The important role of parents in education.
- EMC "Planet of Knowledge", in the opinion of parents and a number of teachers, is a rather complicated system of education for study and assimilation in elementary school. However, in many educational institutions they study according to it, and schoolchildren have to adapt, learning to perceive information in a new way.
- In this they are helped by manuals and textbooks. For example, mathematics, the author of which is M. I. Bashmakov, M. G. Nefedova, and a set of practical aids for this collection. In contrast to the materials used by the parents of schoolchildren, a different approach to the presentation and perception of the material is implemented here. Therefore, in order to study independently, reliable assistants are needed. Indispensable will be the mathematics solution book for grade 4 to the textbook of the above authors, where not only complete and detailed answers to questions, examples and problems of the collection are given, but also the solutions themselves are described in detail. And also - the form of the correct record of the answer is given, since already with elementary school format oriented program final certification graduation classes (OGE, USE).
- Regularly, systematically reviewing GDZ, schoolchildren will acquire useful skills for independent work, visually learn to perceive the current rules for formatting answers and the course of decisions.
- Teachers and parents of fourth-graders have different attitudes towards the elementary school program "Planet of Knowledge", but all, nevertheless, recognize the fairly understandable material in mathematics included in the teaching materials. Visual and colorful material, a variety of manuals that complement the basic textbook, allow you to easily master a number of difficult topics and create a solid foundation for further study of the discipline in the middle school. In order to instill in fourth-graders a useful skill of self-preparation and self-control, you will need manuals from this complex and solution books for them. Plus - a sufficient amount of time for regular training.
- Learn with GDZ fascinating enough. In addition, it is also very useful because:
- allows you to work out the skills of independent work, without the involvement of outside assistants - tutors, course teachers. In addition to the fact that it is beneficial, many teachers consider this type of mastering the material to be the most effective and efficient;
- you can see and automatically remember the principle and order of the correct recording of the answer. What is especially important for mathematics, where not only the progress of the solution is evaluated, but also the fixation of the result;
- teaches to work with information - to choose the right one, to analyze, to draw deep and complete conclusions. - Among the collections-sets on the discipline included in the EMC "Planet of Knowledge" - textbooks and workshops in mathematics for grade 4, compiled by M. I. Bashmakov. When compiling these materials, the author relied on:
- advanced technologies for teaching science at the primary school level;
- modern knowledge and society's needs for it;
- competent combination of theory and the order of its practical application;
- the possibility of combining lesson and extracurricular activities into a single system that allows fourth-graders to more deeply and fully master the course of mathematics. - In addition to Bashmakov's basic textbook, the mathematics kit includes various practicums and manuals of an information and control nature. Among them are workbooks in mathematics for the fourth grade, independent work for the current and final control and tests on the subject, diagnostic and control, training notebook, collections of tasks. For those on a family form of education will come in handy methodological developments to educational materials, technological maps of lessons, work programs in mathematics for fourth-graders.
"Planet of Knowledge" - mathematics for fourth graders
3rd ed. - M.: 2017.- 256 p. M.: 2014.- 256 p.
The textbook was written in accordance with the program for studying mathematics in institutions of NPO and SPO and covers all the main topics: number theory, roots, powers, logarithms, lines and planes, spatial bodies, as well as the basics of trigonometry, analysis, combinatorics and probability theory. For students in primary and secondary institutions vocational education.
Format: pdf(2017, 256s.)
The size: 8.6 MB
Watch, download:drive.google
Format: pdf(2014, 256s.)
