Organizing a Word ProblemDate: 03/21/2000 at 13:28:00 From: G Wimbley Subject: Re: Math - subtracting/trading/borrowing How can I get my 3rd grade son to understand and know where to start on word problems? Sometimes he doesn't know whether to add, subtract or multiply. For example: Backstreet Boys tickets are on sale. Front-row tickets cost $35, center stage $25, balcony $15, T-shirts $10, and posters $8. John bought 2 front-row tickets for himself and his brother, 2 T-shirts, and 2 posters. How much did John spend? How can I get him to understand where to start and how to figure out what to do first? Do you have any sample word problems and explanations of how to do them? Date: 03/21/2000 at 16:57:17 From: Doctor Peterson Subject: Re: Math - subtracting/trading/borrowing Hi, Gloria. Our FAQ includes a section on Word Problems, with some general hints and links to other places to look for examples: http://mathforum.org/dr.math/faq/faq.word.problems.html The archives on Elementary Word Problems may also be useful: http://mathforum.org/dr.math/tocs/wordproblem.elem.html Some people like to give lists of keywords to look for, like "each" which suggests you'll want to multiply, or "less than" which suggests subtraction. I prefer to focus not on words but on concepts; if a child knows well what each operation does, and can visualize what is being done in the problem, it should be easy enough (though sometimes tricky) to match up the right operation with each part of the problem. If he is not good at visualizing and imagining (or maybe even if he is), he might want to draw or act out the situation; if he has trouble organizing his thoughts, he might want to use a table or chart to list what he knows and see how it fits together. Whatever fits his own style of thinking will be best for him. The first thing to do is to look at the goal: what question do you have to answer? Sometimes that can save work if there's a lot of extraneous information that might lead you in the wrong direction. Once you understand the goal, you can take a look around and see what resources you can use to get you there. Let's try your problem as an example: >Backstreet Boys tickets are on sale... We can make a chart of prices, or just imagine one; if nothing else. This helps to make sense of the wording of the problem, namely the idea that there are three different kinds of tickets in the list: Tickets Front row $35 Center stage $25 Balcony $15 T-shirts $10 Posters $8 If we see what's coming, and have a little experience with this sort of problem, we can make up a shopping list, which combines our goal and our givens: Item Count Price Cost ---- ----- ----- ---- Front row tickets 2 $35 T-shirts 2 $10 Posters 2 $8 (Note that some of the paperwork adults take for granted, invoices and forms and so on, are really problem-solving tools that save a lot of thinking, by helping to organize data; just getting used to some of these real-world devices can be a useful experience. Do some shopping together, and look at bills and invoices and receipts.) Now we can go through the problem one step at a time, as if we were really shopping. If we buy two tickets for $35 each, what will they cost? This should trigger the word "multiplication" -- not so much because of the word "each," but because of what is happening, two identical things being added together. We can multiply to find how much is being spent on each item, and then add the results together. If even the idea of adding isn't obvious, we can picture actually spending the money: put down $35, then another $35, then two $10 bills, then two $8 piles. Eventually the idea of addition will pop into our minds. To sum up: the goal is to associate an action with the corresponding arithmetic operation: putting together adds, separation subtracts, repetition multiplies, splitting into groups divides, and so on. There are other tricks for problem solving that help with more complicated problems that have multiple steps, but it sounds as if we're dealing with fairly basic problems in which the goal is simply to learn when to use each operation. If making subtraction concrete helped your son, then probably acting out these problems will help, too. Many children seem to just see the numbers and ask "What can I do to them?" rather than seeing the actions in the problem and asking "What is being done?" By focusing on the concrete problem rather than the abstract numbers, you can make the connection more easily. Let me know if there are any specific kinds of mistakes he makes that might suggest a more specific remedy. - Doctor Peterson, The Math Forum http://mathforum.org/dr.math/ |
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