Hands-on math!

Washington State Math Olympiad
Hints and Solutions
2010 Grade 5 Measurement

Problem
Hint
1) Mr. Barry thought he was ordering square linoleum tiles that measured exactly 1 foot along the edge. He bought five cases of twelve tiles because the hallway he wants to tile is 15 feet long by 4 feet wide. It turns out that all the linoleum squares are 0.03 feet less than 1 foot along each edge. When he lays a single row of tiles the length of the hallway, what length gap will he have at the end? Express your answer to the nearest inch. The number of cases and how many tiles are in the case and how wide the hallway is are all irrelevant!
The gap is 15 times how much each tile is short =
    ____ ft. = _____ in.

2) Kam is playing with a balance. On one side he has a rock. On the other side he has 15 quarters and 10 dimes. The rock side is heavier. When he adds a penny the coin side is heavier. A quarter weighs 5.67 grams. A dime weighs 2.268 grams. A penny weighs 2.5 grams. What is the range of possible weights for the rock to the nearest hundredth of a gram? Give a lower and an upper value for the range.
1. Add up the weight of 15 quarters _____ gms +
    10 dimes ____.
    Total first weight = _____ grams.
2.Add the weight of a penny to the above weight = _____ grams.
3. The range is between these two numbers:
    = _____ to ________.

3) Does 9/10 of one cent matter? If 10,000 people buy 10 gallons of gas at the price of $2.85 9/10 cents per gallon at a gas station, how much money does the 9/10 of one cent contribute to the total amount? Express your answer in dollars and cents.
Compute how much 10,000 x 10 gallons x 9/10 cents/gallon is: _____

Problem
Hint
4) Jillian's backyard is 1200 square feet. She just bought a rectangular trampoline that is 16 feet long. If the trampoline covers 12% of the backyard, then how wide is the trampoline? 1. Compute the area of the trampoline as 12% of the backyard size = _____ sq. ft.
2. Divide the trampoline area by its length to get the width = ______ ft.
5) The diagram shows the dimensions in feet of a hallway. The hallway is 4 feet wide the whole way. What is the area of the hallway floor?
1. Label the unlabeled sides using the fact that the hallway is 4 feet wide.
2. Cut the hallway into 5 rectangles with vertical cuts.
3. Compute the areas of each of the 5 rectangles:
4. Add the 5 areas to get the total area of the hallway = _____ sq.ft.