Hands-on math!

Washington State Math Olympiad
Hints and Solutions
2008 Grade 5 Measurement
Problem
Hint
1) How much carpeting is needed to cover the floor of an L shaped room with the dimensions shown in the figure?

    		Write in the dimensions of the missing sides on the diagram.
Methods 1 & 2: Cut the figure into two rectangles.
    (Either vertically or horizontally, your pick!)
Find the area of each rectangle and add them together.

Method 3: Use area subtraction:
Complete the outer rectangle, determine it's area and then subtract the 11 X 12 missing rectangle.

Method 4: Cut into 2 trapezoids!
1. Draw a line diagonally from the upper left corner to the opposite corner, dividing the figure into 2 trapezoids.
2. Use the formula for the area of a trapezoid to compute the area of these 2 trapezoids, and add:
    A = (b1 + b2) h / 2.
Area = _____
2) The right triangle BAC has a base of 4 centimeters and a height of 5 centimeters. A new triangle is created by increasing the angle at A by 60o and moving point C to point D. AD has the same length as AC. What is the sum of the angles DBA and BDA in triangle BAD?
1. The new (larger) angle at A is
    90o + 60o = _____
2. The sum of the angles of a triangle is ____
3. The angles DBA and BDA form the other two angles of the triangle with the above 3rd angle at A, so their sum is ____

Problem
Hint
3) A loop of rope has a total length of 30 feet. Stevie creates a rectangle with the loop that has length 8 ft. Taneisha takes the loop and creates a rectangle that has length 10 ft. What is the difference in the area between Stevie's and Taneisha's rectangle? 1. If Stevie's rectangle has a side 8 ft, then with a perimeter of 30 ft the other (shorter) side is _____ ft.
2. If Taneisha's rectangle has a side 10 ft, then with a perimeter of 30 ft the other (shorter) side is ____ ft.
3. Compute the areas of the two rectangles and then subtract.
    Difference = _____ sq. ft.
4) Tina's walk home from work is 2 miles. After leaving work she walks 1000 feet and stops to get a drink of water. Tina then walks an additional quarter of a mile and gets her mail. How much further does she need to walk? Give your answer in feet. 1 mile = 5280 feet. 1. Tina's total walk in feet is _____
2. Subtract the first walk to get a drink: _____
3. Compute how many feet are in 1/4 mile: ______ ft
4. Subtract this to get the answer: _____
5) Rocks are being put in an empty well at a rate of 5 rocks per second. After one hour and fifteen minutes how many rocks are in the well? 1. Compute the number of seconds in 1 hour and 15 minutes: _____
2. Multiply this by the number of rocks per second: ______