BYOM Lesson Workbooks
# BYOM 3rd Grade Workbook

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• to simplify algebraic expressions.

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The proposed Russian Math Books for elementary school is part of a unified continuous mathematics course for preschoolers, elementary school, and grade 3 of secondary school. It is designed to achieve new educational goals, including the development of personal, cross-subject, and subject-specific educational outcomes, as well as readiness for self-development based on the formation of students' cognitive motivation, universal learning actions, and overall learning abilities.

1) The focus is on the development of personal and cross-subject educational outcomes, the enhancement of a child's spiritual potential, creative abilities, and interest in the subject.

Mathematical knowledge in the curriculum is not viewed as an end in itself but as a means of fostering specific personal and cross-subject educational outcomes, mathematical activity, the development of children's thinking, their senses and emotions, creative abilities, and motivational factors.

The set goal is achieved through the use of the didactic system of the activity method developed by L. Peterson.

The activity-based method technology assumes the following structure for introducing new knowledge in lessons:

- Motivation (self-determination) for activity.
- Activation of prior knowledge and identification of difficulties through a trial learning action.
- Identification of the location and cause of the difficulties.
- Construction of a project to overcome the difficulties.
- Implementation of the constructed project.
- Initial consolidation through verbalization in external speech.
- Independent work with self-assessment based on a standard.
- Integration into the knowledge system and review.
- Reflection on the activity (lesson summary).

The complex pedagogical
conditions that ensure the implementation of the activity-based method
technology include the following didactic principles: activity, continuity,
holistic representation of the world, minimax, psychological comfort, variability,
and creativity. These principles retain their significance within the system of
educational work and management supporting children's health. Thus, L.
Peterson's educational system enables the establishment of a unified
educational and health-preserving process of an activity-based nature.

2) Levels of Implementation of the Educational System

L. Peterson's educational system can be implemented at different levels: basic, technological, and systemic-technological.

The basic level of the activity-based method (ABM) includes the following 7 steps:

- Motivation for learning activity.
- Activation of prior knowledge.
- Problematic explanation of new knowledge.
- Initial consolidation through verbalization.
- Independent work with self-assessment.
- Integration of new knowledge into the knowledge system and review.
- Lesson summary.

When working at the basic level of ABM within the framework of didactic principles, the principle of activity is transformed into the principle of activating activity in the traditional teaching system. Special attention should be paid to the principles of minimax and psychological comfort. Proper utilization of these principles allows each student to progress at their own pace, facing challenges at the "maximum" level of difficulty that is manageable for them. Ignoring these principles, on the other hand, can lead to student overload.

3) Connection with practice, real-world problems

Comprehensive learning of mathematics is impossible without children understanding the origin and significance of mathematical concepts and the role of mathematics in the system of sciences. Therefore, one of the main tasks of the school curriculum is to reveal to students all three stages of forming mathematical knowledge.

These stages are:

- The stage of mathematization involves constructing a mathematical model of a certain fragment of reality.
- The stage of studying the mathematical model involves constructing a mathematical theory that describes the properties of the constructed model.
- The stage of applying the obtained results to the real world.

For example, natural numbers are not initial abstractions, so their study is preceded by familiarity with finite collections of objects.

Similarly, the study of addition and subtraction of natural numbers begins with the consideration of particular operations of combining finite collections and removing parts of a collection, and the basis for studying formal operations of addition and subtraction of two-digit numbers is the operations on the symbolic representation of these numbers using dots and shapes (in accordance with the historical development of these operations).

4) Continuity between preschool preparation, primary school, and secondary school

Continuity between preschool preparation, primary school, and main school is realized in terms of technology, content, and methods, ensuring a seamless educational process across all levels of education.

The selection of content and the sequence of learning key mathematical concepts were based on a systematic approach. They constructed a multi-level system of foundational mathematical concepts in order to introduce fundamental concepts, ensuring continuity between them and the continuous development of all content and methodological aspects of the mathematics curriculum.

