Hands-on math!

Washington State Math Olympiad
Hints and Solutions
2012 Grade 6 Number Sense

Problem

1) If this pattern continues, in which column will 500 appear?


2) Jimmy and Carlos are at a meeting with eight other people. They are all hungry, but there are only seven bagels. Jimmy divides each bagel in half and gives each person a half of a bagel. He takes the remaining pieces and keeps dividing them all in half until he can again give everyone an equal size piece. He repeats this again with the remaining pieces he now has until everyone has gotten 3 of the same size pieces, a large piece, a medium piece and a small piece. If Jimmy takes his fair share and any remaining pieces, what fraction of the bagels does Jimmy get? Express your answer to the nearest 1/16th of a bagel.

3) Juan decided to go shopping at the grocery store. He spends half of his money on ground hamburger. He then spends a third of his remaining money on fruit. Juan then spends $3.00 on a gallon of milk and the remainder of his money on candy. If Juan had $30.00 to spend how much did he spend on candy?

Problem

4) Using exactly four 3's and any operations [+, -, x, /, ( )] find an expression to equal each of the following:
4 = 3 ___ 3 ___ 3 ___ 3
    6 = __ 3 ___ 3 ___ 3 ___ 3

5) Jodi divided a number by 0.02. Then she divided the resulting number by 0.1. What is the ratio of her original number to her final number?