2). Adapted Mathematics Work Program for Children with ASD (8.2) Curriculum 8.2

A child with an autism spectrum disorder goes to school. What should parents, school, teacher be ready for?

Autism is called the syndrome of the century for a reason: at the moment, this diagnosis is becoming more common. Despite the efforts of public and medical organizations, there is still much we do not know about autism.

Our freelance correspondent Alexandra Chkanikova had a conversation with the director of the NPC PZDP them. G. E. Sukhareva, a psychotherapist of the highest qualification category Marina Alexandrovna Bebchuk, with the director of the Federal Resource Center for the Organization of Comprehensive Support for Children with Autism Spectrum Disorder Artur Valeryevich Khaustov, as well as with some teachers of Moscow schools.

The result is an express guide for a teacher on how the education of a child with autism in a public school can be organized, what parents and teachers should prepare for.

What is autism?

Today, childhood autism is viewed as a general developmental disorder, that is, it is not a disease, but a severe disorder of mental development. There are several variants of autistic disorders. According to the international classification of diseases ICD-10, there are four types:

F84.0 - childhood autism (autistic disorder, infantile autism, infantile psychosis, Kanner's syndrome);

F84.1 - atypical autism;

F84.2 - Rett's syndrome;

F84.5 - Asperger's syndrome, autistic psychopathy.

Recently, all autistic disorders began to be united under the general abbreviation ASD - Autism Spectrum Disorder.

The manifestations of autism are very diverse, but the most common characteristics are the inability to establish full contact with people, extreme isolation from the outside world, a weak reaction to external stimuli, a stereotypical and rather narrow range of interests. Often in the literature one can come across a metaphor that a person with autistic disorder lives, as it were, under a dome, detached from the outside world and very few people are ready to “let in” to him under the dome.

So, a child with ASD goes to school…

Who decides where and how to study for a child with ASD?

In fact, the decision is always made by the parents, and two scenarios are possible here. The first is if the parents managed to notice, recognize and accept the fact that their child has autism. They went to the doctor in time, the child was diagnosed, the medical commission clarified that the child's intellect was preserved (intelligence disorders are the only actual obstacle). The future student was regularly observed by specialists and received the necessary psychological and pedagogical correction. Thus, by the age of seven, many of the child's autistic symptoms are already smoothed out and, most likely, he is ready for school as far as his disorder allows.

The second scenario is when parents do not know, do not see, deliberately keep silent about the illness of their child. Naturally, in this case there were no commissions, consultations, no psychological and pedagogical work, and a child with a neglected disorder ends up in a school where no one is warned either. This is a more difficult story for everyone involved: painful for the child, difficult for educators, and ultimately unpleasant for parents, because ASD is not one of those diagnoses that will go away on its own. Sooner or later, it will become clear to all participants in the educational process that the child has health problems.

In the first case, parents will listen to the advice of specialists, choosing an educational path for the child, in the second, it will be a “one-sided game”, until the parents realize, and then they will have to start all over again: diagnosis, correction etc.

If we are responsible parents, then...

It is best if, at the time of enrollment in the school according to the main list (that is, by March-April), the parents had all the documents related to the developmental features of the child ready. To do this, in November-December, it is worth showing the child to the PMPK - the psychological, medical and pedagogical commission.

This is a permanent body, the task of which is a comprehensive examination of the child for the presence of a particular diagnosis, an assessment of the general level of his development and recommendations on the organization of his education. The commission consists of diversified specialists - defectologists, speech therapists, doctors (neurologists, psychiatrists). They will give advice to the child's parents on what form of education is suitable for him and what program the child will be able to study.

A kindergarten can send a child to the PMPK by submitting his characteristics to the commission, or parents can enroll him on their own initiative.

Before undergoing PMPK, a child with ASD undergoes a medical commission at a medical institution. The purpose of the medical commission is to determine the diagnosis, in order to then choose the type of educational program that corresponds to the characteristics and intellectual level of the child's development.

It is important that the PMPK works in continuity with the medical commission. For example, at the medical commission, the child demonstrates a sufficient level of intelligence to study under the 8.1 or 8.2 program, but at the PMPK he does not cope with the tasks - then the PMPK is obliged to recommend him to study under the inclusive program anyway.

Should parents tell the school that their child has ASD?

By law, no, no one obliges parents to inform the school that their child has autism. They do not have to provide any certificates - but in order for the child to get into suitable conditions for him, it is important to inform the school administration that the child is special. If the parents did not inform the school in a timely manner about the child's difficulties, the school will not be ready to teach a child with ASD, and this will eventually lead to serious difficulties in organizing the educational process - both for the child himself and for the whole class.

Usually, the first meeting of the school administration representatives with the future student and his parents takes place during the formation of the first classes, in April-May. At this moment, and without any information, it will become clear to specialists (school psychologist, speech therapist, defectologist) that not everything is fine with the child. Further clarifications will come in the academic year (autumn), and it is not known how many unpleasant moments will have time to happen to the child during the educational process.

How do children with ASD learn?

Studying programs

In accordance with the Federal State Educational Standard, there are four different options for the education program for children with ASD, subdivided according to the degree of intellectual development of the child.

Program 8.1: it teaches children with intact intelligence. The level of their final achievements should be the same as that of their peers. Children study according to ordinary textbooks, according to the usual program and the standard curriculum. The difference lies in the fact that they must additionally deal with a psychologist, a speech therapist. For the period of adaptation to school, the child may need a tutor.

Program 8.2: children with ASD with mental retardation are trained. Their level of final achievements should also correspond to the level of their peers, but they study for a longer period of time. If a child has previously attended a pre-school organization and received psychological and pedagogical correction, the period of his education in primary school will be five years. If he did not attend a preschool organization, he will study for six years.

Program 8.3- This program caters for children with mild to moderate intellectual disabilities. This is a borderline situation: on the one hand, such children could study in specialized schools, on the other hand, at the request of their parents, they can also be enrolled in a mass school. The expected level of their final achievements does not correspond to the level of their peers, they study according to adapted textbooks. The term of education in elementary school for such children is 6 years.

Program 8.4- for children with severe intellectual retardation and multiple developmental disorders. As a rule, such children have serious speech therapy problems (do not speak at all or have severe speech delays). The duration of the program is 8.4 - 6 years, the expected level of achievement differs significantly from the level of peers, while the main emphasis is placed more on the socialization of the child than on academic success. Approximately 70% of the educational program will be aimed at mastering household skills and life competencies by the child.

How can training be organized?

As for the options for organizing education for children with ASD, they can be as follows:

Full inclusion. The child is taught in a regular class with peers.

Inclusive education using resource zone technology. The child is enrolled in a regular class, but when he has difficulties, he can receive individual support in a separate room - a resource zone. This form is possible if a tutor is assigned to the child and if the school is equipped with a resource zone - a large room where each child with special needs works individually with his tutor.

Correctional classes in a general education or special correctional school, or the child is studying in a special school. And here options are possible - for example, a child with autism can get into a class where very different children with very different developmental disorders are gathered (an integrated class). Or, if he has an intellectual retardation, he may be in a class with children with intellectual disabilities. Or the class is fully staffed with children with ASD - in different forms and manifestations.

Individual training at home. Some children, due to their behavioral disorders, are recommended to study individually at home, but even in this situation it is worth thinking about socialization - for example, connecting to a peer class at least once a week for certain subjects, for outdoor events.

Individual plan

Please note that there is no direct connection between the level of the program and the form of organization of training. It is important that the form of organization of training is selected individually, in accordance with the needs and level of socialization of the child.