Preschool preparation within the framework of a comprehensive indicative educational program for preschool preparation helps develop children's thinking and cognitive motivation, form positive communication experiences, and collaborative problem-solving based on the method of reflexive self-organization. In other words, it provides the necessary foundation for a quick and successful adaptation to school learning.

5) Formation of a thinking style necessary for the successful use of Technology.

The computerization of the surrounding world leads to a reevaluation of the importance of many skills and abilities. Of particular importance, for example, is the ability to create and implement an action plan, strictly adhere to given rules and algorithms, assess the plausibility of the obtained answer, consider alternative solutions, organize the search for information necessary to solve a given task, and more.

Thus, in the BYOM curriculum, all tasks in the subject area "Mathematics and Informatics" are successfully solved.

6) Multi-level nature of the textbook

The material in the textbook allows for work with children of various levels of preparation in schools and classes of all types, based on the principles of minimax and psychological comfort. No children are selected to work with the textbook based on their level of preparation; instead, the teacher's level of preparation is important.

Teaching is conducted at a high level of difficulty (the "maximum" level), meaning it is in the "zone of proximal development" of the most prepared children, while taking into account their individual characteristics and abilities, and fostering each child's belief in themselves and their abilities.

Practically, this means that the textbook presents tasks and a sufficiently high pace of learning. From the very first lesson, all children are placed in situations that require intellectual effort and productive actions. However, in instructional tasks and independent work, only the child's success and progress relative to themselves are evaluated. Errors, on the other hand, are considered working situations that require correction, identification of their causes, and rectification.

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Ongoing and final assessments are conducted at a lower level than the work done in class, which practically leads to the disappearance of low grades. Final grades are determined based on the number of "achievements" (which are evaluated only with A and B) and grades for tests. Bad grades may appear very rarely, only when a child has shown negligence or failed to complete a task that is clearly within their capabilities. It is better if the child assigns themselves a negative grade in accordance with the norms established in the class.

At the same time, the high level of material presentation is considered not as a mandatory requirement but as an offering, an opportunity for each child to achieve success, encouraging them to take action. Therefore, the teacher should notice and support any, even the smallest, success of the child - their activity, involvement in the process of finding a solution, their correct judgment, or simply an attempt to propose their own hypothesis. A student's incorrect answer should not trigger a negative reaction from the teacher, annoyance, or moralizing. It is better if one of the students corrects the answer: "What do you guys think?" It is the teacher’s role in this situation to morally support the one who made the mistake: "Well done! You helped us understand!" "Do you agree now?

Did you understand? Well done!" and so on.

The minimax principle is a self-regulating mechanism for multi-level learning, which is why, as mentioned above, there is no special selection of children to work with it. Furthermore, involvement in educational activities, internal engagement, and the development of a habit of reflecting on each step is particularly important for children with developmental difficulties. However, working at a high level of difficulty must be accompanied by creating an atmosphere of trust, respect, and friendliness in the classroom, allowing each student to believe in their own abilities. "You can do it!" - the teacher must believe in the student, "I can do it!" - the student must believe in themselves, "They can do it!" - all the other students in the class must believe. Otherwise, learning will lose personal significance for the child, and the school will not be able to fulfill its main mission - to help them reach their individual maximum.

The volume of tasks in the textbook sets the level of the individual educational trajectory for the most advanced children. Therefore, it is not expected that every child will complete all the tasks in the textbook. Only 3-4 key assignments on a new topic and review tasks are mandatory for everyone, where the essential learning outcomes are practiced. The range of tasks can be expanded for more advanced children. However, overloading children, including homework, should be avoided.

The consolidation and reinforcement of knowledge of the main content and methodological lines of the course (numerical, text problem solving) are carried out simultaneously with the exploration of new mathematical ideas from additional lines (geometric, algebraic, data analysis, etc.). Therefore, the practice exercises do not tire the children, especially since they are usually presented in a playful form (code decoding, riddles, etc.). Each child with a lower level of preparation has the opportunity to practice the necessary skill from the required learning outcomes at their own pace, while more advanced children constantly receive intellectual stimulation. This makes math lessons appealing to all children, both those who are strong in math and those who are less prepared.

