The Dishes Problem
"How many guests are there?" said the official.
"I don't know.", said the cook, "but every 2 used a dish of rice, every 3 used a dish of broth, and every 4 used a dish of meat between them". There were 65 dishes in all. How many guests were there?
Taken from A puzzle from 4th century CE, China from the Sunzi Suan Jing 孙子算经
Please consider:
• Whether it makes a difference to our students to offer examples, puzzles and histories of mathematics from diverse cultures (or from 'their' cultures!)
• Whether the word problem/ puzzle story matters or makes a difference to our enjoyment of solving it.
Solution:
Let x be the number of guests, then we know that there are x/2 dishes of rices ("every 2 used a dish of rice"), x/3 dishes of broth ("every 3 used a dish of broth"), and x/4 dishes of meat. Then we can have the following equation:
x/2 + x/3 + x/4 = 65.
13x/12 = 65
x = 60
After solving the equation above, we have x equals to 12, which means there are 60 guests in total.
I think it will makes a difference to our students if we offer examples, puzzles and histories of math from divers cultures. It might be difficult for students to understand the problem related to unfamiliar. It remains me of my experience of tutoring a Chinese student. The student struggled with one complicated word problem related to burger making, because she had not made a burger. Burger is from western culture which my student is not familiar with.
And I think integrate story into the word problem/puzzle will make the problem more interesting, which will help student engage in solving it. For instance, the dishes problem, we were told that it this a puzzle from 4th century CE, China from 孙子算经. This history background makes the puzzle feel more significant.
"I don't know.", said the cook, "but every 2 used a dish of rice, every 3 used a dish of broth, and every 4 used a dish of meat between them". There were 65 dishes in all. How many guests were there?
Taken from A puzzle from 4th century CE, China from the Sunzi Suan Jing 孙子算经
Please consider:
• Whether it makes a difference to our students to offer examples, puzzles and histories of mathematics from diverse cultures (or from 'their' cultures!)
• Whether the word problem/ puzzle story matters or makes a difference to our enjoyment of solving it.
Solution:
Let x be the number of guests, then we know that there are x/2 dishes of rices ("every 2 used a dish of rice"), x/3 dishes of broth ("every 3 used a dish of broth"), and x/4 dishes of meat. Then we can have the following equation:
x/2 + x/3 + x/4 = 65.
13x/12 = 65
x = 60
After solving the equation above, we have x equals to 12, which means there are 60 guests in total.
I think it will makes a difference to our students if we offer examples, puzzles and histories of math from divers cultures. It might be difficult for students to understand the problem related to unfamiliar. It remains me of my experience of tutoring a Chinese student. The student struggled with one complicated word problem related to burger making, because she had not made a burger. Burger is from western culture which my student is not familiar with.
And I think integrate story into the word problem/puzzle will make the problem more interesting, which will help student engage in solving it. For instance, the dishes problem, we were told that it this a puzzle from 4th century CE, China from 孙子算经. This history background makes the puzzle feel more significant.
Nice! Do you think you could solve this puzzle using another method rather than modern algebra (which Sunzi and colleagues would not have had available to them, as it had not been invented yet)? Good reflection on integrating story and history into math class!
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