Hands-on math!

Washington State Math Olympiad
Hints and Solutions
2013 Grade 5 Measurement
Problem
Solution
1) Molly and her mom are training for a 75 mile bike marathon. She can now do 6 miles in 30 minutes. How long would it take her to do the 75 mile bike marathon if she can keep that pace for the whole marathon? Express your answer in hours and minutes. 1. Compute the number of miles per minute that Molly and her mom do =
6/30 = 1/5 mile/minute.
2. Divide the number of miles by this rate to get the number of minutes for the entire race =
75/(1/5) = 75 x 5 = 375 min.
3. Convert this to hours and minutes =
    6 hours 15 minutes.

2) A farm has a rectangular field. The width of the field is 32 yards long. The area of the farm is 2,048 square yards. How much fencing is needed to surround the whole field?		 1. Compute the length of the field given the area
    and the width = 2048/32 = 64 yards.
2. Compute the perimeter of the rectangle,
    given this length and the width =
    2 x 64 + 2 x 32 = 192 yards.

3) Sara asks Ryan to figure out the total area of the two sails for the 16 foot sailboat she is making. She draws a scaled picture of the sail she wants to make from a photograph and adds the lengths she wants. What will the total area of the two sails be?		 1. Compute the area of triangle ABE given that sail's measurements =
    (8 x 13)/2 = 52 sq. ft.
2. Compute the area of triangle CDF given that sail's measurements =
    (5 x 10)/2 = 25 sq. ft.
3. Add the 2 areas to get the total =
    52 + 25 = 77 sq. ft.

Problem
Solution
4) Roald Dahl's BFG, Big Friendly Giant, thinks people sleep too much. Stan knows he sleeps about 10 hours a day. He wants to know if he converts the total number of hours he sleeps in a year to days, how many days would that be to the nearest day? 1 year is 365 days. 1. Multiply the number of sleep hours per day by the number of days in a year
  (you should be able to do this in your head!) =
    3650 total hours.
2. Divide this number of hours by the number of hours in a day =
    3650/24 = 152 days.

5) Shona is going to help her dad lay a brick patio. The patio measures 10 ft by 8 ft. The bricks have dimensions 1/6 ft by 1/3 ft by 1/4 ft. They plan to lay them in a single layer with the largest surface facing up so that they need the fewest number of bricks. How many bricks will they need?		 1. Multiply the two largest brick dimensions to get the surface area of 1 brick =
    (1/3) x (1/4) = 1/12 sq. ft.
2. Find the total area of the patio = 80 sq. ft.
3. Divide this total patio area by the area of 1 brick to get the number of bricks needed = 80/(1/12) = 80 x 12 = 960 bricks.