It is crucial for every child to experience the joy of discovery during each lesson and to develop self-confidence and intellectual curiosity. Interest and success in learning are the main parameters that determine the holistic moral, intellectual, and physiological development of the child and, thus, the quality of working with children.

7) Creative tasks in the work system

An effective means of allowing each child in the class to unfold and realize their potential is through creative work. Creative tasks, where children come up with ideas, create, and invent, should be regularly offered, up to 2-3 times a week. In these tasks, children can come up with examples for the learned computational technique, create a problem based on a given expression (e.g., 85 + 5 ∙∙ 9 or x ∙∙ 5 + y ∙∙ 8), create a problem of a specific type (involving multiples, sums, differences, etc.), or based on a given theme (about sports, animals, a story problem, etc.). They can also draw patterns or geometric shapes with specified properties (e.g., ray KM intersecting straight line AB and not intersecting segment CD), decode or encode the name of a city, book, or movie using computational examples, and so on.

Creative tasks are usually assigned as additional homework alongside the mandatory assignments and are never given a poor grade.

The most successful creative works can be collected at the end of the year in a "Problem Book," with the students themselves being the authors of these works. Such tasks, where children act not only as performers but as creators, have a profoundly positive impact on the development of their personalities and contribute to a deeper and more solid assimilation of knowledge.

8. Volume and difficulty level of homework assignments

It is recommended to provide students with two-level homework assignments, consisting of a mandatory and an optional (additional) part.

The mandatory part should be manageable for the child to complete independently and should not exceed 15-20 minutes of their

independent work time. It is also recommended to give assignments based on the children's own choice, for example: "Choose and

complete one task from # 4-7 that you like."

The optional part, which is done at the student's discretion, may include additional tasks marked with an asterisk, etc.

9. Types and forms of work in the lesson

It is necessary to diversify the types and forms of work in the lesson. The lesson should include collective, group, and individual forms of work, oral work, and work in squared notebooks. The practice of computational skills should be systematic and sufficiently intensive during lessons, but should not exceed 3-4 minutes. It is advisable to give computational exercises a developmental character by selecting answer numbers in such a way that the resulting series can be analyzed, classified, and patterns can be identified. This will not only help consolidate counting skills but also prepare children's thinking for activity-based methods.

When forming concepts using the methods adopted in the curriculum, all types of memory are engaged in students - not only visual and auditory but also motor, visual-spatial, tactile, and others. Working in the exercise book should generally not exceed 10-12 minutes. It mainly involves students independently completing tasks that have been prepared in advance during frontal work with similar but different tasks. The time for independent task completion is usually limited (typically, from one to 3-4 minutes). Then the task is checked. Children compare their solutions with the model answer for self-checking and give themselves a corresponding "+" or "-". As a result, the child deliberately develops the ability to self-test.

Since children check their independently completed tasks themselves, when the teacher checks them, the focus is primarily on the development of self-control skills and the neatness of note-taking.

10) Knowledge assessment system

The curriculum incorporates a multi-level knowledge assessment system: self-assessment when introducing new material, peer assessment during its practice, instructional assessment in the form of independent assignments, ongoing assessment through periodic tests during the academic year, and the final assessment, which includes two stages - a transfer test ("minimum") and a final test (assessment and self-assessment of program mastery level).

The independent assignments are conducted at a high level of difficulty, so only success is evaluated. Specifically, if the entire independent work is completed without errors (usually by 3-5 children in the class), an excellent grade is awarded. After each independent assignment, children who made mistakes work on correcting them.

If the error correction is successful and the teacher sees that the child has understood the material, B or even A can be given for that assignment. Low grades are not given for independent assignments. "No grade" (no reason to assign a grade, "not earned") serves as a more significant signal for the child to be active and correct their own activities than poor grades. The teacher's task is to encourage each child to understand their mistakes and correct them.

The level of tests should be lower than the level of independent assignments, and all children should be evaluated. It is recommended that tasks for tests be selected so that approximately three-quarters of the class can achieve an A or B.