And further! Each child has the opportunity to create an individual curriculum. This is a special schedule for the child - where, what and at what moment he will study. For example, mathematics is extremely difficult for a child with ASD, so he spends almost all the time in an inclusive class, and during mathematics lessons he goes to individual lessons with a defectologist.

An individual plan for the child is made by the school, by a joint decision of specialists within the organization - a class teacher, a psychologist, a speech therapist, subject teachers. As a rule, a decision on an individual plan is made after the diagnostic period, which lasts about a month. Thus, by the end of the first quarter, the child can already receive his individual plan.

Do children with ASD need special textbooks?

This is a sore point, since there is no universal textbook for children with ASD, and it will probably be almost impossible to create one: the manifestations of this disorder are too diverse. Every child with ASD needs an individual approach.

At the moment, when teaching children with ASD under programs 8.1 or 8.2, teachers can take as a basis the ruler for a general education school, but even in this situation, textbooks need to be adapted. If the child is studying according to program 8.3 or 8.4, then textbooks for children with intellectual disabilities are taken as the basis, which also need to be adapted. For example, reduce the number of exercises on one sheet, make the font larger, reduce the number of small, insignificant details in the drawings, add visual support (drawings that make it easier to understand).

Usually, teachers of inclusive schools themselves, as best they can, adapt certain chapters of textbooks to the needs of students. But, of course, if a textbook for children with ASD ever appeared, at least an average one, it would be very valuable.

How to choose the most convenient way for the child?

There is an opinion that studying in a regular class is always better than in a correctional one. In this regard, many parents of children with ASD set themselves the goal of fighting for the opportunity to study in the mode of full inclusion.

All experts are unanimous in their opinion: before fighting, parents should calmly, slowly consider all the pros and cons of each form of educational organization - in relation specifically to their child, to their case. In particular, be sure to ask yourself the following questions:

What is more important to you - social or educational inclusion? Quite often, the same form of training will not give you both. For example, in a correctional class, a child will feel like a fish in water, where everyone understands him, indulgent to his features. But, of course, in terms of education, everything is simpler and weaker here. And in an ordinary class, he will receive more knowledge, but he will feel like a stranger among his peers, which, of course, is detrimental to his socialization.

Is the game worth the candle? More precisely, is studying in a regular class worth the effort and stress. For children with ASD, excessive stress is simply contraindicated.

What exactly can your child get from a regular class? For example, it is possible to form an individual plan, according to which the basic subjects (Russian, reading, mathematics) the child takes under a light program in a correctional class or even at home, and comes to school in a regular class for those subjects that develop him physically, are associated with manual labor and general development (music, technology, physical education).

And please accept as an axiom: the choice of the level of inclusion and form of education is not the factor by which it is fair to evaluate your child or you as a parent. You just find the most suitable way, and do not try to prove something to someone, outwit, "achieve" the best, etc. Please, assess the situation sensibly: sometimes a correctional class can give a child much more than an inclusive one.

Parents and school: rules of interaction

Can the school administration refuse to teach a child with ASD?

Difficult question. On the one hand, according to the Law on Education, any child with any degree of ASD with intact intelligence can study in a public school. On the other hand, not every school is able to provide such a child with all the necessary conditions. Inclusion is a very expensive pleasure for the school, which, moreover, is not so easy to organize.

If a school cannot provide a child with ASD with all the conditions for learning, parents have two options: either find another school, or insist on creating special educational conditions for their child in this school.

That is, a student with ASD is an inevitable problem for the school?

If we are dealing with a negative scenario (when parents do not recognize the characteristics of the child) - yes, this is certainly a problem for everyone. If the parents have acquired all the necessary documents, perhaps they have issued a disability to the child, then this is a kind of opportunity for the school. Together with the documents on the child's disability, parents bring additional budgetary funds to the school. In a sense, it is even beneficial for the school to compete for the status of inclusive.

Can all schools guarantee an adequate education for a child with ASD?

Of course, not all. As a rule, at the admission stage, representatives of the school administration honestly explain to parents that the school is not ready to provide the child with adequate opportunities. Then the child may be recommended a special school or given the address of the nearest inclusive school. There are such schools: they invest a lot of effort and money in order to maintain the status of inclusive, resourceful. Parents of children with ASD should look for such a school: it will be much more useful for the child to study in it.

But there are few such schools: for example, in Moscow there are no more than ten of them, but those that exist really know how to work with special children. Here they are really taught, adapted, included in society.

In fact, it is quite normal that a regular school is in no hurry to accept a child with ASD. If the director, teachers, administrators have never dealt with this phenomenon, it is unlikely that the experience of studying in such a school will be useful for the child. It will be more honest to objectively see your resource and understand what you can really give to a child with autism, and what you cannot yet.

It is known that many children with ASD are shown to study with a tutor - a personal assistant and mentor. Where to find a tutor for a child, should the school do this?

If, according to the conclusion of the PMPK, the child is entitled to the assistance of a tutor in learning, then the school must provide him with tutor support. To do this, the school introduces an additional staff unit.

In total there are three forms of tutor support:

The position of a tutor is in the staff list, and then the school provides you with a tutor.

You have an ordinary school, then the parents themselves find and invite a tutor and, most likely, they themselves find a way to pay for his services, but at the same time, the tutor must sign an agreement with the school.

Parents enlist the help of internship students or volunteers. A volunteer can be found by both the school and the child's family by contacting one of the public organizations for the support of children with autism. It is important here that the found person has a sufficient level of understanding of the child.

The most unfavorable option is when one of the child's parents is present as a tutor at the lessons at school. We do not support such a situation, but, unfortunately, if a tutor could not be found, one has to resort to such a measure.

What should the teacher prepare for?

So, a child with an autism spectrum disorder will come to your class ...

The appearance of a child with ASD in the classroom is a serious challenge for the teacher. Most likely, you will be shocked: in front of you will be a student who, for example, has not formed an educational stereotype - that is, he is not ready to sit at a desk, be quiet, listen silently, answer questions. Or he will be constantly distracted, unable to concentrate, his emotions are unpredictable, and often they simply cannot be easily pacified.

We will warn you right away: without special training it will be very difficult for you. If it turned out that you did not have time to complete the training courses, get ready that it will not work out all at once. However, experts can give you some tips to help you deal with the situation more easily.

1. Collect all information- First of all, about the disorder itself. The more you know about the challenges people with ASD face, the easier it will be for you to manage your own anxiety. Ultimately, an autistic child is not so much a threat to you as a person who really needs your help. Try to take a strong position of a patient helper, and not a victim of circumstances, and then it will be easier to get involved in new circumstances.

2. Watch your child. Although you are not a parent or a tutor for him, for successful work you need to know how he behaves in a given situation, what frightens him, annoys him, and calms him down. If the parents of the child are ready for contact, ask them, find out as much as possible about how to help yourself and the child in a difficult situation.

3. Show interest. Yes, a child with ASD is not the easiest student. In a way, his appearance challenges you: do you love children enough to continue doing your job with brilliance? Your interest, attention, dedication to life and the interests of the child is the most appropriate way of interaction.

4. Transform your learning space. You will need to structure the environment in which the child is located in a special way. While a diary schedule is enough for ordinary children, a child with ASD simply needs to see all the important information in front of his eyes. Hang the schedule on the board, stick a piece of paper with hints to the desk, indicate the direction of movement with arrows. You will be able to teach a child with ASD only if the educational environment is predictable and safe for him.

Can a teacher without special training start teaching a child with ASD?

