Hands-on math!

Washington State Math Olympiad
Hints and Solutions
2012 Grade 5 Measurement
Problem
Solution
1) Nicholas loves to run and can burn 400 calories in 15 minutes. At this rate, how many hours would Nicholas have to run to burn 2400 calories? 1. Compute the amount of calories Nicholas burns in 1 hour =
    400 x 4 = 1600 calories.
2. Divide the number of calories Nicholas burns by this amount =
    2400/1600 = 1.5 hours.
2) The area of a square is 25 square feet. What will the area be if the side lengths are tripled? 1. Compute the length of one side of the square = 5 ft.
2. Triple it = 15 ft.
3. Compute the area of a square with this side length =
    225 sq. ft.

3) Heather is using a shoe box for her history project and plans to cover the inside bottom and all the inside walls with fancy paper. The top will be left open. The width of the box is 6 inches. The height is 2/3 of the width and the length is double the width. If Heather could cover the box without any waste, what is the minimum area of the fancy paper she would need? 		1. Compute the height (H) of the box given the width.
    H = 2/3 x 6 = 4 inches.
2. Compute the length (L) of the box given the width.
    L = 6 x 2 = 12 inches.
3. Compute the area of the bottom and all 4 sides =
  • Bottom = L x W = 12 x 6 = 72 sq. in.
  • Ends = 2 x (4 x 6) = 48 sq. in.
  • Sides = 2 x (4 x 12) = 96 sq. in.
Total = 72 + 48 + 96 = 216 sq. in.

Problem
Solution
4) Slim and Sue get paid at the same rate by their farmer uncle for the pints of strawberries they pick. Slim takes 10 minutes to pick a pint on average because he is easily distracted. Sue picks a pint in 4 minutes on average. They each work five hours a day. Sue can only work for 14 days. How many more days than Sue will Slim have to work if he wants to earn as much as Sue? 1. Compute the number of pints that Sue picks in an hour =
    60/4 = 15 pints.
2. At 5 hours per day, Sue picks 75 pints per day.
3. Compute the number of pints that Slim picks in an hour =
    60/10 = 6 pints.
4. At 5 hours per day, Slim picks 30 pints per day.
5. Compute the number of pints that Sue picks for 14 days =
    75 x 14 = 1050 pints.
6. Divide this by the number of pints that Slim picks per day = 35 days
7. Subtract the number of days Sue picks from this =
    35 - 14 = 21 days.
5) Ric is designing a maze for his yard. So far he has the design shown where hedges will be planted in the dotted grey section. He intends to keep them trimmed to a width of 1 yard. The width of the walking path is 1 yard. The dotted segment is the entrance. What is the ratio of the walking area including the inner square to the hedge area shown in dotted grey?
1. Write in the lengths of the unspecified sides using the given lengths. For example, the length of the walking path on the bottom is 8 - 2 = 6 yards.
2. Draw in horizontal and vertical cuts in the walking area, cutting it into a series of rectangles
(See the figure to the left)
3. Add up the area of the white rectangles = WA =
Clockwise from entry:
    2 + 5 + 5 + 4 + 2 + 2 + 2 = 22 sq. yds.
4. Compute the total area of the maze excluding
    that little 2 foot extension in the upper right corner =
    TA = 8 x 7 = 56 sq. yds.
5. Add the area of that little extension and then subtract the walkway area =
    HA = TA - WA = 56 + 2 - 22 = 36 sq. yds.
    This is the hedge area.
6. Compute the ratio of these areas = WA/HA =
    22/36 = 11/18.
Note: there are many ways to cut up the walkway. The figure to the left is just one.