Hands-on math!

Washington State Math Olympiad
Hints and Solutions
2014 Grade 5 Number Sense


Problem
1) Mrs. Roscoe noticed at the dance that for every three boys that walked in the door there were five girls with them. When she counted the tickets she found that the total number of boys and girls at the dance was 248. How many girls attended the dance?

2) William needed to change the oil in his truck. His truck holds 12 and 3/4 quarts of oil. Behind the seat he finds 2 and 3/5 quarts of oil. On the shelf in his garage he finds 3 and 2/3 quarts. How many additional quarts will he need to purchase?

3) Tyree and Huang Fu are studying a set of new words for Spanish class. They both decide to make study cards. Tyree writes 7 words on each card except the last card has 6 words. Huang Fu writes 9 words on each card except the last card has 7 on it. What is the smallest number of words there could be in the whole set?

Problem
4) Tammy is preparing to display all her rocks on a 28 inch by 22 inch poster board. Each rock will be in its own square with side length 3 and 1/4 inches, which fits her largest rock. The maximum number of squares that fit on the poster board is the same as the number of rocks in her collection. How big is her collection?

5) Roni loves to talk. Roni's mom is a tech wiz and programs Roni's phone so that after 7pm, each time she is on her phone it cuts her off at half of the time she spent on her previous conversation. Her first phone call lasts 52 minutes and starts at 7:05 pm. If she talks until she is cut off in every conversation after that, how many minutes has she been on the phone at the end of her sixth call? Express your answer as a mixed number.