Spatial awareness, counting shapes within figures, and perimeter/area "tricks."
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
If you are looking for specific "Podgotovka k olimpiade" (Olympiad Preparation) materials, these are the highly-rated standards for the Russian mathematical tradition: counting shapes within figures
Knight/Knave problems, weighing puzzles, and "magic squares." and "magic squares."