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13 Jul 2005 - 02:18
PreAlgebraFastFactsFromSaxonMath
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I have a question. (I could probably look in the book myself and answer it!) Does Prentice Hall start out with story problems? Saxon starts out--and I thought this was great--with simply subtituting a letter in a regular addition, subtraction, multiplication, or division problem. He has these great problems--kind of a 'trick' question--where he'll have a whole long column of numbers to add, and he'll slip in one variable somewhere inside the column. The first couple of times that happened Christopher didn't kow what to do. He still had that very concrete, inflexible knowledge, and it didn't jump out at him that he needed to add up all the other numbers, and simplify the problem down to 'sum' + variable = total. -- CatherineJohnson - 13 Jul 2005
The other cool thing Saxon does is to introduce the lingo early, in situations where you wouldn't normally use it. He'll say, 'Simplify this expression' and then the 'expression' will be a standard problem in arithmetic. Christopher informed me the other day, rather proudly, 'simplify means do the problem.' I loved it! -- CatherineJohnson - 13 Jul 2005
I find it odd that EVERYDAY MATH never mentioned variables, given all their constant introducing of too-advanced concepts..... -- CatherineJohnson - 13 Jul 2005
You're into Saxon 8/7 with Christopher now, right? Which unit? Prentice Hall jumps right into story problems. And then they back up a bit and do number patterns, which we don't need any more of. And then it's full speed ahead and on into equation solving. Bleah! -- CarolynJohnston - 13 Jul 2005
We need to write the perfect prealgebra text. -- CarolynJohnston - 13 Jul 2005
(That last comment was actually a joke) -- CarolynJohnston - 13 Jul 2005
I've heard Borenson's Hands on Equations mentioned many times by homeschooling parents. Here is a quote from the website, "By using game pieces consisting of pawns and numbered cubes, the student is able to physically represent and solve algebraic linear equations in a manner that makes sense to them. The "legal moves" provide students with a sound, intuitive understanding of fundamental algebraic properties. Elementary school students are fascinated with HANDS-ON EQUATIONS®. They are impressed with their ability to solve algebraic linear equations in a game-like manner. The "legal moves" provide students with a sound, intuitive understanding of fundamental algebraic properties. The early acquisition of algebraic concepts made possible by HANDS-ON EQUATIONS® may be an essential step in helping to raise the level of mathematics education in the United States." Here are examples of problems solved at different levels: Level I: Lessons #1 - #7: 2x + x + x + 2 =2x = 10 2(x+4) + x = 2x + 10 Level 2 Lessons 8-16 2x + (-x) + 3 = 2(-x) + 15 2x - 3(-x) = 20 + x There's more...go to http://www.borenson.com/html/brochure.html 2 x + x + x + 2 = 2 x + 10 2 ( x + 4 ) + x = 2 x + 10 Level II: Lessons #8 - #16 2 x + ( - x ) + 3 = 2 ( - x ) + 15 2 x - 3 ( - x ) = 20 + x Level III: Lessons #17 - #25 2 ( - x ) + 3 = - 6 + x 2 x - 2 ( - x + 4 ) = x + ( - 2 ) -- LoneRanger - 13 Jul 2005
Sorry that post came out so strangely... -- LoneRanger - 13 Jul 2005
I work on this all the time with Daniel. When we have a word problem, I put a box for the unknown. For example, a problem he had today was: Mike bought 12 liters of paint. If he has 2l 450 ml left over, how much did he use? So we write out the equation first in words: total - left over = used. Then we put in a box for the unknown. Later, I'll start substituting letters. In this way, I can use the word problems at his level to start teaching him prealgebra concepts. -- AnneDwyer - 13 Jul 2005
