A puzzle from Sunzi Suanjing:
"今有雉、兔同笼，上有三十五头，下九十四足。问雉、兔各几何？"
Now we have chickens and rabbits in the same cage. There are 35 heads and 94 feet in total. How many chickens and rabbits do we have?
The solution from the book:
"上置三十五头，下置九十四足。半其足，得四十七。以少减多。"
Solving without algebra:
The first step is to find a number that has factors 2, 3 and 4. The smallest number that meets the condition, i.e the least common multiple, is 12. Thus, the solution must be a multiple of 12. The possible solutions can be 12, 24, 36, 48, 60, 72 etc. The next step is to figure out which one meets the other condition: the total number of dishes is 65. By trials and errors, we can find 60 is the final answer as 60/2+60/3+60/4=65.
Math problems, puzzles and histories from diverse cultures foster students’ interests in math. Since these questions could have different approaches, students can practice their mathematical thinkings and have deeper understandings of the development of math. When students from other ethnic groups find that the math questions are from their cultures, they could be more excited and actively engaged in the class. During the interactions, other students could also benefit from the problem-solving process.
Word problems, puzzle stories and imageries play important roles in math learning and teaching. Students could develop essential skills such as understanding the backgrounds of problems, collecting useful information, visualizing problems and utilizing different approaches to solve problems. Moreover, they could feel connections to the ancient time and appreciate the efforts and wisdom of ancient people. By successfully solving these kinds of problems, they could gain more fulfillment and joy than figuring out the solutions to boring equations.
