CAPACITY PROBLEMS Try exploring these additional problems with your class. You can print this page by hitting the "Print" button on your browser. 1. Build a Fence: (related to counting the spaces between beams on the bridge) a. How many posts will it take to build a fence that is 60 feet long if each fence post is ten feet apart? (Answer: 7 posts. There is one more post than space or one less space than post.) b. Based on part a how many posts will it take to build a fence around a rectangular yard that is 50 feet long and 30 feet wide? (Answer: 16 posts) Problem solving strategy: Try an easier problem. Students work on these specific problems and then they make a generalization. 2. Capacity on public transportation: (related to how many cars fit on the bridge) Students estimate how many people (standing, sitting) can fit into a subway car, bus, trolley etc. Students find out the measurements of the vehicle either through research or actual hands-on measurement. Then estimate how much room (area) a person takes up on the average. From there they can estimate the number of people that fit into the vehicle. Issues will arise about how much space to leave between people and rush hour. 3. Jar of screws: Students estimate the number of screws in a jar (volume). Guess and check. Note: This is not quite the same concept of capacity as the cars on the bridge. It's an extension from area to volume. 4. Maximum area from given perimeter. What is the maximum rectangular area you can form given the perimeter of 24 feet? Students can try different perimeters and they should eventually see that a square with a side of 6 feet has the largest area. Let students make a generalization.