Hands-on math!

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

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? 		1. Determine the ratio of Peyton's jumps to Ashlyn's jumps = _____
2. Multiply this ratio to Ashlyn's jumps to get Peyton's jumps in the same period = ____

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 ). 		1. What portion of the pizza is left after Dad takes his piece? ____ of the pizza
2. Take half of this fraction: _____
3. Compute 1/4 of what is left: ______
4. Subtract this from #2 above _____
5. Reduce to lowest terms: ______

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? 		Always work backwards with this type of problem:
1. If 30 grapes weigh as much as 2 peaches, then
90 grapes weigh as much as _____ peaches.
2. If 3 peaches weigh as much as 2 pears, then
______ peaches weigh as much as _______pears.

Problem
Hint

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! 		1. OK, first compute the sum of the numbers from 1 to 12: _____
2. Take 1/3 of this: _____
3. This is how much must be in each third of the diagram,
4. Find consecutive numbers on the clock that add up to this number. Draw a line separating these numbers from the rest of the clock
5. On the other side of the clock from your first line, find consecutive numbers on the clock that add to this same number. Draw a second line separating these numbers from the rest of the clock.
6. As a check, the numbers in between these 2 lines should add to that same number.

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. 		1. In the 10 number system 12 means adding one 10 to 2. The 2 is in the units place and the 1 is in the 10s place.
2. In the 8 number system 12 means adding one 8 to 2 because the 2 is still in the units place and the 1 is in the 8s place, so it is 8 + 2 = 10. Got it?
3. So 37 in the 8 number system is ____ units + ____ 8s = _____ in the 10s system.
4. 45 in the 8 number system is ____ units + ____ 8s = _____ in the 10s system
5. Write these 2 numbers down, one above the other and add. Here is that addition:
6. As a check, your sum should equal to 104 in the 8s system, which is 4 units + no 8s + one 82 = _____