It's extremely difficult. An experienced teacher with a developed professional intuition is really able to quickly "feel" the situation. However, you should not force a good teacher to act by trial and error: it will be much more useful to give him all the necessary knowledge about the development and behavior of children with ASD, to help him master effective methods of correction and education. For example, the teacher should always be able to understand what is happening with the child: is he excited? Scared? Talk to the child about a particular problem, or just show him the right picture? Is it worth it now to explain something to him in detail, or just take him away from other children and let him rest calmly in a quiet place? All these things are easier to digest if you know what to do.

The minimum possible level of training is the passage of short-term refresher courses. On average, the training period is about 2 months, but significant results are achieved already in 1-2 weeks of intensive work. A huge role is played here by the personality of the teacher, and his life attitudes. The key qualities for an inclusive class teacher are patience, determination and readiness for the fact that in such a matter as teaching a child with ASD, there are no quick results. But, when you wait for the results, albeit slow ones, you will feel that you have conquered a real pedagogical Everest.

Alexandra Chkanikova

Mandatory are the organization and expansion of everyday social contacts, the inclusion of special courses for correctional and developmental ...

Option 8.2 assumes that a student with autism spectrum disorders receives an education that is comparable in terms of final achievements with the education of peers who do not have health limitations in an extended period of time. This option assumes extended periods of study: 5 years (with one first additional class) - for children who have received preschool education; 6 years (with the first two additional classes) - for children who have not received a preschool education that contributes to the development of CEO based on the AOOP. This option involves, to a greater extent, the development of life competence among students on the basis of a systematic introduction to a more complex social environment, the gradual formation of educational activities and communicative behavior, the expansion of life experience, social contacts with children and adults.
Mandatory are the organization and expansion of everyday social contacts, the inclusion of special courses in the correctional and developmental direction, special structuring of the content of training based on increased attention to the purposeful development of the emotional-personal sphere and communicative behavior, the formation of life competence, as well as the use of both general and special methods and teaching methods.

Requirements for special conditions for obtaining primary general education are established by the Federal State Educational Standard for Primary General Education for Students with Disabilities (Order of the Ministry of Education and Science of Russia dated December 19, 2014 N 1598):

The structure of the adapted educational program for students with disabilities includes mandatory correctional and developmental courses, which are provided for by federal state educational standards from September 1, 2016 (applicable to relations arising from September 1, 2016, i.e. are valid for first graders in 2016 and subsequent years). The mandatory remedial courses provided for by the standards can be supplemented by an educational organization independently based on the recommendations of the PMPK and taking into account the IPR.

Compulsory remedial courses are an integral part of the adapted educational program and are free for the student.

Mandatory correctional and developmental courses for students with autism spectrum disorders.

From SanPiNs to the conditions and organization of training and education in organizations that carry out educational activities according to adapted basic general educational programs for students with disabilities (Resolution of the Chief State Sanitary Doctor of the Russian Federation of July 10, 2015 N 26):

“Rehabilitation and correctional activities can be implemented both during extracurricular activities and during class activities.

The number of hours allotted for mastering by students with disabilities of the main educational program, consisting of the curriculum of a general educational organization, including the obligatory part and the part formed by the participants in the relationship, as well as from the hours necessary for carrying out rehabilitation and correctional measures, should not in total exceed the value of the weekly educational load of students with disabilities.

Extracurricular activities is formed from the hours necessary to meet the individual needs of students with disabilities and in total is 10 hours per week for each class, of which at least 5 hours are provided for the implementation of compulsory remedial classes, the rest - to the developing area, taking into account the age characteristics of students and their physiological needs.

For the creation of special conditions for education pay in state and municipal educational organizations not charged It's free for the family. Correctional classes are an integral part of educational programs for teaching a child with disabilities and cannot be charged for them either. If the school requires the provision of correctional services included in the educational program to conclude an agreement on paid services, contact the education authority to resolve the situation.

Answers to the questions of school principals about resource classes for children with autism

This document was developed by an initiative parent group of the Inclusive Molecule project aimed at creating and developing resource classes for teaching children with autism in general education institutions. Parents created a closed group on Facebook, where they posted questions from school principals, and then turned to specialists for answers. All of the questions below are real - they were heard by parents when they discussed with the directors of Moscow schools the possibility of opening a resource class.

Project moderator and editor-in-chief Evgenia Lebedeva (PhD in Psychology, Senior Researcher at the Developmental Psychology Laboratory of the Institute of Psychology of the Russian Academy of Sciences and mother of children with ASD), consultants Anastasia Kozorez, Elena Kutepova, Tatiana Medvedeva, Elena Tsyrulnikova and many other specialists interested in so that children with ASD can go to kindergarten and go to school.

Gradually, the document will be finalized, and you can take part in its development. Send questions from your acquaintances to the directors of schools and kindergartens to the address, and we will definitely find those who can answer them meaningfully.

Dear colleagues!

This document contains answers to questions from school principals who are approached by initiative groups of parents with a request to admit children with autism to school. In schools that accept such children, resource classes are often organized in international practice. If the school has such a class, teaching a child with autism becomes possible and effective, and the school implements the principles of inclusive education in practice. Today there are such projects in Russia. We will be glad to expand the list of answers and are ready to accept your questions. The full version with new answers to the questions will be published on the website of the Department of Education of the Voronezh Region, on the website of the Vykhod Foundation and on the website of the Institute for Inclusive Education Problems (MSUPE). Questions were answered by specialists from educational institutions where children with ASD study, as well as representatives of public organizations created by parents of children with autism. Reviewer: Institute for Problems of Inclusive Education (MGPPU).

1. What features can children with autism spectrum disorders (ASD) have?

Sometimes children with ASD differ so little from other children that their features are only noticeable to specialists. But still, more often, the characteristics of children with ASD are clearly manifested when communicating with them.

The child may never look at the interlocutor or maintain eye contact during the conversation, while not answering anything, so that it seems that he does not notice that he is being addressed.

There is also the opposite situation: the child can talk on topics of interest to him without stopping, without seeing that the interlocutor has lost interest in the conversation and wants to end it. Children with ASD, as a rule, do not understand the hidden motives of the actions of other people, it is almost impossible for them to understand the irony of the interlocutor, as well as the use of words in a figurative sense.

Most often, children with ASD have features of speech development, which can vary from a complete lack of speech to slight intonation differences.

Some children with ASD learn to read quite early, even before they begin to speak in phrases, and read almost the entire school curriculum before they go to school, or are so serious about a subject, such as history, that they know the school curriculum in this subject is no worse than the teacher.

But in most children with autism, intellectual development is uneven: strengths are often visual perception, attention to detail, and a large amount of mechanical memory. Weaknesses often turn out to be a lack of understanding of the general meaning of the text and retelling of what was read by memorized phrases or a fragmentary perception of oral speech, which, for example, can make it difficult to study mathematics, because although the child knows how to perform arithmetic operations, he fails to understand the condition of the problem.

Many children with ASD have sensory developmental features. Some children cannot stand loud noises or bright lights, smell or touch can also become a strong irritant (and all this, as a rule, does not cause any inconvenience to those around them). What may be perceived as odd behavior is often the child's reaction to sensory stimuli that cause him great discomfort and sometimes even pain.

Children with ASD can soothe themselves with habitual stimulation. For example, when exposed to bright lights or loud music, some children may shake their hands, or jump in place, or roll the wheels of a toy car as close to their eyes as possible. The mechanisms of these actions are similar to those that we demonstrate by shaking our legs or twisting our hair around our fingers during an unpleasant conversation or a long wait.

Odd behavior in a child with ASD (as well as any strange behavior in a child without ASD) can be explained by a specialist, and through practice with the child and his parents, such behavior can be changed.

