Hands-on math!

Washington State Math Olympiad
Hints and Solutions
2007 Grade 5 Number Sense

Problem
1) Toffee Yums are chocolate and caramel toffees. Each package has a ratio of 5 chocolate to 3 caramel toffees. How many caramel toffees total will Amy have if she bought only enough so that all 30 students in her class could have a chocolate toffee?

2) HT6 is a 3 digit number that is a multiple of 3 and 14. The sum of H + T is a multiple of what number?

3) Damian has a 7 digit phone number. The first 3 digits are consecutive in strictly decreasing order and sum to 6. The last 4 digits is a number that is the product of the squares of two consecutive numbers and it is as large as possible. What is Damian's phone number?

4) It's Joni's lucky day and she finds $2.88 in coins while walking across a parking lot. She decides to share a little of it with her two friends. They each get 1/8 of the amount and she keeps the rest. What is the fewest number of coins she could give one of her friends and what are they?

5) Using the operations addition, subtraction, multiplication, or division in any order you need to how can you get the number 1 using exactly five 2s? Insert the operations you need and parentheses to make the equation true or tell us what you did.
2 __ 2 __ 2 __ 2 __ 2 = 1