Hands-on math!

Washington State Math Olympiad
Hints and Solutions
2013 Grade 5 Number Sense


Problem
1) Carla baked 36 cookies for the bake sale. She called Daniel and discovered that he baked 45. They decide to combine their cookies and put them into packages with an equal number of cookies in each package. How many cookies should they put in a package if they decide on more than 1 cookie per package, and how many packages could they sell?

2) Kelly and Kylie are swimming. Kelly is much faster than Kylie and swims 5 laps to every 2 laps Kylie makes. In the time Kelly swims 35 laps, how many laps does Kylie swim?

3) Sally is thinking of a three digit number and tells you this:
The greatest common factor of the three digits is 1.
The least common multiple of the three digits is 12. The number is also the area of a square with a whole number side length. What is her number?

Problem
4) Eric dropped a ball from his deck. On the 1st bounce it bounced up one-half the distance of the drop and fell back to the ground. On the 2nd bounce it bounced one-third the distance of the 1st bounce and fell back to the ground. On the 3rd bounce it bounced one-fourth of the distance of the 2nd bounce and fell back to the ground. On the 4th bounce it bounced one-fifth of the distance of the 3rd bounce and fell one inch to the ground before rolling away. How high off the ground was the ball when Eric dropped it?

5) Susan set a whole pizza in a circular pan on the dinner table. Sam took one fourth of the pizza. Keenan took half of what was left. Miguel then cut one third of what remained. What portion of the pizza is left in the pan? Express your answer as a fraction in lowest terms (i.e. as a reduced fraction) .