Hands-on math!

Washington State Math Olympiad
Hints and Solutions
2012 Grade 6 Measurement
Problem
Solution
1) Rectangle A and rectangle B both have area 72 sq.cm. The lengths and widths of both rectangles are integers. The width of rectangle B is 5 cm greater than the width of rectangle A. The length of rectangle B is 15 cm less than the length of rectangle A. Which rectangle has the greater perimeter and how much greater is it? Let L = length of rectangle A
      W = width of rectangle A
1. The perimeter of rectangle A is 2L + 2W
2. The perimeter of rectangle B is
    2(L - 15) + 2(W +5)
3. Perimeter of B is 2L + 2W - 20
4. So A is greater by 20 cm.
2) Mr. Clear likes cutting things. He has a piece of paper 1/400th of an inch thick, which he cuts in half and stacks on top of the other half. Mr. Clear cuts and stacks a total of 15 times. How tall is the stack of paper now? Express your answer in feet and inches rounded to the nearest whole number. It helps if you have a calculator that can do exponents.
If you do, compute 215 = 32768
1. Divide 215 by 400 = 32768/400 = 81.92 inches
2. Rounded = 82 inches = 6 feet 10 inches
3) At Pizza-R-Us, you can buy a circular pizza with a diameter of 14 inches or a square pizza with 13 inch side lengths. For both pizzas, the baker pours sauce on the entire pizza except for a 1 inch border around the edges. What is the difference in areas between the sauce covered regions of the two pizzas? Express your answer to the nearest square inch.
You may use = 3.14 		1. Take 2 inches off each dimension and compute the areas of the two pizzas:
    Round: 3.14 x 62 = 113.04 sq. in.
    Square: 11 x 11 = 121 sq. in
2. Take the difference between these two areas =
    121 - 113.04 - 7.96 rounds to 8 sq. in.

Problem
Solution
4) Michelle draws a circle in a garden area in preparation for circular garden. She decides it's too small. If she increases the length of its radius by 4 feet, the area is quadrupled. What is the radius of her original circle? When you double the radius of a circle it quadruples its area.
For example, take a circle of radius 2.
It's area is 22 = 4
A circle of radius 4 has an area of
42 = 16, 4 times greater.
Radius of the original circle = 4 ft.
5) John always drives at a constant rate of 60 miles per hour. In the United States he drives for 120 miles. He then crosses the border into Canada where all the distances are in kilometers and drives for 175 kilometers. How long was his trip in hours and minutes? Round the minutes to the nearest whole number.
Note: 1 mile = 1.609 kilometers.		 1. Compute the number of hours John drives in the U.S. = 2 hrs.
2. Convert 60 miles per hour to km/hour and divide the kilometers by this value to get the Canadian time = 1.812 hr.
3. Add the two to get the total time =
    3.812 hr = 3 hr 49 min