We hope you enjoyed the Three Brothers and the Oak Casks problem. Every Middle School team submitted a correct response. The submissions were exuberant, artful and joyful.
And here is the teaser! You can see them on display on March 1 at the next Conversation with Parents called Math: The Art of Explanation. Some of the submissions were on paper; some on poster board; some on foam board. A few were digital. One team provided a Google Doc presentation. Two teams submitted a video demonstrations.
In case you tried to work it out, the solutions were variations on this theme:
One brother would get 3 full casks, 1 half-full cask, and 3 empty casks.
The other brothers would each get 2 full casks, 3 half-full casks and 2 empty casks.
The best submissions provided this solution, and one other alternative. Some teams explained why there could be no further solutions. Very powerful mathematics. Very powerful thinking.
Below you will find the next problem, The Aunt and Her Nephew. My brother, the physics professor at University of Chicago, sent me the problem last summer and was having trouble completing the solution. Before I could figure it out, my daughter had it!
If you have a Middle School student, ask how they did with it. And see if they will give you any hints. Enjoy!
Tuesday, January 24, 2012
The Next I Love Math Problem
The Aunt and Her Nephew
Aunt Annie and her nephew Neal were walking down the street. In the distance, they saw three well-dressed people disappear down an alley. Aunt Annie asked Neal if he knew how old they were. Neal did not.
The three were well-known to Aunt Annie, so she was able to give two helpful clues:
The product of the three ages is 2,450.
The sum of their ages is twice Neal’s age.
Neal was grateful, and went away to think for a few minutes. Being a clever and creative mathematician, he was able to make good use of the clues.
When Neal returned, he told his Aunt that the clues were very helpful, but they were not enough information. She agreed.
Aunt Annie added one more clue:
All three of the ages are less than hers!
Neal was delighted. He already knew how old Aunt Annie was, and he now had enough information to determine the ages of the three well-dressed people.
How old are the three?
How old is Neal?
How old is Aunt Annie?
Tuesday, January 17, 2012
Welcome to I Love Math 2012
Welcome! I Love Math Day is coming up on February 14. In the preceding weeks, middle school students work in small teams to solve challenging problems. They are given one week to solve each problem and prepare a solution to submit to the judges.
By way of this blog we encourage all school families to read the problems and join in the fun. We hope parents and students at all grades will find ways to talk about these problems, puzzle over them, and enjoy the pursuit together. Click on the Older Posts button below to see the three problems posted so far.
These problems are published for the school community with a one week delay, so middle school students have already submitted their presentations. However, we love getting solutions from parents and all school families. Please email Mr. Lawrence with any questions or comments you have, and please send in solutions (glawrence@mustardseedschool.org).
The problem that really counts for the first week is Three Brothers and the Oak Casks. The other two are just for fun. They are great for warming up and thinking outside the box.
I look forward to hearing from you! Enjoy. Mr. Lawrence
By way of this blog we encourage all school families to read the problems and join in the fun. We hope parents and students at all grades will find ways to talk about these problems, puzzle over them, and enjoy the pursuit together. Click on the Older Posts button below to see the three problems posted so far.
These problems are published for the school community with a one week delay, so middle school students have already submitted their presentations. However, we love getting solutions from parents and all school families. Please email Mr. Lawrence with any questions or comments you have, and please send in solutions (glawrence@mustardseedschool.org).
The problem that really counts for the first week is Three Brothers and the Oak Casks. The other two are just for fun. They are great for warming up and thinking outside the box.
I look forward to hearing from you! Enjoy. Mr. Lawrence
Sunday, January 8, 2012
Three Brothers And
The Oak Casks
Long, long ago three brothers did a good deed by saving their small town from disaster. (It had something to do with a fire-breathing dragon, but that’s another story.)
The mayor and all the townspeople rewarded them by presenting 21 beautiful, highly polished oak casks. They were all sealed tight. One third of the casks were filled with a rare, precious oil. One third were half full. The rest were empty. The brothers could easily tell which were which by the weight.
Being well-mannered and fair brothers, they wanted to be sure that each one got exactly the same number of beautiful oak casks, and exactly the same amount of oil. And of course they didn’t want to open the casks just to re-distribute the oil.
They were deep in thought and discussion trying to solve the dilemma. Just then Beremiz came along and declared, “The division, my friends, can be done without much complication. Here is the simplest possible solution ………………………….
What do you think Beremiz proposed?
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