Hands-on math!

Washington State Math Olympiad
Hints and Solutions
2010 Grade 5 Number Sense
Problem

1) On a number line, what fraction is halfway between
3/4 + 1/3 and 3/8 + 5/6?

2) At Raymond's school, Tuesday was jeans day and everyone wore either blue jeans or black jeans. In his math class they collected data and concluded for every 7 children wearing blue jeans there were 4 wearing black jeans. If there were 451 students in the school on Tuesday, how many were wearing black jeans?

3) There are 30 students in Samir's class. They line up in the hall. Samir has a bag of jelly beans. He will hand them out according to the following rule. Each student gets a minimum of 6 jelly beans. However, if your place in line is a prime number then you get 6 jelly beans plus one jelly bean for every prime number spot so far, provided you can tell Samir the number of prime number spots, including yours, he has already visited. As an example, if you were standing in the spot that was the fourth prime number, you could receive ten beans if you were able to tell Samir that you were in the fourth prime number spot. What is the most number of jelly beans Samir could hand out to a student?

Problem

4) Paulina and her Abuela (grandmother) sell eggs at the market. At the end of the day they have less than a half dozen eggs left. Abuela likes math humor. The next customer comes up and Abuela says "I have very few eggs left, but for 10 cents I will give you half of my remaining eggs and give you an extra half an egg without breaking any eggs if you can guess how many eggs I have." What is the most number of eggs Abuela could have?

5) I am a whole number. I am a multiple of 4 and 6. I am divisible by 14. Subtract 100 from me and the result is a negative number. Who am I?