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ESCOT Problem of the Week: Archive of Problems, Submissions, & Commentary |
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ESCOT Problem of the Week: Archive of Problems, Submissions, & Commentary |
The pirate ship has just landed, loaded with diamonds. You've been sent to buy 8 lbs. of diamonds but you only have one 10-lb. and one 6-lb. measuring container.How can you make the purchase?
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Students used two basic methods to solve the problem. One method begins with container A, and the other starts with container B. Since we hadn't specified that we wanted the method using the least number of steps, we counted both methods as correct.Most students' solutions provided only the steps involved in finding 8 lbs. of diamonds, without including the amounts that were poured. Since we thought that the amounts would help people understand the solution, we only gave credit if students included them. Because so many students left out the amounts, it's possible that the wording of the problem didn't clearly ask for what we wanted.
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Page Part 1 Fill A and pour it to B. You should have 6 lbs in the 10 lbs container. Fill A again and pour again into B. Giving you a full ten pound container but leaving you with only two in the six lbs container. Now empty the 10 lbs container.Pour the 2lbs inside A into B. Giving you 2 lbs in the 10 lbs container.Now fill A again, and pour it into B giving you 8 lbs in the 10 lb container. ------------------------------------
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Page Part 1 First we filled A and got 6 lbs. Then we poured A to B to get 6 lbs. in B. A is now empty. Then we filled A so now there was 6 lbs. in each container. Then we poured A to B so now there was 10 lbs. in B and 2 lbs. in A Then we emptied B so there was only 2 lbs. in A. Then we poured A to B so there was 2 lbs.in B. Then we filled A so that there was 6 lbs. in it. Last, we poured A to B so that B contained 8 lbs. ------------------------------------
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Page Part 1 First I filled A, which equaled 6 pounds. Next I poured A to B, now B had the six pounds. After that I filled A again, and poured A to B. That left 2 lbs in the 6 lbs container and the 10 pound container was full. Then I emptied B. So B had nothing and A had 2 pounds. Next I poured A to B. Now A had no pounds and B had 2 pounds. Next I filled A and poured A to B. Now B contained 8 pounds of diamonds. I did the problem in eight steps. ------------------------------------
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Page Part 1 First you fill container A with 6 pounds of diamonds . Pour the 6 pounds of diamonds in container A to container B so that it is filled with 6 pounds of diamonds. Fill container A again with 6 pounds of diamonds. Pour the 6 pounds of diamonds from container A to container B again so that it is filled with 10 pounds of diamonds. You should have 2 pounds of diamonds left in the A container. Empty the B container . Pour the 2 pounds of diamonds in container A to container B so that it has 2 pounds of diamonds. Fill container A again with 6 pounds, Pour container A with the 6 pounds into container B. That's how you make the purchase of 8 pounds. ------------------------------------
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Page Part 1 The first thing we did was was fill the ten pound container. The next thing we did was put the ten pounds of diamonds into the six pound container and four pounds remained in the ten pound container, because the six pound contaner can only hold six pounds. After that we emptied the six pound container. Then we poured what was in the ten pound container into the six pound container. Then we filled the ten pound container again. Then we poured the ten pounds that was in the ten pound container into the six pound container. After that we emptied the six pound container that had six pounds in it and we were left with 8 pounds of diamonds in the 10 pound container. ------------------------------------
Atena A., age 13 - Lionville Middle School, Exton, PA
Mark A., age 13 - Frisbie Middle School, Rialto, CA
Reina A., age 13 - Frisbie Middle School, Rialto, CA
Victoria A., age 13 - JFK Middle School, Port Jefferson Station, NY
Chris B., age 14 - School of the Arts, San Francisco, CA
Jessie B., age 13 - Frisbie Middle School, Rialto, CA
Keturah B., age 13 - Frisbie Middle School, Rialto, CA
Miguel B., age 13 - Frisbie Middle School, Rialto, CA
Alan C., age 13 - School of the Arts, San Francisco, CA
Christina C., age 13 - School of the Arts, San Francisco, CA
Ryan-Grace C., age 13 - JFK Middle School, Port Jefferson Station, NY
Carson D., age 13 - School of the Arts, San Francisco, CA
Honora D., age 13 - School of the Arts, San Francisco, CA
Wil D., age 13 - School of the Arts, San Francisco, CA
Anna G., age 13 - School of the Arts, San Francisco, CA
Consuelo G., age 13 - Frisbie Middle School, Rialto, CA
Jeanette G., age 13 - School of the Arts, San Francisco, CA
Nick G., age 13 - JFK Middle School, Port Jefferson Station, NY
Bryant H., age 13 - Frisbie Middle School, Rialto, CA
Chelsea H., age 13 - School of the Arts, San Francisco, CA
Amanda L., age 13 - JFK Middle School, Port Jefferson Station, NY
Nicole L., age 13 - JFK Middle School, Port Jefferson Station, NY
Heather M., age 13 - JFK Middle School, Port Jefferson Station, NY
Nichole M., age 13 - JFK Middle School, Port Jefferson Station, NY
Kai N., age 13 - School of the Arts, San Francisco, CA
John O., age 25+ - W. R. Coile Middle School, Athens, GA
Noga P., age 13 - JFK Middle School, Port Jefferson Station, NY
Leah R., age 13 - Frisbie Middle School, Rialto, CA
Amanda S., age 13 - JFK Middle School, Port Jefferson Station, NY
Rachael S., age 13 - JFK Middle School, Port Jefferson Station, NY
Niranjani T., age 13 - JFK Middle School, Port Jefferson Station, NY
Alicia W., age 13 - Frisbie Middle School, Rialto, CA
Helen Y., age 13 - School of the Arts, San Francisco, CA