Problem Solving and Mental ProcessDate: 10/03/2002 at 21:19:10 From: Jean Ploughman Subject: Problem solving My daughter is in grade 5. The problem is problem solving. My solution is plain old logic, which is hard for a 10-year-old to comprehend. Is there an equation/formula to simplify the following? These 2 numbers add up to 19. The difference between these 2 numbers is 3. What are the numbers? The answer, of course, is 11 and 8. I arrive at the answer through a mental process. Is there an easier way to teach her? Date: 10/03/2002 at 23:27:14 From: Doctor Ian Subject: Re: Problem solving Hi Jean, What 'mental process' did you use? In many cases, 'problem solving' problems are exercises in trying to articulate slowly what your brain can do quickly. Without using algebra, there are two pretty straightforward ways to approach this problem. One is to start from the fact that the two numbers differ by 3. Then you start examining the possibilities: 1 + 4 = 5 2 + 5 = 7 3 + 6 = 9 Now, you can keep going one by one, or you can see that you can probably skip a few, which lets you arrive more quickly at the answer (8 and 11). The other place to start is with the fact that the two numbers have to add up to 19. 1 + 18 = 19 18 - 1 = 17 2 + 17 = 19 17 - 2 = 15 3 + 16 = 19 16 - 3 = 13 And then you're in sort of the same boat. You can work your way down, but you can also start skipping to speed the process up. To do this with an _equation_, it would look like this. We can use '?' to represent the smaller number, and '(?+3)' to represent the larger number. Then ? + (?+3) = 19 ? + ? + 3 = 19 2*? + 3 = 19 Now, if you add 3 to something and end up with 19, then the something must be equal to 16, right? So 2*? = 16 Now, by the definition of division, this means that ? = 16/2 = 8 So the smaller number must be 8, and the larger one must be 11. Try running these three solutions by your daughter, and see if any of them make sense to her. Write back if she's still stuck, or if you have any other questions. - Doctor Ian, The Math Forum http://mathforum.org/dr.math/ |
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