Hands-on math!

Washington State Math Olympiad
Hints and Solutions
2006 Grade 5 Measurement
Problem
Solution
1) Olivia bought some candy costing exactly $0.58. She paid with a $1.00 bill and received correct change. What is the least number of coins she could have received in change? 1. Compute Olivia's change = 42 cents
2. Starting with quarters, then dimes, etc., figure out her change with the smallest number of coins =
    1 quarter, 1 dime, 1 nickel and 2 pennies =
    5 coins
2) A quilt is created by sewing together unit rectangles that measure 3 inches by 6 inches into blocks as shown. The blocks are then sewn together in a checkerboard pattern where the first block is as you see it and the second is just a rotation of the block by 180 degrees. The final quilt will measure 4 feet by 6 feet. How many unit rectangles will be in the finished quilt? 1. Compute the area of the quilt in sq. inches = 48 x 72 = 3456 sq. in.
2. Divide by the area of a unit rectangle =
    3456/18 = 192 unit rectangles
Note: The fact that they fit together in a pattern is irrelevant.

3) Alex and Zach meet on a track to do a long distance run. They start running from the same point and in the same direction but Alex begins to steadily pull ahead. The first time that Alex passes Zack is at the starting point when Alex has just complete five laps. What fraction of Alex's distance has Zach run at this point? 		1. If Alex has completed 5 laps then Zack has completed 4 laps.
2. The fraction of Alex's distance this represents is 4/5

Problem
Solution

4) Mr. Herbert's fifth grade class is going to do a bake sale and they decide on making only chocolate chip cookies and brownies. The chocolate chip cookie recipe calls for 12 ounces of chocolate chips and the brownies call for 4 ounces of chocolate chips. The chocolate chip cookie recipe makes 3 dozen cookies. The brownie recipe makes 24 brownies. The class decides they'll need about 360 cookies and 240 brownies. How many 24 ounce bags of chocolate chips will they need? 		1. Compute the total ounces of chocolate chips needed to make
    36 cookies and 24 brownies = 12 + 4 = 16 ounces
2. Divide the number of desired cookies
    by this recipe's number of cookies = 360 / 36 = 10
3. Multiply the number of ounces in the recipe (above) by this factor =
    10 x 16 = 160 ounces
4. Divide by the size of the bag = 160/24 = 6 2/3 bags
5. Round up to the next whole bag = 7 bags

5) Joe flies from Seattle to New York and back regularly on business. Joe left on Wednesday at 5 am, local time, to go to New York. He arrives at 2:15 pm, local time, in New York on Wednesday, works for 5 hours, leaves at 8 pm, local time, to fly back to Seattle. He arrives at 11 pm, local time, Wednesday evening. All time between departure and arrival is considered flying time. The time difference between Seattle and New York is 3 hours. How long was he flying? Give your answer in hours and minutes. 		Convert all times to New York time and compute travel time:
  • Depart 5 am (Seattle) = 8 am (New York)
  • Arrive 2:15 pm (New York).
    Travel time = 14:15 - 8 = 6 hr 15 min
  • Depart 8 pm (New York)
  • Arrives at 11 pm (Seattle) = 2 am (New York).
    Travel time = 2 am - 8 pm = 6 hours
  • 6 hours 15 min + 6 hours =
    12 hours 15 min. travel time