I think Anne is hitting this thing correctly. I read blogs of a couple of college level math instructors (with students who are not ready for the pre-calculus classes they teach). They report using the phrase "An equation is a relationship among quantities" practically as a mantra in class. If you have the meaning of this phrase firmly set in your mind, it makes sense that you can do the same operation to both sides of the equation without changing the result. It reminds me, too, of an earlier post where the concrete example of a balance was used to demonstrate the equality of quantities on either side of the balance. None of this, of course, helps with writing the equation, it just helps with the novelty of representing an unknown with a letter. You might also try telling your child that the numerals are just symbols we use to represent numbers, and we similarly use letters to represent numbers when we aren't sure what numeral to use yet. But that might just confuse them even more... -- StephanieO - 13 Jul 2005
I used to use a box instead of a letter all the time in calculus classes. It makes figuring out what f(g(x)) is much easier. the borenson stuff sounds interesting... I'll check it out. -- CarolynJohnston - 13 Jul 2005
looking for prealgebra resources
I've just started introducing Ben to some algebra concepts.. variables, equations, translating story problems into equations with unknowns. I've found that it really is a conceptual hurdle, totally different from what came before it. It's a Big Discontinuity in one's math education. Take a sample word problem like this one: John weighed 78 pounds in 5th grade. When he was weighed in 6th grade, he weighed 86 pounds. How much weight did he gain between 5th and 6th grade? "You want to figure out how much weight he gained, that's what you don't know," I say. "So you give it a letter name. Let's call it w for weight gain. Write w = weight." w = weight, he writes. "So what is that word problem saying about the weight gain?" He sits there silently for a couple of minutes, so quietly you think he's zoned out; that's his way. And then maybe he'll say "Oh, I get it," and write down 78 + w = 86. Very slowly. And maybe I'll need to give him another hint or two before it happens. The very idea that he can give a number that he doesn't know a letter name -- that he is even allowed to do such a thing -- is totally new and revolutionary for him. The idea that he can put that letter name into an equation that he translates from a word problem is just as revolutionary, and it all came at him in just one section in Prentice-Hall Course 1. And the section was labeled just like all the others: it didn't say "Huge New Concept" in flashing letters. Prentice Hall just doesn't quite have enough practice at this new skill, of giving some quantity a letter name that you pick out. The next section is on solving problems like the example above. I just want to take an extra day for Ben to work on the daring act of naming an unknown and putting it into an equation. So I went looking for some online resources, and I wasn't too excited by what I found. There is a lot of software that purports to give help in algebra; most of it costs money, and being cheap, I was looking for free stuff. There are a lot of sites that give explanations and assistance in algebra, and one or two that have online quizzes and the like. Nothing that fit what I was looking for, though; I think I'll have to go to the textbooks for that. Here's a brief rundown of what I found that might be worth having a look at: Algebra section of library.thinkquest.org. I absolutely DETEST the name of this site, which appears to be Math for Morons Like Us. If there were a larger number of good sites out there, I wouldn't recommend it at all, just on principle. However, the site is fairly well organized and the explanations are pretty good, and there are little popup self-quizzes at the end of the sections. All of this puts it ahead of the other sites I looked at. It could be good for a teenager reviewing for SATs, or for a parent trying to brush up before teaching algebra to a child, but they need to lose the awful name. Algebra worksheet generator. This looks pretty good; it's very configurable, and it's free. Word problem worksheets. These are algebra and prealgebra word problem worksheets. There are many of them, and all the ones I looked at looked good, like they would stretch a kid without actually breaking him. However, I've still not found what I was looking for. Any suggestions would be welcome.PreAlgebraFastFactsFromSaxonMath
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Look here for syntax help.