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In the BYOM program for the 3rd grade, universal learning actions (personal, regulatory, cognitive, communicative) are developed through the study of the following main topics: numeration, comparison, addition, and subtraction of multi-digit numbers, written methods of multiplication, and division. Mental calculation skills within 1000 are consolidated and brought to an automated level.

Set-theoretical concepts are introduced, problems involving unit conversion are included, and composite problems covering all four arithmetic operations are given. Special attention is given to developing the ability to independently analyze word problems, forming geometric representations in children, identifying relationships and dependencies (topic: "Formulas"), and promoting cognitive processes, logical thinking, and variation.

Intensive exercises to practice computational skills should be included in almost every lesson. It is advisable to give the computational exercises a developmental character by selecting answer numbers that allow children to analyze, classify, and identify patterns in the obtained series.

PERSONAL RESULTS

The student will develop:

• an understanding of educational and corrective activities, their similarities and differences;

• an understanding of the general nature of mathematical knowledge, its history of development, and ways of mathematical cognition;

• independence and personal responsibility for their performance in executive activities, their own experience of creative activities;

• the ability to perform self-assessment based on a model, detailed example, and standard;

• experience in reflective self-assessment of their own educational actions;

• the ability to correct errors based on a refined error correction algorithm;

• the ability to apply rules for maintaining and supporting their health in educational activities;

• a desire to make maximum personal contributions to collaborative activities;

• the ability to apply the rules of "author," "comprehender," and "critic" during communicative interactions in pairs and groups;

• motivation to develop speech as a means of successful communication in educational activities;

• activity, friendliness, honesty, and patience in educational activities;

• determination in educational activities based on agreed-upon standards;

• interest in mathematics classes and educational activities as a whole;

• an understanding of friendship, self-confidence, self-criticism, and acceptance of them as values that help the student achieve good results;

• respectful and positive attitude towards oneself and others, aiming for maximum personal contribution to the overall result and striving for common success;

• experience in using constructive behavior strategies in difficult situations and resolving disputes based on reflective methods;

• experience in independent successful mathematical activities according to the 3rd-grade curriculum.

The student will have the opportunity to develop:

• the ability to adequately assess their performance and treat negative results as signals prompting them to rectify the situation;

• the ability to establish friendly relationships with classmates and self-assess this ability based on the application of a standard;

• experience in using techniques to mitigate negative emotions when working in pairs or groups;

• experience in distinguishing true and false values;

• positive experience in constructive and creative activities.

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METASUBJECT RESULTS

The student will learn:

• to identify and record the progress of two main stages and steps of educational activities (12 steps);

• to identify individual difficulties in educational activities in various typical situations;

• to determine the place and cause of individual difficulties in educational activities based on the application of a standard;

• to create a plan for their educational activities when encountering new knowledge based on the application of an algorithm;

• to record the result of their educational activities during the lesson on the discovery of new knowledge in the form of a coordinated standard;

• to use the standard to justify the correctness of completing educational tasks;

• to apply the rule of consolidating new knowledge;

• to use given criteria to assess their own work;

• to identify and record the progress of two main stages and steps of corrective activities (12 steps);

• to use the error correction algorithm in their educational activities;

• to apply the refined algorithm for completing homework;

• to use the mathematical terminology learned in the 3rd grade to describe the results of their educational activities.

The student will have the opportunity to learn:

• to perform project activities under the guidance of an adult;

• to conduct self-assessment of the ability to apply rules that foster self-confidence based on the application of a standard;

• to conduct self-assessment of the ability to identify and record the progress of two main stages and steps of educational activities (12 steps);

• to conduct self-assessment of the ability to determine the place and cause of difficulty when constructing a new method of action;

• to conduct self-assessment of the ability to plan their own educational activities;

• to conduct self-assessment of the ability to record the result of their educational activities in the form of a standard;

• to conduct self-assessment of the ability to use the standard to justify the correctness of completing educational tasks;

• to conduct self-assessment of the ability to apply the rule of consolidating new knowledge;

• to conduct self-assessment of the ability to apply given criteria to assess their own work;

• to conduct self-assessment of the ability to identify and record the progress of two main stages and steps of corrective activities (12 steps);

• to conduct self-assessment of the ability to determine the place and cause of their own mistakes;

• to conduct self-assessment of the ability to use the error correction algorithm in their educational activities;

• to conduct a self-assessment of the ability to apply the refined algorithm for completing homework.