2. Why do children with ASD need a comprehensive school? Aren't they better in remedial?

Of course, the mere presence of a child with ASD in a general education school does not guarantee effective teaching of academic skills. But the creation of special conditions (a resource class, an adapted program, the help of a tutor), as well as the presence of typically developing children as a role model and an environment for communication, helps a child with ASD to be more successful in mastering the school curriculum, contributes to the formation of communicative behavior, and the expansion of life experience. and better socialization.

After school, a child with autism will have to live in the same society as regular school graduates. The sooner they get to know each other, the higher the chances that understanding and interaction will develop between them. It will be much easier for a child with autism who goes to school with ordinary children to feel part of society than a graduate of a special school.

3. Why should ordinary children study together with children with autism? What does it give them?

Many scientific works have been written about the benefits of inclusive education for ordinary children by scientists from different countries, where this practice has existed for many years. For example, it has been proven that graduates of inclusive schools have better communication skills, better understanding of others, and greater flexibility and creativity. In addition, working in an inclusive classroom with special educational conditions provides teachers with a unique experience. A teacher who understands the complex characteristics of a child with autism will easily find an approach to the learning problems of an ordinary child, and if this is not enough, he can use the help of resource class specialists, so all children benefit. There are other benefits as well.

In a school where children from an early age learn to understand each other's characteristics, an atmosphere of trust arises - and the best qualities develop: tolerance, care, kindness. And all children feel more comfortable.

4. Will a child with ASD be in a regular classroom?

For children with ASD, resource classes are being created, in which preparations are made for learning in a regular class.

5. What is a resource class?

The resource classroom is a separate room for special studies where students with ASD can study according to a special program designed in accordance with their individual educational needs.

Students with ASD attend part of the lessons in the resource class, and part - together with their classmates in the general education class. The resource class teacher can teach in small groups or work with the child individually.

Students of general education classes can also receive additional help from specialists in the resource class.

6. Who decides when a student with ASD is ready to be included in a regular class?

The decision that a child with ASD is ready to be included in a regular class is made by the resource class teacher.

Decisions about the choice of lessons that the child will attend, about increasing the amount of time spent in the classroom, about reducing tutor support, are agreed with the teachers of the general education class. If necessary, the teacher of the resource class adapts the teaching materials to the needs of the student.

7. What tasks does the resource class teacher solve? What are his responsibilities?

The resource class teacher is the leading specialist in organizing work with students with ASD in the school. He must have a higher specialized pedagogical education. The teacher-defectologist is optimal for working in the resource class.

If the work of the resource class is built on the basis of Applied Behavior Analysis (ABA), the teacher must have additional education in this direction.

Responsibilities of the resource class teacher include:

- diagnosing the developmental features of students in the resource class;

– conducting individual and group classes with students attending the resource class;

– organization of work on the correction of undesirable forms of behavior in students with ASD;

– drawing up, adaptation and adjustment of educational and correctional programs and curricula;

- drawing up lesson plans for the resource class;

- adaptation of educational materials taking into account the individual characteristics of students;

— adaptation of the curricula of general education classes for students with ASD;

— training of tutors;

- Counseling parents and school staff;

— monitoring the effectiveness of the educational process for students with ASD.

8. What program will a child with ASD study?

Program requirements are described in the Federal State Educational Standard for Primary General Education for Students with ASD. At the moment, there are four options for the educational program, according to which students with ASD can study. The teacher of the resource class, in cooperation with teachers of general education classes, when drawing up the program, must determine what knowledge, skills and abilities are the most priority for this student and in what format their assimilation will be most effective: in individual forms of work, in a resource class or in a general education class, as well as what materials, methods and techniques should be used in his training.

Requirements for AOOP IEO for students with autism spectrum disorders

8.1 Adapted basic educational program of basic general education. This option assumes that a student with ASD receives an education that is fully consistent with the final achievements by the time of completion of education, the education of peers who do not have disabilities, being in their environment and in the same terms of study (grades 1–4).

8.2 Adapted educational program of basic general education. This option assumes that a student with ASD receives an education comparable in final achievements to the education of peers without disabilities in a prolonged period. This option assumes extended periods of study: five years (grades 1–5) for children who have received preschool education; six years (grades 1-6) - for children who have not received preschool education.

8.3 Adapted educational program for students with mental retardation. This option assumes that a student with ASD receives an education that, in terms of the content of the final achievements, does not correlate with the content and final achievements of peers with ASD, who do not have additional health limitations, by the time they complete schooling, in a prolonged period. This option involves a prolonged period of study: six years (grades 1–6).

8.4 Special individual development program. This option assumes that a student with ASD complicated by mental retardation (moderate, severe, profound, severe and multiple developmental disorders) receives an education that, in terms of content and final achievements, does not correlate with the content and final achievements of peers by the time of completion of schooling, does not having additional restrictions on health capabilities, in a prolonged period. This option involves a prolonged period of study: six years (grades 1–6).

9. There are non-speaking children among school-age children with ASD. When will they speak, and on what does it depend?

There are children who will never use spoken language. But for communication and transmission of information, we do not always use oral speech. We have different ways. We can gesture, write, type, chart.

For children who do not use oral speech, various alternative communication systems have been created, using which they can answer questions, express requests, talk about something interesting, and chat with friends.

The school should create conditions under which the child can use all possible means of communication, and then the lack of oral speech will not become an obstacle to learning or communicating with peers.

10. Can children with ASD be a danger to normal children?

Aggression is not a hallmark of children with ASD. However, they may become defensive in response to what they perceive as a threat or ridicule.
Sometimes a child with autism may appear aggressive when they try to communicate their discomfort, such as loud noises or strong smells.

It is important to remember that children who have potentially dangerous behaviors are not included in the educational process in the general education class.

11. Children tend to repeat words and actions one after another. Will children with ASD become an example of bad behavior for other children? Are there ways to avoid this?

It is possible that other children will sometimes repeat some of the actions of their classmates with ASD. But they will not adopt and appropriate this behavior, because they have formed their own habitual forms of behavior for emerging life situations.

If children have questions about why their classmate with ASD behaves the way they do, it is important to explain to them the reasons for this behavior and how they can be helped to learn to behave differently.

We hope that the information on our website will be useful or interesting for you. You can support people with autism in Russia and contribute to the work of the Foundation by clicking on .

Adapted work program

mathematics

Course “Mathematics. 1-4 class "

Explanatory note

The work program in mathematics was developed for ____________________ (a child with an autism spectrum disorder), based on an exemplary adapted basic general education program of primary general education for students with autism spectrum disorders (option 8.2), the Concept of the second generation standard, requirements for the results of mastering the main general education program of primary general education , the fundamental core of the content of general education, an exemplary program taking into account inter-subject and intra-subject relationships, the logic of the educational process, the task of developing the ability to learn in younger students, the author's program in mathematics

The program is aimed at achieving the planned results, the implementation of the program for the formation of universal educational activities.

2 hours a week are allotted for the study of mathematics,

1st class - 66 hours,

Grades 2-4 - 68 hours each, for a total of 336 hours for the primary school course.

Material and technical support of the educational process in the subject "Mathematics"

Library fund (printed products):

Textbooks: "Mathematics" in 2 parts for grades 1-4 of a four-year elementary school (authors Rudnitskaya V.N., Kochurova E.E., Rydze O.A.), M: Ventana-Graf

The main educational program of a general education institution working according to the system of textbooks "Primary School of the XXI century". (http://www.vgf.ru/tabid/186/Default.aspx)

Information and communication means

Digital information tools and sources (on the main topics of the program): electronic reference and training aids www.vgf.ru

Screen and audio aids

Video clips and other information objects (images, audio and video recordings) reflecting the main topics of the mathematics course

Games and toys

Board educational games

Constructors

General characteristics of the subject

A mathematics course in elementary school provides sufficient training for continuing education and expands students' understanding of mathematical relations and patterns of the world around them, develops erudition, and fosters mathematical culture.

