Abstract
One of the fundamental knowledge in mathematics in Primary school is related to the arithmetic operations addition and subtraction. According to the educational programs in mathematics in the Republic of Bulgaria, students start studying these operations in grade 1.
 The article presents theoretical concepts affecting studying the arithmetic operations addition and subtraction in the education in mathematics at a primary school.
 The research work identified the specifics of studying the inverse connections between the arithmetic operations addition and subtraction in the education in mathematics for grade 1 are also presented. Some of the significant tasks with importance for discovering the relations between the forward operation addition and the reverse operation subtraction were proposed in the study. A new methodology system of work with tasks where these relations are used was developed and tested.
 The author studied the knowledge, skills, and competencies of the grade 1 students to solve arithmetic operations addition and subtraction tasks. After the exit diagnostic, it was found out that the students of the class where the new methodology system of work was applied during their education in mathematics have got a higher level of knowledge and skills from competency Cluster Numbers in respect of the arithmetic operations addition and subtraction. 
 The use of mathematical tasks with reverse relations between the arithmetic operations addition and subtraction help the students to develop both the overall mathematical knowledge and the logical thinking of the first-graders.
Highlights
IntroductionThe expected results from the education in mathematics for grade 1 are specified in the respective educational program approved by the Ministry of Education
During their Primary school education in mathematics in the Republic of Bulgaria, students acquire knowledge from arithmetic, geometry, and algebra and lead is the knowledge in arithmetic.The expected results from the education in mathematics for grade 1 are specified in the respective educational program approved by the Ministry of Education
After applying the new methodology system of work, the students from the experimental class achieved higher results in solving tasks related to the arithmetic operations addition and subtraction
Summary
The expected results from the education in mathematics for grade 1 are specified in the respective educational program approved by the Ministry of Education According to this program, students are expected to acquire knowledge and skills to perform the arithmetic operations addition and subtraction of natural numbers up to 20 and to use the relationship between addition and subtraction to find the value of numerical expressions. The foundations of the reverse relations between addition and subtraction are laid in grade 1 Their use facilitates the students to develop knowledge, skills, and competencies for the arithmetic operations addition and subtraction, overcoming the most frequent mistakes which they do in subtraction of numbers up to 20 with passing the ten. This interrelation is getting updated and applied during the education in mathematics in the years of education
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