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Weekly students will be given the opportunity to solve mathematical word problems. Once they solve the problem they come up with a rule. This rule is a result of looking for a pattern. Where there is a pattern, there is a rule. The following are problems students have solved or on which they will be working:

1. Eight adults and 2 children try to cross a river in a canoe. The canoe will only hold at one time, 2 children or 1 child and 1 adult. How many trips will it take to get everyone across the river? How many trips would it take with 10 adults? 100 adults? (always just 2 children) 8/23

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2. A canoe has eleven seats. There are ten fishermen in the canoe, five at each end with the middle seat vacant. They decide to switch ends. They cannot move the canoe. They can only move to an empty seat next to them or around one person to an empty seat or the canoe will tip over. Can they make the switch? If so, how many moves will it take to get the fishermen to the opposite end of the canoe? What about a canoe with 21 seats? 51 seats? 101 seats? 8/24

3. The Mangoes Problem: One night the King couldn't sleep, so he went down into the Royal kitchen, where he found a bowl full of mangoes. Being hungry, he took 1/6 of the mangoes. Later that same night, the Queen was hungry and couldn't sleep. She, too, found the mangoes and took 1/5 of what the King had left. Still later, the first Prince awoke, went to the kitchen, and ate 1/4 of the remaining mangoes. Even later, his brother, the second Prince, ate 1/3 of what was then left. Fnally, the third Prince ate 1/2 of what was left, leaving only three mangoes for the servants. How many mangoes were originally in the bowl? 8/31

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4. Sailors and Coconuts: Three sailors were marooned on a deserted island that was also inhabited by a band of monkeys. The sailors worked all day to collect coconuts but were too tired that night to count them. They agreed to divide them equally the next morning. Duing the night, one sailor woke up and decided to get his share. He found that he could make three equal piles, with one coconut left over, which he threw to the monkeys. Thereupon, he had his own share, and left the remainder in a single pile. Later that night, the second sailor awoke and, likewise, decided to get his share of coconuts. He also was able to make three equal piles, with one coconut left over, which he threw to the monkeys. Somewhat later, the third sailor awoke and did exactly the same thing with the remaining coconuts. In the morning, all three sailors noticed that the pile was considerably smaller, but each thought that he knew why and said nothing. When they then divided the remaing coconuts equally, each sailor received seven and one left over, which they threw to the monkeys. How many coconuts were in the original pile? 8/31--9/4

5. How can you carry exactly four gallons of water from a river if only a three-gallon jug and a five-gallon jug are available? 9/24-9/28

To solve this problem, students worked in groups with tubs of water and "faux" buckets, aka, two different size cups, and poured back and forth until they came up with a solution. Actually the students came up with two different ways to solve the task! Students then wrote about how they solved the task.

6. **Desert Crossing:** You live in a desert oasis and grow miniature watermelons that are worth a geat deal of money, if you can get them to the market 15 kilometers away across the desert. Your harvest this year is 45 melons, but you have no way to get them to the market, except to carry them acros the desert. You have a backpack that holds up to 15 melons, the maximum number that you can carry at a time. To walk across the desert, you need a certain amount tof fluid and nourishment that is supplied by the melons you carry. For each kilometer you walk (in either direction), on melon must be eaten. Your challenge is to find a way to get as many melons as possible to market**. 10/5**

Last Modified on October 5, 2012

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