In the process of studying the course of mathematics, younger students form ideas about numbers as a result of counting and measurement, about the principle of writing numbers. Students learn to perform verbal and written arithmetic operations with numbers, find an unknown component of an arithmetic operation, compose a numerical expression and find its value in accordance with the rules of the order of operations; gain experience in solving arithmetic problems. In the process of observations and experiments, they get acquainted with the simplest geometric shapes, acquire the initial skills of depicting geometric figures, and master methods for measuring lengths and areas. In the course of working with tables and diagrams, they develop skills that are important for practice-oriented mathematical activity related to the presentation, analysis and interpretation of data.

As a result of mastering the subject content of a mathematics course, general learning skills and methods of cognitive activity are formed. Simple memorization of rules and definitions gives way to the establishment of the distinctive features of a mathematical object, the search for common and different, the analysis of information, the comparison (comparison) of the characteristic features of mathematical objects (numbers, numerical expressions, geometric shapes, dependencies, relationships). Students use the simplest subject, symbolic, graphical models, tables, diagrams, build and transform them in accordance with the content of the task (task).

In the process of studying the course of mathematics, younger students get acquainted with the mathematical language. They learn to make judgments using mathematical terms and concepts, to ask questions in the course of completing the task, to choose evidence for the correctness or incorrectness of the completed task, to substantiate the stages of solving the educational problem, to characterize the results of their educational work.

Mathematical content allows you to develop organizational skills: the ability to plan the stages of the upcoming work, determine the sequence of educational activities; monitor and evaluate their correctness, search for ways to overcome errors.

In the process of teaching mathematics, students learn to participate in joint activities: to negotiate, discuss, come to a common opinion, distribute responsibilities for information search, take initiative and independence.

The study of mathematics in primary school aims to achieve the following goals:

mathematical development junior schoolchildren - the development of logical and symbolic thinking, spatial imagination, mathematical speech (the ability to build reasoning, choose an argument); development of the ability to distinguish between reasonable and unreasonable judgments, to search for information (facts, grounds for ordering, options, etc.);

development basic mathematical knowledge - understanding the meaning of quantities and methods of measurement; the use of arithmetic methods to resolve plot situations; formation of the ability to solve educational and practical problems by means of mathematics; work with algorithms for performing arithmetic operations;

- upbringing interest in mathematics, the desire to use mathematical knowledge in everyday life.

To achieve the goals, it is necessary to organize work to develop the thinking of students, to contribute to the formation of their creative activity, to master a certain amount of mathematical knowledge and skills that will enable them to successfully study mathematical disciplines in high school. The originality of the initial stage of education lies in the fact that during this period the elements of educational activity are formed in students. On the basis of this activity, the child develops theoretical consciousness and thinking, and the corresponding abilities develop.

(reflection, analysis, mental planning); at this age, children also develop the need and motives for learning.

In this regard, the following methodological methods are used as the basis for the selection of training content. principles:

analysis of specific educational material in terms of its general educational value and the need to study in elementary school;

the relationship of the introduced material with the previously studied;

ensuring continuity with preschool mathematical training and the content of the next stage of education in secondary school;

enrichment of the mathematical experience of younger students by including new questions in the course that were not previously studied in elementary school;

development of interest in mathematics.

an organic combination of education and upbringing.

mastering mathematical knowledge.

development of cognitive abilities of younger students.

formation of the foundations of logical thinking and speech of children.

the practical orientation of training and the development of the skills necessary for this.

taking into account the age and individual characteristics of children.

differentiated approach to learning

The main content lines of the course (sections, structure)

Numbers and quantities

Arithmetic operations

Working with text tasks

Geometric quantities

Working with information

The following sections are distinguished in the structure of the studied program:

Numbers and magnitudes. Item count. Reading and writing numbers from zero to 20 . Comparison and ordering of numbers, comparison signs. Quantities and units of their measurement. Units of mass (kilogram), capacity (liter), time (hour). Relations between units of measurement of homogeneous quantities.

Arithmetic operations. Addition and subtraction . Names of components of arithmetic operations, signs of actions. Addition table. Arithmetic operations with numbers 0 and 1. The relationship of arithmetic operations. Numeric expression. Finding the value of a numeric expression. Using the properties of arithmetic operations in calculations (permutation and grouping of terms in the sum) . Ways to check the correctness of calculations.

Work with text tasks. Solving text problems in an arithmetic way. Tasks containing relations "more by ...", "less by ...".

Spatial relations. Geometric figures. The mutual arrangement of objects in space and on a plane (above - below, left - right, top - bottom, closer - further, between, etc.). Recognition and image of geometric shapes: point, line (curve, straight line), segment, broken line, polygon, triangle, rectangle, square, circle. Using drawing tools to perform constructions.

Geometric quantities. Geometric quantities and their measurement. Measuring the length of a segment. Units of length (centimeter, decimeter). Measuring the length of a segment.

Working with information. Collection and presentation of information related to the account, measurement of quantities; recording the results of the collection.

Numbers and quantities

Item count. Reading and writing numbers from zero to a million. Classes and ranks. Representation of multi-valued numbers as a sum of bit terms. Comparison and ordering of numbers, comparison signs.

Measurement of quantities; comparison and ordering of quantities. Units of mass (gram, kilogram, centner, ton), capacity (liter), time (second, minute, hour). Relations between units of measurement of homogeneous quantities. Comparison and ordering of homogeneous quantities. Share of value (half, third, quarter, tenth, hundredth, thousandth).

Arithmetic operations

Addition, subtraction, multiplication and division. Names of components of arithmetic operations, signs of actions. Addition table. Multiplication table. Relationship between addition, subtraction, multiplication and division. Finding an unknown component of an arithmetic operation. Division with remainder.

Numeric expression. Establishing the order of performing actions in numerical expressions with and without brackets. Finding the value of a numeric expression. Using the properties of arithmetic operations in calculations (permutation and grouping of terms in the sum, factors in the product; multiplying the sum and difference by a number).

Algorithms for written addition, subtraction, multiplication and division of multi-digit numbers.

Methods for checking the correctness of calculations (algorithm, reverse action, reliability assessment, estimation of the result, calculation on a calculator).

Working with text tasks

Solving text problems in an arithmetic way. Tasks containing relations "more (less) by ...", "greater (less) by ...". Relationships between quantities characterizing the processes of movement, work, sale and purchase, etc. Speed, time, path; volume of work, time, labor productivity; the quantity of goods, its price and cost, etc. Planning the course of solving the problem. Representation of the text of the task (scheme, table, diagram and other models).

Tasks for finding the share of the whole and the whole by its share.

Spatial relations. Geometric figures

The mutual arrangement of objects in space and on a plane (above-below, left-right, top-bottom, closer-further, between, etc.). Recognition and display of geometric shapes: point, line (curve, straight line), segment, polyline, angle, polygon, triangle, rectangle, square, circle, circle. Using drawing tools to perform constructions. Geometric shapes in the environment. Recognition and naming: cube, ball, parallelepiped, pyramid, cylinder, cone.

Geometric quantities

Geometric quantities and their measurement. Measuring the length of a segment. Units of length (mm, cm, dm, m, km). Perimeter. Calculating the perimeter of a polygon.

