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What is a 'Problem'?

What is a 'Problem'?. A problem is a doubtful or difficult question; a matter of inquiry, discussion, or thought; a question that exercises the mind ( Oxford English Dictionary ) A problem is a situation or task for which a. the person wants or needs to find a solution

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What is a 'Problem'?

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  1. What is a 'Problem'? • A problem is a doubtful or difficult question; a matter of inquiry, discussion, or thought; a question that exercises the mind (Oxford English Dictionary) • A problem is a situation or task for which a. the person wants or needs to find a solution b. the person does not have a solution for the problem right at that moment c. the person makes an attempt to find the solution

  2. Different Types of Problems • Our ideas:

  3. BEING A MATHEMATICAL PROBLEM SOLVER

  4. Ron’s Recycle Shop was started when Ron bought a used paper-shredding machine. Business was good so Ron bought a new shredding machine. The first machine could shred a truckload of paper in 4 hours. The new machine could shred the same truckload of paper in half the time. How long will it take to shred a truckload of paper if Ron runs both shredders at the same time?

  5. Stuck? • Are you overlooking anything? Do the two machines work simultaneously? Do they run just as fast when working together as when they work alone? • Have you tried to predict or guess about how much time you think it should take the two machines? For example, will it be closer to 1 hour or closer to 4 hours? Why? Checking a guess can sometimes lead to a new insight into the problem. • Did you try drawing a picture to help you solve the problem? • Perhaps you could use something that you could move or change. For example, you might draw a rectangle or line segment to stand for the truckload of paper, or you might get some counters and make a collection that stands for the truckload.

  6. Problem Solving Steps • Understand the problem. • Devise a plan for attacking the problem. • Carry out the plan. • Look back at the problem, the answer, and what you have done to get there.

  7. The 3-Read Strategy • A special strategy for reading math problems is called the 3-Read Strategy. • It involves reading a problem several times in order to try to understand the problem clearly. • It then involves devising a plan or strategy, carrying it out, and then checking your ideas. • Work on the assigned activity in order to practise this strategy.

  8. The 3-Read Strategy • The first read is designed so that you can understand the general idea of the problem. • The second read is designed so that you can focus in on the separate facts and the actual question. • The third read is designed so that you can recheck the problem to make sure you have not misunderstood anything.

  9. The 3-Read Strategy • After understanding the problem, you need to think of possible ways to solve it. You need to think about the best strategy to use. • Next, you must put into action the strategy or plan you have come up with. Record your thinking using pictures, symbols, and/or words. • Lastly, you need to check over what you have done to make sure that you have answered the question and explained your thinking.

  10. Now practise the 3-Read strategy on some new problems. Examine the checklist for Problem Solving given to you by the teacher. (Van de Walle, page 58)

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