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From: Loyd <email@example.com> To: Teacher2Teacher Public Discussion Date: 2001122214:27:22 Subject: Problem-solving difficulties; making a table may help My only full time classroom experience has been with 9th and 10th grade math classes. However, i have taught GED classes and also tutored quite a few elementary and middle school students in small groups of 1 to 3. Here are a couple of things a I think can help. 1. Make sure the students know their add, subtract, multiplication and division facts before they enter the 4th or 5th grade. I have tried to teach many students who still didn't know all their multiplication facts. This slows them down so much in almost everything they do. For example, can't convert 24/36 to 2/3. 2. Many students have trouble understanding when to use multiplication or division. Some times they can get the correct answer if the numerals are small. or example, if you say eggs are 2 cents each, how much will 3 eggs cost. They know that the answer is 6, but they often don't know that multiplication will result in the answer. One thing you can do is to make the problem harder with say, eggs are 5 cents each, how much does 12 eggs cost. Often they are confused and give completely illogical answers. I try to teach students to make a table and make them take the time to complete: Number of eggs Cost 1 egg 5 cents 2 eggs 10 cents 3 eggs 15 cents ... 12 eggs. ? Often they still don't know the answer, but if you continue to make them complete the cable, they will usually see the solution is a simple multiplication. So, start with simple tables with small numbers and then progress to ones with larger numerals. The way I worked these type of problems during my life time was to try to solve the problem and If I had trouble, substitute small simple numbers in place of the larger more complex looking numbers. Then ask yourself what you did to solve the simple problem. Do the same for the complex problem. For example, if you said Santa had to visit 10 homes in 10 hours, how much time would he have for each home including the travel time. This problem is easy, but if you substitute numbers as follows: Santa had to visit 31,256,132 homes in 14 hours, how much time would he have for each home including the travel time. With this problem you may get silly answers even if students use a calculator. That is why it is often profitable to substitute simple numbers to see the procedure for obtaining the solution. 3. Division problems are just as difficult but if you can relate the problem to life experiences, that can help. For example if you bought three pizzas cut into 8 slices each, how many slices will each person get if there are 8 people to eat the pizza. If they can work that problem, you can progress to more complicate problems to make sure they know to use division. A student will often know the answer is three slices each, but may not know they used division. You can check that by making a hard problem such as if there are 57 slices of pizza for 19 kids, how many do each kid get. 4. Students don't understand subtraction vocabulary many times. For example, "take 8 from 9" is often misunderstood. Often they will write 8-9 fof that problem. One needs to express each problem in a variety of ways for it to sink in.
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