The area of ​​a geometric figure. Area units (cm2, dm2, m2). Accurate and approximate measurement of the area of ​​a geometric figure. Calculating the area of ​​a rectangle.

Working with information

Collection and presentation of information related to the account (recalculation), measurement of quantities; fixation, analysis of the received information.

Construction of the simplest expressions using logical connectives and words (“and”; “not”; “if ... then ...”; “true / false that ...”; “each”; “all”; “some”); the truth of the statements.

Drawing up a final sequence (chain) of objects, numbers, geometric shapes, etc. according to the rule. Compilation, recording and execution of a simple algorithm, information search plan.

Reading and filling the table. Interpretation of table data. Reading a bar chart. Creation of the simplest information model (scheme, table, chain).

Planned results of mastering the adapted basic general education program of primary general education by students with autism spectrum disorders

The results of mastering with students with RASAOOP are evaluated as final at the time of completion of general education.

The development by students of the AOEP, which was created on the basis of the Federal State Educational Standard, implies the achievement of two types of results: personal and subject.

In the structure of planned results, the leading place belongs to personal results, since it is they that ensure the mastery of a set of social (life) competencies necessary to achieve the main goal of modern education - introducing students with ASD into culture, mastering their socio-cultural experience.

Personal Outcomes development of AOOP IEO of students with ASD, complicated by mild mental retardation (intellectual impairments), taking into account individual capabilities and special educational needs, include individual personal qualities, special requirements for the development of life and social competence and should reflect:

1) development of a feeling of love for parents, other family members, for the school, acceptance of the teacher and students of the class, interaction with them;

2) development of motivation for learning;

3) development of adequate ideas about essential life support;

4) mastering the social skills used in everyday life (imagining the arrangement of home and school life; the ability to get involved in a variety of everyday school activities);

5) possession of elementary communication skills and accepted rituals of social interaction;

6) development of positive properties and qualities of a person;

7) readiness for the student to enter the social environment.

AOOP defines two levels of mastery of subject results: minimal and sufficient. A sufficient level of mastering the subject results is not mandatory for all students.

The minimum level is mandatory for all students with ASD.

The minimum and sufficient levels of assimilation of subject results at the end of education in the lower grades:

Subject Results:

Minimum level:

know the number series 1-100 in direct order and set aside, using counting material, any numbers within 100;

understand the meaning of the arithmetic operations of addition and subtraction, multiplication and division (into equal parts).

know the multiplication table of single digit numbers up to 5;

know the order of actions in examples in two arithmetic operations;

distinguish between numbers obtained by counting and measuring, write down numbers obtained by measuring with two measures;

use a calendar to establish the order of months in a year, the number of days in months;

determine the time by the clock in at least one way;

solve, compose, illustrate studied simple arithmetic problems;

solve compound arithmetic problems in two steps (with the help of a teacher);

recognize, name, model the mutual position of two straight, curved lines, figures, find intersection points without drawing;

know the names of the elements of quadrangles, draw a rectangle (square) using a drawing triangle on unlined paper (with the help of a teacher).

distinguish between a circle and a circle, draw circles of different radii.

Enough level:

know the number series 1-100 in forward and reverse order, count, counting, counting by one and in equal numerical groups of 2, 5, 4, within 100; set aside, using counting material, any numbers within 100;

know the names of the components of addition, subtraction, multiplication, division;

understand the meaning of the arithmetic operations of addition and subtraction, multiplication and division (into equal parts and by content), distinguish between two types of division at the level of practical actions, know how to read and write each type of division;

know the multiplication tables of all single-digit numbers and the number 10, the rule for multiplying numbers 1 and 0, by 1 and 0, dividing 0 and dividing by 1, by 10;

understand the relationship between multiplication and division tables, use multiplication tables on a printed basis, both to find the product and the quotient;

know the order of actions in examples in 2-3 arithmetic operations;

know and apply the commutative property of addition and multiplication;

perform oral and written addition and subtraction of numbers within 100;

know the units (measures) of measuring cost, length, mass, time and their ratio;

distinguish between numbers obtained by counting and measuring, write down the numbers obtained by measuring with two measures, with a full set of characters in small measures: 5 m 62 cm,

know the order of the months in the year, the numbers of the months from the beginning of the year, be able to use the calendar to establish the order of the months in the year, the number of days in the months;

determine the time by the clock in three ways with an accuracy of 1 minute;

solve, compose, illustrate all studied simple arithmetic problems;

write briefly, simulate content, solve compound arithmetic problems in two steps;

distinguish between closed, open curves, broken lines, calculate the length of a broken line;

recognize, name, draw, model the mutual position of two straight lines, curved lines, polygons, circles, find intersection points;

know the names of the elements of quadrangles, draw a rectangle (square) using a drawing triangle on unlined paper;

draw circles of different radii, distinguish between a circle and a circle.

Calendar - thematic planning Grade 1

№ lesson

Lesson topic

Basic results

Activities

Notes

Initial ideas about sets of objects

Comparison, identification of similarities and differences. The concept of "set", the selection of its elements.

Be able to describe the relative position of objects in space and on a plane. Compare objects in different ways (in direction, in the chosen order, element by element, by color, shape, size)

Reveal similarities and differences. .

Drawing up sentences on drawings using the words above, below, thicker, thinner. Comparison of objects by length, height, thickness. Comparison of geometric shapes using the words form, color, size. Designation by a chip of each element of the set (modeling). Classification of the elements of the set. Selection of elements of a set.

Compare objects by shape, color and size.

Be able to describe the relative position of objects in space and on a plane. Compare on a given or self-established basis.

Reveal similarities and differences. Distribute objects into groups Draw a closed line, inside which the objects of the selected group are located.

Drawing up sentences on drawings using the words above, below, thicker, thinner. Comparison of objects by length, height, thickness. Comparison of geometric shapes using the words form, color, size. Designation by a chip of each element of the set (modeling). Classification of the elements of the set. Selection of elements of a set.

Classification of objects. Distinguishing concepts: from left to right, from right to left, before, behind, between.

Be able to describe the relative position of objects in space and on a plane. Select elements of a set according to a given description. Know the concept of "left to right", "right to left" . Draw closed lines, inside which the objects of the selected group are located.

Distinguishing concepts: from left to right, right to left Selection of elements of a set, recalculation of objects Classification of objects Distinguishing concepts: before, behind, between.

(2 hours)

Introduction to the table.

Be able to describe the relative position of objects in space and on a plane. Distinguish concepts: row, column, right, left, top, bottom, inside, outside.

Distinguishing concepts: line, column, top left, bottom right Designation with a chip for each element of the set (modeling) Drawing a line from a point in a given direction Clarifying the spatial arrangement of objects.

Distinguishing concepts inside, outside, intersection.

Be able to distinguish between the concepts of "inside", "outside"; - writes the number 1; - gives examples of geometric shapes (circle, square, triangle, polygon).

Distinguish between inside and outside. Arrangement of objects inside and outside the "ring" Work on the distinction between the concepts: "left to right", "right to left" Designation by a chip of each element of the set (modeling) Drawing a line from a point in a given direction; modeling the composition of the number. Changing the size of a figure while maintaining color and shape: working with the didactic manual "machine"; a description of the location of the cubes in space using the words above, below.

Number and count (2 hours)

Introduction to numbers and numbers from 1 to 5.

Be able to distinguish between the concepts of "number", "number"; "longer", "shorter", "between";

Write number 2.

Able to correlate numbers and numbers within 5, 9.

