Duct Tape & Fence Posts
Students in my Algebra classes chose their own problem to use to investigate ratios and proportional relationships. My 7th period chose to see how far down the parking lot they could stretch a roll of duct tape, except that instead of measuring it in feet or meters or some traditional unit of measurement, they measured the distance in terms of fence posts. Students had to determine a unit rate of feet per fence post. They then graphed the relationship between linear feet and the number of fence posts and wrote an equation modeling that relationship. They used fractional ratios of a small roll of duct tape to determine the length of the big roll (i.e., 1 ft = 1/90th of a small roll, 1 big roll is 150% of a small roll). Then they used that calculation and their equations and graphs to determine how many fence posts long the roll of duct tape is (they were only off by a few inches in their final calculations, which is a very tiny fraction in terms of unit rates!)