The size: 52.6 MB
Watch, download:drive.google
Table of contents
Basic notation 3
Preface 4
Chapter 1. DEVELOPMENT OF THE CONCEPT OF NUMBER 7
Lesson 1. Integers and rational numbers 7
Lesson 2. Real numbers 11
Lesson 3. Approximate calculations 15
Lesson 4. Complex numbers 18
Conversation. Numbers and roots of equations 22
Chapter 2
Lesson 1 Review 26
Lesson 2. nth root degree 29
Lesson 3. Degrees 33
Lesson 4. Logarithms 37
Lesson 5. Exponential and logarithmic functions 40
Lesson 6. Exponential and logarithmic equations and inequalities 46
Conversation. Calculating powers and logarithms 49
Chapter 3. LINES AND PLANES IN SPACE 52
Lesson 1. Mutual arrangement straight lines and planes 52
Lesson 2. Parallelism of lines and planes 56
Lesson 3. Angles between lines and planes 58
Conversation. Geometry of Euclid 61
Chapter 4. COMBINATORICS 66
Lesson 1. Combinatorial constructions 66
Lesson 2. Rules of combinatorics 69
Lesson 3. Number of orbits 72
Conversation. From the history of combinatorics 77
Chapter 5. COORDINATES AND VECTORS 79
Lesson 1 Review 79
Lesson 2. Coordinates and vectors in space 83
Lesson 3. Dot product 85
Lesson 4. Perpendicularity of lines and planes 88
Conversation. Vector space 90
Chapter 6. BASICS OF TRIGONOMETRY 93
Lesson 1: Angles and rotation 93
Lesson 2, Trigonometric operations 98
Lesson 3. Transformation trigonometric expressions 103
Lesson 4. Trigonometric functions 109
Lesson 5. Trigonometric equations 114
Conversation. From the history of trigonometry 120
Chapter 7. FUNCTIONS AND GRAPHICS 122
Session 1 Review general concepts 122
Lesson 2. The scheme of the study of function 127
Lesson 3. Function transformations and actions on them 131
Lesson 4. Symmetry of functions and transformation of their graphs 136
Lesson 5: Function Continuity 139
Conversation. Development of the concept of function 141
Chapter 8, Polyhedra and Round Bodies 143
Lesson 1. Dictionary of geometry 143
Lesson 2. Parallelepipeds and prisms 145
Lesson 3. Pyramids 148
Lesson 4. Round bodies 151
Lesson 5. Regular polyhedra 154
Conversation. Platonic Solids 157
Chapter 9. BEGINNINGS OF MATHEMATICAL ANALYSIS 159
Lesson 1. Process and its modeling 159
Lesson 2 Sequences 165
Lesson 3. The concept of a derivative 171
Lesson 4. Differentiation formulas 176
Lesson 5. Derivatives elementary functions 180
Lesson 6. Applying the derivative to the study of functions 183
Lesson 7. Applications 187
Lesson 8. Antiderivative 193
Conversation. Taylor Formula 195
Chapter 10. THE INTEGRAL AND ITS APPLICATIONS 198
Lesson 1. Areas of plane figures 198
Lesson 2. Newton-Leibniz theorem 201
Lesson 3. Spatial bodies 207
Conversation. Integral quantities 213
Chapter 11. ELEMENTS OF THE THEORY OF PROBABILITY AND MATHEMATICAL STATISTICS 219
Lesson 1. Probability and its properties 219
Lesson 2: Retesting 222
Lesson 3. Random value 225
Conversation. The origin of the theory of probability 228
Chapter 12. EQUATIONS AND INEQUALITIES 230
Lesson 1 Equivalence of Equations 230
Lesson 2. Basic techniques for solving equations 233
Lesson 3 Systems of Equations 238
Lesson 4. Solving inequalities 242
Conversation, Resolvability algebraic equations 247
Answers 249
Foreword
Mathematics for 2500 years of its existence has accumulated the richest tool for the study of the world around us. However, as Academician A.N. Krylov, an outstanding Russian mathematician and shipbuilder, noted, a person turns to mathematics "not to admire innumerable treasures." First of all, he needs to get acquainted with "centuries of proven tools and learn how to use them correctly and skillfully."
This book will teach you how to use mathematical tools such as functions and their graphs, geometric figures, vectors and coordinates, derivative and integral. Although you may have had your first exposure to some of these concepts earlier, the book presents x anew. This is convenient for those who have forgotten the previously studied material a little, and is useful for everyone, since even familiar things will reveal new aspects and connections.
To facilitate the work with the textbook, the most important provisions and formulations are highlighted. Illustrations play an important role, therefore it is necessary to carefully consider the drawing related to the text for a better understanding of the text (even in ancient times they used this method of studying mathematics - they drew a drawing and said: “Look!”).
In addition to the undoubted practical value of the mathematical knowledge obtained, the study of mathematics leaves an indelible mark on the soul of every person. With mathematics, many associate objectivity and honesty, the desire for truth and the triumph of reason. Many people have a lifetime of self-confidence, which arose when overcoming the undoubted difficulties that they encountered in the study of mathematics. Finally, most of you are open to the perception of the harmony and beauty of the world that mathematics has absorbed, so you should not approach each page of the textbook, each task with an assessment of whether it will be used in the new life that awaits you after graduation .
The topics to which the textbook is devoted - the theory of numbers, spatial bodies, the foundations of mathematical analysis, the beginnings of probability theory - are not only of applied importance. They contain rich ideas, familiarization with which is necessary for every person.
It is hoped that the study of mathematics, which / textbook should help, will allow you to make sure high level of their abilities, will strengthen the desire to continue their education and bring many joyful minutes of communication with the "unshakable laws that mark the entire order of the universe."
AT fourth grade The kids have a lot to learn. They will pass inequalities, solving the most simple equations with one unknown, learn new terms and for the first time get acquainted with an important section of the exact sciences - geometry. All this is detailed in "GDZ in Mathematics Grade 4 Textbook Bashmakov, Nefedova Planet of Knowledge", released by the famous Drofa publishing house. Among the many topics and sections in this tutorial, there are some that can be difficult.
