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
Spatial awareness, counting shapes within figures, and perimeter/area "tricks." and sequences. Spatial awareness
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. counting shapes within figures
Often considered the "gold standard" for early competitive math. Her series focuses on "non-standard" problems that require logical leaps rather than just computation.
If you are looking for specific "Podgotovka k olimpiade" (Olympiad Preparation) materials, these are the highly-rated standards for the Russian mathematical tradition: