Logic to Algorithm
Here is a question in Edmonotn Grandview Height School for Grade 8 students:
A and B are two runners, A's speed is 15km/h, B's speed is 20km/h. 1 hour after A ran, B started to run to catch up A. How long would take B to catch up A?
This is probably a simple math question for element school kids in China. I, totally trained in Chinese thinking, will get answer by doing (1*15)/(20-15) = 3 hrs.
If we want to do the X way, so we can solve the problem as the following, which is taught in Math Power book:
1.let x be the time for B to catch up A
2.then by the time A catches B, A's total running time would be x+1
3.when A catchs B, their running distances are equal, so the following equation wil be used to solve the problem: 15(x+1) = 20x -> x = 3 hrs, same answer.
But the school math teacher's solution is as the following: (of course it's right!)
1. let x be the A's running time (why not be B's time?!)
2. let's think about nagative, since time is passed!
3. so the equation would be 15x = 20(x+1) -> x = -4
4. since time is nagative, so the A's time is 4 hrs.
5. Don't forget this step! since question asks B's time, so B's time is (4-1) = 3 hrs.
We can see the different solutions/logics for this simple question, the answers are same. Which is best? It all depends. From logic to algorithm, it is a long, interesting, challenging way for kids. Hope every kid will be enjoy this, which is the responsiblity of teachers and parents.
A and B are two runners, A's speed is 15km/h, B's speed is 20km/h. 1 hour after A ran, B started to run to catch up A. How long would take B to catch up A?
This is probably a simple math question for element school kids in China. I, totally trained in Chinese thinking, will get answer by doing (1*15)/(20-15) = 3 hrs.
If we want to do the X way, so we can solve the problem as the following, which is taught in Math Power book:
1.let x be the time for B to catch up A
2.then by the time A catches B, A's total running time would be x+1
3.when A catchs B, their running distances are equal, so the following equation wil be used to solve the problem: 15(x+1) = 20x -> x = 3 hrs, same answer.
But the school math teacher's solution is as the following: (of course it's right!)
1. let x be the A's running time (why not be B's time?!)
2. let's think about nagative, since time is passed!
3. so the equation would be 15x = 20(x+1) -> x = -4
4. since time is nagative, so the A's time is 4 hrs.
5. Don't forget this step! since question asks B's time, so B's time is (4-1) = 3 hrs.
We can see the different solutions/logics for this simple question, the answers are same. Which is best? It all depends. From logic to algorithm, it is a long, interesting, challenging way for kids. Hope every kid will be enjoy this, which is the responsiblity of teachers and parents.
omfg.
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