Cognitive

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The student will learn:

• to understand and apply mathematical terminology to solve educational tasks according to the 3rd-grade curriculum;

• to apply algorithms of generalization and classification of a set of objects based on a given property;

• to apply simple techniques for developing their memory;

• to use observation as a method of cognition in their educational activities in simple cases;

• to identify types of models (object models, graphical models, symbolic models, algorithm flowcharts, etc.) and use them as a method of cognition in their educational activities in simple cases;

• to differentiate between the concepts of "knowledge” and "skill”; • to understand and apply basic interdisciplinary concepts in accordance with the 3rd-grade curriculum (set, element of a set, subset, union, and intersection of sets, Euler-Venn diagram, enumeration of options, decision tree, etc.);

• to create and solve their own problems, examples, and equations according to the 3rd-grade curriculum;

• to understand and apply the signs and symbols used in the 3rd-grade textbook to organize their educational activities.

The student will have the opportunity to learn:

• to conduct self-assessment of the ability to apply algorithms of generalization and classification of a set of objects based on a given property, based on the application of a standard;

• to conduct self-assessment of the knowledge of the stages of the observation method in their educational activities, based on the application of a standard;

• to conduct self-assessment of the ability to identify the type of model and knowledge of the stages of the modeling method in their educational activities, based on the application of a standard;

• to conduct self-assessment of the ability to apply simple techniques for developing their memory, based on the application of a standard;

• to use the learned methods and means of cognition to solve educational tasks;

• to identify and correct errors of arithmetic nature (during calculations) and logical nature (in solving word problems and equations);

• to apply knowledge from the 3rd-grade curriculum in modified conditions;

• to solve creative and exploratory problems in accordance with the 3rd-grade curriculum.

Communicative

The student will learn:

• to distribute roles in communicative interactions, formulate the functions of "author," "comprehender," and "critic," and apply the rules of working in these positions;

• to offer their own solutions in collaborative work, and evaluate different options based on the common goal;

• to apply basic techniques of public speaking in order to express their thoughts clearly to others during dialogues;

• to apply the rules of dialogue when working in pairs or groups;

• to apply simple techniques for managing negative emotions in collaborative activities;

• to exercise mutual control, provide assistance, and support classmates when necessary.

The student will have the opportunity to learn:

• to conduct self-assessment of the ability to perform the role of "critic" in communication, based on the application of a standard;

• to conduct self-assessment of the ability to express their thoughts clearly to others based on the studied techniques of public speaking;

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• to conduct self-assessment of the ability to apply the rules of dialogue when working in pairs or groups, based on the application of a standard;

• to conduct self-assessment of the ability to manage and control negative emotions in collaborative work, based on the application of a standard;

• to conduct self-assessment of the ability to exercise mutual control;

• to demonstrate friendliness when working in pairs or groups.

Subject Outcomes

Numbers and Arithmetic Operations

The student will learn:

• to count in thousands, name place values and classes: units class, thousands class, millions class, etc.;

• to name, compare, add, and subtract multi-digit numbers (up to 1,000,000,000,000), represent a natural number as the sum of its place value parts;

• to multiply and divide numbers by 10, 100, 1000, etc., multiply and divide (without remainder) round numbers within the range of 100;

• to multiply multi-digit numbers (all cases) and write multiplication in columns;

• to divide a multi-digit number by a single-digit number and write division in the form of long division;

• to check the accuracy of operations with multi-digit numbers using algorithms, inverse operations, and calculator calculations;

• to mentally add, subtract, multiply, and divide multi-digit numbers in cases within the range of 100;

• to perform specific cases of all arithmetic operations with 0 and 1 on the set of multi-digit numbers;

• to apply the properties of arithmetic operations to the set of multi-digit numbers; • to evaluate the values of numerical expressions involving the studied natural numbers, containing 4-5 operations (with and without parentheses) based on the knowledge of the order of operations;

• to simplify calculations with multi-digit numbers based on the properties of arithmetic operations.

