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Monday, September 7, 2009


"These are some of my favorite things..." Particular Problems of the Week that I enjoy working on with my 8th graders:

POW #1: Tie and Lift

Take a long rope; tie it to the bottom of the goal post at one end of a football field.

Then run it across the length of the field (120 yards) to a goal post at the other end.

Stretch it tightly, and then tie it to the bottom of that goal post, so that it lies flat against the ground.

Now suppose that I add just 1 foot of slack to the rope, so that now I can lift it off the ground at the 50-yard line. How high can I lift it up?

POW #2: Motorcycle vs. horse

A motorcyclist was sent by the Post Office to meet a plane at the airport. The motorcyclist knew exactly how much time he needed to reach the airport when the plane arrived, so he waited until the last possible minute to leave for the airport. However, one day, the plane landed ahead of schedule, and its mail was taken toward the Post Office by horse. After half an hour, the horseman met the motorcyclist on the road and gave him the mail. The motorcyclist returned to the Post Office 20 minutes before he was expected. How many minutes early did the plane land? (your solution probably needs a diagram as part of it, at least)

POW #3: Which Barrel?

Ali Baba’s arch rival, the leader of the 40 thieves, had 6 barrels containing either oil or vinegar. One barrel contained 15 gallons, another 8 gallons, another 17 gallons, another 13 gallons, another 19 gallons and the last one contained 31 gallons. He was able to sell the oil for twice as much per gallon as the vinegar. A customer buys $14 work of each, leaving one barrel untouched. Which barrel was left?

POW #4: Ripple in a pond

Juanita and Kelly were tossing pebbles into a pond, and noticed that each pebble's splash made a circular ripple which grew larger and larger. Juanita observed that the ripple traveled at a steady speed as it moved outwards. In other words, the diameter of the circle increased by the same amount each second. Kelly wondered if the area of the circle also increased at a steady speed. What do you think?

In particular, with this problem you need to strive to show your answer with multiple representations (equations, graphs, tables, diagrams ect.)

POW #5: Dog Sledding in the Yukon

Jack London, (1876-1916) the San Francisco novelist who wrote so eloquently about Alaska at the turn of the century, tells in one of his stories how he raced from Skagway out to a remote camp where his friend was dying. For the first 24 hours four huskies pulled his sled at top speed, but then two dogs ran off and he was slowed proportionately, reaching the camp in 48 hours later rather than the 24 hours more he had been planning on. If the huskies had stayed in harness for another 100 miles, London wrote, he would have made it in time. How far away was the camp?

POW #6: COW + GOAT + GOOSE = ?

A farmer found that his cow and goat would eat all the grass in a certain field in 45 days, that his cow and goose would eat it in 60 days, but that it would take his goat and goose 90 days to eat it all. If he turns the cow, the goat, and the goose into the field together, how long will it take them to eat all the grass? Assume that the grass is not growing each day.

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