Acquaintance with numbers and numbers from 1 to 5. Establishing a correspondence: a lot of objects (chips) - a number; number - a set of objects (chips). Writing a number 1. Search for numbers on the ruler scale. Distinguishing the concepts of "to the left", "to the right". Drawing up sentences on drawings using words longer, shorter.

Introduction to numbers and numbers from 6 to 9.

Be able to match numbers and numbers within 9.

Acquaintance with numbers and numbers from 6 to 9. Establishing a correspondence: a lot of objects - a number. Searching for numbers on a ruler scale. Establishing a correspondence between a lot of objects and a number. Writing the number 2. Drawing a line from a given point along a specified route. Counting within 9 . Classification of figures by color and shape Designation of each element of the set with a chip (modeling).

Geometric concepts

The development of geometric observation: work with the details of the designer "Corners" and "Tangram". Numbers and figures from 1 to 5.

Be able to write the numbers 1, 2;

works with the "Corners" and "Tangram" sets.

The development of geometric observation: work with the details of the constructor "Corners" and "Tangram"

The location of the numbers "inside" and "outside" the closed line. Distinguishing numbers and numbers from 1 to 9. Finding numbers on the ruler scale.

Drawing a line from a given point along a specified route

Writing numbers 1, 2. Clarification of concepts inside, outside the "ring".

Number and count. (1 hour)

Acquaintance with the composition of numbers: 2,3,4,5.

Preparation for performing addition, solving addition problems. Numbers and figures. fifteen. Writing number 2.

Be able to name and distinguish between the numbers 2,3,4,5; determines the spatial position of the numbers 2,3,4,5 and the number of items in the set.

Union of sets. Compilation of records corresponding to the scheme (orally):

The composition of each of the numbers: 2, 3, 4, 5. Complementing records of the form:  and  is 4, in accordance with the figure. Building a model: drawing chips. Drawing lines from a point along the pattern; according to the given algorithm. Writing the number 3. Arrangement of numbers on the scale of the ruler. Naming numbers in a given order. Grouping (classification) by color, by size.

Relations between objects and between sets of objects

Finding geometric shapes in space

Letter of numbers 1,2,3.

Be able to find shapes in a polygon;

composes and models tasks according to drawings;

establishes patterns and continues the pattern.

Development of geometric observation: comparison of the whole (quadrilateral) and its parts (triangles). Search for triangles in figures of complex configuration

Modeling (with the help of chips) a situation formulated orally; establishing a correspondence between the drawing and the model. Building a model (drawing chips). Writing the numbers 1, 2, 3. Checking the completed part of the task. Establishing a pattern and continuing the "pattern".

Learning to use the ruler scale for ordinal counting. Movement along the ruler scale to the right, to the left.

Be able to move along the ruler scale to the right, to the left;

is oriented in concepts on the scale of the ruler "to the right", "to the left".

The transition from one number to another when "moving" along the ruler to the right (left): "step" to the right (left). Compilation of sentences according to given samples using the words "right", "left"

Modeling (with the help of chips) the composition of the number 6. Building a model (drawing chips) and filling in the scheme with numbers:  and  is 6. Writing a number 4. Description of the location of objects in the structure (using the words above / below according to a given plan). Consideration of possible options for building "towers" of three cubes according to a given condition. Enumeration of all possible options for building "towers" from three cubes of different colors.

Arithmetic operations (1 hour)

Establishing a correspondence between a drawing and a record:

6 minus 2 is .

Getting ready to do the subtraction. Preparation for solving subtraction problems.

be able to write down the numbers 1-4;

stacks the results with the cut material.

Selection from the set of its subsets. Removing a part of a set. Compiling (verbal) records corresponding to the scheme:

Establishing a correspondence between a drawing and a record: 6 without 2 is . Addition of entries in accordance with the figure. Complementing the model (crossing out chips) in the situation of deleting a part of the “Movement” set along the scale of the ruler. Independent laying out of the results using cutting material. Checking the correctness of the task. Writing the numbers 1, 2, 3, 4 Search for "triangles" in the given figures.

Comparison of numbers. (4 h) Familiarity with the concepts of "more", "less".

Number 5 letter.

Be able to write number 5

Makes pairs of elements of two sets.

Demonstrates the difference between a number and a digit.

Comparison by pairing the elements of two sets. Orientation in terms: "more", "less", "equally"

Selection and compilation of a model (with the help of chips) for a given plot situation. Comparison of models. Writing the number 5. Copying the specified image (number 5) on the checkered part of the sheet. The arrangement of geometric shapes in the table according to a given plan. Changing the shape of a figure while maintaining the size and color (working with the "machine"). Selecting an element of a set that satisfies a given condition.

Comparison by the method of pairing of elements of two sets and the formulation of the conclusion.

The concept of "more by ...", "less by ..."

Letter number 6.

be able with leave and solve problems according to the drawing.

Know the composition of the number 6. Compares sets of objects. Knows the concept of "more by ...", "less by ...". Can write the number 6.

Comparison by pairing the elements of two sets and formulating the conclusion “... by  more than ...”, “... by  less than ...” Drawing up questions with the words “by how much”

Building models (drawing chips) to the situation of increasing (decreasing) the number of elements of the set. Set comparison. Addition of records of results of comparison. Writing a figure 6. Justification of the choice of a model corresponding to a given situation. Modeling (with the help of chips) the composition of the number 7.

Simulation of the plot situation. Establishing a correspondence between: drawing and model; drawing and diagram.

Be able to compose and solve problems from drawings.

Applies the ability to move along the ruler scale to the right, to the left. Converts shapes.

Writes numbers: 1, 2, 3, 4, 5, 6.

Using chips when answering a question

Correlation of records and drawings

Establishing a pattern for writing numbers in each line and writing numbers in accordance with the identified pattern

"Journey" from a point according to a given program. Finding triangles in a shape. Construction of houses according to the rule.

Preparation for solving problems, including the concepts of "more on ...",

"less by..."

Be able to explore, compose and write down the solution of the problem according to the drawing.

Argues the movement along the scale of the ruler and writes down the results.

Can write the number 7.

Modeling a situation formulated orally. Establishing correspondence between text and model. Choice of the method of complementing the model (coloring, strikethrough, etc.) Modeling (with the help of chips) the composition of the number 8. Filling in the scheme with numbers: 8 is  and . Comparison of two sets and formulation of the conclusion "... by  more (less) than ...". "Movement" on the ruler scale. Writing the number 7.

Arithmetic operations. (2 hours)

Learning how to write and solve addition problems.

Be able to write and solve addition problems based on pictures.

Simulates the conditions of the problem and writes down the solution. Oriented in the concepts of "inside", "outside", "intersection"

Addition of numbers. View record

corresponding to the scheme

Drawing up and supplementing entries in accordance with the figure and question

"Movement" on the ruler scale

Training in writing learned numbers. Establishing a pattern in writing numbers and continuing to work in accordance with the identified pattern. The location of objects and geometric shapes inside and outside the "ring". Work with the reverse "machine": detection of figures that have been entered into the "machine" Continuation of the pattern according to a given program.

Learning how to write and solve subtraction problems.

Be able to write and solve subtraction problems.

Models the condition of the problem and writes down its solution. Knows the composition of the number 8.

Know how to write the number 8.

Subtraction of numbers. View record

corresponding to the scheme

Compilation and addition of records in accordance with the figure and question. Establishing a correspondence between the figure and the diagram  -  = . Writing the number 8

Search for polygons of the same shape and location

Compiling a question with the words “How much ...?” to the subject matter

Search for triangles in a figure (development of geometric observation).

