Hands-on math!

Washington State Math Olympiad
Hints and Solutions
2017 Grade 8 Measurement
Problem
Solution
1) Mia travels 8⁄3 miles in 4⁄9 hours. What is her speed in miles per hour? 8⁄3 ÷ 4⁄9 = 8⁄3 x 9⁄4 = 72⁄12 = 36⁄6 = 6 mph

2) A pizza with an 8 inch diameter will feed five people. At this rate, how many people will a pizza with a 24 inch diameter feed?
  1. Area of 8 inch pizza = 16
  2. Area of 24 inch pizza = 144
  3. Area served by 1 person = (16/5)
  4. 144 ÷ (16/5) =
    144 x (5/16) = 45
3) A rectangular box has a surface area of 126 square meters, and a volume of 216 cubic meters. A smaller scale model of the box is made. The smaller box has a surface area of 14 square meters, what is its volume?
  1. The scale model's area is 1⁄9 of the larger rectangle's area.
  2. This means their side lengths are in the ratio of 1:3
  3. Their volumes are in the ratio of 1:27 so the scale model's volume is 216/27 = 8 cu. m.

Problem
Solution
4) Along the race route Giselle places a black marker every 88 feet. Zakaria places a red marker every 156 feet. What is the shortest distance from the start where a black marker and a red marker at at the same spot? This is a least common multiple problem.
  1. Factor both numbers to find their greatest common factor:
    • 88 = 2x2x2x11
    • 156 = 2x2x3x13
  2. Their greatest common factor is 2x2=4
  3. Using the GCF-LCM equation:
        LCM(88,156) = (88x156) / 4 = 3432
5) ABCD is a square with an area of 56 sq. in. Each square in the figure is formed by joining the midpoints of the next larger square. What is the area of QRST?
  1. A square formed by connecting the midpoints of the sides of a larger square has 1⁄2 the larger square's area.
  2. Square QRST is 1⁄2 of 1⁄2 of 1⁄2 of 1⁄2 of the largest square =
    1⁄16 x 56 = 3.5 sq. in.