THE IMPORTANT ROLE OF PARENTS IN LEARNING
master school curriculum it will be easier if you always have at hand "GDZ in Mathematics 4th grade Shoes". The book contains detailed answers to all tasks from the textbook with notes from the authors and additional materials. With the help of this manual, you can check homework and sort out mistakes with your child. In addition, you can learn together the topic that the student missed at school good reason, but it is necessary to "catch up" with the class. In addition, any child can, even sitting in a lesson, simply listen to the teacher's explanations, look at him, but think about his own, without listening to the explanation of the material.
BRIEFLY ABOUT THE BENEFITS
The publication consists of two parts, in the first one hundred and nineteen, and in the second one hundred and forty-two pages. On them, the author managed to place educational and auxiliary material on all topics of the main course mathematics for the fourth grade:
- Area calculation.
- Addition of thousands and millions.
- How to add and subtract bit terms.
Each exercise is accompanied by a detailed sample solution that allows you to understand and reliably remember all the topics of the course. mathematics this school year.
ADVANTAGES
Undoubtedly, fourth grader- this is already a student so mature that at the end of the school year he will take the first real exams in his life - all-Russian verification work. But at the same time, he is still at a very young age, he cannot always coordinate his work correctly, and parents must explain to the child very simple, but important things:
- GDZ cannot serve as a cheat sheet;
- you need to do the exercises yourself before looking at the finished answer;
- if your version differs from the version solver, then you cannot copy the correct solution, you need to find and correct the error yourself.
It is this way of working that will allow you to master the subject reliably, but with minimal time.
The study guide contains tasks but general exchange rate mathematics to study the discipline on basic level regardless of the profile of the received professional education. The choice and arrangement of topics correspond to the textbook by M.I. Bashmakov "Mathematics", which, together with teaching aids"Maths. Collection of problems of profile orientation”, “Mathematics. A book for a teacher ”by the same author and this problem book forms an educational and methodological set.
Tasks contain simulators for the main studied algorithms, matrix tests, independent work and control tests with a choice of answers.
For students of institutions of secondary vocational education.
Examples.
Dan regular tetrahedron. A section is constructed in it by a plane parallel to its two intersecting edges. Prove that a quadrilateral in such a section is a rectangle. Can it be a square?
Through a point on an edge triangular pyramid two planes are drawn parallel to two faces of the pyramid. Cut the remaining polyhedron into two triangular prisms.
On the diagonals of adjacent cube faces lying on skew lines, find two such points K and L so that the line KL is parallel to the cube face. What are the limits of the length of the segment KL in a cube with edge 1?
Free download e-book in a convenient format, watch and read:
Download the book Mathematics, Zadachnik, Bashmakov M.I., 2014 - fileskachat.com, fast and free download.
- Mathematics, Collection of specialized tasks, Bashmakov M.I., 2013
- Algebra and the beginnings of analysis, Problems and solutions, Bashmakov M.I., Bekker B.M., Golkhovoi V.M., 2004
- Problems in mathematics and physics offered at the entrance exams in 1974-76, Nikolsky Yu.S., Fedosov B.V., Chekhlov V.I., Kozel S.M., Belonuchkin V.E., Shelagin A.V. ., 1977
The following tutorials and books:
- Mathematics, Testing and tests, Grade 3, Fedorova T.L., 2005
- Mathematics, Grade 4, Problems with sample solutions, Mezhueva Yu.V., 2015
- Developing mathematical abilities, Workbook, 6-7 years old, Gavrina S.E., Kutyavina N.L., Toporkova I.G., Shcherbinina S.V., 2006
The closer the end of school, the greater the burden experienced by the student in obtaining education. Performance even in core subjects like math can suffer if there is no time for rest. This subject belongs to the exact sciences, which raise many questions. How to be in such a situation? GDZ in mathematics for grade 4 Bashmakov allows fourth-graders to do their homework independently, without outside help. Its content is fully consistent with the underlying source. All solutions are detailed and contain the correct answers that you can check online.
The manual helps to solve typical test papers for several options, as well as a variety of thematic tasks. Many differentiated tasks are fully consistent with those required working programm. It helps to develop and consolidate cognitive abilities.
The workshop provides a detailed solution to the tasks of the mathematical course. The student can use them both in preparation homework, and for self study basics of mathematics.
GDZ is useful!
It is a mistake to think that GDZs harm learning. Of course, if you use them thoughtlessly, it will. Often a student experiences big problems of a psychological nature: is the exercise done correctly or not? Fear of going to class and getting a bad grade provokes stressful situation which is detrimental to academic achievement.
Ready-made answers allow you to:
- self-checks (it is easy for the student and parents to check any number);
- effectively organize educational process(the teacher or tutor may, at their discretion, use the workshop information to create additional material to the lesson)
- obtaining deeper knowledge (the resource was compiled taking into account the Federal State Educational Standard).
Answer book in mathematics for the fourth grade (M.I. Bashmakov, M.G. Nefyodova) Suitable for arranging various shapes educational activities: from self-education to tutoring. The opportunity to practice once again guarantees excellent preparation and good marks for future test papers.