Hands-on math!

Washington State Math Olympiad
Hints and Solutions
2012 Grade 5 Number Sense
Note: In this editor's opinion, problem #5 is way too difficult for a 5th grader. Although I provide a hint and a solution for it, I don't recommend giving this problem to 5th graders.
If you choose to give it, black out this comment before making copies. LDM

Problem

1) What is the time exactly half way between 9:37 pm and 2:43 am?

2) A bowling ball and a bag together cost $88. The ball costs three times as much as the bag. How much does the bowling ball cost?

3) Kyle baked at least two dozen cookies but fewer than 60 cookies. If he divides the cookies evenly among 7 plates, 4 cookies are left over. If he divides the cookies evenly among 6 plates, 5 cookies are left over. How many cookies did Kyle bake?

Problem

4) The sum of two numbers is 16 and their product is 48. What is the ratio of the two numbers when expressed as an improper fraction in lowest terms ?

5) Four friends have their birthdays in the same month. This year the squares containing their birthdates on the calendar touch each other such that they make a larger square. Two of their birthdates are multiples of six. The horizontal sums and the vertical sums are prime. What is the sum of the four birthdates?