Hands-on math!

Washington State Math Olympiad
Hints and Solutions
2010 Grade 7 Number Sense
Problem
1) What is the smallest exponent n for which the following expression is true?
    (0.5)3 > (0.6)n

2) In Mr. Hemple's orchestra there are 4/7 as many boys as girls. 1/4 of the girls wear glasses, and 2/7 of the girls who wear glasses also have braces. If 2 girls have glasses and braces, how many students are in Mr. Hemple's orchestra?
3) On a number line, what fraction is halfway between
    1 - 3 and   -3 + 5 ?
    3   4           8     6

Problem
4) Liz was playing with a pile of pennies. She noticed when she stacked them in piles of three there was 1 left over. When she stacked them in piles of five there were 2 left over. When she stacked them in piles of seven there were 3 left over. What is the smallest number of pennies she could have?

5) It is the end of market day and Grandma Wilcox wants to sell all her remaining eggs. One at a time to the last two customers come to her stand. To the first customer she sells half of all of the eggs she has right then plus half an egg without breaking any eggs. To the last customer she sells half of all her remaining eggs plus half an egg without breaking any eggs. She's now out of eggs. What is the smallest number of eggs she could have had left at the time the last two customers came?