Hands-on math!

Washington State Math Olympiad
Hints and Solutions
2011 Grade 5 Number Sense
Problem

1) Peyton and Ashlyn are jumping rope. Ashlyn is much faster than Peyton and makes 5 jumps to every 2 jumps Peyton makes. In the time Ashlyn jumps 35 times, how many times does Peyton jump?

2) Mom set a whole pizza in a pan on the dinner table. Dad took one third of the pizza. Mom took half of what was left. Dad then cut one fourth of what remained and served it to their daughter. What portion of the pizza is left in the pan? Express your answer as a fraction in lowest terms (ie. as a reduced fraction ).

3) If 2 pears weigh as much as 3 peaches, and 2 peaches weigh as much as 30 grapes, how many pears weigh as much as 90 grapes?

Problem

4) How could you use two lines to create three separate regions on the clock shown so that the sum of the numbers in each region is equal? Draw in your lines on the provided clock on the answer sheet.
Note: Your lines do not have to go through the clock center like hands on a clock!

5) Wizzo comes from a planet with a base 8 number system that came from their having eight fingers. Our 10 is Wizzo's 12. He shows you the following calculation:
    37
  +45
   104
What is the same calculation in our base 10 number system? You need to show the two numbers being added as well as the sum.