BYOM Lesson Workbooks
# BYOM 3rd Grade Workbook

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.

The complex pedagogical conditions that ensure the implementation of the activity-based method technology includes 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.

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 established order for introducing
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.
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, the ability to strictly adhere
to given rules and algorithms, assess the
plausibility of the obtained answer, the ability to 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. There is no selection of children to work with the
textbook based on their level of preparation; instead,
the teacher's level of preparation is of importance.
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 the pace of learning that are of a sufficiently
high level. 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 their progress relative to themselves are evaluated.
Errors, on the other hand, are considered working situations
that require correction, identification of their causes, and rectification.
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 crucially important for every child to experience the joy of discovery during each lesson and for them 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, and so on.
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 for 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 are
evaluated. It is recommended to select tasks for tests so that
approximately three-quarters of the class can achieve A or B.
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, developing the ability to identify 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 in a way that allows
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.
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
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;
• 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;
• 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;
• use new units of mass - 1 gram,
1 kilogram, 1 centner, 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 analogues: 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 < b to verify the
correctness of the operation on the set of multi-digit numbers.
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 < b;
• based on the general properties
of arithmetic operations in simple cases:

• 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;
• 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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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 includes 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.

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, which involves constructing a mathematical theory that describes the properties of the constructed model.
- The stage of applying the obtained results to the real world.

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Private Lessons | | | Group Lessons |

Would you like to book private or group online lessons?

Private Lessons | | | Group Lessons |

Would you like to book private or group online lessons?

Private Lessons | | | Group Lessons |

Would you like to book private or group online lessons?

Private Lessons | | | Group Lessons |

Would you like to book private or group online lessons?

Private Lessons | | | Group Lessons |

Would you like to book private or group online lessons?

Private Lessons | | | Group Lessons |

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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

• 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;
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