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Negative Exponents (Dolciani Pre-Alg)


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DD12 has struggled with the lessons about exponents a bit in Chapter 2 of Dolciani pre-algebra.   She was a bit shaky and eventually got most of the problems correct (including basic problems with negative exponents), but she got really stuck on the problems with both a negative exponent and a variable.  Is this a topic to camp out on and really "get" ... or is it one that's okay to come back and revisit later?  Is it covered again in Algebra 1?  It has been so long since I have done Pre-Algebra/Algebra that I don't feel like I have a good sense for what are the critical skills she needs to master before moving on, and what can just be introduced at this stage. 

 

 

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I'm not familiar with the Dolciani books, but since you have no other answers, I'll weigh in with my opinion. YMMV!

 

Exponents are vitally important. But it seems weird to focus on them so early in a pre-algebra course. They will almost surely be covered again later (check the table of contents?) and revisited in even more depth when she gets to algebra.

 

Sometimes seeing a different presentation can help with tricky math topics. Your daughter might like the Math is Fun page on exponents, which is a quick overview/review using numbers only (no variables). Or the more detailed Purplemath pages, designed for algebra students.

 

I don't think you need to stop and camp out on exponents. Have her make a reminder sheet summarizing the exponent rules and let her use that as needed with future homework. Eventually, she will get used to how exponents work, just from sheer repetition, but the rules are not intuitive to beginners.

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AoPS also puts exponents really early in pre-algebra. I don't know how much you'll use them in algebra, but if you want a practical application, you can use them to do metric conversions. You can probably find videos about metric conversions that use negative exponents, and having something concrete to think about might help your student to see how it works.

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My ds is in Algebra 1 using a Harcourt Brace book (in public school) right now. It assumes *some* knowledge of exponents including negative exponents (how to multiply and divide them or raise a number with an exponent to another exponent), but not negative exponents with variables.

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That's funny - we also just did that a few weeks ago and it was one of the few things that I felt like didn't have enough practice. And having tons of practice options is usually one of the best things about Dolciani!

 

Obviously Denise had great suggestions... we did some practice but mostly just moved on with the assumption that it would come up again.

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That's funny - we also just did that a few weeks ago and it was one of the few things that I felt like didn't have enough practice. And having tons of practice options is usually one of the best things about Dolciani!

 

Obviously Denise had great suggestions... we did some practice but mostly just moved on with the assumption that it would come up again.

 

So true!  We will probably practice a bit on exponents while moving on to the next chapter.  I looked at the first couple lessons in chapter 3 and they seem much easier than what we just did with exponents.  The next chapter looks to be almost all review for DD12, which will be good since she was starting to feel like I had thrown her into something she wasn't ready for.  I think an easier chapter will be a good confidence builder. 

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So true!  We will probably practice a bit on exponents while moving on to the next chapter.  I looked at the first couple lessons in chapter 3 and they seem much easier than what we just did with exponents.  The next chapter looks to be almost all review for DD12, which will be good since she was starting to feel like I had thrown her into something she wasn't ready for.  I think an easier chapter will be a good confidence builder. 

 

I've been giving BalletBoy the Chapter Test first and if he passes it easily, then we skip ahead. I had him do some of the challenge stuff for the first chapter, then just exponents and some of the word problems for the second. Then just a couple topics for the third. Then we went on vacation. When we pick back up in a week, he'll probably need to do everything in Chapter 4, but I guess we'll see...

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We stalled out on negative exponents in aops last year, spent way too much time finding other resources, finally moved on, and when we got to negative exponents in the fractions chapter, he said, "oh, that makes perfect sense." It just clicked. Made me wish we could have had the weeks back that we had spent struggling with the concept earlier. Or maybe all that struggling had primed him to understand it the next time it came up :)

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We're running behind everyone, but my dd just did lesson 2-8 today. She missed page 74 numbers 41-46 (the ones with variables too) because she didn't correctly interpret the instruction. When I said, they mean rewrite it as a fraction, like all the class exercises we just did, she got it. Hopefully your dd reached a similar epiphany as you moved on.

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