Hands-on math!

Washington State Math Olympiad
Hints and Solutions
2014 Grade 6 Measurement
Problem
Hint
1) A satellite orbits the earth at a height of 343 kilometers. If it makes 8 revolutions around the earth, how many kilometers does it travel? Give your answer to the nearest kilometer. Earth's diameter is 6,371 kilometers.
Use = 3.14.		 1. Compute the radius of the earth and add the satellite height to it =
    _____ km.
This is the radius of the satellite orbit from the center of the earth.
2. Double this to get the orbital diameter = _____ km.
3. Compute the circumference of the orbit = _____ km.
4. Multiply by the number of orbits = _____

2) Trevon's family drove in Canada at a speed of 110 km per hour for 45 minutes. They crossed the border into Washington and drove for 2 hours and 20 minutes at a speed of 60 miles per hour. How far did they travel? Express your answer to the nearest tenth of a mile.
1 mile = 1.6 km.		 1. Compute the distance traveled in Canada by multiplying the speed X the time = ____ kilometers.
2. Convert this to miles = _____ mi.
3. Compute the distance traveled in the U.S. by multiplying the speed times the time = _____ mi.
4. Add these 2 = _____

3) Ronin finds an old punch recipe from his grandma. It calls for 1 gallon of apple juice, 3 quarts of grape juice, 7 pints of cherry juice, 5 cups of pomegranate juice. How many ounces of punch would that make? There are 4 quarts in a gallon, 2 pints in a quart, 2 cups in a pint, and 8 ounces in a cup.		 1. Compute the number of ounces in a pint = _____
2. Compute the number of ounces in a quart = _____
3. Compute the number of ounces in a gallon = _____
4. Convert all the amounts into ounces and add = _____

Problem
Hint
4) Kara's family plans to construct a tiled patio of 20 x 31 square feet. The choices of the tiles are 1 x 1 sq ft tiles for $2.50 per tile and 2 x 2 sq ft tiles for $9 per tile. Assume the tiles can be cut (at no cost) to fit small areas. Which option is cheaper and how much cheaper, all 1 x 1 sq ft tiles or all 2 x 2 sq ft tiles? 1. Compute the area of the patio = _____
2. Compute the number of 1 x 1 tiles = _____ tiles.
3. Divide the area of the patio by the area of one 2 X 2 tile = _____ tiles.
4. Multiply the number of 1 x 1 tiles by their cost = _____
5. Multiply the number of 2 x 2 tiles by their cost = _____
6. ______ is cheaper and by $_____

5) A math contest began at noon one day and ended 1000 minutes later. At what time did the contest end? 		1. Divide the number of minutes by the number of minutes in an hour to get the number of hours = _____. The remainder is _____ of an hour.
2. Convert this fraction of an hour to minutes = _____
3. Add this to noon to come up with the ending time = _____