I have a question. (I could probably look in the book myself and answer it!) Does Prentice Hall start out with story problems? Saxon starts out--and I thought this was great--with simply subtituting a letter in a regular addition, subtraction, multiplication, or division problem. He has these great problems--kind of a 'trick' question--where he'll have a whole long column of numbers to add, and he'll slip in one variable somewhere inside the column. The first couple of times that happened Christopher didn't kow what to do. He still had that very concrete, inflexible knowledge, and it didn't jump out at him that he needed to add up all the other numbers, and simplify the problem down to 'sum' + variable = total. -- CatherineJohnson - 13 Jul 2005
The other cool thing Saxon does is to introduce the lingo early, in situations where you wouldn't normally use it. He'll say, 'Simplify this expression' and then the 'expression' will be a standard problem in arithmetic. Christopher informed me the other day, rather proudly, 'simplify means do the problem.' I loved it! -- CatherineJohnson - 13 Jul 2005
I find it odd that EVERYDAY MATH never mentioned variables, given all their constant introducing of too-advanced concepts..... -- CatherineJohnson - 13 Jul 2005
You're into Saxon 8/7 with Christopher now, right? Which unit? Prentice Hall jumps right into story problems. And then they back up a bit and do number patterns, which we don't need any more of. And then it's full speed ahead and on into equation solving. Bleah! -- CarolynJohnston - 13 Jul 2005
We need to write the perfect prealgebra text. -- CarolynJohnston - 13 Jul 2005
(That last comment was actually a joke) -- CarolynJohnston - 13 Jul 2005
I've heard Borenson's Hands on Equations mentioned many times by homeschooling parents. Here is a quote from the website, "By using game pieces consisting of pawns and numbered cubes, the student is able to physically represent and solve algebraic linear equations in a manner that makes sense to them. The "legal moves" provide students with a sound, intuitive understanding of fundamental algebraic properties. Elementary school students are fascinated with HANDS-ON EQUATIONS®. They are impressed with their ability to solve algebraic linear equations in a game-like manner. The "legal moves" provide students with a sound, intuitive understanding of fundamental algebraic properties. The early acquisition of algebraic concepts made possible by HANDS-ON EQUATIONS® may be an essential step in helping to raise the level of mathematics education in the United States." Here are examples of problems solved at different levels: Level I: Lessons #1 - #7: 2x + x + x + 2 =2x = 10 2(x+4) + x = 2x + 10 Level 2 Lessons 8-16 2x + (-x) + 3 = 2(-x) + 15 2x - 3(-x) = 20 + x There's more...go to http://www.borenson.com/html/brochure.html 2 x + x + x + 2 = 2 x + 10 2 ( x + 4 ) + x = 2 x + 10 Level II: Lessons #8 - #16 2 x + ( - x ) + 3 = 2 ( - x ) + 15 2 x - 3 ( - x ) = 20 + x Level III: Lessons #17 - #25 2 ( - x ) + 3 = - 6 + x 2 x - 2 ( - x + 4 ) = x + ( - 2 ) -- LoneRanger - 13 Jul 2005
Sorry that post came out so strangely... -- LoneRanger - 13 Jul 2005
I work on this all the time with Daniel. When we have a word problem, I put a box for the unknown. For example, a problem he had today was: Mike bought 12 liters of paint. If he has 2l 450 ml left over, how much did he use? So we write out the equation first in words: total - left over = used. Then we put in a box for the unknown. Later, I'll start substituting letters. In this way, I can use the word problems at his level to start teaching him prealgebra concepts. -- AnneDwyer - 13 Jul 2005
I think Anne is hitting this thing correctly. I read blogs of a couple of college level math instructors (with students who are not ready for the pre-calculus classes they teach). They report using the phrase "An equation is a relationship among quantities" practically as a mantra in class. If you have the meaning of this phrase firmly set in your mind, it makes sense that you can do the same operation to both sides of the equation without changing the result. It reminds me, too, of an earlier post where the concrete example of a balance was used to demonstrate the equality of quantities on either side of the balance. None of this, of course, helps with writing the equation, it just helps with the novelty of representing an unknown with a letter. You might also try telling your child that the numerals are just symbols we use to represent numbers, and we similarly use letters to represent numbers when we aren't sure what numeral to use yet. But that might just confuse them even more... -- StephanieO - 13 Jul 2005
I used to use a box instead of a letter all the time in calculus classes. It makes figuring out what f(g(x)) is much easier. the borenson stuff sounds interesting... I'll check it out. -- CarolynJohnston - 13 Jul 2005
| WebLogForm | |
|---|---|
| Title: | looking for prealgebra resources |
| TopicType: | WebLog |
| SubjectArea: | MiddleSchoolMath |
| LogDate: | 200507122218 |