Date: 04/02/2009 at 08:08:33 From: Aileen Subject: teaching inequalities using greater than or equal to Hi. We're looking for the best way to help students understand the idea of greater than or equal to, including some real-life examples of how it might be used. Can you help us?
Date: 04/02/2009 at 09:42:23 From: Doctor Peterson Subject: Re: teaching inequalities using greater than or equal to Hi, Aileen. I think the usual difficulty is what "or" means here, and why the idea is needed. When you first give a simple example, it can seem almost silly: 7 >= 6 and 6 >= 6 (I'm using ">=" to mean "greater than or equal to") To say "7 is greater than or equal to 6" seems redundant; why bother saying "or equal"?? And to say "6 is greater than or equal to 6" seems even sillier. So why bother with the idea? It becomes meaningful when you aren't talking about specific numbers, but about a variable. Then it starts making sense to have options connected by "or". Let's take an ordinary English statement that incorporates the same idea: I am 6 feet tall or more. (Or, I am at least 6 feet tall) I know my own height, and so in describing myself I would not need to be so vague; I could just say "I am 6 feet tall." A situation that might call for this statement would be Only people who are 6 feet tall or more can go on this ride. This is a general description of ALL people who are allowed to do something, and does not just cover one person with a specific height. It says that someone 6 feet tall may go, and also someone 6 feet 1 inch, and so on. Anyone whose height is EITHER 6 feet OR greater fits the description. In the same way, using a variable, if I say x >= 6 I am saying that x can be any number from 6 up: 6, 6.0001, 7, 1023, or whatever. As long as EITHER x > 6 OR x = 6, the statement (inequality) is true. At this point you could present examples like this, asking for examples of numbers for which an inequality is true and numbers for which it is false, and then presenting specific numbers and asking whether it is true for them. This might be done in the context of examples like mine of height. You could also translate some English statements like "The president must be at least 40 years old" into symbols. Graphing inequalities can also help to clarify their meaning, since this emphasizes the idea that many numbers satisfy the inequality, and that the "or equals" part causes the boundary point (6 in my example) to be part of the solution set. - Doctor Peterson, The Math Forum http://mathforum.org/dr.math/
Date: 04/02/2009 at 14:25:32 From: Aileen Subject: Thank you (teaching inequalities using greater than or equal to ) Thank you. This is very helpful.
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