The student will have the opportunity to learn:

• to independently develop and use algorithms for mental and written operations with multi-digit numbers;

• to express multi-digit numbers in various larger units of measurement;

• to see the analogy between the decimal system of representing natural numbers and the decimal system of measurement.

Problem-Solving with Word Problems

The student will learn:

• to solve problems involving uniform processes (i.e., containing relationships between quantities of form a = b · c: distance - speed - time problems (motion problems), amount of work - work rate - time problems (work problems), cost - price - quantity problems (price problems), etc.;

• to solve problems involving determining the start, end, and duration of an event;

• to solve problems involving calculating the areas of shapes composed of rectangles and squares;

• to solve problems involving finding numbers based on their sum and difference;

• to analyze word problems involving multi-digit numbers and 2-4 operations of all studied types, construct graphical models and tables, plan and implement solutions, explain the solution process, explore different solution methods, relate the obtained result to the problem statement, and assess its plausibility;

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• to solve problems of all studied types with letter data and vice versa, create word problems based on given letter expressions.

• recognize the analogy of solving word problems with externally different plots but a unified mathematical approach to solving them;

• independently create their own problems of the studied types based on a given mathematical model - numerical and algebraic expressions, diagrams, tables;

• perform all arithmetic operations with the studied quantities when solving problems.

The student will have the opportunity to learn:

• independently construct and use algorithms for solving the studied cases of word problems;

• classify simple problems of the studied types by model type;

• apply a general method of analysis and solution for composite problems (analytical, synthetic, analytical-synthetic);

• analyze, model, and solve word problems involving 5-6 steps using all arithmetic operations within the range of 1,000,000;

• solve non-standard problems related to the topics being studied.

Geometric shapes and quantities

The student will learn:

• perform on grid paper the transfer of shapes by a given number of cells in a given direction;

• determine the symmetry of points and shapes with respect to a line based on essential symmetry features;

• construct symmetric shapes on grid paper with respect to a line;

• identify and name shapes that have an axis of symmetry;

• recognize and name rectangular parallelepiped, cube, their vertices, edges, and faces;

• find the volume of a rectangular parallelepiped and a cube using formulas; • find the areas of shapes composed of squares and rectangles;

• read and write the studied geometric quantities, convert them from one unit of length to another, compare their values, add, subtract, multiply, and divide them by natural numbers.

The student will have the opportunity to learn:

• construct nets and physical models of a cube and a rectangular parallelepiped;

• find the surface areas of a rectangular parallelepiped and a cube;

• independently derive properties of geometric shapes being studied;

• use measurements to independently discover properties of geometric shapes.

Quantities and relationships between them

The student will learn:

• recognize, compare, and order the quantity "time"; use units of time measurement: 1 year, 1 month, 1 week, 1 day, 1 hour, 1 minute, 1 second - to solve problems, convert them, compare them, and perform arithmetic operations with them;

• tell time, name months and days of the week, and use a calendar;

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• use new units of mass - 1 gram, 1 kilogram, 1 center, 1 ton - among the studied units, convert them, compare them, and perform arithmetic operations with them;

• observe relationships between quantities using tables and models of motion on a coordinate line, verbally express relationships, and using formulas (such as the formula for distance: s = v · t, and its analogs: the formula for cost: C = a · n, the formula for work: A = w · t, etc.; formulas for the perimeter and area of a rectangle: P = (a + b) · 2 and A = a · b; formulas for the perimeter and area of a square: P = 4 · a and A = a · a; formulas for the volume of a rectangular parallelepiped: V = a · b · c; formula for the volume of a cube: V = a · a · a, etc.);

• construct a generalized multiplication formula a = b · c, describing uniform processes;

• build models of object motion on a number line, observe relationships between quantities describing motion, and create formulas based on these relationships;

• compose and compare simple expressions with variables, find their values for given variable values in simple cases;

• apply relationships between the components and results of arithmetic operations to compare expressions.

