6:
-models illustrating the digitization of numbers,
-trainers aimed at strengthening oral counting skills and comparing natural numbers,
-tasks for finding divisors and finding the NOD and NOC of several numbers,
-models illustrating the concepts of fractions and common fractions,
-models illustrating arithmetic operations with integers and their properties,
-tasks for representing numbers on the number axis.
In addition, the tasks in this section allow students to familiarize themselves with the method of brute force.
The 'Algebra' section offers models devoted to algebraic expressions (order of operations, their properties, calculation, formulas of reduced multiplication) and linear dependence (solution of linear equations and their systems, physical meaning of linear dependence). The main purpose of these models is to develop skills of 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 specifying functions,
labs for studying linear, quadratic, fractional linear and step functions, their properties and graphs, as well as geometric properties of parabolas and hyperbolas,
exercises on graph transformations.
The largest section of the collection is devoted to planimetry. It includes:
- demonstration models illustrating different types of polygons, including triangles and quadrilaterals,
- laboratories for studying quadrilaterals and circles,
- construction exercises, including classical problems of construction with a circular and ruler, non-standard ways of performing the simplest constructions in the smallest number of operations, tasks with a limited set of tools, construction of geometric places of points, construction exercises using geometric transformations,
- illustrations of geometric transformations,
- illustrations of geometric diagrams,
- exercises of geometric constructions, etc. They contribute to the development of geometric observation, mathematical culture, as well as skills in solving geometric problems for construction, calculation, and proof.
The materials on stereometry include:
- 3D models of the simplest geometric bodies, which can be used as templates for creating tasks,
- entertaining puzzle tasks on defining a figure by its three types,
- tasks on constructing sections of polyhedrons.
The 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 familiarizing with the basics of stereometry in the introductory course in the 9th grade, and puzzle tasks will be interesting and accessible even to fifth-graders.
The 'Probability and Statistics' section contains models designed specifically for studying the new probability-statistics line of the school mathematics course. They allow
- to visualize the process of conducting a random experiment with the possibility of changing its parameters,
- to conduct a series of random tests and demonstrate the basic probabilistic-statistical regularities,
- to check the theoretically obtained results through a statistical experiment,
- to process the data obtained in the experiment with the help of statistical functions and show them on graphs,
- to perform an independent statistical study.
Probabilistic models presented in the Collection can be divided into discrete, related to the classical approach to the definition of probability, and continuous, based on the so-called 'geometric probability'. A separate class is devoted to the study of random variables and their distributions