Number and count. (2 h)

Introduction to numbers and numbers from 1 to 9.

Be able to consolidate knowledge of numbers and numbers from 1 to 9.

Know the ingredients 8.

Lists the steps for writing the number 9.

Number. Number. Distinguish between numbers and numbers. Writing the number 9 and other numbers in accordance with the task. Modeling (with the help of chips) the composition of the number 9. Correspondence: drawing - diagram; drawing is a model. Justification for the choice of arithmetic operation and scheme:  -  =  or  +  = . Compiling sentences of the form: “If ..., then ...”

Analysis of the sample and the arrangement of geometric shapes in a rectangular table. Working with the reverse "machine": finding shapes.

Introduction to the number and number 0.

Know the number and number 0, the concepts of "more by ...", "less by ...". Compare numbers using a ruler scale. Remember the order of writing the numbers 7, 8, 9.

Transfer figures into cells in a notebook

Acquaintance with the number and number 0. Comparison of the studied numbers with zero (without registration). Writing the number 0

Making questions with the word "How much?" by drawing. Working with records of the form: 3 and 0 is 3. Comparison by making pairs of elements of two sets and formulating the output "  more than ...", "...  less than ...". Correlation of diagram and drawing . Finding triangles in a shape. Establishing patterns in the record and writing numbers in accordance with the established pattern.

Geometric concepts

Introduction to the unit of length, the centimeter.

Know“recording” the solution of the problem in numbers.

Know the unit of length is the centimeter.

Measure line lengths with a ruler.

Introduction to the unit of length, the centimeter. Plan (algorithm) for measuring the length of a segment. Measuring the lengths of objects and segments using a ruler; recording results. Connecting points using a ruler (drawing a segment). Number ordering. Drafting questions and notes for story situations. Modeling the composition of the number 7.

Finding the length of segments. Recording the lengths of segments.

Be able to find the length of the segments.

Write numbers.

To solve problems.

Compare objects by height and length.

Draw shapes that are equal to the given one. Know composition of the number 9.

Checking the correctness of the length measurement. Using measurements to compare the lengths of objects (segments) Drawing a segment of a given length Making records corresponding to models. Movement along the scale of the ruler Compilation of questions and notes for plot situations Description of the comparison result using the words above and below Search for “triangles” in given figures Search for polygons of the same shape and location.

Number and count. (3 h)

Distinguishing concepts: "as much ...", "more

(less) by…”.

Incrementing and decrementing a number by 1.

Be able to distinguish between the concepts of "as much ...", "more

(less) by…”.

Clarification of the meaning of the expression: “more (less) by 1” Different ways to obtain the result of an arithmetic operation (drawing up a model; using a ruler) Compiling and reading entries like: “Adding one to six makes seven”; “Subtract one from six, you get five” Modeling (with the help of chips) a situation of increasing (decreasing) a number by 1 Working out the results of increasing and decreasing a number by 1 Finding patterns when filling out a table Compiling an example from the details of a mosaic (difficult task) Applying simulation to find answers to questions.

Clarification of the meaning of the expression "more (less) by 2".

Increasing and decrementing a number by 2.

be able to increase and decrease numbers by 2.

Distinguishing concepts: "the same amount ...", "more (less) by ...". Different ways to get the result of an arithmetic operation (drawing up a model; using a ruler)

Compilation and reading of records of the form: “Add two to five, you get seven”; “Subtract two from five will make three” Modeling (with the help of chips) a situation of increasing (decreasing) a number by 2 Adding and subtracting the number 2: choosing a method for obtaining a result (drawing up a model; using a ruler), recording actions Rationale for choosing an arithmetic operation and scheme:  –  =  or  +  =  corresponding to the figure.

Distinguish between a number and a digit Analysis of records of the form: 3  2 = 5 and the choice of the sign + or -.

Acquaintance with the notation and composition of the number 10.

Know number 10 and be able to write it down. Know composition of the number 10. Compares numbers using a ruler scale

Modeling (with the help of chips) the composition of the number 10. Filling in the scheme with numbers:  and  is 10. Location of the number 10 on the scale of the ruler. Comparison with the number 10. Finding the missing number based on the composition of the number 10 Recording the number 10. Adding the model of the composition of the number 10 (drawing chips) and writing the solution Arrangement of objects in the table Establishing a correspondence between the arithmetic operation and the set of objects in the figure Adding and subtracting numbers 1, 2 Comparison of results Orientation on the checkered part of the sheet: the execution of the task according to the given plan.

Values ​​(1 h)

Introduction to the concept of "decimeter".

Known the concept of a decimeter.

The unit of length is decimeter. Measurement of lengths of segments in decimeters. Comparison of the length of a segment with a decimeter (more (less) than a decimeter) Comparison of the length of objects "by eye", verification by measurement. Drawing a segment 1 dm long (with and without a dotted line) Preparing to work with the task (working with models, writing questions, etc.) Using different methods to calculate and check the results. Writing numbers. Finding an answer to a question based on a model.

Geometric concepts

Generalization of ideas about the polygon.

Have an idea about polygons.

Makes a drawing problem for addition and subtraction. Counts geometric shapes.

Generalization of ideas about the polygon. Distinguishing polygons (triangle, quadrilateral, pentagon, etc.) Working with the “Colored Shapes” set (Supplement to the textbook): classifying geometric shapes Sample analysis and doing the task according to the model: painting the corners of the figure and counting the number of corners. Determining (according to the figure) the basis of the classification and continuing the classification of geometric shapes Preparation for solving problems: searching for a situation corresponding to the record Using different methods of calculating and verifying the results Supplementing records based on figures.

Arithmetic operations (3 hours)

Consideration of the condition and question as mandatory elements of the task.

Know all parts of the task.

Consideration of the condition and the question as obligatory elements of the task. Addition of text to the task. Search for a rule (patterns) in compiling a series of numbers, in filling out a table. Work according to a given rule. Establishing correspondence Work with models.

Establishing a sequence of learning activities to answer the question of the task.

Solving addition and subtraction problems.

Be able to solve addition and subtraction problems.

Detection of a task by its main elements. Solving the problem according to the algorithm Establishing a correspondence: between the problem and its solution, written using the equality between the picture and the question to it; between the object and its height, measured in centimeters Finding the result of addition (subtraction). Checking the correctness of the action Comparison of the lengths of the segments "by eye"; verification of comparison result by measurement

Solution of the problem according to the algorithm. Finding the length of objects.

Solving addition and subtraction problems. Drawing tasks.

Be able to compose and solve problems drawn up according to the picture.

Drawing up a question in accordance with the entry Selecting a problem corresponding to the solution scheme. Solving a problem based on a drawing Comparing numbers in different ways (using a ruler scale, based on an account) Distinguishing geometric shapes. A way to find the number of triangles in a given figure. Description of the procedure for counting triangles, when drawing the second half of the figure (letter) Comparison of the lengths of the segments "by eye"; checking the result of comparison by measurement Compiling an equality record according to the rule.

Number and count. (2 h)

Acquaintance with the formation of numbers from 11 to 20; their reading and writing.

Know formation of numbers from 11 to 20, be able to read and write them. Models numbers from 1 to 20. Be able to compose and solve a drawing problem.

The decimal composition of each of the numbers of the second ten. Supplementing the entry “10 and £ is £” according to the picture) Ordering numbers, ordering entries of numerical expressions Description of the procedure for counting triangles Compilation of questions on figures with the words “how much”, “how much”. Making notes for answering the questions “How much?”, “How much?” Task solution planning

Performing practical work on measuring the lengths of objects depicted in the textbook and real objects.