Problem Solving in Mathematics
Mathematics plays a practical role within individuals and society. Through problem-solving, math is developed. Presenting problems and developing skills needed to solve problems is quite motivational. Rather than being taught skills without context, problem solving gives a special value to learning new concepts and skills. Using problem solving techniques to approach mathematics creates a context that simulates real life and therefore justifies the mathematics.
The following non-traditional problems connect to the core and
therefore, can be used in an algebra course.
Problem: Legs on Bus
There is a bus with 7 girls.
Each girl has 7 backpacks.
Inside each backpack, there are 7 big cats.
Each big cat has 7 small cats.
All the cats have 4 legs each.
Question: How many legs are inside the bus?
Hints
There is a bus with 7 girls.
Each girl has 7 backpacks.
Inside each backpack, there are 7 big cats.
Each big cat has 7 small cats.
All the cats have 4 legs each.
Question: How many legs are inside the bus?
Hints
Solution
Apple Problem:
Three tired and hungry people had a bag of apples. While the other two were asleep, one of the three awoke, ate one-third of the apples, and went back to sleep. Later a second person awoke, ate one-third of the remaining apples and went back to sleep. Finally, the third person awoke and ate one-third of the remaining apples, leaving 8 apples in the bag.
Question: How many apples were in the bag originally?
Three tired and hungry people had a bag of apples. While the other two were asleep, one of the three awoke, ate one-third of the apples, and went back to sleep. Later a second person awoke, ate one-third of the remaining apples and went back to sleep. Finally, the third person awoke and ate one-third of the remaining apples, leaving 8 apples in the bag.
Question: How many apples were in the bag originally?
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