Tuesday, March 12, 2013

Got a Problem?

We used to teach children to find key words in word problems that would tell them which operation to use to solve tehm. We also used to tell them to look at the numbers; they'll "tell" you which operation to use;  "altogther" means add and the numbers 30 and 5 probably means divide since there will be no remainder. We know now that such misguided advice does nothing to help children know which algorithmic operation to use, or, more importantly these days, which key to press on the cell phone calculator feature; add, sub, mult. or div. For example, simple one step addition/subtraction  problems of the type found in the elementary school can usually be classified  as joining, separating, part-part-whole or comprison. The key to solving such problems is to work out what is happening, find the question, select the operation to use to asnwer the question, then check and decide if it seems a reasonable answer. To help children work out what good problems look like we should share examples of  poor problems, or un-problems. In addition to being humorus such problems help us teach children what constitutes a solvable, meaningful problem.

Here are some examples of un-problems;

  1. If it rains for 3 hours on Monday how much will it rain for the next 4 days?
  2. If it takes ½ an hour for 3 friends to walk home how long will it take 5 friends? 
  3. If 2 students have 5 pet gerbils how many gerbils does each student have? 
  4. If 2 girls have 3 brothers how many brothers do 4 girls have? 
  5. What is the area of your hand if your thumb is 3 inches long and your middle finger is 4 inches long? 
  6. If the temperature is 62F today what will it be for the next 3 days? 
  7. If 2 squares have 8 sides how many sides do 3 triangles have? 
  8. If it’s 60F in Vermont and 72F in Maine what is the temperature  in New Hampshire? 
  9. If one train is traveling at 35 mph (clearly an AMTRAC train) and another similar train is going at 45mph what time will they pass each other? 
  10. If you eat 2 slices of your birthday cake today and ½ of what’s left tomorrow how much will you eat the next day? 
  11. If 140 students are going on a field trip and a school bus will hold 60 students how many school buses will you need?
  12. If 2 friends have 5 pets and one of them has 2 cats how many dogs does her friend have?


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