Hands-on math!

Washington State Math Olympiad
Hints and Solutions
2009 Grade 5 Measurement
Problem
Hint
1) What is the area of this garden?
(dimensions are in feet)
 Method 1:Cut it up into rectangles
1. Determine the length of the unlabeled horizontal side (bottom) by using the 3 horizontal measurements given. Length = _____ ft.
2. Determine the length of the unlabeled vertical side by using the 3 vertical side measurements (you need all 3). Length = ____ ft.
3. Now, you can cut the garden into 3 rectangles, either with vertical or horizontal cuts.
4. With all the sides measured, you should be able to determine the area of each of the 3 parts. Then add the areas together.
Total area = ______ sq. ft.

Method 2:Use area subtraction
1. Complete the outer rectangle and determine it's area =
    outer area = ______ sq. ft.
2. Determine the length of the unlabeled side on the bottom cutout: = _____ ft.
3. Determine the area of the cutouts and subtract.
    Total area = _____ sq. ft.
2) Eugene and Florence are both reading books and they read for 20 minutes a day during an after school program that runs Monday through Friday.
Eugene reads 3 pages every 6 minutes and Florence reads 2 pages every 5 minutes.
If it takes Eugene 4 whole weeks to finish his book, and Florence takes 6 whole weeks, whose book is longer and by how many pages? 		1. Determine the amount of time Eugene reads by multiplying the amount of reading time per day times the number of days.
    Eugene's reading time = _____ minutes.
2. Determine the amount of time Florence reads by multiplying the amount of reading time per day times the number of days.
    Florence's reading time = _____ minutes.
3. Multiply each student's reading time by their reading rate to get their total number of pages read:
    Eugene = _____ pages. Florence = _____ pages.
4. Subtract the longer book length from the shorter book length to get how much longer the longer book is:
    ______'s book has ______ more pages.

Problem
Hint
3) A room is 25% full. If 900 more people enter the room it will be at full capacity. Full capacity is determined by one person per 1.5 square meters. The length of the room is 60 meters. What is the width of the room? 1. If the room is 25% full and 900 more people enter, it, then the 900 people must be _____% of the room's capacity.
2. Given that percentage, compute the room's capacity: ______ people.
3. At one person per 1.5 square meters, the room's area is _____ sq. meters.
4. If the room is 60 meters wide, then to have this area the length must be _____ meters.
4) Aleisha is exercising her business talents as the go to classmate to get things from. She trades:
  • 2 bags of chips = 1 candy bar
  • 1 bag of chips = 5 pencils
  • 3 pencils = 2 gel pens
How many gel pens can she get for 1 candy bar? 		Work backwards:
  1. If 3 pencils = 2 gel pens, then
    1 pencil = ____ gel pens.
  2. If 1 bag of chips = 5 pencils, then
    1 bag of chips = ____ gel pens.
  3. If 1 candy bar = 2 bags of chips, then
    1 candy bar = ____ gel pens.
5) In this diagram the two white triangles have height 7 cm and are congruent
What is the area of the dark parallelogram? 		"Congruent" means the 2 white triangles are the same size.
Method 1: Compute areas of triangles and subtract.
1. Compute the area of the outer rectangle = ____ sq. cm.
2. Compute the area of one white triangle = ______ sq. cm.
3. Subtract the white areas from the outer rectangle area to get the area of the parallelogram = _____ sq. cm.

Method 2: Compute area of parallelogram:
1. Subtract height of a triangle from the length of the rectangle to get the width of the parallelogram = ____.
2. Compute the area as base (4) times this height = ____.