Hands-on math!

Washington State Math Olympiad
Hints and Solutions
2011 Grade 5 Measurement
Problem
Solution

1) Farmer Judy is creating an oddly shaped rotationally symmetric raised garden bed. For every square foot of garden, she needs 1 pound of manure. How many pounds of manure will she need for this bed? (The dashed lines are to indicate lengths and are not part of the framing.) 		1. "Rotationally symmetric" means that the unlabeled triangles are the same as their labeled copies.
2. Determine the lengths of the unlabeled sides and write them on the diagram.
3. Compute the area of the inner rectangle =
    6 x 5 = 30 sq. ft.
4. Compute the area of the larger triangle =
    (5 x 3)/2 = 7.5 sq. ft.
5. Compute the area of the smaller triangle =
    (2 x 2)/2 = 2 sq. ft.
6. Add the following:
  • Area of the rectangle = 30 sq. ft.
  • 2 of the small triangles = 4 sq. ft.
  • 2 of the larger triangles = 15 sq. ft.
  • Total = 49 sq. ft.
7. Compute the amount of manure by multiplying the total area by the number of pounds of manure per square foot =
    49 pounds

2) A gingerbread recipe calls for 1 and 1/3 cups of flour and an 8 inches by 10 inches baking pan. Jodi wants to increase the recipe so that she can use her 9 by 13 inch pan. How much flour should she use to the nearest 1/8 cup?
1. Compute the area of the smaller pan = 80 sq. in.
2. Compute the area of the larger pan = 117 sq. in.
3. Divide the larger pan's area by the smaller pan's area to get the ratio of their areas = 1.4625
4. Convert the amount of flour to an improper fraction =
    1 1/3 = 4/3
5. Multiply this fraction times the ratio above
    to get the new amount of flour = (4/3) x 1.4625 = 1.95 cups
6. Round to the nearest 1/8 cup = 2 cups

Problem
Solution
3) This figure is made up of 13 congruent squares. The perimeter of the figure is 140 cm. Find the area of the figure in square centimeters. The figure is not to scale. "Congruent" means all the little squares are the same size.
1. Count up the number of small squares in the figure = 13 squares.
2. Count up the number of edges of the squares that comprise the outer edge of the figure = 28 edges.
3. Divide the total perimeter of the figure by this number of edges to get the length of one square edge = 140/28 = 5 cm.
4. Compute the area of one square = 5 X 5 = 25 sq. cm.
5. Multiply by the number of squares to get the total area = 13 X 25 =
    325 sq. cm.
4) Ayden claims his dad can count to 1,000,000 saying each number. If on average it takes 2 second to say each number, how long does it take to count to 1,000,000 without taking any breaks? Round your answer to the nearest day. 1. Multiply 1,000,000 by the time to say each number =
  2,000,000 seconds.
2. Compute the number of seconds in an hour = 3600
3. Compute the number of seconds in a day = 86,400
4. Divide the total number of seconds to say each number by the number of seconds in a day = 23.148 days.
5. Round to the nearest day = 23 days.
5) The PTA is organizing an ice cream extravaganza with 8 flavors of ice cream. They need a total of 5 gallons of ice cream. The 1.75 quarts containers of ice cream are on sale at 2 for $6.00. How much will they spend on ice cream? 1. The number of flavors of ice cream is irrelevant to this problem!
2. Compute the number of quarts in 5 gallons = 20 quarts.
3. Divide this number of quarts by the size of the container to get the total number of containers = 20/1.75 = 11.428 containers.
4. Round this up to the next highest whole number of containers = 12
5. Compute the cost of a single container = 6/2 = $3.00 per container
6. Multiply this cost per container by the total number of containers to get the total cost = 3 x 12 = $36.