1. Hundred and thousand table, investigations.

2. Decimal number system and system of other bases. Calculations in these systems.

3. Divisibility tests.

4. Divisibility. Primes, composite numbers, divisors, multiples.

5. Fractions and rational numbers.

6. Diophantine equations.

By solving submitted tasks students' ability to experiment, to organize partial results, to make use of patterns, to formulate and verify hypothesis will be developed. The ability to pose new tasks related to the given problem on basis of asking questions like What if ...? will also be developed.

Stress will be put on the development of ability of argumentation, that means to explain Why...? Why does the given algorithm work? The development of abilities mentioned above is a key requirement in the future teachers training. Thus the conception of subject Arithmetic qualitatively differs from that conception which the students met in their secondary school education.