For a 4th-grader a good introduction to contest math may be problems from the Continental Math League, from a book such as
Math Contests-Grades 4, 5 & 6: School Years: 1979-80 through 1985-86 (Volume 1) by Steven R. Conrad and Daniel Flegler (2003)
available for about $5 from Amazon used, including shipping. There are other books in the series. Each has book has several multiple choice contests, with answer keys and solutions.
Also good are the "Math Olympiad Contest Problems" books related to MOEMS.