The student will have the opportunity to learn:

• create and present their own project on the history of the development of concepts related to measuring time, the history of calendars, the peculiarities of the Julian and Gregorian calendars, and more;

• observe relationships between variables using tables, number lines, and express them in simple cases using formulas;

• independently construct a scale with a given division value, a coordinate axis, and create formulas for the distance between points on the coordinate axis, the relationship between the coordinate of a moving point and the time of motion, and more;

• determine the parameters of motion (starting point, direction, speed) using formulas of the form x = a + bt, x = a - bt, which express the dependency of the coordinate x of a moving point on the time of motion t.

Algebraic Representations

The student will learn:

• to express the properties of arithmetic operations on the set of multi-digit numbers using algebraic notation;

• to solve simple equations of the form a + x = b, a - x = b, x ∙∙ a = b, a ∙∙ x = b, a + x = b, x + a = b, providing commentary on the steps of the solution;

• to solve compound equations that can be reduced to a chain of simple equations (2 steps), and provide commentary on the steps of the solution;

• to apply the formula for division with remainder a = b ∙∙ c + r, r

The student will have the opportunity to learn:

• to read and write expressions containing 2-3 arithmetic operations, starting from the name of the last operation;

• to independently identify and write in algebraic notation the formula for division with the remainder a = b ∙∙ c + r, r

• based on the general properties of arithmetic operations in simple cases:

• to determine the set of roots of non-standard equations;• to simplify algebraic expressions.

Mathematical Language and Elements of Logic

The student will learn:

• to use symbolic notation for multi-digit numbers, indicate their digits and classes, and represent spatial shapes;

• to recognize, read, and apply new symbols of mathematical language: set notation and its elements, symbols ∈, ∉, ⊂, ⊄, ∅, ∩, ∪.

• to define sets by their properties and by listing their elements;

• to determine the membership of elements in a set, equality and inequality of sets, and to determine if one set is a subset of another set;

• to find the empty set, union, and intersection of sets;

• to represent relationships between sets and their elements, as well as set operations, using Euler-Venn diagrams;

• to differentiate between statements and propositions that are not statements;

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• to determine true or false statements in simple cases;

• to construct simple statements using logical connectors and words such as "true/false, that...", "not", "if...then...", "each", "all", "exists", "always", and "sometimes".

The student will have the opportunity to learn:

• to justify their judgments using the rules and properties learned in 3rd grade and make logical deductions;

• to justify statements of a general nature and statements of existence in simple cases based on common sense;

• to explore the commutative and associative properties of set union and intersection, represent them using mathematical symbols, and establish an analogy between these properties and the commutative and associative properties of addition and multiplication;

• to solve logical problems using Euler-Venn diagrams; • to solve logical problems (with guidance from an adult and independently) and master problem-solving techniques in accordance with the 3rd-grade curriculum.

Working with Information and Data Analysis

The student will learn:

• to use tables for analyzing, representing, and organizing data, and to interpret data from tables;

• to classify elements of a set based on a given property;

• to find information on a given topic from different sources (textbooks, reference books, encyclopedias, controlled Internet space, etc.);

• to carry out project work on topics such as "From the History of Natural Numbers" and "From the History of the Calendar," plan information search in reference books, encyclopedias, controlled Internet space, and present the results of project work;

• to complete creative projects on the theme of "Beauty and Symmetry in Life"; • to work in the material and informational environment of primary education (including educational models) in accordance with the content of the subject "Mathematics, Grade 3".

The student will have the opportunity to learn:

• to independently carry out extracurricular project work under the guidance of an adult, gather information from literature, reference books, encyclopedias, controlled internet sources, and present information using available technical means;

• to create their own problems based on the 3rd-grade curriculum, become a co-author of the "Problem Book for Grade 3" which includes the best problems invented by students, and compile a portfolio of a 3rd-grade student.

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