Traditional Russian math preparation (MechMat style) emphasizes: Russian Math - Amazon.com
Basic divisibility rules, patterns, and sequences. podgotovka k olimpiade po matematike 3-4 klass
If you are looking for specific "Podgotovka k olimpiade" (Olympiad Preparation) materials, these are the highly-rated standards for the Russian mathematical tradition: podgotovka k olimpiade po matematike 3-4 klass
This is the most popular international math competition for this age group. Reviewing past papers is the best way to understand the "tricks" used in competitive math. podgotovka k olimpiade po matematike 3-4 klass
While often for slightly older kids, the elementary versions (Grade 3-4) introduce "circle-style" problems: parity, logic puzzles, and "backwards" reasoning.
Often considered the "gold standard" for early competitive math. Her series focuses on "non-standard" problems that require logical leaps rather than just computation.